Transcript
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Radio Channel Measurements and Modeling for Smart Antenna Array Systems Using a

Software Radio Receiver

William G. Newhall

Dissertation submitted to the Faculty of Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in

Electrical and Computer Engineering

Committee Jeffrey H. Reed (Chairman)

Warren L. Stutzman William H. Tranter Brian D. Woerner

C. Patrick Koelling

April 2003 Blacksburg, Virginia

© 2003 William G. Newhall

Keywords: Propagation Measurement, Channel Modeling, Vector Channels, Smart Antenna, Software Radio,

Multipath, Wireless Communications.

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Radio Channel Measurements and Modeling for Smart Antenna Array Systems Using a

Software Radio Receiver

William G. Newhall

Abstract

This dissertation presents research performed in the areas of radio wave propagation measurement and modeling, smart antenna arrays, and software-defined radio development. A four-channel, wideband, software-defined receiver was developed to serve as a test bed for wideband measurements and antenna array experiments. This receiver was used to perform vector channel measurements in terrestrial and air-to-ground environments using an antenna array. Measurement results served as input to radio channel simulations based on three geometric channel models. The simulation results were compared to measurement results to evaluate the performance of the radio channel models under test. Criteria for evaluation include RMS delay spread, excess delay spread, signal envelope fading, antenna diversity gain, and gain achieved through the use of a two-dimensional rake receiver.

This research makes contributions to the wireless communications field through analysis, development, measurement, and simulation that builds upon past theoretical and experimental results. Contributions include a software-defined radio architecture, based on object oriented techniques, that has been developed and successfully demonstrated using the wideband receiver. This research has produced new wideband vector channel measurements to provide extensive characterization results facilitating simulation of emerging wireless technology for commercial and military communications systems. Original ways of interpreting multipath component strength and correlation for antenna arrays have been developed and investigated. A novel geometric air-to-ground ellipsoidal channel model has been developed, simulated, and evaluated. Other contributions include an evaluation of two popular radio channel models, a geometric channel simulator for producing channel impulse responses, and analytical derivation results related to channel modeling geometries and multipath channel measurement processing.

In addition to new results, existing theory and earlier research results are discussed. Fundamental theory for antenna arrays, vector channels, multipath characterization, and channel modeling is presented. Contemporary issues in software radio and object orientation are described, and measurement results from other propagation research are summarized.

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To those who steadfastly encourage life accomplishments.

Family, and friends close enough to call family.

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Acknowledgements

I have received an enormous amount of support from colleagues, friends, and family throughout

my graduate work. I would like to thank Jeff Reed, Bill Tranter, Brian Woerner, Warren

Stutzman, and Pat Koelling for their direction and participation on my committee. I also greatly

appreciate many other professors and staff at Virginia Tech for their input and support,

especially Tim Pratt, Bill Davis, Charles Bostian, Bob Boyle, Dennis Sweeney, and Krishnan

Ramu.

I am thankful for the friendship and assistance of my fellow graduate students and Virginia Tech

graduates, including Max Robert, James Hicks, Fakhrul Alam, Sesh Krishnamoorthy, Raqib

Mostafa, Ramesh Palat, Mostafa Howlader, Roger Skidmore, Ran Gozali, Tom Biedka, Chris

Anderson, Jody Neel, Philip Balister, Carl Dietrich, Gaurav Joshi, Kai Dietze, Neiyer Correal,

Matt Valenti, and Kathyayani Srikanteswara. I greatly appreciate the help of the MPRG staff,

including Jenny Frank, Hilda Reynolds, Shelby Smith, Beth Huffman, and Cindy Graham.

I could not have accomplished so much without my colleagues and friends at Grayson Wireless.

I thank Ken Talbott, Greg Bump, Jon Dubovsky, Casey Elder, Ron Bryan, Mark Priest, Steve

Trice, Tom Conley, Tim Garrett, and Terry Garner.

To my terrific friends, Mike Metzgar, Jennifer Lesser, Michele Kolet, and Neal Kegley, I owe

thanks for your friendship and a space in your lives.

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Bob Newhall and Barbara Ruebush, my brother and sister, have provided an immeasurable

amount of encouragement, and I thank them for being there for me.

I would mostly like to thank my parents, Robert and Roberta Newhall, whose constant and

limitless support, encouragement, and advice had a great part in bringing my work and dreams to

completion.

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Table of Contents

List of Figures ..........................................................................................................................xi List of Tables........................................................................................................................xxiii Chapter 1 Introduction .......................................................................................................1

1.1 Motivation and Challenges in Wireless ........................................................................1 1.2 Foundations of Progress in Wireless ............................................................................4 1.3 Research Issues Covered .............................................................................................5 1.4 Organization of This Dissertation ................................................................................7

Chapter 2 Signal Fundamentals for Antenna Arrays ........................................................9 2.1 Complex Signal Fundamentals ....................................................................................9

2.1.1 The Complex Envelope......................................................................................10 2.1.2 Converting Bandpass Signals to Complex Envelopes.........................................11 2.1.3 The Narrowband Approximation........................................................................13

2.2 Signals for Smart Antennas .......................................................................................16 2.2.1 The Purpose of Smart Antennas .........................................................................16 2.2.2 A Signal Model for Antenna Arrays...................................................................18 2.2.3 Vector Channels ................................................................................................23 2.2.4 Array Steering Vectors ......................................................................................25 2.2.5 Spatial Signatures ..............................................................................................26

2.3 Channel and Signal Characteristics in Multipath Environments .................................27 2.3.1 Multipath Amplitude and Time Delay................................................................28 2.3.2 Number of Multipath Components.....................................................................30 2.3.3 Fading Envelope ................................................................................................31 2.3.4 Direction of Arrival ...........................................................................................33 2.3.5 Signal Envelope Correlation Coefficient ............................................................34

2.4 Summary...................................................................................................................35 Chapter 3 A Multi-Channel, Software-Defined Measurement Receiver ........................37

3.1 Architecture Motivation.............................................................................................37 3.2 The Software Radio Methodology .............................................................................39

3.2.1 Physical Architecture.........................................................................................40 3.2.2 Division of Hardware and Software ...................................................................41 3.2.3 Benefits of the Methodology..............................................................................42

3.3 The Measurement Receiver Concept..........................................................................43 3.3.1 Processing Tradeoffs..........................................................................................43 3.3.2 Examples and Applications................................................................................44

3.4 System Specifications and Analysis ...........................................................................45 3.4.1 Target Applications............................................................................................45 3.4.2 Design Goals .....................................................................................................46 3.4.3 RF Specifications...............................................................................................47 3.4.4 System Specifications ........................................................................................48 3.4.5 Link Analysis ....................................................................................................49 3.4.6 RF Section Analysis...........................................................................................49 3.4.7 Noise Analysis...................................................................................................50

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3.5 Measurement Receiver Hardware ..............................................................................51 3.5.1 RF Front End .....................................................................................................52 3.5.2 Sampling Section...............................................................................................53 3.5.3 Complete System...............................................................................................54

3.6 Theory and Application of Object Orientation ...........................................................54 3.6.1 Objects ..............................................................................................................55 3.6.2 Object Orientation Concepts ..............................................................................55 3.6.3 Application of Object-Oriented Methods to Software Radios .............................57

3.7 Measurement Receiver Software ...............................................................................59 3.7.1 Signal Acquisition with the Hardware-Specific Receiver Object ........................60 3.7.2 Radio Receiver and Processing Functions ..........................................................62 3.7.3 Display/File Interface Functions ........................................................................62 3.7.4 Multithreading and Inter-Object Communications..............................................63 3.7.5 Automatic Gain Control.....................................................................................65 3.7.6 Example of Measurement Receiver Software Application..................................66

3.8 FPGA-Based Transmitter ..........................................................................................69 3.8.1 Transmitter Hardware........................................................................................69 3.8.2 Transmitter Verification.....................................................................................70

3.9 Summary...................................................................................................................72 Chapter 4 Multipath Channel Models for Antenna Arrays ............................................75

4.1 The Purpose of Radio Channel Models ......................................................................76 4.2 Channel Model Classification....................................................................................78 4.3 Existing Geometric Channel Models..........................................................................79

4.3.1 Multipath Channel Impulse Response ................................................................79 4.3.2 Geometrically Based Single-Bounce Elliptical Model........................................81 4.3.3 Geometrically Based Single-Bounce Circular Model .........................................86 4.3.4 Elliptical Sub-Regions Model ............................................................................88 4.3.5 Other Channel Models .......................................................................................92

4.4 Three-Dimensional Ellipsoidal Channel Model..........................................................95 4.4.1 The Ellipsoidal Scattering Region......................................................................95 4.4.2 Applications of the Bounded Ellipsoid ...............................................................96 4.4.3 Axis Lengths and Normalized Excess Delay ......................................................99

4.5 Geometric Air-to-Ground Ellipsoidal Channel Model..............................................101 4.5.1 Analytical Specification of Scattering Region..................................................103 4.5.2 Generating the Ellipsoid and Scatterers on the Rotated Axes............................107 4.5.3 Direction-of-Arrival Statistics ..........................................................................111 4.5.4 Joint Direction-of-Arrival and Time-Delay Statistics .......................................114

4.6 Summary.................................................................................................................119 Chapter 5 Channel Measurements .................................................................................121

5.1 Survey of Radio Channel Measurements .................................................................121 5.1.1 Terrestrial Measurements.................................................................................122 5.1.2 Air-to-Ground Measurements ..........................................................................127

5.2 Rooftop-Level Measurement Campaign...................................................................131 5.2.1 Measurement Overview ...................................................................................131 5.2.2 Multipath RMS Delay Spread ..........................................................................132 5.2.3 Distribution of Multipath Components.............................................................135

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5.2.4 Multipath Strength Correlation Coefficients Versus Delay...............................137 5.3 Dense Scatterer Measurement Campaign.................................................................148

5.3.1 Measurement Overview ...................................................................................148 5.3.2 Multipath RMS Delay Spread ..........................................................................151 5.3.3 Multipath Excess Delay Spread........................................................................160 5.3.4 Distribution of Multipath Components.............................................................161 5.3.5 Strength of Multipath Components Versus Delay.............................................169 5.3.6 Multipath Strength Correlation Coefficients Versus Delay...............................186

5.4 Air-to-Ground Measurement Campaign...................................................................188 5.4.1 Measurement Overview ...................................................................................190 5.4.2 Multipath RMS Delay Spread ..........................................................................191 5.4.3 Multipath Excess Delay Spread........................................................................194 5.4.4 Distribution of Multipath Components.............................................................195

5.5 Summary.................................................................................................................200 Chapter 6 Wideband Vector Channel Simulation .........................................................203

6.1 Simulation Overview...............................................................................................204 6.2 Simulation Geometries ............................................................................................207

6.2.1 Simulating the ESR Model Geometry ..............................................................207 6.2.2 Simulating the GBSBE Model Geometry.........................................................209 6.2.3 Simulating the GAGE Model Geometry...........................................................209

6.3 Multipath Component Distribution, Strength, and Delay..........................................213 6.3.1 Distribution of Multipath Components in Delay...............................................213 6.3.2 Multipath Delay...............................................................................................214 6.3.3 Strength Modeling for ESR and GBSBE..........................................................216 6.3.4 Strength Modeling for GAGE ..........................................................................218 6.3.5 Line of Sight Components ...............................................................................220 6.3.6 Log-Normal Multipath Strength Variation .......................................................221 6.3.7 Rayleigh Fading...............................................................................................223

6.4 Direction of Arrival .................................................................................................226 6.4.1 Direction of Arrival for ESR and GBSBE ........................................................226 6.4.2 Direction of Arrival for GAGE ........................................................................228

6.5 Summary.................................................................................................................228 Chapter 7 Channel Model Evaluation............................................................................229

7.1 Elliptical Sub-Regions Channel Model ....................................................................231 7.1.1 Simulation Parameters .....................................................................................231 7.1.2 Multipath Signal Strength ................................................................................233 7.1.3 RMS Delay Spread ..........................................................................................242 7.1.4 Excess Delay Spread........................................................................................246 7.1.5 Multipath Fading .............................................................................................248 7.1.6 Antenna Diversity............................................................................................250 7.1.7 Two-Dimensional Rake Receiver.....................................................................256 7.1.8 ESR Comparison Summary .............................................................................264

7.2 Geometrically Based Single-Bounce Elliptical Channel Model................................266 7.2.1 Simulation Parameters .....................................................................................266 7.2.2 Multipath Signal Strength ................................................................................268 7.2.3 RMS Delay Spread ..........................................................................................275

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7.2.4 Excess Delay Spread........................................................................................278 7.2.5 Multipath Fading .............................................................................................280 7.2.6 Antenna Diversity............................................................................................281 7.2.7 Two-Dimensional Rake Receiver.....................................................................288 7.2.8 GBSBE Comparison Summary ........................................................................295

7.3 Geometric Air-to-Ground Ellipsoidal Channel Model..............................................296 7.3.1 Simulation Parameters .....................................................................................297 7.3.2 RMS Delay Spread ..........................................................................................299 7.3.3 Multipath Signal Strength ................................................................................301 7.3.4 Excess Delay Spread........................................................................................304 7.3.5 Multipath Fading .............................................................................................305 7.3.6 Antenna Diversity............................................................................................305 7.3.7 Two-Dimensional Rake Receiver.....................................................................308 7.3.8 GAGE Comparison Summary..........................................................................311

7.4 Summary.................................................................................................................312 Chapter 8 Conclusion......................................................................................................315

8.1 Summary of Research..............................................................................................315 8.2 Original Contributions .............................................................................................317 8.3 Future Work ............................................................................................................319 8.4 Closing....................................................................................................................320

Epilogue.................................................................................................................................321 Appendix A Measurement Receiver MATLAB Signal Interface .................................323

A.1 MATLAB Interface Overview.................................................................................323 A.2 Workspace Variables...............................................................................................324 A.3 Real-Time Plotting ..................................................................................................325 A.4 Example M-File.......................................................................................................326 A.5 Steps for Developing m-files for the Measurement Receiver....................................329

Appendix B VT-STAR Development.............................................................................331 B.1 Overview.................................................................................................................331 B.2 VT-STAR Transmitter.............................................................................................331 B.3 VT-STAR Receiver .................................................................................................333

Appendix C Channel Model Simulator Parameters......................................................337 C.1 Top Level Structures ...............................................................................................337 C.2 Channel Parameters Structure..................................................................................338 C.3 Intermediate Plots....................................................................................................339 C.4 Vector Channel Structure.........................................................................................340 C.5 Multiple Simulation Runs ........................................................................................341

References .............................................................................................................................343 Author Biographical Notes ...................................................................................................351

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List of Figures

Figure 2-1. Block diagram of the down-conversion process for extracting in-phase and quadrature signal components from a bandpass signal. ......................................................13

Figure 2-2. Location of elements of an antenna array. .............................................................18 Figure 2-3. Signal sources surrounding antenna array...............................................................20 Figure 2-4. Geometry for a uniformly spaced, linear antenna array...........................................20 Figure 2-5. Transmitted signal and impulse response of a multipath vector channel.................28 Figure 2-6. Relative strengths of multipath components used to determine excess delay spread.

..........................................................................................................................................29 Figure 2-7. Isoprobability contours for the composite complex signal envelope due to Rayleigh

and Rician fading in a multipath environment....................................................................33 Figure 3-1. Block diagram of the major components of a practical software radio receiver........41 Figure 3-2. Functionality distribution of software radios versus legacy radio methodology. .....42 Figure 3-3. Block diagram of the measurement receiver hardware, including the RF hardware

that performs a frequency translation to a band that can be sampled by the 1 gigasample/sec sampling section................................................................................................................52

Figure 3-4. (a) The RF front end of the four-channel receiver, showing the tubular filters and connectorized RF components. (b) The complete system, showing the oscilloscope used for sampling, a signal generator used for the local oscillator, and another signal generator used to generate a test signal. ............................................................................................54

Figure 3-5. Flow of signal data through the processing of the measurement receiver software. .60 Figure 3-6. Class hierarchy of hardware-specific receiver objects.............................................62 Figure 3-7. Relationships among the measurement system software modules and external

interfaces...........................................................................................................................63 Figure 3-8. Block diagram of hardware and software components of automatic gain control. ...66 Figure 3-9. Block diagram of the software module that measures the strength, delay, and phase

of multipath components arriving at the receiver. ..............................................................68 Figure 3-10. Power-delay profile (amplitude and phase) computed by measurement receiver...68 Figure 3-11. Block diagram of the measurement system transmitter, including a PLD that is

programmable to produce the data required for the particular experiment..........................69 Figure 3-12. Wideband transmitter used for generating BPSK-modulated signal. .....................70

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Figure 3-13. Output of transmitter acquired with measurement receiver (in-phase component, quadrature component, and relative phase shown). ............................................................71

Figure 3-14. Signal constellation as demodulated by measurement receiver (phase rotation of constellation has not been applied for illustration purposes; the diagonal dashed line indicates the decision boundary)........................................................................................71

Figure 3-15. Transmitter signal acquired with measurement receiver after symbol decisions have been made. ........................................................................................................................72

Figure 4-1. Uses for channel models shown from the standpoints of functionality and system implementation. ................................................................................................................76

Figure 4-2. Physical layout of the geometrically based single-bounce model. ...........................82 Figure 4-3. Ellipses E1 and E2 that define scattering region between delays τ and τ+∆τ for the

GBSBE model...................................................................................................................83 Figure 4-4. Geometry for the geometrically based single-bounce circular model. .....................86 Figure 4-5. Probability density function for direction of arrival for the GBSB macrocell model

with d=5 km and r=100, 300, 1000 m................................................................................87 Figure 4-6. Geometry for the elliptical sub-regions channel model. ..........................................90 Figure 4-7. Base station and mobile station orientation for Lee's geometric model. ..................92 Figure 4-8. Geometry of base station, mobile station, and scatterers for the typical urban model.

..........................................................................................................................................93 Figure 4-9. Geometry of base station, mobile station, and two scattering regions for the bad

urban model. .....................................................................................................................93 Figure 4-10. Orientation of mobile station and base station among city streets for the urban

street geometric model, indicating types of propagation.....................................................94 Figure 4-11. Geometry of the ellipsoid (a=2, b=1) bounding surface for maximum multipath

delay: (a) three-dimensional view, (b) top view, (c) side view. ..........................................97 Figure 4-12. Locations of uniformly distributed scatterers throughout the ellipsoide bounding

surface; transmitter and receiver are located at foci............................................................98 Figure 4-13. An urban model based on the ellipsoidal geometry useful for three-dimensional

direction of arrival simulation and analysis........................................................................99 Figure 4-14. Scatterer distribution boundaries around transmitter and receiver for normalized

excess delay of 0.05, 0.3, and 0.9. ...................................................................................100 Figure 4-15. Ratio of minor to major axis of elliptical scatterer boundary versus normalized

excess delay. ...................................................................................................................101 Figure 4-16. Geometry, distance, and angle definitions for the geometric air-to-ground

ellipsoidal model. ............................................................................................................102 Figure 4-17. Unit vectors that define the axes for the ellipsoid model geometry. ....................108 Figure 4-18. Views of the ellipsoid, ground plane, and scattering region: (a) The oblique view

shows the overall geometry of the model and the ellipse outlining the scattering region, (b) The end view shows the y-axis width of the scattering region, (c) The side view shows the x-length of the scattering region which is clearly dependent upon the major axis elevation angle, (d) The top view shows the perfectly elliptical shape of the scattering region, (e) The ground-bounded view limits the ellipsoid to z<0 to show that the analytical scattering region exactly matches the ground-ellipsoid intersection. ...........................................................110

Figure 4-19. Marginal probability density function of direction of arrival for ψ=30 and ψ=80.........................................................................................................................................113

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Figure 4-20. Joint probability density functions for direction of arrival and normalized multipath delay for several elevation angles El................................................................................117

Figure 4-21. Marginal DOA and delay PDFs for the air-to-ground model...............................118 Figure 5-1. The measurement system was positioned on the roof of Whittemore near the corner

of the building, and the receiver array was mounted on a stand approximately six feet above roof level. ........................................................................................................................131

Figure 5-2. Sample power-delay profiles recorded at elements 2 and 3 of the antenna array. The solid line is the channel 2 PDP, and the dotted line is the channel 3 PDP.........................133

Figure 5-3. Complementary CDF for RMS delay spread based on measurements...................135 Figure 5-4. Number of signal components versus excess propagation delay. ..........................136 Figure 5-5. One set of power-delay profiles acquired simultaneously at each antenna element for

multipath magnitude correlation processing.....................................................................139 Figure 5-6. Delay bins evenly divide the delay between the first arriving signal component and

the last arriving signal component. ..................................................................................141 Figure 5-7. Map of the plaza where measurements were performed........................................149 Figure 5-8. Photo of measurement site with transmitter in the foreground at the LOS1 location.

........................................................................................................................................149 Figure 5-9. Sample power-delay profile from dense scatterer measurement site (NLOS1)......150 Figure 5-10. RMS delay spread CCDF for NLOS1.................................................................153 Figure 5-11. RMS delay spread CCDF for NLOS2.................................................................153 Figure 5-12. RMS delay spread CCDF for NLOS3.................................................................154 Figure 5-13. RMS delay spread CCDF for NLOS4.................................................................154 Figure 5-14. RMS delay spread CCDF for NLOS5.................................................................155 Figure 5-15. RMS delay spread CCDF for NLOS6.................................................................155 Figure 5-16. RMS delay spread CCDF for LOS1. ..................................................................158 Figure 5-17. RMS delay spread CCDF for LOS2. ..................................................................158 Figure 5-18. RMS delay spread CCDF for LOS3. ..................................................................159 Figure 5-19. RMS delay spread CCDF for LOS4. ..................................................................159 Figure 5-20. Average number of signal components using 16 delay bins for NLOS1..............161 Figure 5-21. Average number of signal components using 16 delay bins for NLOS2..............162 Figure 5-22. Average number of signal components using 16 delay bins for NLOS3..............162 Figure 5-23. Average number of signal components using 16 delay bins for NLOS4..............163 Figure 5-24. Average number of signal components using 16 delay bins for NLOS5..............163 Figure 5-25. Average number of signal components using 16 delay bins for NLOS6..............164 Figure 5-26. Average number of signal components using 16 delay bins for LOS1. ...............164 Figure 5-27. Average number of signal components using 16 delay bins for LOS2. ...............165 Figure 5-28. Average number of signal components using 16 delay bins for LOS3. ...............165 Figure 5-29. Average number of signal components using 16 delay bins for LOS4. ...............166 Figure 5-30. Average number of signal components using 16 delay bins for all NLOS

measurements..................................................................................................................166 Figure 5-31. Average number of signal components using 16 delay bins for all LOS

measurements..................................................................................................................167 Figure 5-32. Relationship between two multipath components arriving with different delays with

all other factors held constant. .........................................................................................171

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Figure 5-33. NLOS1 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................173

Figure 5-34. NLOS1: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................173

Figure 5-35. NLOS2 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................174

Figure 5-36. NLOS2: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................174

Figure 5-37. NLOS3 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................175

Figure 5-38. NLOS3: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................175

Figure 5-39. NLOS4 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................176

Figure 5-40. NLOS4: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................176

Figure 5-41. NLOS5 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................177

Figure 5-42. NLOS5: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................177

Figure 5-43. NLOS6 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................178

Figure 5-44. NLOS6: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................178

Figure 5-45. LOS1 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................181

Figure 5-46. LOS1: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................181

Figure 5-47. LOS2 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................182

Figure 5-48. LOS2: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................182

Figure 5-49. LOS3 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................183

Figure 5-50. LOS3: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................183

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Figure 5-51. LOS4 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values. ..........................................................................................................184

Figure 5-52. LOS4: PDF created using data points and corresponding theoretical Gaussian distribution. .....................................................................................................................184

Figure 5-53. Location of the transmitter antenna under aircraft fuselage and wing..................190 Figure 5-54. Ground location of the receiver array for the air-to-ground measurements..........190 Figure 5-55. Sample power-delay profile for 7.5 degree elevation angle.................................192 Figure 5-56. Sample power-delay profile for 15 degree elevation angle..................................192 Figure 5-57. Sample power-delay profile for 22.5 degree elevation angle...............................193 Figure 5-58. Sample power-delay profile for 30 degree elevation angle..................................193 Figure 5-59. RMS delay spread CCDF for all measured elevation angles. ..............................194 Figure 5-60. Average number of signal components using 16 delay bins for 7.5 degree elevation

angle. ..............................................................................................................................196 Figure 5-61. Average number of signal components using 16 delay bins for 15 degree elevation

angle. ..............................................................................................................................196 Figure 5-62. Average number of signal components using 16 delay bins for 22.5 degree

elevation angle. ...............................................................................................................197 Figure 5-63. Average number of signal components using 16 delay bins for 30 degree elevation

angle. ..............................................................................................................................197 Figure 5-64. Average number of signal components using 16 delay bins for each elevation

angle. ..............................................................................................................................198 Figure 5-65. Average number of signal components using 16 delay bins for all air-to-ground

measurements..................................................................................................................199 Figure 6-1. Block diagram of wideband vector channel simulator. .........................................204 Figure 6-2. Geometry plot produced by the simulator for the ESR model showing a top view of

transmitter (+) and receiver (o) locations, elliptical boundaries, scatterer locations, and propagation paths. ...........................................................................................................208

Figure 6-3. Geometry plot produced by the simulator for the GBSBE model showing a top view of transmitter (+) and receiver (o) locations, elliptical boundary, scatterer locations, and propagation paths. ...........................................................................................................208

Figure 6-4. Geometry plot produced by the simulator for the GAGE model showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and propagation paths. Elevation angle in this case is 45 degrees. .....210

Figure 6-5. Geometry plot produced by the simulator for the GAGE model, showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and propagation paths. Elevation angle in this case is 90 degrees. .....211

Figure 6-6. Geometry plot produced by the simulator for the GAGE model, showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and propagation paths. Elevation angle in this case is 0 degrees........212

Figure 6-7. Dense uniform distribution of scatterers in the seventh scattering region for the GAGE model. .................................................................................................................214

Figure 6-8. Absolute propagation delay for the GBSBE and ESR models is calculated using (a) the distance from the transmitter to the center of the receiver array by way of the scatterer and (b) the distance between parallel lines through the receiver array center and the array element drawn orthogonally to the propagation path........................................................215

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Figure 6-9. Absolute propagation delay for the GAGE model is calculated using (a) the distance from the transmitter to the center of the receiver array by way of the scatterer and (b) the distance between parallel lines through the receiver array center and the array element drawn orthogonally to the propagation path. ....................................................................216

Figure 6-10. Typical strength-versus-delay plot (ESR model) for a channel impulse response affected only by log-distance path loss and reflection loss (non-line-of-sight channel).....217

Figure 6-11. Top and side view of propagation environment for air-to-ground radio channels.........................................................................................................................................219

Figure 6-12. Example strength-versus-delay plot (GAGE model) for a channel impulse response affected only by log-distance path loss and reflection loss. ..............................................220

Figure 6-13. Simulated channel impulse response for the ESR model after the LOS component is added. ..........................................................................................................................221

Figure 6-14. Simulated channel impulse response for the ESR model after the log-normal strength variation has been applied. .................................................................................222

Figure 6-15. Channel impulse response of four array element superimposed on one plot after correlated Rayleigh fading has been applied. ...................................................................226

Figure 6-16. Definition of direction of arrival for the ESR and GBSBE models......................227 Figure 6-17. Definition of direction of arrival for the GAGE model. ......................................227 Figure 7-1. A block diagram of the process for evaluating channel models.............................230 Figure 7-2. Example of geometric channel simulation (elliptical sub-regions model) showing

transmitter location (plus symbol at focus), receiver location (circle at other focus), scatterers (dots), propagation paths (yellow lines), and elliptical sub-region boundaries. .233

Figure 7-3. NLOS 1 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................235

Figure 7-4. NLOS 2 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................235

Figure 7-5. NLOS 3 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................236

Figure 7-6. NLOS 4 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................236

Figure 7-7. NLOS 5 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................237

Figure 7-8. NLOS 6 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................237

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Figure 7-9. NLOS 6 simulated multipath strength (ESR) for 1000 impulse responses (without Rayleigh fading): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown............................................................238

Figure 7-10. NLOS 6 simulated multipath strength (ESR) for 1000 impulse responses (Rayleigh fading, no log-normal deviation): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. Standard deviation about best-fit line of 5.4 dB results ..................................................................................239

Figure 7-11. LOS 1 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................240

Figure 7-12. LOS 2 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................240

Figure 7-13. LOS 3 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................241

Figure 7-14. LOS 4 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................241

Figure 7-15. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS1 (b) NLOS2.243 Figure 7-16. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS3 (b) NLOS4.243 Figure 7-17. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS5 (b) NLOS6.244 Figure 7-18. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS6 simulated

using log-normal variation about best-fit power (dB) versus log-delay line, and (b) NLOS6 simulated using log-normal variation and Rayleigh fading for multipath components......244

Figure 7-19. RMS delay spread CCDF for simulated (ESR) channels (a) LOS1 (b) LOS2......246 Figure 7-20. RMS delay spread CCDF for simulated (ESR) channels (a) LOS3 (b) LOS4......246 Figure 7-21. Signal strength CDF for each NLOS location derived from (a) channel impulse

response simulations (ESR) and (b) measured channels. ..................................................249 Figure 7-22. Signal strength CDF for each LOS location derived from (a) channel impulse

response simulations (ESR) and (b) measured channels. ..................................................249 Figure 7-23. CDF of received signal strength using maximal ratio combining and using a single

antenna for NLOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................251

Figure 7-24. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................251

Figure 7-25. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................252

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Figure 7-26. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................252

Figure 7-27. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS5 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................253

Figure 7-28. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS6 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................253

Figure 7-29. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................254

Figure 7-30. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................255

Figure 7-31. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................255

Figure 7-32. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................................................................................................256

Figure 7-33. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................257

Figure 7-34. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................258

Figure 7-35. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................258

Figure 7-36. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................259

Figure 7-37. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS5 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................259

Figure 7-38. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS6 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................260

Figure 7-39. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................261

Figure 7-40. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................262

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Figure 7-41. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................262

Figure 7-42. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels. .........................................263

Figure 7-43. Example of geometric channel simulation (GBSBE model) showing transmitter location (plus symbol at focus), receiver location (circle at other focus), scatterers (dots), propagation paths (yellow lines), and elliptical boundary for uniformly distributed scatterers. ........................................................................................................................268

Figure 7-44. NLOS1 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. .............................................................................................................269

Figure 7-45. NLOS2 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. .............................................................................................................270

Figure 7-46. NLOS3 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. .............................................................................................................270

Figure 7-47. NLOS4 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. .............................................................................................................271

Figure 7-48. NLOS5 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. .............................................................................................................271

Figure 7-49. NLOS6 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. .............................................................................................................272

Figure 7-50. LOS1 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................273

Figure 7-51. LOS2 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................273

Figure 7-52. LOS3 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................274

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Figure 7-53. LOS4 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown..............................................................................................................................274

Figure 7-54. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS1 (b) NLOS2.........................................................................................................................................276

Figure 7-55. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS3 (b) NLOS4.........................................................................................................................................276

Figure 7-56. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS5 (b) NLOS6.........................................................................................................................................277

Figure 7-57. RMS delay spread CCDF for simulated (GBSBE) channels (a) LOS1 (b) LOS2.278 Figure 7-58. RMS delay spread CCDF for simulated (GBSBE) channels (a) LOS3 (b) LOS4.278 Figure 7-59. Signal strength CDF for each NLOS location derived from (a) channel impulse

response simulations (GBSBE) and (b) measured channels. ............................................280 Figure 7-60. Signal strength CDF for each LOS location derived from (a) channel impulse

response simulations (GBSBE) and (b) measured channels. ............................................281 Figure 7-61. CDF of received signal strength using maximal ratio combining and using a single

antenna for NLOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................282

Figure 7-62. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................282

Figure 7-63. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................283

Figure 7-64. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................283

Figure 7-65. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS5 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................284

Figure 7-66. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS6 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................284

Figure 7-67. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................................285

Figure 7-68. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................................286

Figure 7-69. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................................286

Figure 7-70. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels. .........................................................................................................................287

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Figure 7-71. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................288

Figure 7-72. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................289

Figure 7-73. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................289

Figure 7-74. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................290

Figure 7-75. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS5 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................290

Figure 7-76. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS6 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................291

Figure 7-77. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................292

Figure 7-78. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................293

Figure 7-79. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................293

Figure 7-80. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.....................................294

Figure 7-81. Example of geometric air-to-ground channel model simulation showing transmitter location (plus symbol at elevated ellipsoid focus), receiver location (circle at ellipsoid and ground ellipse shared focus), scatterers (dots), propagation paths (green lines), and sub-region boundaries of constant propagation delay. ............................................................298

Figure 7-82. CDF of RMS delay spread for four elevation angles for (a) simulated (GAGE) channel impulse responses and (b) measured channels. A constant reflection loss was used.........................................................................................................................................299

Figure 7-83. CCDF of RMS delay spread for four elevation angles for (a) simulated (GAGE) channel impulse responses and (b) measured channels. Reflection loss was defined to be a function of elevation angle. .............................................................................................300

Figure 7-84. Scatter plot of multipath strength versus log of propagation delay for the 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles........................................................................................................302

Figure 7-85. Scatter plot of multipath strength versus log of propagation delay for the 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles........................................................................................................302

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Figure 7-86. Scatter plot of multipath strength versus log of propagation delay for the 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles. .......................................................................................303

Figure 7-87. Scatter plot of multipath strength versus log of propagation delay for the 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles........................................................................................................303

Figure 7-88. Signal strength CDF for each air-to-ground elevation angle derived from (a) channel impulse response simulations and (b) measured channels. ..................................305

Figure 7-89. CDF of received signal strength using maximal ratio combining and using a single antenna for 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels. .............................................................................................306

Figure 7-90. CDF of received signal strength using maximal ratio combining and using a single antenna for 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels. .............................................................................................306

Figure 7-91. CDF of received signal strength using maximal ratio combining and using a single antenna for 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels...............................................................................307

Figure 7-92. CDF of received signal strength using maximal ratio combining and using a single antenna for 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels. .............................................................................................307

Figure 7-93. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels. ................309

Figure 7-94. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels. ................309

Figure 7-95. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels. ................310

Figure 7-96. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels. ................310

Figure A-1. Data flow through measurement receiver to MATLAB workspace. .....................324 Figure A-2. Sample m-file listing showing how to use the signal data and produce real-time

plots. ...............................................................................................................................327 Figure A-3. MATLAB interface application launched from the measurement receiver software.

........................................................................................................................................328 Figure A-4. Spectrum plot produced by m-file listed in Figure A-2. .......................................328 Figure B-1. Transmitter section of VT-STAR. .......................................................................332 Figure B-2. Photograph of VT-STAR transmitter section. ......................................................333 Figure B-3. Receiver section of the VT-STAR. ......................................................................334 Figure B-4. Photograph of VT-STAR receiver RF section......................................................334

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List of Tables

Table 2-1. Comparison of relative signal bandwidth for a 1.25 MHz-wide CDMA signal used for voice and data services, where the base information bit rate is 19.2 Kbps and the carrier frequency is 825 MHz, in a multipath environment with a 4 µs excess delay. ....................15

Table 2-2. Advantages of using smart antennas at a transmitter or receiver...............................17 Table 2-3. Expressions for computing signals incident on the elements of an antenna array. ....23 Table 3-1. Target applications of measurement receiver. ..........................................................46 Table 3-2. High-level design goals for measurement receiver...................................................47 Table 3-3. Radio frequency (RF) specifications for measurement receiver. ..............................48 Table 3-4. System specifications for measurement receiver......................................................49 Table 3-5. Measurement system link analysis for outdoor radio channel (1 mile, line-of-sight).49 Table 3-6. Measurement receiver RF section analysis for outdoor radio channel. .....................50 Table 3-7. System noise analysis and noise results for outdoor radio channel. ..........................51 Table 3-8. Description of the generic hardware-specific receiver object interface functions......61 Table 4-1. Requirements of channel models versus radio access technology.............................77 Table 4-2. Equations that describe the intersection of a tilted, three-dimensional excess delay

bounding volume and a planar surface containing scatterers. ...........................................106 Table 5-1. Results of a wideband measurement campaign in a suburban environment [Wil01].

........................................................................................................................................122 Table 5-2. Results of a spatial-temporal measurement campaign [Lar99]. ..............................124 Table 5-3. Summary of results of campaign to measure correlation of spatial signatures [Kav00].

........................................................................................................................................125 Table 5-4. Results of a measurement campaign using a light aircraft to study land mobile

satellite communications [Smi91]....................................................................................127 Table 5-5. Summary of results for a campaign that measured land mobile satellite channels

[Jah96]. ...........................................................................................................................129 Table 5-6. Results of an air-to-ground measurement campaign [Dye98].................................130 Table 5-7. Details of the measurement system setup and transmitter/receiver locations for the

Whittemore roof measurements. ......................................................................................132 Table 5-8. RMS delay spread statistics. ..................................................................................134 Table 5-9. Distribution of multipath components among delay bins of power-delay profiles. .136

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Table 5-10. Processing details for signal component correlation processing. ..........................144 Table 5-11. Correlation coefficients for signal component magnitude across antenna elements (4

delay bins).......................................................................................................................145 Table 5-12. Correlation coefficients for signal component magnitude across antenna elements (8

delay bins).......................................................................................................................145 Table 5-13. Correlation coefficients for signal component magnitude across antenna elements

(16 delay bins).................................................................................................................146 Table 5-14. Transmitter-receiver separation for each transmitter location. ..............................150 Table 5-15. Link budget for terrestrial measurements on the VT campus................................151 Table 5-16. RMS delay spread results for NLOS locations for the dense scatterer measurement

campaign.........................................................................................................................152 Table 5-17. Summary of RMS delay spread results for dense-scatterer measurement site. ......156 Table 5-18. RMS delay spread results for LOS locations for the dense-scatterer measurement

campaign.........................................................................................................................157 Table 5-19. Excess delay spread values for NLOS locations...................................................160 Table 5-20. Excess delay values for LOS locations. ...............................................................160 Table 5-21. Average number of signal components per delay bin per profile for NLOS

measurements..................................................................................................................167 Table 5-22. Average number of signal components per delay bin per profile for LOS

measurements..................................................................................................................168 Table 5-23. Average number of signal components per power-delay profile for LOS and NLOS

measurements..................................................................................................................169 Table 5-24. Path loss exponent, standard deviation of multipath strength about best-fit line, and

intercept of best-fit line for NLOS measurements. ...........................................................179 Table 5-25. Path loss exponent, standard deviation of multipath strength about best-fit line,

intercept of best-fit line, and LOS strength above best-fit line for LOS measurements. ....185 Table 5-26. Summary of multipath strength results for all measurements at the dense-scatterer

site. .................................................................................................................................186 Table 5-27. NLOS Measurement Results (4 propagation delay bins). .....................................187 Table 5-28. NLOS Measurement Results (8 propagation delay bins). .....................................187 Table 5-29. NLOS Measurement Results (16 propagation delay bins). ...................................188 Table 5-30. Link budget calculations for each of the four elevation angles measured. ............189 Table 5-31. RMS delay spread results for the air-to-ground measurement campaign. .............191 Table 5-32. Excess delay spread values for air-to-ground measurements. ...............................195 Table 5-33. Average number of signal components per delay bin per profile for air-to-ground

measurements..................................................................................................................199 Table 5-34. Average number of signal components per power-delay profile for each elevation

angle measured during air-to-ground measurements. .......................................................200 Table 6-1. Input parameters used by the wideband vector channel model simulator................206 Table 6-2. Relationship between correlation coefficients of Gaussian random variables and

correlation coefficients of Rayleigh random variables computed from the envelope of the Gaussian random variables. .............................................................................................224

Table 7-1. Major simulation parameters for elliptical sub-regions model for NLOS channels. 232 Table 7-2. Major simulation parameters for elliptical sub-regions model for LOS channels....232 Table 7-3. RMS delay spread results for simulations (ESR) and measurements of NLOS dense

scatterer locations............................................................................................................242

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Table 7-4. RMS delay spread results for simulations (ESR) and measurements of LOS dense scatterer locations............................................................................................................245

Table 7-5. Excess delay spread values for simulated (ESR) and measured NLOS channel impulse responses. ..........................................................................................................247

Table 7-6. Excess delay spread values for simulated (ESR) and measured LOS channel impulse responses.........................................................................................................................247

Table 7-7. Approximate diversity gain for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels. .........................................................254

Table 7-8. Approximate diversity gain for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels. .........................................................256

Table 7-9. Approximate fading levels differences between 2-D rake output and single channel output for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels. .........................................................................................................260

Table 7-10. Approximate fading levels differences between 2-D rake output and single channel output for LOS locations computed from simulated (ESR) channel impulse responses and measured channels. .........................................................................................................263

Table 7-11. Major simulation parameters for GBSBE model for NLOS channels. ..................267 Table 7-12. Major simulation parameters for GBSBE model for LOS channels. .....................267 Table 7-13. RMS delay spread results for simulations (GBSBE) and measurements of NLOS

dense scatterer locations. .................................................................................................275 Table 7-14. RMS delay spread results for simulations (GBSBE) and measurements of LOS

dense scatterer locations. .................................................................................................277 Table 7-15. Excess delay spread values for simulated (GBSBE) and measured NLOS channel

impulse responses. ..........................................................................................................279 Table 7-16. Excess delay spread values for simulated (GBSBE) and measured LOS channel

impulse responses. ..........................................................................................................279 Table 7-17. Approximate diversity gain for NLOS locations computed from simulated (GBSBE)

channel impulse responses and measured channels. .........................................................285 Table 7-18. Approximate diversity gain for NLOS locations computed from simulated (GBSBE)

channel impulse responses and measured channels. .........................................................287 Table 7-19. Approximate fading levels differences between 2-D rake output and single channel

output for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels. ...................................................................................................291

Table 7-20. Approximate fading levels differences between 2-D rake output and single channel output for LOS locations computed from simulated (GBSBE) channel impulse responses and measured channels. ...................................................................................................294

Table 7-21. Major simulation parameters for geometric air-to-ground ellipsoidal channel model.........................................................................................................................................298

Table 7-22. Reflection losses as a function of elevation angle used to produce the most accurate RMS delay spread results for the GAGE model. ..............................................................300

Table 7-23. RMS delay spread results for air-to-ground simulations using the GAGE model versus measurements.......................................................................................................301

Table 7-24. Excess delay spread values for simulated and measured air-to-ground channel impulse responses. ..........................................................................................................304

Table 7-25. Approximate diversity gain for simulated and measured air-to-ground channel impulse responses. ..........................................................................................................308

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Table 7-26. Approximate fading levels differences between 2-D rake output and single channel output for air-to-ground channels computed from simulated channel impulse responses and measured channels. .........................................................................................................311

Table A-1. Description of variables passed into MATLAB workspace by measurement receiver.........................................................................................................................................326

Table B-1. Specifications for VT-STAR transmitter and receiver. ..........................................335

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1

Chapter 1 Introduction

Wireless communications has enabled the creation of a world once only dreamed about in

fiction. Wireless devices and capabilities that are commonplace today but were unimaginable in

the not-too-distant past are the result of an unrelenting quest for understanding through research

and development in radio technology. Wireless has become pervasive throughout advancements

in fields ranging from farming to medicine. With the emergence of every new mobile

application involving storing, displaying, or communicating information, a new application for

wireless is born.

1.1 Motivation and Challenges in Wireless

Commercial wireless communication is a primary driver of the development of radio technology.

One of the biggest challenges in commercial wireless is satisfying an enormous and growing

demand for mobile communications with a limited and fixed amount of resources. Expectations

for mobile communications have risen to the point where wireless quality of service needs to

equal or exceed that of wire line. The success of early voice cellular systems had whetted the

appetite of consumers who now crave instant messaging, web browsing, electronic mail, and

many other types of services normally offered through wired Internet access but until just

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CHAPTER 1 – INTRODUCTION

2

recently not truly practical over wireless links. As the wireless subscriber base grows and

service offerings expand, the simple fact is that wireless networks need to provide more bi-

directional bits-per-second in any given area.

Voice communication capabilities over wireless networks has matured to a level of acceptable

quality and reliability where wireless phones have become an acceptable replacement for home

and office. Widespread coverage and acceptable unit costs drive the more adventurous to

exclusive use of wireless, forgoing diminishing advantages of wire line. Up until recently, a

major drawback was the loss of reasonable data connectivity speeds for those who chose the

wireless route. While the maximum wire line modem speed of 53.3 kbps1 falls short of blazing

data speed, circuit-switched wireless phone transfer rates of 19.2 kbps or less dissatisfy even the

most modest of Internet enthusiasts. Emerging today are not only paper standards that promise

higher data rates but also actual system deployments whose delivered capabilities rival those of

wire line in at least a stochastic sense. Early deployments of CDMA-2000-1xRTT [IS2000],

known in the field by a variety of nicknames for obvious conversational reasons, have

demonstrated payload data rates exceeding 100 kbps.

However, challenges in addressing bits-per-second issues are only aggravated by a growing

acceptance of high-speed, home Internet access offered by DSL, cable modem, direct satellite,

and even Ethernet directly to residences. As more of the population goes online with fast wired

connections, expectations for quick data access will rise and Internet service developers will

become less concerned with building low transfer rate requirements into their applications.

Developments are needed in wireless to permit continued growth in the application and use of

wireless for commercial services. Practical smart antennas that fit the forms of contemporary

devices need to be developed to fully exploit spatial properties of signals, since all received

energy not transmitted by the desired sender is interference to the desired recipient, and all

transmitted energy not received by the desired recipient is interference to all other users.

Modulation schemes that tolerate coexistence in the frequency and time domains need to be

pursued. New multiple access techniques and spectrum sharing algorithms need to be developed

1 Although modems are capable of 56 kbps, U.S. law restricts transmission speeds over analog telephone lines to 53.3 kbps.

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so that frequency spectrum can be fully occupied, since vacancies observed within allocated

bands on a spectrum analyzer equate to wasted resources. Developments in these areas are

essential to industry, or we risk being decelerated to a state analogous to trying to conduct

business today with the voice and data communication capabilities of decades ago.

A less visible but important driver of technical advances in wireless involves development for

military and civil applications related to national defense, law enforcement, public safety, and

navigation, where performance of wireless systems concerns not productivity and profit but life

and limb. Increasingly burdening requirements are being placed on military wireless

communication systems, as tactical military operations today rely on video from unmanned

drones, intercepted communications, and airborne communications nodes for relaying voice and

data from the field. Efficient and safe operations require reliable, uninterrupted radio links that

achieve low probability of detection and low probability of intercept while simultaneously

achieving the highest performance possible.

Outside of the military, civilians rely on wireless communication systems for safety so that

emergency personnel, law enforcement agents, utilities employees, air traffic controllers, and a

variety of other service personnel can do their jobs. While deficiencies may be tolerable today, a

rise in demand and capability requirements will accelerate the need for wireless engineers to

strive for faster and more efficient communication systems. As an example, present day civilian

aviation radio communication is a snapshot of history, where large airliners and general aviation

aircraft alike use amplitude modulation (resulting in signal quality similar to that of broadcast

AM radio) for communications with air traffic control. This relatively low quality and congested

system is the primary method that most commercial and private pilots use for collision avoidance

to steer clear of other aircraft, for weather avoidance to circumnavigate weather phenomena such

as thunderstorms, and for navigational guidance to descend to altitudes as low as 200 feet above

ground during instrument approaches. Developments in aviation data communications are

needed to more effectively get weather data, clearances, and traffic information into the cockpit.

Developments in wireless technologies that serve the public and the nation in other ways are

likewise needed.

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Indeed, we have become a society dependent upon wireless to sate our appetite for

communications and mobility. Advances in wireless communications facilitate advances in all

areas of civilization, moving us forward as fast as our growing expectations for quality and ease

of life and work.

1.2 Foundations of Progress in Wireless

Frequency spectrum is the raw material with which wireless services are built. Long before a

swarm of electromagnetic fields exponentially consumed the frequency spectrum around the

planet, pioneering experimenters in radio produced the first intentional manmade disturbances in

the spectrum distinguishable from noise with crude but inventive devices. Wireless

communications was truly born when the first spark gap transmitters splattered energy into RF

bands, but accounts of wireless experiments started to become noteworthy in public memory

around the time following the first wireless transmission across the English Channel in 1899 by

Guglielmo Marconi. The world seriously took notice on December 12, 1901, the date when

global wireless communications was born by Marconi’s first successful reception of radio signals

across the Atlantic between the Poldhu station in Cornwall, England, and Signal Hill in

Newfoundland.

In these early days of radio, preservation of frequency spectrum was not a concern and

government regulation of the airwaves as we know it today was nonexistent. In the Radio Act of

1912, which mandated federal licensing of all radio stations [DoC14] and banished amateur use

to the “less useful” radio bands above 1.5 MHz [Wes00], the United States government showed

its first bit of concern over this newly discovered natural resource called radio frequency

spectrum. Over the next several decades, all of the radio frequency spectrum between 9 KHz

and 300 GHz would be allocated for commercial, military, and private use [DoC96]. The price

tag placed on spectrum would truly be realized in the 1990s when the average consumer

developed a perceived need for anywhere, anytime, instant communications. During this time

period, the privilege to use spectrum throughout a particular geographical region by service

providers could cost millions of dollars after outbidding a competitor in an auction for slices of

bandwidth.

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Advances since the early exploration of radio have been made in many sub-fields of wireless

communications, all working towards the goal of more efficient use of radio resources. Multiple

access techniques have evolved to allow users to share spectrum in a manner that allows soft,

sometimes imperceptible degradation of service to occur when capacity is taxed rather than

forcing hard failures of mobile links. Adaptive antenna array systems have aged through a

period of adolescence in academia and have been accepted in industry as a viable path to

increased quality and capacity for commercial networks. Software-defined radios, once a

concept merely evangelized but not realized because of digital signal processing constraints,

have found their way in early form into commercial products. Developments in coding

algorithms, RF hardware, integrated circuits, and many other areas have all improved the quality

of personal communications devices in terms of reliability, cost, function, form factor, and

overall desirability of integrating such devices into everyday life. As applications for wireless

become more plentiful, development of wireless technology through academic and industrial

research must continue to ensure capacity never reaches the point of saturation.

1.3 Research Issues Covered

As with all focused research, the work described in this dissertation was performed with the

intent of contributing to the mosaic of wireless developments directed toward advancing basic

theory and practical knowledge in the field. The research presented here reaches into the

coupling among three areas in wireless communications: radio channel measurements and

modeling; smart antenna arrays; and design, development, and application of software radio

technology.

Behaviors of the actual hardware and software that implement radio communications devices are

either deterministic in nature or, at least, well understood stochastic processes. Once designed, a

piece of hardware can generally be modeled and implemented in a simulator, and changes to

model are likely related to changes in the hardware. Behavior of radio channels, however, is

typically a moving target, requiring evolutions of modeling and characterization to support

leading-edge developments in technology and the latest applications of wireless. To support this

evolution, this research addresses channel measurement and modeling related to smart antenna

arrays.

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Literature on basic signal and antenna array theory was gathered and reviewed to provide a

foundation of well understood and accepted theory. This dissertation reviews complex signal

fundamentals, signal representations for smart antenna arrays, and channel characteristics related

to smart antenna performance. Vector channels, a term used to describe multidimensional

channel impulse responses for antenna arrays, are a common theme throughout all discussions of

new and old developments.

A large part of the initial research was dedicated to the development of a software-defined

measurement receiver for characterizing wideband vector channels. Measurement results from

this system were required in order to pursue subsequent research topics. The design of the

measurement system receiver and transmitter included provisions to serve as a test bed for

antenna array experiments and as a platform for experiments requiring high-speed sampling and

wideband signal acquisition.

Once the operational measurement system had been developed, channel modeling literature was

reviewed. Of interest were existing channel models that base results on propagation environment

geometry; these geometric channel models provide spatial and temporal signal information for

simulating wireless communications systems. Through this research, accepted channel modeling

techniques were used to produce a new geometric channel model for air-to-ground

communications.

With channel modeling techniques and considerations in mind, measurement campaigns were

designed and conducted using the new measurement system to characterize channels and collect

received signal data relevant to evaluation of a subset of the channel models studied. Three

multipath environments were characterized with information on channel impulse responses and

the effect of the channel on received signals. Two terrestrial environments were measured. The

first environment was used to characterize vehicular rooftop-to-ground environment, and the

second was used to characterize a dense-scatterer ground-to-ground environment. An airborne

measurement campaign was conducted to measure air-to-ground channels, where the ground-

based receiver was surrounded by structures that obstructed and reflected radio signals.

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Traditional and newly developed methods of processing signal data were employed to produce

measurement results.

A channel model simulator was developed to produce channel impulse responses using the three

channel models under evaluation. The simulator accepts as input sets of results from the

terrestrial and airborne measurement campaigns. Methods used to simulate strength, delay, and

direction of arrival of multipath components are described.

Finally, three geometric channel models were evaluated by comparing their output with

measurements of the channels they were intended to represent. Comparisons were made

between simulations and measurements with regard to processed parameters including RMS

delay spread, excess delay spread, multipath component strength distributions, multipath fading

characteristics, antenna diversity gain, and gain achieved through the use of a two-dimensional

rake receiver. Accuracies and discrepancies are discussed for each result.

1.4 Organization of This Dissertation

Chapter 2 provides a review of signal representation and radio channels from the perspective of

analysis and design of antenna arrays. Notation is defined and key concepts related to antenna

arrays are discussed, and parameters for characterizing signals and channels are presented.

Chapter 3 describes the development of the vector channel receiver antenna array test bed and

wideband measurement system, explaining system specifications and capabilities of the software

and hardware. Topics related to software-defined radio, object orientation, RF hardware, and

software architecture are covered. The FPGA-based transmitter used to produce wideband

signals for power-delay profile measurement is also described. Chapter 4 begins with a review

of existing radio channel models and an introduction to new models. The newly developed

geometric air-to-ground model is documented, including analytical and simulated results for

temporal-spatial multipath characteristics. Chapter 5 gives a review of past channel

measurements and presents results of the new measurements completed for this research. In

Chapter 6, details of the channel simulator used to implement three geometric channel models

are presented. Finally, Chapter 7 presents evaluations of channel models based on their ability to

accurately produce results in comparison to measured channels. Output from the channel model

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CHAPTER 1 – INTRODUCTION

8

simulator and results of the measurement campaigns described in the earlier chapters serve as the

basis for this comparison.

Together, these chapters unite theory, simulation, and measurement. Detailed data presented in

each chapter provides opportunities for additional analysis. Documentation of the measurement

system hardware and software supports evolution of the current system or development of new

systems. As much as it is the author’s intent to provide answers and information to solve

problems, it is also the intent to raise new questions and launch further research.

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Chapter 2 Signal Fundamentals for Antenna Arrays

Analysis and simulation of antenna arrays requires consideration of multiple time-domain signals

simultaneously. With a single signal source present, the minimum number of signals that needs

to be represented is equal to the number of array elements. When multiple signals are present in

a multipath environment, the number of signals that must be considered grows rapidly. This

chapter reviews fundamental signal concepts and introduces signal representations for antenna

arrays. Also, characterization of signals and radio channels through which they propagate is

discussed.

2.1 Complex Signal Fundamentals

In this section, basic signal principles that form the foundation for antenna array signal

processing are presented. For a given bandpass signal2, all of the information is contained in its

complex envelope representation. Phase, amplitude, and relative frequency (time-varying phase)

characteristics can be preserved when the carrier is removed from a bandpass signal. The

2 A bandpass signal is a waveform that has a spectral magnitude that is nonzero for frequencies concentrated in a band about a frequency ω = ±ωc and that has negligible spectral magnitude elsewhere [Cou90]. The frequency ωc is the carrier frequency. The bandpass signal generally has negligible spectral magnitude at ωc = 0 (DC).

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CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

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complex representation of signals simplifies analysis and simulations of systems without

compromising accuracy of results.

2.1.1 The Complex Envelope

Sinusoids provide a set of basis functions with which all wireless communication signals can be

represented. In formation is conveyed using sinusoidal signals by time-varying their amplitude,

phase, and/or frequency. Let us first define the signal ( )tr~ , which is a real-valued, bandpass

signal given by

( ) ( ) ( )( )tttRtr c θω += cos~ . ( 2.1 )

This signal has a carrier frequency cω , and the time-varying amplitude and phase are given by

( )tR and ( )tθ , respectively. This signal can also be expressed as

( ) ( ) ( ){ }tjtrtr cωexpRe~ = . ( 2.2 )

The complex-valued signal ( )tr is called the complex envelope of signal ( )tr~ , and ( )tr contains

all of the information of ( )tr~ except for the carrier frequency cω . The time varying amplitude

( )tR in equation ( 2.1 ) is related to the complex envelope ( )tr by

( ) ( ) ( ){ }( ) ( ){ }( )22 ImRe trtrtrtR +== . ( 2.3 )

The time varying phase ( )tθ in equation ( 2.1 ) is related to the complex envelope ( )tr by

( ) ( ) ( ){ }( ){ }

=∠=

trtr

trtReIm

arctanθ . ( 2.4 )

The complex envelope ( )tr can be represented using two real-valued functions, ( )trI and ( )trQ ,

given by

( ) ( ){ } ( ) ( )( )ttRtrtrI θcosRe == ( 2.5 )

and

( ) ( ){ } ( ) ( )( )ttRtrtrQ θsinIm == . ( 2.6 )

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CHAPTER 2 – SIGNAL FUNDAMENTALS FOR ANTENNA ARRAYS

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The function ( )trI is called the in-phase component or simply the I-component. The function

( )trQ is called the quadrature component or simply the Q-component. The in-phase and

quadrature components are combined to form ( )tr using

( ) ( ) ( )tjrtrtr QI += . ( 2.7 )

If we combine equation ( 2.7 ) with equation ( 2.2 ), a direct relationship between the bandpass

signal and the I- and Q-components is produced,

( ) ( ) ( ){ }tjtrtr cωexpRe~ =

( ) ( )( ) ( )( ){ }tjtrtr cQI ωexpRe +=

( ) ( )( ) ( ) ( )( ){ }tjttrtr ccQI ωω sincosRe ++=

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ){ }ttrttjrttjrttr cQcQcIcI ωωωω sincossincosRe −++= .

( 2.8 )

Therefore,

( ) ( ) ( ) ( ) ( )ttjrttrtr cQcI ωω sincos~ −= . ( 2.9 )

The use of real-valued in-phase and quadrature signal components allows processing in analog

circuits, where only real-valued voltages and currents exist; also, native instructions of digital

signal processors generally only operate on real-valued arguments.

The complex envelope ( )tr is typically a baseband signal, since the carrier has been removed

from the signal. As such, the complex envelope ( )tr may be called a complex baseband signal.

2.1.2 Converting Bandpass Signals to Complex Envelopes

Bandpass signals can be converted to their equivalent baseband complex envelops using a

process known as quadrature down-conversion (or complex down-conversion). Consider the

bandpass signal of the form

( ) ( ) ( )( )tttRtr c θω += cos~ . ( 2.10 )

The in-phase component can be extracted by multiplying the bandpass signal ( )tr~ by ( )tcωcos2

and low-pass filtering the result. This is demonstrated by first performing the multiplication:

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( ) ( )( ) ( ) ( )( ) ( )( )tttRttr ccc ωτθωω cos2coscos2~ +=

( ) ( )( ) ( )ttttR cc ωθω coscos2 +=

( ) ( )( ) ( )( )

−++++= tttttttR cccc ωθωωθω cos

21

cos21

2

( ) ( )( ) ( )( )( )ttttR c θθω cos2cos ++=

( ) ( )( ) ( ) ( )( )ttRtttR c θθω cos2cos ++= .

( 2.11 )

Then, the low-pass filtering attenuates components with frequencies near tcω2 :

( ) ( )( ){ } ( ) ( )( )ttRttrLPF c θω coscos2~ =

( )trI= . ( 2.12 )

The quadrature component can be extracted by multiplying the bandpass signal ( )tr~ by

( )tcωsin2− and low-pass filtering the result.

( ) ( )( ) ( ) ( )( ) ( )( )tttRttr ccc ωτθωω sin2cossin2~ −+=−

( ) ( )( ) ( )ttttR cc ωθω sincos2 +−=

( ) ( )( ) ( )( )

−+−++−= tttttttR cccc ωθωωθω sin

21

sin21

2

( ) ( )( ) ( )( )( )ttttR c θθω sin2sin ++=

( ) ( )( ) ( ) ( )( )ttRtttR c θθω sin2sin ++= .

( 2.13 )

As in the previous case, the low-pass filtering attenuates components with frequencies near

tcω2 :

( ) ( )( ){ } ( ) ( )( )ttRttrLPF c θω sinsin2~ =−

( )trQ= . ( 2.14 )

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( ) ( ) ( )( )tttRtr c θω += cos~

LPF

ccutoff ωω 2<<

( )trI

( )tcωcos2

LPF

ccutoff ωω 2<<

( )trQ

( )tcωsin2−

( ) ( ) ( )( )tttRtr c θω += cos~

LPF

ccutoff ωω 2<<

( )trI

( )tcωcos2

LPF

ccutoff ωω 2<<

( )trQ

( )tcωsin2−

Figure 2-1. Block diagram of the down-conversion process for extracting in-phase and quadrature signal components from a bandpass signal.

Figure 2-1 illustrates the process of extracting in-phase and quadrature signal components from a

bandpass signal using conventional signal processing blocks. This process can be performed

using analog components or in the digital domain after a signal has been sampled and quantized.

2.1.3 The Narrowband Approximation

Signals can be classified as wideband or narrowband, but the wideness or narrowness of a

signal’s bandwidth is a relative measure and must be defined in a particular context. The

bandwidth of signals can be measured relative to several quantities, including carrier frequency,

information rate, multipath delay, and antenna bandwidth.

First consider a signal symbol (or chip) period relative to the period of its carrier. Define a time

shift τ that is large compared to the period of the sinusoidal carrier. That is, the time shift τ

may be up to a few carrier periods in duration. The resulting real, bandpass signal with a time

shift τ can be written as

( ) ( ) ( )( ){ }τωττ ++=+ tjtrtr cexpRe~ . ( 2.15 )

Now assume that the symbol period of the modulating signal is very large compared to the

period of the sinusoid. For example, the symbol period may be 20 or more times the carrier

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period3. This large ratio in periods implies that the symbol period is also very large compared to

the time shift τ. If the modulating signal is filtered such that the filter bandwidth is on the order

of the symbol (or chip) rate, as is usually the case4, then because of the slowly varying nature of

the modulating signal compared to the short duration of τ, the following approximation can be

made for the complex envelope

( ) ( )trtr ≈+τ . ( 2.16 )

This approximation is called the narrowband array approximation [Ree02]. Therefore, equation

( 2.16 ) may be rewritten as

( ) ( ) ( )( ){ }τωτ +≈+ tjtrtr cexpRe~ . ( 2.17 )

Since the carrier is purely sinusoidal, the time shift in the exponential argument can be rewritten

as a phase shift, where the phase shift is given by

τωψ c= . ( 2.18 )

Therefore, the expression for the real, bandpass signal given in equation ( 2.15 ) can be written as

( ) ( ) ( )( ){ }ψωτ +≈+ tjtrtr cexpRe~ . ( 2.19 )

The salient point of this discussion is to show that a time shift τ, which is small compared to the

symbol period, can be represented solely by a phase shift of the carrier frequency.

Antenna array elements are typically spaced at distances equal to fractional wavelengths of the

carrier frequency, implying that a time shift τ due to excess propagation delay between elements

is on the order of the carrier period. If the symbol period is large compared to this time shift,

then the narrowband array approximation applies. However, the signal may still be considered

wideband in certain contexts. For example, consider an IS-2000 bandpass signal. A 1.2288

Mcps (megachip per second) PN sequence modulates an 825 MHz carrier to produce a bandpass

signal filtered to a bandwidth of approximately 1.25 MHz. The signal carries data at a rate up to

3 A good example is the proposed IS-2000/CDMA-2000 3X standard, which specifies a 3.75 Mcps chip rate at a carrier frequency in the 800 MHz band. Even at this high chip rate (considered “wideband” by today’s standards), the ratio of the chip period to carrier period is still very large, (1/3.75)/(1/800) = 213. 4 For example, the IS-95 and IS-2000 1X standards specify a chip rate of 1.2288 Mcps and a filter bandwidth of approximately 1.25 MHz.

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19.2 kbps and is received by a monopole antenna (with 2% bandwidth relative to center

frequency) in a multipath environment with excess propagation delays up to 4 µs in duration.

Table 2-1 shows the contexts in which the signal may be considered wideband. The ratio of the

signal bandwidth (approximately the chip rate) to the carrier frequency is small, so that the signal

can be considered narrowband relative to the carrier, and therefore, the narrowband

approximation actually is valid regardless of context. The ratio of the signal bandwidth to the

information bit rate is large, and in this context the signal can be considered wideband. The ratio

of the bandwidth to the inverse of the multipath excess delay is large, so that this signal may be

considered wideband and may experience frequency-selective fading. With regard to the

antenna bandwidth, the ratio of signal bandwidth to antenna bandwidth is very small, and the

signal would be considered narrow band in this context.

Table 2-1. Comparison of relative signal bandwidth for a 1.25 MHz-wide CDMA signal used for voice and data services, where the base information bit rate is 19.2 Kbps and the carrier frequency is 825 MHz, in a multipath environment with a 4 µs excess delay.

Signal bandwidth relative to… Ratio Wideband?

Carrier frequency 1.25 MHz / 825 MHz = 0.0015 No

Information rate 1.25 MHz / 19.2 KHz = 65 Yes

Multipath delay 1.25 MHz / ( 1 / (4µs) ) = 5 Yes

Antenna bandwidth 1.25 MHz / ( (2%)(825 MHz) )= 0.076 No

Measurements discussed in following chapters used a signal produced by phase modulating a

2050 MHz carrier with chip rate of 80 Mcps, which is unquestionably wideband compared to

today’s common communication systems. However, in the context of antenna arrays, the

narrowband approximation still applies because the chip period is large compared to the carrier

frequency, (1/80)/(1/2050) = 25.6, and equations ( 2.16 ) through ( 2.19 ) still hold true.

Therefore, even when using a signal modulated by a 80 Mcps data source for measurements, the

narrowband approximation can be applied to represent time shifts due to array element spacing

as phase shifts of the carrier.

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2.2 Signals for Smart Antennas

A smart antenna at a receiver is an antenna array system that uses signal processing algorithms to

adapt to radio environments by selecting or combining in some way the signals received by each

element of the antenna array [Ree02]. A smart antenna at a transmitter transmits different

signals at each element to produce a desired effect at a receiver on the other end of the radio link.

Unless otherwise specified as a transmitter antenna, the term smart antenna will be used in most

cases to describe a receiver antenna.

Smart antennas are far advanced compared to their passive ancestors whose processing

capabilities included at most statically combining signals from different elements. Rather than

existing as a resonant conductor designed to passively capture the surrounding electromagnetic

fields, smart antennas have the ability to actively select desired signals out of an environment of

interferers and noise. The smart antenna encompasses not only the elements of the array, but

also the signal processing that lies behind the array.

2.2.1 The Purpose of Smart Antennas

Smart antennas provide a means of strengthening desired signals and suppressing unwanted

signals at a radio receiver using an array of two or more antennas as elements of the array

through spatial filtering, often called beamforming [Ng02]. The overall purpose of using a smart

antenna array in a wireless system is to improve the ability of a wireless system to efficiently

convey error-free information over a radio channel and to increase the capacity of the system.

A smart antenna system requires a receiver or transmitter to have additional processing

capabilities. The burden of additional processing may be offset by the advantages listed in Table

2-2.

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Table 2-2. Advantages of using smart antennas at a transmitter or receiver.

Factor Effect of using smart antennas

Capacity The intentional direction of energy from transmitter antennas reduces the amount

of interference throughout the wireless network. The ability to perform spatial

filtering at receiver antennas reduces the effect of remaining interfering signals. In

interference-limited system, this means that more users can be active on the

network for a given level of performance.

Reliability Smart antennas increase reliability (or equivalently lower error rates) by providing

an increase in antenna gain for the signals of a desired user and a decrease in gain

for undesired signals and environmental noise. The result is a higher quality radio

link for stations in the fringe region of reception.

Data rates For a given error rate, the amount of data that can be transmitted through a

wireless link is limited by the energy-per-bit and the noise-plus-interference level.

The reduction of interference and the increase in antenna gain (an increase of

received power at the receiver) means that shorter bit periods (higher data rates)

can be used compared to that of a system without smart antennas.

Energy An increase in antenna gain through the use of smart antennas means that lower

transmitter power can be used for a given situation, resulting in longer battery life

for mobile stations. The reduction of interference at the receiver has the same

effect of requiring a lower transmitter power.

Bandwidth While smart antennas may not directly affect the bandwidth of signal, smart

antennas enables a communications system to use its allocated bandwidth more

efficiently. By reducing the amount of transmitted and received interference

throughout the band, a larger number of users can operate within the allocated

bandwidth of an interference-limited wireless network.

Location Smart antennas can provide direction of arrival information, which can be used by

geo-location systems to locate a mobile station in the coverage area of a wireless

network.

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2.2.2 A Signal Model for Antenna Arrays

In order to study channel measurement and modeling techniques for smart antennas, it is

necessary to understand conventional signal models for smart antennas. Widely used definitions

compiled from several sources (including [Chr00] [Ert99] [Ng02] [Ree02] [Vib02]) are used to

set many of the conventions for the rest of this work. However, the notation used here rigorously

keeps track of the signals at each antenna element as well as the sources from which they

originate. In this section, a general expression is derived for determining the complex envelope

of a signal at any element of an antenna array.

First consider the antenna array with elements located as shown in Figure 2-2. This figure shows

the general case of L antenna elements, and the location of the lth element is specified by position

vector lr , which extends from the axis origin to element l.

= Antenna array element

z…

Element 1Element 2

Element 3

Element L

lr

xy

Element l

= Antenna array element

z…

Element 1Element 2

Element 3

Element L

lr

xy

Element l

Figure 2-2. Location of elements of an antenna array.

Now consider a set of M point signal sources surrounding the antenna array as shown in Figure

2-3. The assumption is made that the distances between all pairs of elements is much less than

the distance between signal sources and the antenna array (i.e., the array is small compared to the

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distances between the array and the signal sources). Given this assumption, signals radiated

from the point sources appear as plane waves when reaching the array. The location of signal

source m is defined by position vector mm , which extends from the axis origin to source m.

Next consider the relative time of arrival of signals received by the antenna elements from each

signal source. Because relative time of arrival, not absolute time of arrival, is of importance, the

choice of a reference point is arbitrary. For simplicity, the axis origin is chosen. The relative

time of arrival observed at the lth element of a signal from the mth source is given by the scaled

dot product of the source position vector with the element position unit vector,

( ) ( )c

mmlmmlml

θφθφττ

,ˆ,,

mr ⋅== ( 2.20 )

where

( ) mmmm mmm /,ˆ =θφ . ( 2.21 )

The vector ( )mm θφ ,m is a unit vector in the direction of the mth source given by the angles

( )mm θφ , , and c is the speed of propagation of the plane wave (the speed of light in free space,

3x108 m/s). A negative ml ,τ means that the signal arrives at the origin before arriving at the

antenna element; a positive ml ,τ means that the signal arrives at the antenna element before

arriving at the origin.

The expression for delay given by equation ( 2.20 ) is very useful for antenna arrays with

elements located in two or three dimensions, such as a square or circular array, and for situations

where signal sources surround an array in three dimensions. A more specific and common

antenna geometry is the case of a uniformly spaced, linear antenna array surrounded by sources

that lie on a plane5. Figure 2-4 shows the case where the antenna elements are located along the

x-axis, and the sources line on the x-y plane.

5 Such is the case when an antenna array is used at a base station and the signal sources are mobile stations surrounding the base station at a distance much greater than the height of the base station antenna array.

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= Signal source…

Source 1

Source 2

Source 3

Source M

Source m

AntennaArray

xy

z

mm

= Signal source…

Source 1

Source 2

Source 3

Source M

Source m

AntennaArray

xy

z

mm

Figure 2-3. Signal sources surrounding antenna array.

1 2 l Lφm

Source m

… …x

y

d

(l-1)d cos(φ m

)

1 2 l Lφm

Source m

… …x

y

d

(l-1)d cos(φ m

)

Figure 2-4. Geometry for a uniformly spaced, linear antenna array.

The time of arrival relative to the axis origin for the plane waves from source m at antenna

element l is given by

( ) ( ) ( )c

dl mmlml

φφττ

cos1,

−== . ( 2.22 )

Now consider expressions for the signals incident on the antenna array elements. Let ( )txl~ be

the bandpass output signal of the lth of L isotropic antenna elements. The signal ( )txl~ consists of

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a bandpass signal contribution ( )tsl~ and a bandpass additive noise contribution ( )tnl

~ , expressed

by

( ) ( ) ( )tntstx lll~~~ += . ( 2.23 )

The signal ( )tsl~ may be the sum of multiple signals incident on the array, so that

( ) ( )∑=

=M

mmll tsts

1,

~~ , ( 2.24 )

where ( )ts ml ,~ is the contribution of the mth signal source at the lth antenna element. Using the

time shift ml ,τ computed using ( 2.20 ) or ( 2.22 ), the signal contribution from each source can

be expressed as

( ) ( )mlmml tsts ,,~~ τ+= , ( 2.25 )

where ( )tsm~ is the signal from the mth source at the axis origin; for the case of the linear array in

Figure 2-4, the first element is located at the origin, so ( ) ( )tsts mm ,1~~ = . Now, equation ( 2.24 )

can be rewritten so that the signal at the lth element is sum of time shifted signals from each of

the M sources, given by

( ) ( )∑=

+=M

mmlml tsts

1,

~~ τ , ( 2.26 )

where ml ,τ is the time shift governed by ( 2.20 ) or ( 2.22 ). The mth signal from each source can

be expressed as a complex envelope ( )tsm in the equation

( ) ( ) ( ){ }tjtsts cmm ωexpRe~ = . ( 2.27 )

The time-shifted version of the signal from the mth source is expressed as

( ) ( ) ( )( ){ }mlcmlmmlm tjtsts ,,, expRe~ τωττ ++=+ . ( 2.28 )

By applying the narrowband approximation from equation ( 2.17 ), the time-shifted signal from

the mth source can be approximated with

( ) ( ) ( )( ){ }mlcmmlm tjtsts ,, expRe~ τωτ +≈+ . ( 2.29 )

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The time shift ml ,τ is equivalently expressed using a phase shift ml ,ψ where

mlcml ,, τωψ = ( 2.30 )

so that the time-shifted signal from the mth source can be written as

( ) ( ) ( ){ }mlcmmlm tjtsts ,, expRe~ ψωτ +≈+

( ) ( ) ( ){ }mlcm jtjts ,expexpRe ψω= . ( 2.31 )

From here forward the approximation will be assumed to be an equality. Using ( 2.31 ), the

expression in ( 2.26 ) for the signal at the lth element can be rewritten as

( ) ( ) ( ) ( ){ }∑=

=M

mmlcml jtjtsts

1,expexpRe~ ψω . ( 2.32 )

Because the real part of a sum of complex numbers is equal to the sum of the real parts, ( )tsl~ can

be written as

( ) ( ) ( ) ( )

= ∑=

M

mmlcml jtjtsts

1,expexpRe~ ψω , ( 2.33 )

which is equivalent to

( ) ( ) ( ) ( ) ( ) ( ){ }tjtstjjtsts clc

M

mmlml ωωψ expReexpexpRe~

1, =

= ∑

=

. ( 2.34 )

From this equality, it is seen that the complex envelope ( )tsl~ of the signal at the lth element of

the array is equal to the sum of phase-shifted complex envelopes of the signals at the origin from

the M signal sources. This relationship can be written as

( ) ( ) ( )∑=

=M

mmlml jtsts

1,exp ψ . ( 2.35 )

Table 2-3 summarizes the expressions for computing the complex envelope of signals at

elements of an antenna array given arbitrary locations of elements and sources.

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Table 2-3. Expressions for computing signals incident on the elements of an antenna array.

Array and Signal Source Parameters Expression

Number of antenna elements L

Number of signal sources M

Index of antenna element l

Index of signal source m

Position vector for lth antenna element lr

Position vector for mth signal source mm

Unit vector in the direction of the mth source ( )mm θφ ,m

Complex envelope of signal from mth source at lth

antenna element

( )ts ml ,

Complex envelope of signal from mth source at axis

origin

( )tsm

Time shift of signal from mth source at lth element relative

to axis origin ( ) ( )

cmml

mmlml

θφθφττ

,ˆ,,

mr ⋅==

Phase shift of signal from mth source at lth element

relative to axis origin mlcml ,, τωψ =

Complex envelope of signal received by lth element ( ) ( ) ( )∑=

=M

mmlml jtsts

1,exp ψ

2.2.3 Vector Channels

Received signals, noise contributions, and channel impulse responses can be represented in

vector notation (as in [Ree02] and [Vib02]) to facilitate analysis and processing for antenna

arrays. The signals ( )tsl arriving at an antenna array with L elements can be expressed in vector

form using

( )

( )( )

( )

=

ts

tsts

t

L

M2

1

s . ( 2.36 )

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The output of the array is represented in vector form as the sum of signal sources and

independent noise sources, given by

( )

( )( )

( )

( )( )

( )

( )( )

( )

( ) ( )tt

tn

tntn

ts

tsts

tx

txtx

t

LLL

nsx +=

+

=

=MMM

2

1

2

1

2

1

. ( 2.37 )

The elements of the noise vector ( )tn are assumed to contribute independent and additive noise

signals. Each noise contribution can be a noise source based on the system noise figure of each

receiver branch referenced to the output port of each antenna element.

To relate the received signal to the transmitted signal, the concept of the vector channel is

introduced. Elements of the vector channel consist of the channel impulse response between the

mth source and the lth antenna element. If ( )tmm is the transmitted signal and ( )th ml , is the

impulse response between the mth source and lth antenna element, then the received signal at

element l contributed by the mth source is given by

( ) ( ) ( )tmthts mmlml ∗= ,, . ( 2.38 )

where ∗ represents convolution. In vector form, the received signal is written as

( )

( ) ( )( ) ( )

( ) ( )

( ) ( )tmt

tmth

tmthtmth

t mm

mmL

mm

mm

m ∗=

∗∗

= hs

,

,2

,1

M. ( 2.39 )

The vector ( )tmh is a vector channel impulse response and represents a vector channel. Using

( )tmh , the output of the array due to the mth source can be related to the transmitted signal of the

mth source with

( )

( ) ( ) ( )( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )ttmt

tntmth

tntmthtntmth

t mm

LmmL

mm

mm

m nhx +∗=

+∗

+∗+∗

=

,

2,2

1,1

M. ( 2.40 )

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One vector channel exists between each source and the antenna array. If M sources are present,

then the output of the array is given by

( ) ( ) ( ) ( )∑=

∗+=M

mmm tmttt

1

hnx . ( 2.41 )

Equation ( 4.41 ) completely describes the output of an isotropic-element antenna array that is

surrounded by M signal sources transmitting through M vector channels.

Vector channels modeled by ( )tmh simply express a relationship between the signal radiated by

a transmitter antenna and the signals (plane waves) incident on a receiver antenna array. Vector

channels do not describe the effects of antenna radiation patterns (amplitude and phase

characteristics), but if ideally isotropic array elements are assumed, then the output of the array

can be computed.

2.2.4 Array Steering Vectors

Array steering vectors express the relationship between the signals (plane waves) incident upon

an antenna array and the output of the antenna array. This relationship is a function of the

radiation patterns of the antenna elements and the relative positions of the elements. Let

( )θφ ,lG be the radiation pattern of the lth antenna element. If this radiation pattern is included in

the expression in ( 2.35 ), then signal contribution to the output of the lth antenna element due to

all M sources is given by

( ) ( ) ( ) ( )∑=

=M

mmlmmlml jGtsts

1,exp, ψθφ , ( 2.42 )

where mφ and mθ specify the angles to the mth source from the antenna array. The radiation

pattern and phase shift terms, which are functions of array geometry and element radiation

pattern, can be expressed by a single term ( )θφ ,la given by

( ) ( ) ( )mlll jGa ,exp,, ψθφθφ = , ( 2.43 )

so that ( )tsl can be expressed as

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( ) ( ) ( )∑=

,=M

mlml atsts

1

θφ . ( 2.44 )

By including the noise contribution term in ( 2.44 ), the output of the lth of the antenna array is

given by

( ) ( ) ( ) ( ) ( ) ( )∑=

,+=+=M

mlmllll atstntstntx

1

θφ . ( 2.45 )

In vector form, this relationship can be written as

( ) ( ) ( ) ( )∑=

,+=M

mm tstt

1

θφanx . ( 2.46 )

If only once source ( )ts1 is present, then the a common result is obtained, given by

( ) ( ) ( ) ( )ttst nax +,= θφ1 . ( 2.47 )

The vector ( )θφ ,a is called the array steering vector. The array steering vector includes two

influences: the antenna element radiation pattern and phase differences due to relative

propagation distances among the antenna elements. In practical antenna arrays, the effect of

mutual coupling of antenna elements should be included in the array steering vector. Mutual

coupling has the effect of changing the radiation pattern of the individual array elements.

2.2.5 Spatial Signatures

In a multipath channel, multiple plane waves will be incident on an antenna array even if only

one source is present. Let K be the number of multipath components arriving from a single

source that would cause signal ( )ts1 to be incident on the array along the direct path. Then the

output of the array can be expressed as

( ) ( ) ( ) ( ) ( )∑=

,−+=K

kkkkk tsttt

11 θφτα anx . ( 2.48 )

The factor ( )tkα is a (possibly time-varying) complex value that describes the strength and phase

of the multipath component, and ( )kk θφ ,a specifies the steering vector for each of the multipath

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components. If multipath delays are much smaller than the reciprocal of the signal bandwidth,

then following approximation can be made

( ) ( )tsts k 11 ≈−τ for ( )( )tsBWk1

1<<τ . ( 2.49 )

Using this approximation, the output of the array can be written as

( ) ( ) ( ) ( ) ( )tstttK

kkkk 1

1

,+= ∑

=

θφα anx , ( 2.50 )

since ( )ts1 is no longer dependent upon k because kτ is removed from its argument. This

expression can be written more simply as

( ) ( ) ( ) ( )tsttt 1anx += , ( 2.51 )

where

( ) ( ) ( )∑=

,=K

kkkk tt

1

θφα aa . ( 2.52 )

The function ( )ta is called the spatial signature of ( )ts1 . Spatial signatures are influenced by

three factors: the antenna element radiation pattern; phase differences due to relative

propagation distances among the antenna elements; and the summation of multipath components

incident on the array. Because of the approximation made in ( 2.49 ), the definition of spatial

signature is valid only for signals that are narrowband with respect to excess multipath delays of

the channel.

2.3 Channel and Signal Characteristics in Multipath Environments

Several attributes of signals and channel responses must be characterized in a manner that is

relevant to the performance of radio systems. Signal strength and propagation delay is an

important factor for all communications systems. Antenna arrays add the requirement for joint

characterization of signals where relative signal strengths and channel characteristics can have an

impact on potential gains in multipath environments. The characteristics discussed in this

section lay a foundation for measurement processing and channel modeling discussed later.

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2.3.1 Multipath Amplitude and Time Delay

Multipath strength and time delay must be considered together when characterizing a radio

channel. Let the transmitted signal from a single source be an impulse with unity magnitude at

t=0 as shown in Figure 2-5. The signal is transmitted through the L-dimensional vector channel

to an antenna array with L elements. The impulse response of each channel is the corresponding

received signal shown in Figure 2-5. The delay and amplitude of multipath components in each

dimension of the vector channel can be quantified using excess delay spread, mean delay, and

RMS delay spread.

t

t

( )th1

( )th2

t

( )thL

… …

1

t

Tran

smitt

edSi

gnal

1,1α2,1α

3,1α4,1α

1,2α2,2α

3,2α4,2α

1,Lα2,Lα

3,Lα4,Lα

t

t

( )th1

( )th2

t

( )thL

… …

1

t

Tran

smitt

edSi

gnal

1,1α2,1α

3,1α4,1α

1,2α2,2α

3,2α4,2α

1,Lα2,Lα

3,Lα4,Lα

Figure 2-5. Transmitted signal and impulse response of a multipath vector channel.

Excess delay spread is a measure of the spread of multipath components based on some defined

threshold. The impulse response is normalized so that the strength of multipath components is

expressed as a dB-level relative the strongest component, as shown in Figure 2-6. For the

response shown in the figure, the excess delay spread dB10τ∆ for the 10 dB level is the time

difference between the first and third signal components. The excess delay spread dB20τ∆ for the

20 dB level is the time between the first and fifth components. Excess delay spread values are

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important for defining input parameters for geometric channel modeling. Excess delay spreads

determine, for example, the range around the transmitter and receiver within which multipath-

causing reflectors must be modeled (discussed in detail in Chapter 4).

t

0 dB

-10 dB

-20 dB

dB10τ∆

dB20τ∆

t

0 dB

-10 dB

-20 dB

dB10τ∆

dB20τ∆

Figure 2-6. Relative strengths of multipath components used to determine excess delay spread.

Mean delay is a measure of the average propagation delay between a transmitting antenna

element and a receiving antenna element. The delay of each component is weighted by its

strength. Mean delay is calculated using

=

==K

kk

K

kkk

1

2

1

2

α

τατ , ( 2.53 )

where K is the number of multipath components to be included in the calculation. While mean

delay may not have a direct impact on inter-symbol interference (ISI) like RMS delay spread,

mean delay does have an effect on system planning in wireless networks that require precise

synchronization of clocks at transmitting and receiving stations6.

6 Direct-sequence spread-spectrum systems require synchronization of chip clocks at the transmitter and receiver, and the amount of relative lead or lag of the clocks is determined by mean delay. This relative lead or lag becomes important for handoffs in mobile communication systems.

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RMS delay spread is a measure of the spread of multipath components about the mean delay.

RMS delay spread [Cav00] is the second central moment of the received multipath components

computed using

( )

=

=

−= K

kk

K

kkk

1

2

1

22

α

ττασ τ . ( 2.54 )

When RMS delay spread becomes larger than approximately 10% of the symbol period, inter-

symbol interference causes an increase in symbol error rate for an unequalized receiver [Chu87].

Realizable measurements systems cannot resolve multipath components with infinitely small

time delay resolution. As a result, the impulse responses for vector channels shown in Figure 2-5

can never be exactly measured. Measured impulse responses consist of the true impulse

response convolved with the time response of the finite-bandwidth system; therefore, multipath

components in the impulse response are represented with relatively wide components rather than

ideal impulses7. In practice, equations ( 2.53 ) and ( 2.54 ) can be used for the measured

responses to achieve good approximations for mean delay and RMS delay spread.

2.3.2 Number of Multipath Components

The number and distribution of multipath components has been statistically characterized by past

research efforts based on measured data. A Poisson distribution [Cou97] is used, whose

probability density function is given by

( ) ( ) ( )∑∞

=

−=0k

Poisson kxkPxf δ , ( 2.55 )

where

( ) ( )λλ

−= exp!k

kPk

. ( 2.56 )

7 Although a finite-bandwidth system would in theory have an infinitely wide time response, noise floors limit the time-domain response of the measurement system to a finite width.

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The mean of the distribution λ is the single parameter that needs to be characterized for this

distribution.

The number of multipath components in a theoretical impulse response is limited only to the

number of reflecting objects that induce multipath in the environment. In practical systems,

multipath components may arrive at an antenna with a strength undetectable by the receiver. The

count of multipath components is dependent upon the amplitude threshold selected. For

measurements, this implies that the measurement system needs to have a sensitivity better than

that of the target communication systems for which the measurements are being performed. This

ensures that multipath components detectable by the target system will be detectable by the

measurement system.

2.3.3 Fading Envelope

When an antenna element receives multipath components from a narrowband source, the

envelope of the resultant signal will fluctuate in amplitude due to constructive and destructive

combination of the narrowband signals. The time varying nature of the envelope is due to the

motion of the receiver, transmitter, or reflectors in the environment. This motion causes minute

frequency shifts (time varying phases of multipath components) known as Doppler shifts. The

time-varying phase of each multipath component changes at different rates depending upon the

directions of motion, and the resulting amplitude fluctuation is called fading.

A model developed by Clarke [Cla68] showed that a mobile receiver experiences Rayleigh

fading when a large number of narrowband multipath components arrive with equal strength and

from uniformly distributed angles in azimuth. Let the complex received signal envelope at a

single antenna element be ( )tr , and let the received signal envelope magnitude8 be ( )tre , where

( ) ( ) ( )( )tjtrtr e φexp= . ( 2.57 )

The Rayleigh distribution for signal envelope fading [Cav00] is then given by

8 The magnitude of the complex envelope is frequently called simply the signal envelope. As such, re is used to represent this real-valued envelope.

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( )

−=

2

2

2 2exp

r

e

r

eeRayleigh

rrrp

σσ , 0≥er , ( 2.58 )

where 2rσ is the variance of ( )tr , which is the power in the composite signal. This distribution

assumes that there is no dominant component incident on the antenna element; a dominant line-

of-sight contribution disqualifies the Rayleigh distribution.

If a dominant signal component is present, then a Rician distribution is observed for the fading

envelope [Cav00]. The dominant component is defined to have a power larger than the diffuse

components by a factor of K. This factor is called the Rician K-factor, and if K=0, then Rayleigh

fading results. The Rician probability density function is given by

( )

−−

= K

rKrI

rrp

r

e

r

e

r

eeRician 2

2

02 2exp

2σσσ

, 0≥er and 0≥K , ( 2.59 )

where ( )⋅0I denotes the modified 0th-order Bessel function of the first kind given by

( ) ( )∫−

ππdttyyI cosexp

21

0 . ( 2.60 )

The difference between the Rayleigh and Rician cases can be visualized using isoprobability

contours for the complex signal ( )tr shown in Figure 2-7. The Rician-fading signal consists of a

specular component ( )trs and a zero-mean Gaussian diffuse component ( )trd , and the composite

signal is given by

( ) ( ) ( )trtrtr ds += . ( 2.61 )

If the variance of the diffuse component is 2rσ , then the magnitude of the specular component is

given by

( ) Ktr rs 2σ= . ( 2.62 )

The result is a nonzero mean that produces the offset in the isoprobability contours. Note that

the phase of the composite signal is dependent on the relative amplitude between the specular

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and diffuse components, and the phase distribution for the Rician case is no longer uniform like

the Rayleigh case.

……

……

……

……

{ }rRe

{ }rIm

Rayleigh

Rician

Kr 2σ

……

……

……

……

……

……

{ }rRe

{ }rIm

Rayleigh

Rician

Kr 2σ

Figure 2-7. Isoprobability contours for the composite complex signal envelope due to Rayleigh and Rician fading in a multipath environment.

2.3.4 Direction of Arrival

The direction of arrival of multipath around a receiver can be characterized in a way similar to

that for multipath time delay. The concept of center of gravity and square root of the second

central moment can be used for the angles of incident multipath components. Let angle kφ be

the azimuthal angle of arrival for the kth of K multipath components. The mean angle of arrival

is compute using

=

==K

kk

K

kkk

1

2

1

2

α

φαφ , ( 2.63 )

where kα is the voltage amplitude of the kth multipath component. The angle spread of the

multipath components [Ber02] is given by

( )

=

=

−=

K

kk

K

kkk

1

2

1

22

α

φφασ φ . ( 2.64 )

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This definition of angle spread is not the only one used by researchers. While in general, angle

spread parameters are used to characterize spatial power distributions for arriving multipath, the

metrics may vary. For example, the concept of excess delay spread can be adopted from time

delay characterization and applied to direction of arrival characterization, whereby the angle

spread is the widest difference in angle between two multipath components arriving with a power

above a particular threshold.

Measurements have shown a high correlation between angle spread and delay spread [Mas00].

In both line-of-sight and non-line-of-sight environments, angle spread tends to increase with

delay spread. The correlation coefficient between angle spread and delay spread computed from

a set of measurements in a metropolitan environment was 0.7. As would be expected, angle

spread φσ measured in non-line-of-sight environments is typically wider than angle spread

measured in line-of-sight environments.

2.3.5 Signal Envelope Correlation Coefficient

Spatial separation of antenna elements causes fading due to multipath to be different at each

element. The correlation coefficient computed for signal envelopes at pairs of antenna elements

is a factor in determining the potential gains of using smart antennas. For example, appreciable

diversity gain is achieved when envelope correlation coefficients exceed 0.7 [Kit95]. If ( )tr1 and

( )tr2 are the envelopes of received signals from two antenna elements, then the correlation

coefficient 12ρ can be computed directly using

( )( ) ( )( )

( )( ) ( )( )∫∫

−−

−−

=2

1

2

1

2

1

222

211

2211

12 t

t

t

t

t

t

dtrtrdtrtr

dtrtrrtr

ρ , ( 2.65 )

where

( )∫−=

2

1

112

1

1 t

t

dttrtt

r , 12 tt > ( 2.66 )

and

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( )∫−=

2

1

212

2

1 t

t

dttrtt

r , 12 tt > . ( 2.67 )

When performing measurements in practice, the means 1r and 2r may be time-varying values

due to large-scale path loss changes and shadowing. As such, the values of t1 and t2 are chosen

for a time period during which large scale path loss does not vary significantly but a long

duration of signal fading due to multipath is observed.

2.4 Summary

The metrics of antenna array signal characteristics, including multipath delay, multipath strength,

signal envelope fading, direction of arrival, and correlation coefficient, are fundamental concepts

for measurement and modeling radio channels for antenna arrays. For measurements systems

built on a digital signal processing platform, the actual implementations of processing routines to

compute the referenced characteristics adhere closely to the definitions in theoretical discussions.

Understanding these characteristics is important for analysis of algorithms, development of

systems, interpretation of measurement results, and use of channel models based on

measurements.

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Chapter 3 A Multi-Channel, Software-Defined Measurement Receiver

In this chapter, the development of a new measurement receiver is described. The measurement

receiver was built to serve channel measurement and radio test bed needs as they had arisen

throughout the research presented in this dissertation. First, the motivation behind the

architecture and methodology is discussed. Principles of the concept of software radio are

emphasized. This chapter combines modern techniques from the fields of wireless

communications and software development to describe a unique approach to receiver design.

The hardware and software of the receiver are described, and the bases for major hardware and

software design decisions are discussed. An example application of the measurement receiver is

also presented.

3.1 Architecture Motivation

The wideband, multi-channel, software-defined measurement receiver (herein simply called the

measurement receiver) was designed to meet the needs of performing measurements for modern

communications systems. Early radio communications systems, such as narrowband analog and

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digital wireless telephone networks, could rely largely upon single-channel signal envelope

measurements or simple multipath delay characterization. As wireless communications

technology enters an era of widespread use of complex antenna array algorithms and very wide

bandwidth modulation to handle a growing number of high-data-rate users, a more advanced

measurement receiver is required. The measurement receiver discussed here was developed to

meet the requirements of current channel modeling and smart antenna research and was designed

to be scalable for future needs.

The salient features that demonstrate the design to be a novel approach to measurement receiver

architecture include:

• Software-defined radio functionality

• Object-oriented, multi-threaded software implementation

• Standardized internal communications interface

• External signal data interface

• Forward compatibility for algorithm development

• Network support for external simulations

Software-defined functionality means that most of the functions performed by the receiver are

executed in software that can be controlled and modified while the receiver is operating. Multi-

threading allows several processing algorithms to operate on received signals in parallel. Object-

oriented software implementation affords a programmer a template and interface for developing

new radio modules. The measurement system’s internal communications interface controls the

delivery of signal data to each of the processing modules and relieves the programmer of the

responsibility of synchronizing data reading and writing events. The external signal data

interface gives an engineer the ability to connect existing MATLAB or C simulations to actual

radio signal data, providing a straightforward way to test simulations and processing algorithms

in real world environments. The signal data collected by the measurement system is forward

compatible in that the data is stored in a raw format that can be used by future processing

algorithms; all signal information is preserved using this raw format. The measurement system

supports supplying signal data to external simulations (simulations executed on another PC or

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other processing platform) by providing a TCP/IP network interface for exporting data in real

time.

3.2 The Software Radio Methodology

Widespread acceptance of the concept of a software-defined radio, frequently called simply a

software radio9, began in the 1990s when digital signal processors were developed that could

provide sufficient processing capability. Between 1990 and 2000, an abundance of technical

articles appeared that began to define the characteristics, requirements, and applications of the

nebulous software radio concept (e.g., [Bur00], [Erb98], [Lee00], [Mit93], [Mit95]). Because of

the versatility and mutability of the software radio, no exact definition has ever been universally

accepted and probably never will be. However, commonalities among definitions suggest that

the following characteristics describe the core of the software radio concept:

• Definition and implementation of radio functions in software

• Dynamic reconfigurability of processing at every layer of protocol stack at runtime

• Placement of the A/D (or D/A) converter close to the antenna (i.e., minimization of

hardware functionality between A/D or D/A and the antenna)

In a software radio, a majority of the radio functions are performed by some type of signal

processor. The processor may use sequential instruction execution (in the case of a traditional

digital signal processor integrated circuit), combinational logic (in the case of a programmable

logic device or a field-programmable gate array), or a combination of both. In each case, the

radio functionality is defined in a software radio by a program of instructions or logic gates that

completely specify how the radio will operate on sampled signal data and how it will behave at

all protocol layers. The programming of a software radio is reconfigurable as the radio is

operating, allowing the radio to adapt to changing channel conditions or conform to

communication standards with agile protocol characteristics. Placement of the A/D converter

operationally close to the antenna is an indication that hardware functionality is minimized.

9 Some literature, for example [Wol00], distinguishes between “software radio” and “software-defined radio” by excluding radios that perform RF/IF frequency conversion from the class of “software radio.” However, in this dissertation, frequency conversion is considered to be signal conditioning, and hence “software radio” and “software-defined radio” are used interchangeably.

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While in its purest form, a software radio would sample signals directly from the receiver

antenna port without the aid of analog RF components, the use of a frequency down-conversion

stage is generally an acceptable practice10 in software radio design [Bad00], [Dix01], [Mit95].

The fact that a that a radio employs digital techniques is not a sufficient condition for the radio to

be considered software-defined. For example, while the phase-locked loop (PLL) of a receiver

may be digitally controlled, the frequency channel selection would in actuality be implemented

using the PLL hardware, which is only incidentally controlled by the digital portion of the

receiver (supported by [Mit95]). However, a radio that samples an entire frequency band,

crossing multiple frequency channels, and then extracts individual channels through software

processing would be using software radio techniques for channelization.

3.2.1 Physical Architecture

The physical architecture of a practical software radio receiver can be represented by the block

diagram shown in Figure 3-1. (adapted from [Bur00] and [Mit95]). The antenna is a hardware

component required by all radio systems for receiving electromagnetic signals transmitted

through the wireless channel. RF signal conditioning is performed on the received signals to

produce a signal acceptable for the input of the A/D converter. Signal conditioning includes

functions such as amplification, filtering, and frequency translation (frequency conversion).

Generally, analog amplification is required to make the received signal span the desired number

of amplitude levels of the A/D converter, and filtering is required to satisfy the Nyquist criterion

based on the A/D converter sample rate.

10 The use of a frequency down-down conversion stage can improve radio performance compared to using direct sampling of high frequency signals. As discussed in [Bad00], A/D converters may become more limited in dynamic range at higher frequencies.

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RF SignalConditioning

A/DConversion

Antenna

AnalogConditioning

DigitalProcessing

Processorand

Software

DataSink

RF SignalConditioning

A/DConversion

Antenna

AnalogConditioning

DigitalProcessing

Processorand

Software

DataSink

RF SignalConditioning

A/DConversion

Antenna

AnalogConditioning

DigitalProcessing

Processorand

Software

DataSink

Figure 3-1. Block diagram of the major components of a practical software radio receiver.

3.2.2 Division of Hardware and Software

While functions of a radio can be classified as hardware or software, a sharp boundary does not

exist to determine whether a radio is truly a software radio. Radios whose functionality is

weighted heavily in the direction of software implementation, and yet implement some of their

functionality hardware, may arguably be classified as software radios. In [Mit99], the

continuum of radio classifications is represented in a phase space plot, illustrating the subspace

of software radio as a function of the digital access bandwidth and the type of programmable

hardware used. In order to further mitigate the opacity caused by the loose definition of software

radio, an alternative representation is presented in Figure 3-2, which shows a plot that depicts the

relationship between the type of functionality used for a radio and the degree to which it is used.

Functionality that is purely implemented in hardware, such as the reception of signals by the

antenna, is represented on the left side of the plot. Functionality that is purely software is

represented on the right side of the plot. Many radio functions, such as filtering, fall in the center

of the plot because the filtering operations performed in a particular radio might be performed in

both hardware and software. This plot of radio functionality distribution can be viewed to aid in

determining (albeit subjectively) the degree to which a radio is software-defined. Software-

defined radios will be heavily weighted to the right of the plot, and legacy hardware radios will

be heavily weighted to the left side of the plot.

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Deg

ree

of F

unct

iona

lity

PureHardware

PureSoftware

AntennasHardware FiltersMixers

Adaptive processingSoftware filters

RF Sampling

Digital Control Digital Processing

Type of Functionality

Software

RadioLegacy Radio

Deg

ree

of F

unct

iona

lity

PureHardware

PureSoftware

AntennasHardware FiltersMixers

Adaptive processingSoftware filters

RF Sampling

Digital Control Digital Processing

Type of Functionality

Software

RadioLegacy Radio

Figure 3-2. Functionality distribution of software radios versus legacy radio methodology.

3.2.3 Benefits of the Methodology

While the favorable implications of software radio are often included in the definition, they often

depend upon the application of the system and are therefore not truly inherent to software radio

design; the implications are, however, worth noting ([Bur00], [Mit95], [Wol00], [Jon00]):

• Flexible operation of the radio and its subcomponents

• Downloadable air interface (over-the-air or otherwise)

• Multiple mode and air interface standard support

• Programmable parameters at all protocol layers (e.g., RF bandwidth, modulation and

coding scheme, radio resource and mobility management)

• Reduction of hardware size, weight, and power consumption

These benefits form the foundation for the movement toward the use of software radio in user

terminals and base stations alike. Technologists envisage the universal radio that will operate on

any standard using any modulation and will be entirely defined by the software load. The

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wideband measurement receiver developed for the research described here was designed using

software radio methodology to take advantage of these benefits and to further develop the

methodology itself.

3.3 The Measurement Receiver Concept

In order to provide an unambiguous vocabulary for the development of the receiver presented

here, the term measurement receiver is defined. A measurement receiver is a radio receiver

whose purpose is to measure the characteristics of received signals and the channels through

which the signals propagate. A real-time measurement receiver produces signal data and

channel results as measurements are performed and at a rate sufficient to characterize the time-

varying nature of the signals and channels, specific to the characterization parameters used.

Unlike a communications receiver, which is typically required to receive and demodulate a

continuous or regularly time-slotted signal, the processing in a measurement receiver may

tolerate gaps in received signals without corrupting the desired measurement results. For

example, while a communications receiver (operating on a continuously transmitted signal) is

required to sample signals continuously at a rate that satisfies the Nyquist criterion in order to

maintain a communications link, a measurement receiver designed to measure multipath delay

characteristics only needs to acquire signal data at a rate determined by the change of channel

conditions that affect multipath delay (the actual sampling instants would depend upon factors

such as the coherence time of the channel and the physical propagation environment).

3.3.1 Processing Tradeoffs

The processing objectives of the measurement receiver allow the sampling continuity and timing

requirements to be relaxed compared to that of the communications receiver, thereby permitting

a tradeoff in resources that let the measurement receiver outperform the communications receiver

in several regards.

Bandwidth: Because a measurement receiver may tolerate gaps in received signal data,

the sample rate and bandwidth can generally be higher than that of a communications

receiver employing the same processing platform. By buffering necessary data and

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ignoring redundant data, a measurement receiver can allow bottleneck processing to

perform at a rate slower than the sample rate.

Algorithm complexity: By retaining only the signal data that a processing algorithm

needs and ignoring other signal data, a measurement receiver can devote more processing

resources to accommodate algorithms with increased complexity.

Data storage requirements: The omission of unnecessary signal data reduces the

capacity needed to store measurement data. Data often can be stored in its rawest,

unprocessed form, while doing this with a communications receiver would require

prohibitively large storage capacity.

Processing platform: For a software radio application of a given complexity, the

processing speed and available resources of a processing platform can be reduced

compared to that required for a communications receiver. This means that processing

platform that is less powerful but more versatile and easier to program can be selected, in

important consideration for measurement receiver test bed systems.

3.3.2 Examples and Applications

A simple example of a measurement receiver is a receiver that logs narrowband received signal

strength data in order to gather fading statistics. At the expense of losing waveform shape and

frequency spectrum data, the receiver can log data at a slower rate; instead of continuously

sampling the signal faster than the Nyquist rate, the receiver can sample received power at a rate

sufficient to compute the signal envelope for detailing fading characteristics.

Measurement receivers can also be well suited to act as test beds for new algorithms. Instead of

computing received signal strength from a signal, a measurement receiver can be used to

compute the performance gains resulting from algorithms programmed into the receiver. For

example, the output of a measurement receiver could be diversity gain, computed from an

antenna combining algorithm programmed into the receiver.

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A measurement receiver exhibits high utility for testing new wideband measurement techniques

or processing algorithms, where historically the wide bandwidth of the new measurements or the

complexity of the new algorithms prohibits full-scale implementation on a real-time

communications receiver. For example, in the early- to mid-1990s multipath characterization

measurements were performed using bandwidths greater than 10 MHz [Bod97][Dev95][New97],

resulting from the rule of thumb that wideband measurements are performed using a bandwidth

of greater than ten times the communications signal bandwidth of the system for which the

measurements are being performed; in the early 1990s, the frequency channel bandwidth of the

IS-95-A cellular and J-STD-008 PCS systems was 1.25 MHz [IS95A][JSTD8]. This “ten-times-

bandwidth” rule results in the need to measure channels using a bandwidth much wider than the

radio test beds designed for the target communications system.

The concept of the measurement receiver is the basis for the receiver developed for this research.

Wide bandwidth, raw data storage, and an easily programmed processing platform are

characteristics of this receiver designed to accommodate testing of measurement and processing

algorithms.

3.4 System Specifications and Analysis

In this section, the specifications for the measurement receiver are discussed, and link-budget

and noise analyses are presented. The specifications are based on meeting the requirements of a

wideband measurement receiver for propagation research and test bed for smart antenna array

experiments.

3.4.1 Target Applications

Table 3-1 lists the target applications of the measurement receiver. The applications shown in

the table require the RF section of the receiver to be multi-channel and wideband. Also, the

variety of processing required for the applications suggest that a software-defined architecture

should be used, enabling the receiver to execute multiple signal processing applications. The use

of MATLAB and C++ interfaces is specified for the software radio test bed applications because

high-level languages provide a more structured and easier way for designers to program radio

algorithms; DSP development tools and software radio designers have moved in the direction of

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using high-level programming languages over assembly language for software radio applications

[Dix01].

Table 3-1. Target applications of measurement receiver.

Application Category Specific Applications

Channel measurement and modeling support • Multi-element antenna channel modeling

• Power-delay profile measurements

• Multipath delay statistics

• Wideband signal envelope measurements

Smart antenna research • Antenna diversity

• Adaptive combining

• Direction of arrival

Wideband data collection • Multi-channel raw received signal samples

• Processed data logging

Software radio test bed • MATLAB interface for use with m-files

• C code interface using C++ base class

3.4.2 Design Goals

Table 3-2 summarizes the high-level design goals for the overall system and its hardware and

software. The hardware goals include minimizing the amount of RF and non-configurable

components to give the receiver the greatest amount of flexibility. The bandwidth of the system

is maximized to give the best time-domain resolution for multipath power-delay profile

measurements with which multipath radio channels are characterized. Although the

maximization of bandwidth results in higher noise power at the A/D converter input, it affords

the largest flexibility in bandwidth control by allowing the software to control and implement

filtering and channelization of the spectrum. The software goals include maximizing the radio

processing functions performed in software to accommodate the minimization of functions

performed in dedicated hardware. To take advantage of organized and maintainable

programming techniques and parallel processing, the software uses an object-oriented and

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multithreaded design methodology, described further in sections 3.6 and 3.7. The interface

between the radio hardware and signal processing software of the measurement receiver is

simplified by encapsulating the hardware interface software in classes to enable standard

interface methods, also described further in section 3.6.

Table 3-2. High-level design goals for measurement receiver

Overall design goal • Develop a multi-channel, wideband

receiver whose functionality is primarily

implemented in software

Hardware design goals • Minimize functions performed by hardware

• Minimize amount of RF hardware

• Maximize bandwidth of sampled spectrum

Software design goals • Maximize receiver functions performed by

software

• Apply an object-oriented, multithreaded

approach to receiver design

• Encapsulate hardware functionality so that

software processes are largely independent

of specific hardware receiver

3.4.3 RF Specifications

Table 3-3 lists the RF specifications for the measurement receiver. The center frequency of 2050

MHz was used to be able to compare measurements with other measurements performed by

Virginia Tech at this frequency11. A bandwidth of 100 MHz is required to perform power-delay

profile measurements with a multipath time delay resolution of 10 ns, an acceptable resolution

for both indoor and outdoor channel sounding [New97]. The IF bandwidth was designed wider

than the initially chosen RF bandwidth so that other RF filters could be used to select a wider

11 Virginia Tech has performed multiple narrowband experiments and measurements at 2050 MHz. Results from measurements and experiments at this frequency can be extended to nearby bands, such as the 1900 MHz U.S. PCS band and the 2.4 GHz unlicensed band.

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bandwidth. Also, the wide IF bandwidth of 400 MHz allows the RF spectrum to be down-

converted to a wide range of center frequencies selectable by the signal processing software.

Four RF channels serve to acquire signals from a four element array; at the time of development,

a four-channel, high speed A/D converter was available.

Table 3-3. Radio frequency (RF) specifications for measurement receiver.

RF Parameter Value

Primary center frequency 2050 MHz

RF Bandwidth 100 MHz

IF bandwidth accommodated (max RF BW) 400 MHz

Number of RF channels 4

Dynamic range > 40 dB

RF section input/output impedance 50 ohms

3.4.4 System Specifications

Table 3-4 shows the system specifications for the measurement receiver. The single-stage down-

conversion architecture was chosen because it requires a minimal amount of RF hardware

compared to down-conversion using more stages. Direct RF sampling was not specified because

of bandwidth limitations of the A/D converter12, which would not sample frequency bands above

1 GHz. The four-channel A/D converter that was selected was used to sample each 400 MHz-

wide channel at 1 Gsps. The A/D converter stored in memory continuous sequences of signal

samples taken simultaneously from the four channels. These sequences of signal samples are

defined to be snapshots of the received signal.

12 The A/D converter had a bandwidth of 1 GHz and a sample rate of 1 Gsample/sec per channel. The A/D converter could have been used for bandpass sampling for bands up to 1 GHz, but the band of interest for this measurement system was 2.05 GHz.

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Table 3-4. System specifications for measurement receiver.

System Parameter Specification

Frequency translation Single-stage down-conversion

Sampling type IF sampling

Intermediate Frequency 0.2 MHz to 400 MHz (selected by software)

Sample rate 1 Gsample/sec per channel

A/D converter resolution 8 bit

Number of A/D converter channels 4

Signal snapshot record length (buffer size) 2 Msamples per channel

3.4.5 Link Analysis

A link analysis for the measurement system is shown in Table 3-5, in which the path loss and

received power are computed for an outdoor channel. A line-of-sight (LOS) channel was used to

determine the upper bound on the range of the measurement system. The log-distance path loss

model was used with a path loss exponent of 2 to determine the LOS path loss. The link analysis

results in the received power at the antenna ports of the receiver.

Table 3-5. Measurement system link analysis for outdoor radio channel (1 mile, line-of-sight). Parameter Sub-Param Sub-P Sym Sub-P Val Symbol Value Units CommentsTransmit Power Pt 28 dBm TX Amp ZHL-4240WTransmit Antenna Gain Gt 0 dBReceive Antenna Gain Gr 0 dBPath Loss (Log-Distance)

Ref Dist do 1 mFrequency fo 2.05E+09 Hz Center of channelRef Loss Lp(do) 38.7 dB Calculated for free space at ref distancePL Exponent n 2 2=free space, ~3.5 outdoor obs, ~5 indoor ofcDistance d 1610 m 1610m = 1miPath Loss PL 102.81 dBm

Receive Power (Ant Port) Pr -74.81 dBm

3.4.6 RF Section Analysis

Table 3-6 shows an analysis for the RF section of the measurement receiver. RF component

specifications were used to determine the power at the input to the A/D converter block. The

A/D converter block includes an internal, variable-gain amplifier that is not included in this table

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because the amplifier is part of the automatic gain control (AGC) loop, which is assumed to be in

a maximum gain state for the maximum range computations. This AGC loop is discussed in

section 3.7. The A/D converter block required a sinusoid with a magnitude of approximately -30

dBm (into 50 ohms) to have all levels of the A/D converter spanned.

Table 3-6. Measurement receiver RF section analysis for outdoor radio channel. Parameter Sub-Param Sub-P Sym Sub-P Val Symbol Value Units CommentsReceive Power (Ant Port) Pr -74.81 dBm From Link BudgetAntenna Cable Loss Lc1 2 dBRF Filter Loss Lrf 4.4 dB LARK SM-Series 0.2G-3G (fo=2.05G, 5%BW)RF Amp Gain Grf 25 dB ZHL-1042J, 10M-4.2GMixer Loss Lm 6.7 dB ZEM-4300, L-R 300M-4.3G, I DC-1GIF Filter Loss Lif 0.6 dB LARK LHP-Series 60M-700M (fc=200M)IF Amp 1 Gain Gif 20 dB ZFL-500, 50K-500MIF Amp 2 Gain Gif 20 dB ZFL-500, 50K-500MConnector Loss Lcn 3 dB SMAA/D Input Power Pad -26.51 dBm

3.4.7 Noise Analysis

An analysis of system noise is shown in Table 3-7. The noise figure specifications for each

component were used to compute an overall system noise temperature. The system noise power,

referenced to the input of the RF amplifier, is approximately –88 dBm; this noise power is

considerably higher than that of a conventional narrowband receiver because of the wide

bandwidth of the measurement receiver. When using the measurement receiver to perform

channel sounding measurements, a direct-sequence spread-spectrum signal is used, benefiting the

receiver with a large amount of processing gain. For the case of a 2047-chip sequence run at a

chip rate of 100 MHz and integrated over the entire sequence period at the receiver, a 33 dB

processing gain is realized. The resulting signal to noise ratio, accounting for processing gain, is

approximately 40 dB. The resulting power-delay profile would have a maximum theoretical

signal-to-correlation-noise ratio (interval of discrimination) of approximately 66 dB.

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Table 3-7. System noise analysis and noise results for outdoor radio channel. Parameter Sub-Param Sub-P Sym Sub-P Val Symbol Value Units CommentsRF Amp NF NFrf 6 dB ZHL-1042J, 10M-4.2GIF Amp 1 NF NFif1 5.3 dB ZFL-500, 50K-500MIF Amp 2 NF NFif2 5.3 dB ZFL-500, 50K-500MOscilloscope NF Nfo N/A dB Spec by accuracy, N/A since high RF/IFgainReceiver Noise Bandwidth B 1.00E+08 Hz 100MHz RF Filter, Filter 100 MHz IF in softwareSystem Noise Temperature

Antenna Noise Temp Ta 100 K EstimateAnt Cable Noise Temp Tc 107 K Calc from lossRF Filter Noise Temp Tfrf 185 K Calc from lossRF Amp Noise Temp Trf 865 K 290(10^NFrf/10 - 1)Mixer Noise Temp Tm 228 K ZEM-4300, Calc from conv lossIF Amp 1 Noise Temp Tif1 693 K ZFL-500, 50K-500M, Calc from NFIF Amp 2 Noise Temp Tif2 693 K ZFL-500, 50K-500M, Calc from NFIF Filter Noise Temp Tfif 37 K Calc from lossO-scope Noise Temp To N/A K Spec by accuracy, N/A since high RF/IFgainEqu. T into RF Amp Tin 246 K Eq noise temp at input to RF AmpSystem Noise Temp Ts 1122 K At input to RF Amp

Total Noise Power N -88.1 dBm At input to RF Amp (kTB*1000)Signal Power S -81.21 dBm At input to RF Amp (Pr-Lc1-Lrf)Signal to Noise Ratio SNR 6.89 dB Signal to thermal noise ratioProcessing Gain

PN Sequence Length l 2047 chips 11 bit shift regChip Rate Rc 1.00E+08 chips/secIntegration Period Ti 2.05E-05 sec 20.5us = 1 seq period for 2047 chipsChip Period Tc 1.00E-08 secProcessing Gain P 33.1 dB Int Period / Chip Period

Despread Sig to Therm Noise SNRt 40.0 dB SNR + Proc GainDespread Sig to Corr Noise SNRc 66.2 dB 20*log10(chip length)

Through this analysis, the maximum range for the system in an outdoor, LOS channel was

determined to be approximately one mile (1.6 km). Other analyses were performed to

demonstrate the performance of the system in an outdoor obstructed channel (n=3.5) and an

indoor, non-LOS channel (n=5). These analyses assumed a path loss reference distance of one

meter, indicating obstructions in close proximity to the antennas, and demonstrated the system to

be usable to approximately 100 m in an obstructed outdoor channel and approximately 25 m in a

severely obstructed indoor channel.

The specifications presented above were developed through an iterative process, with

consideration placed on the measurement requirements, equipment availability, equipment cost,

development time, and usability of the system (including portability and maintainability). The

analysis demonstrates the theoretical feasibility of constructing the measurement receiver.

3.5 Measurement Receiver Hardware

The measurement receiver hardware consists of three sections: an RF front end, a sampling

section, and a processing platform. Figure 3-3 illustrates a block diagram of the hardware. The

purpose of the RF front end is to condition the signals for sampling by the sampling section. The

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sampling section samples and stores snapshots of signals from the four RF front end channels

simultaneously. A personal computer (PC) is used as the processing platform to acquire the

samples from the sampling section and perform all of the software processing. The PC also logs

signal data and displays processed results.

RFBPF

IFLPF

Multi-Channel

ADC

Ch 1

Antenna

LARK SMFo=2050MHzBrf=100MHzL=4.4dB

ZHL1042JG=25dBNF=6dB

ZEM-4300L=6.7 dB

(2) ZFL-500G=20dBNF=5.3dB

LARK LHPfc=400MHzL=0.6dB

Ch 4

. . . . . .

Ch 2

Ch 3

High-SpeedRAM

TDS 580D

ReceiverControl

SignalAcquisition

PC

Vector ChannelData

RFBPF

IFLPF

Antenna

LARK SMFo=2050MHzBrf=100MHzL=4.4dB

ZHL1042JG=25dBNF=6dB

ZEM-4300L=6.7 dB

(2) ZFL-500G=20dBNF=5.3dB

LARK LHPfc=400MHzL=0.6dB

RFBPF

IFLPF

Multi-Channel

ADC

Ch 1

Antenna

LARK SMFo=2050MHzBrf=100MHzL=4.4dB

ZHL1042JG=25dBNF=6dB

ZEM-4300L=6.7 dB

(2) ZFL-500G=20dBNF=5.3dB

LARK LHPfc=400MHzL=0.6dB

Ch 4

. . . . . .

Ch 2

Ch 3

High-SpeedRAM

TDS 580D

ReceiverControl

SignalAcquisition

PC

Vector ChannelData

RFBPF

IFLPF

Antenna

LARK SMFo=2050MHzBrf=100MHzL=4.4dB

ZHL1042JG=25dBNF=6dB

ZEM-4300L=6.7 dB

(2) ZFL-500G=20dBNF=5.3dB

LARK LHPfc=400MHzL=0.6dB

Figure 3-3. Block diagram of the measurement receiver hardware, including the RF hardware that performs a frequency translation to a band that can be sampled by the 1 gigasample/sec sampling section.

3.5.1 RF Front End

Each channel of the four-channel RF front end translates the 2000 MHz to 2100 MHz spectrum

down to an IF below 400 MHz. The RF front end uses an RF filter with a 100 MHz bandwidth

to select the desired reception band and reject the image band. The RF filter is intentionally

located at the input of the RF amplifier, which is wide band and could be saturated if strong out-

of-band signals exist at the measurement site. The mixer is driven by a 1900 MHz local

oscillator, translating the 2050 MHz RF center frequency down to the 150 MHz IF center

frequency. Two IF amplifiers are used to provide sufficient gain for the sampling section. The

IF filter is a low pass filter with a 400 MHz cutoff frequency. The use of these wide low pass

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filters allows the software algorithm designer to choose IF center frequencies other than 150

MHz (between approximately 0.2 MHz and 400 MHz)13, and only tuning of the local oscillator is

then necessary.

3.5.2 Sampling Section

The four IF signals at the output of the RF front end are sampled at 1 gigasample per second. A

Tektronix TDS 580 digital oscilloscope with extended memory serves as the sampling section.

The sampled IF signals are stored in high-speed RAM buffer until acquired by the PC for

processing. The data transfer rate between the sampling section and the PC is a maximum of 8

Mbyte/sec. This transfer rate necessitates the use of signal snapshots, which are acquired by the

sampling section at each channel simultaneously and buffered before delivery to the PC. When

the sampling section buffer is full and the PC is acquiring the signal data from the sampling

section, the sampling section ignores subsequent incoming signals. This process allows the

sampling bandwidth to be extremely high while using a practical data transfer rate and realizable

processing platform. The RAM can buffer up to 8 Msamples of signal data (2 Msamples per

channel).

All raw IF samples are acquired and logged by the PC. The PC uses an IEEE 488 GPIB (general

purpose interface bus) card to communicate with the sampling section. More information about

signal processing and communication between the PC and the sampling section are presented in

section 3.7.

Performing IF sampling versus using in-phase and quadrature (I/Q) sampling allows the greatest

flexibility in software processing while minimizing hardware requirements. When using IF

sampling for the four channels, only four IF channels need to be sampled instead of eight

quadrature baseband channels. This reduction in sampling channels is at the cost of a higher

sampling rate and places the responsibility of a down-conversion stage on the software.

Software modules perform the final filtering, automatic gain control (control of the final

hardware amplification stage), and complex baseband down-conversion.

13 The 0.2 MHz restriction is due to the AC coupling cutoff of the sampling section and not the low pass filter frequency response.

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3.5.3 Complete System

Figure 3-4 illustrates the RF front end assembly and the entire measurement receiver system. As

shown in Figure 3-4 (a), eight-section tubular filters perform the hardware filtering operations.

Wideband RF amplifiers allow the RF filters to be exchanged for filters covering other bands for

future measurements. The mixers are driven by a common local oscillator through a signal

splitter to maintain phase coherence among the channels. The amplifiers in the RF front end are

powered by a 15 volt power bus supplied from a single point on the assembly. Figure 3-4 (b)

shows the entire measurement receiver and a signal generator used to produce a test signal.

(a) (b)

Figure 3-4. (a) The RF front end of the four-channel receiver, showing the tubular filters and connectorized RF components. (b) The complete system, showing the oscilloscope used for sampling, a signal generator

used for the local oscillator, and another signal generator used to generate a test signal.

The measurement system hardware provides a versatile channel measurement and test bed

system. While most of the functionality of the measurement receiver is performed by software,

and is therefore configurable, the RF components are connectorized and can be exchanged for

other components to accommodate other center frequencies and bandwidths (up to 400 MHz

wide).

3.6 Theory and Application of Object Orientation

In this section, a foundation for the object-orientated design of the measurement system software

is presented. A knowledge of the concepts and terminology of object oriented programming is

very helpful for understanding the measurement receiver software. The theory of object oriented

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programming relevant to the development of the measurement receiver software and its

processing modules is discussed.

3.6.1 Objects

Object-oriented programming is an organized approach to large-scale software development

based on abstract data types, encapsulation, hierarchical organization, polymorphism, and a

generic activation mechanism for message passing [p.21 Kri96]. In object-oriented

programming, data members and functional methods are packaged into groups known as objects

[p.2 Sul94]. An object is a metaphorical representation of entities that need to be abstracted into

a programmatic context. Objects give programmers a way of defining the characteristics and

actions of entities (physical or conceptual) using data members and methods, respectively.

Stated similarly, “an object is a meaningful group of process requirements and data

requirements.” [p.27 Sul94]

Objects consist of two components that allow them to store data and perform actions [p.22

Kri96]. Attributes form the static component of an object to store the object’s data, which

describes the characteristics and state of that object. Attributes are the object’s variables, which

are contextually sensitive. Methods form the dynamic component of an object, defining the

behavioral and functional characteristics of the object. Methods are the functions belonging to

the object that comprise all that an object can do. The data type of an object is called a class. A

class combines the attributes and methods of an object into one package [p.21 Ent90]. Classes

are used to define the attributes and methods of the objects they describe.

3.6.2 Object Orientation Concepts

The following five concepts of object-oriented programming are important to understanding the

significance of applying object orientation to software radio applications:

Encapsulation: The hiding of the internal structure of an object, including its internal

data and functions, is known as encapsulation [p.24 Kri96]. Encapsulation allows the

designer to purposefully determine which components of the object should be exposed

and which components should be hidden as the integral workings of the object.

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Programming can be greatly simplified and protected using encapsulation; for example, a

large set of low level commands can be encapsulated by an object, and access to

functional groups of those commands can be given to the programmer in the form of

methods. In this way, a specific set and order of low level commands can be predefined

and provided to the programmer, relieving the programmer of the responsibility of

determining the correct set and order of commands to perform a particular task.

Encapsulating benefits the programmer at the cost of reduced freedom to prod at low

level operations, but transparent interfaces can be developed for objects where low level

command manipulation is warranted.

Abstract data types: Abstraction is the act of representing something without including

background or inessential detail [p.10 Gra94]. An abstract data type is an abstraction that

encapsulates the components of a set of objects. Abstract data types are defined by the

programmer rather than being specified in the particular programming language. The

abstract data type defines both attributes and methods for objects, and hence the

programmer can completely define the behavior of objects.

Hierarchical Organization (Inheritance): Classes of objects are organized in a

hierarchical fashion, where one class can inherit the methods and attributes from other

classes. If Class D (a derived class) is derived from Class B (a base class), then some or

all of the methods and attributes of Class B can be made available for use by Class D.

This allows derived classes to become more specific in their abstraction while

maintaining commonality with the base class and other classes derived from the same

base class. Inheritance provides a method of distinction between the general properties of

an entity and the properties of a specific entity [p.21 Str91].

Polymorphism: Polymorphism allows selection between redundant methods or

attributes using the context in which the methods or attributes are referred [p.70 Sul94].

This concept allows software modules to be developed separately and provides a

mechanism for forward compatibility software. With polymorphism, calls to methods

that do not yet exist can be handled, and those methods can be added or modified in the

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future. Polymorphic references are resolved within a particular class hierarchy, allowing

a base class to handle references that are not resolved in the derived classes, and

permitting derived classes to override the methods and attributes in their own base

classes.

Message-passing mechanism: Generically defined in the context of object-oriented

programming, a message is a query given to an object that requests execution of one of

the members of that object [p.23 Kri96]. A message consists of a selector and

arguments, which specify which method should be called and the parameters to be passed

to the method. Objects can use messages to perform an operation or to transfer

information, between two objects or among multiple objects.14

3.6.3 Application of Object-Oriented Methods to Software Radios

The overhead of object-oriented design and programming makes object orientation appropriate

only for large software systems. Because of the multifaceted complexity of software radio

programming, it is a probable candidate for object orientation, especially if the software is

developed by a group of programmers, or if the software is intended to be reusable and have a

long life with multiple revisions. The following list summarizes the more important benefits of

using object-oriented programming for software radio projects, adapted from the generic object

orientation benefits [p.31 Gra94]:

• Classes designed for object-oriented software radios form a library of reusable modules

that can be used by future projects, resulting in a reduction of redundant effort and an

increase in development productivity.

• As reusable software modules become mature through use, the quality and reliability of

the modules increases, resulting in fewer software deficiencies and a more useable library

of software radio blocks.

14 For generic object-oriented design, it is implied in [Kri96] that passing messages is the only method of communication among objects. However, in practice, programming languages such as C++ and development environments such as those using Microsoft Foundation Classes distinguish between calling of methods and passing of messages. Methods of an object can be called directly using the function name and associated parameters, while messages are received by an object’s message handler methods, which may call other methods of the object.

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• Using object-oriented programming allows software radio modules to be developed

independently or in parallel through inheritance. Developers can interface with

functionally incomplete classes until such time in development or testing where the

objects need to perform a required operation or provide required data.

• The message passing mechanism of object orientation provides a straightforward

interface to software modules and defines a clean break between modules for minimal

coupling and interdependency.

• Encapsulation inherent in object orientation naturally divides a complex programming

task into manageable subtasks, increasing the likelihood of successful completion and

yielding modules that are scalable for other projects of more or less complexity.

The benefits of object orientation come at the cost of planning time, development speed, and

software overhead:

• Variable referencing and function calling are context-sensitive, requiring overhead

embedded in the program [p.5 Sul94].

• Reliance on a compiler to be efficient in minimizing processor instruction cycles and

occupied code space.

• Increased effort required for planning, organization, and preparation at the beginning of

the software development cycle.

• Reduction in upfront development speed when attention is devoted to the architecture

rather than signal processing functionality [p.5 Sul94].

As more functionality is integrated in to the software of radios, and as additional radio

communication standards need to be handled by a single device, the size and complexity of

software radio projects will continue to increase. Because of this trend, the benefits of object-

oriented programming techniques will progressively outweigh the costs, an assertion supported

by case studies of other large scale software applications and their migration to object technology

[p.50 Gra94].

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The applicability of object technology to the growing complexity of wireless communications is

evidenced by emerging wireless architectures. In [Moe99], the network entities rather than

internal radio entities are abstracted to objects. The same methodology applies, however, in that

the functionality of a network object is encapsulated, and external entities are separated from the

object’s workings and behavior. An interface is defined for use by outside objects and is the

means by which communications occur. While [Moe99] defines objects to be wireless network

nodes between which network traffic is passed, the measurement receiver described here defines

objects to be radio modules between which signal data is passed. In another reference [Dav99],

concepts of abstraction, encapsulation, messaging, and object-orientation in general are used in

the communication architecture of a software radio to allow portability of software radio

applications and dynamic instantiation of objects. In both references cited, object orientation is

aimed at organizing the components of complex radio systems and facilitating scalable and

maintainable architectures.

3.7 Measurement Receiver Software

The architecture of the measurement receiver software was designed in such a way as to allow

implementation of a variety of radio applications. The functionality of the software can be

broken into several stages as shown in Figure 3-1. This figure shows a data flow representation

of the measurement receiver, where signal data is distributed and processed successively through

the software modules, beginning at the hardware receiver object and ending at the user interface

that displays processed results. In this section the following topics are covered to explain the

measurement receiver software:

• Signal acquisition with the hardware-specific receiver object

• Radio receiver and processing functions

• Display/file interface functions

• Multithreading and inter-object communications

• Automatic gain control

• Example of measurement receiver software application

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The architecture described here, including the logical division of functionality into objects and

the method of inter-object communications within a software radio, was originally developed for

the research presented in this dissertation.

SW Receiver 1

SW Receiver 2

. . .

SW Receiver n

SignalAcquisition

Radio ReceiverFunctions

SW Processor 1

SW Processor 1

SW Processor m

Hardware-SpecificReceiverObject

Receiver H

ardware

Hardware Software

Display/FileFunctions

Interface 1

Interface 2

Interface k

. . .

. . .

ProcessingFunctions

• Oscilloscope-based acquisition• Multi-channel PC acquisition card

• DS-SS receiver• Narrowband receiver

• Channel characterization• Wideband diversity• Narrowband diversity• DOA algorithms

• Impulse responses• Diversity metrics• DOA displays

SW Receiver 1

SW Receiver 2

. . .

SW Receiver n

SignalAcquisition

Radio ReceiverFunctions

SW Processor 1

SW Processor 1

SW Processor m

Hardware-SpecificReceiverObject

Receiver H

ardware

Hardware Software

Display/FileFunctions

Interface 1

Interface 2

Interface k

. . .

. . .

ProcessingFunctions

• Oscilloscope-based acquisition• Multi-channel PC acquisition card

• DS-SS receiver• Narrowband receiver

• Channel characterization• Wideband diversity• Narrowband diversity• DOA algorithms

• Impulse responses• Diversity metrics• DOA displays

Figure 3-5. Flow of signal data through the processing of the measurement receiver software.

3.7.1 Signal Acquisition with the Hardware-Specific Receiver Object

The hardware-specific receiver object is responsible for communications between the external

hardware and the measurement receiver software. Hardware configuration routines and signal

acquisition functions are encapsulated by the receiver object in order to sever coupling between

the radio processing objects and the RF hardware. This means that the processing objects can

work independently and without knowledge of the type of RF hardware to which they are

connected. To exploit the benefits of polymorphism, the hardware object is defined in a

hierarchical class structure, and a standard set of interface methods are defined. These standard

methods allow new hardware to replace old hardware without breaking code downstream in the

data flow.

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Table 3-8. Description of the generic hardware-specific receiver object interface functions.

Receiver

Object

Interface

Functions

• CReceiver(.) – This constructor (and derived-class constructors) sets up the

initial state of the object and the hardware to which it is connected.

• Configure(.) – Sets the state of the receiver object based on the user’s

input. This method defines which configuration options are presented to

the user based on the hardware type with which the class is associated.

• Initialize(.) – Prepares the hardware by setting up the hardware with the

desired configuration and confirming that hardware has been set up

successfully.

• GetSignal(.) – Retrieves raw signal data from the hardware, scales the data

with calibration constants, and obtains the sample rate of the data snapshot.

The hierarchical relationships among the receiver object classes are illustrated in Figure 3-6.

The CReceiver class handles the generic methods for all classes that are derived from CReceiver.

CReceiver and CGpibDevice are abstract classes and therefore cannot be instantiated alone. The

CGpibDevice class handles GPIB (IEEE-488) interface functions; the GPIB interface is used for

communications with the oscilloscope that samples the IF channels. The CGpibDevice class

handles opening the connection to the GPIB device, checking for errors, and managing GPIB

addresses. Any GPIB device can use an object derived from this class for communications. The

CTekScope class is derived from the CGpibDevice class and provides methods specific to

interface with a Tektronix oscilloscope. The CTekScope class has been tested with the Tektronix

TDS 580 and TDS 520 oscilloscopes. Specific routines for communicating with the TDS

oscilloscopes are encapsulated in the CTekScope object and are far removed from the software

radio processing code, relieving the signal processing programmer from the need to fully

understand the hardware interface software. The measurement receiver software uses a pointer

to a CReceiver object, so that through polymorphism any object of a class derived from

CReceiver can be used transparently, and the correct methods for the appropriate class will be

called.

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CReceiver

CGpibDevice

CTekScope

Handles generic methods for all receiver objects.

Handles methods for GPIB devices.

Handles methods for Tektronix devices.

CReceiver

CGpibDevice

CTekScope

Handles generic methods for all receiver objects.

Handles methods for GPIB devices.

Handles methods for Tektronix devices.

Figure 3-6. Class hierarchy of hardware-specific receiver objects.

3.7.2 Radio Receiver and Processing Functions

The radio receiver and processing modules perform all of the signal processing on the acquired

signal data. The modules exist in the form of objects in the measurement receiver, and multiple

processing objects can be instantiated simultaneously to operate on data in parallel. Radio

receiver functions are classified as operations that are performed on raw signal data at the

modulation or waveform level. Processing functions are categorized as operations that require

processed data to perform statistical characterization or symbol-level decoding. These objects

together implement both simple and complex operations such as narrowband receivers, direct-

sequence spread-spectrum receivers, channel characterization algorithms, and antenna diversity

algorithms. Radio receiver functions and processing functions can be combined into a single

object depending upon the complexity of the operations. Generally, functionally complex

algorithms should be compartmentalized to facilitate design and maintenance of the software.

3.7.3 Display/File Interface Functions

After processing, the data generally needs to be displayed or stored to disk. The interface objects

are responsible for this task, and multiple objects can operate on the same processed data. The

interface objects take the processed data and display it on a graph or table, or alternatively the

processed data can be stored to disk. Existing display interfaces include plots of power-delay

profiles, histograms, cumulative distribution functions (CDFs), and frequency spectra. Displays

also include tables of computed signal data (for example, received power). A data logging object

has also been developed that stores raw IF samples, sample rates, time stamps, and calibration

parameters to disk continuously as the measurement receiver is running.

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3.7.4 Multithreading and Inter-Object Communications

Objects in the measurement receiver communicate through messaging and shared memory space.

An illustration of the communication paths within the receiver software is shown in Figure 3-7.

The RF hardware of the measurement receiver is represented by the box on the left side of the

figure, and the display and storage media is represented by the boxes on the right side of the

figure. In between these components is the software of the measurement receiver, with each oval

representing an object or module of the system.

The operations of the entire system are either controlled or launched by the System Exe object at

the top of the diagram. This object is responsible for accepting instructions from the user for

configuring the receiver, launching processing objects, logging data to disk, and overall control

of the measurement receiver. The System Exe object is the central point in the software through

which all objects can communicate.

MatlabApplications

Data Logging

System Exe

Receiver

Playback

FrequencySpectrum

ChannelSounding

AsynchronousMessaging

Hardw

are

Display

Hard D

isk

MATLAB

MatlabApplications

Data Logging

System Exe

Receiver

Playback

FrequencySpectrum

ChannelSounding

AsynchronousMessaging

Hardw

are

Display

Hard D

isk

MATLAB

Figure 3-7. Relationships among the measurement system software modules and external interfaces.

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Each of the objects represented by the ovals in Figure 3-7 operates on signal data in an

independent thread15. The usage of multiple threads offers several advantages [Coh98], namely,

Maximization of parallel processing: When a process needs to execute tasks that are

independent activities, performance of the overall process can be improved by assigning

tasks to different threads and executing the threads in parallel. This is especially true for

tasks that involve a user interface or tasks that wait for events to occur.

Reduction of overall idle time: Separating tasks that consume idle time into separate

threads reduces the amount of idle time consumed by the entire process. For example, a

separate thread that waits for data due to relatively slow I/O (input/output) can be

designed so that the whole process does not need to wait for the I/O to complete, as might

be the case with a single-threaded process performing the same task.

Responsiveness: Separating the interface functions and processing functions yields a

more responsive user interface. By doing this, a processing function that takes a long

time to complete will not freeze user input functions or output displays.

Simplified design: A design can be simplified using multiple threads by assigning

unique threads to independent and well defined tasks. The use of separate threads

naturally modularizes the software into manageable portions.

Communication between the System Exe object and other objects shown in Figure 3-7 is

performed using asynchronous messaging. Each object has message handler methods that

respond to messages posted into the message queue of the measurement receiver software.

These messages start and stop processing, alert objects new data that new data is ready, and send

indexing parameters used as references for each processing object. Communications between

the measurement receiver user interface and the objects is also performed using messaging.

15 A thread is a path of execution through software code. Each thread has its own call stack and register state independent from the rest, but all exist within the code and address space defined by the process that has launched the threads [Coh98].

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Before the measurement receiver is started, the Receiver object in Figure 3-7 is sent

configuration information to set up the hardware. The receiver object configures the hardware

and alerts the System Exe object that the hardware is ready to perform. While the measurement

receiver is running, the Receiver object executes its primary responsibility of acquiring signal

data from the receiver hardware. Signal data is acquired in snapshots up to two megasamples in

length per channel, and the data is placed in memory space that is shared with the processing

objects.

Synchronization of data reading and writing is an important consideration when shared memory

space is used among multiple threads. A technique must be used in order to eliminate the

possibility of one thread overwriting data space while another thread is reading the same data

space. The measurement receiver software uses synchronization objects to handle data reading

and writing by multiple objects (each managing an independent thread). The receiver object and

the playback object are the source of the received signal data, and the processing objects are the

recipients of the data. When the source objects are writing data, they first check the

synchronization object to see if any processing object is reading data. If no object is reading

data, then the source object locks out the common memory space from the processing objects

using the synchronization object, and then the source object writes data to the memory space.

Once done writing, the source object unlocks the memory. Processing objects follow a similar

process, using the synchronization object to check if a source object is writing to the common

memory space and only reading if no source object is writing. Processing objects that implement

time-intensive algorithms can copy the data to local memory space to free the synchronization

lock in a minimum amount of time.

3.7.5 Automatic Gain Control

Automatic gain control (AGC) is accomplished using a combination of hardware and software

components. Figure 3-8 illustrates a block diagram of the AGC components, distributed between

hardware and software sections. The AGC for each of the four measurement receiver channels is

independent of those of the other channels.

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From RFFrontEnd

Final AmpStage –AdjustableGain

ADCSignalRAM

GainController

Device C

omm

unications

SoftwareSampling HardwareAGC

Signal LevelDetection

Gain AdjustmentFactor

RadioProcessing

From RFFrontEnd

Final AmpStage –AdjustableGain

ADCSignalRAM

GainController

Device C

omm

unications

SoftwareSampling HardwareAGC

Signal LevelDetection

Gain AdjustmentFactor

RadioProcessing

Figure 3-8. Block diagram of hardware and software components of automatic gain control.

The Sampling Hardware block represents the digital oscilloscope in the current measurement

receiver implementation. The oscilloscope has an internal amplifier that is used as the final gain

stage in the analog signal path. This amplifier has an adjustable gain and is controllable from the

communications port of the oscilloscope. While the hardware is responsible for the actual signal

gain, the entire AGC algorithm is implemented in software (illustrated within the Software block

in Figure 3-8).

The AGC signal level detection can respond to any computed value of the signal; for example, it

can operate using values of signal power or peak amplitude. The gain adjustment factor is then

used to scale the absolute gain of the final analog amplifier stage. The AGC software includes

the option of throwing out snapshots that are far out of range before signal data is passed to the

radio processing objects.

3.7.6 Example of Measurement Receiver Software Application

Presented here is an example radio application developed for the measurement receiver. The

application is designed to measure multipath channel characteristics using the measurement

receiver and a separate transmitter (see section 3.8 for information on the transmitter).

To detect individual multipath components, the measurement system transmitter transmits a

BPSK-modulated PN sequence through the radio channel. The autocorrelation function of an m-

length PN sequence produces a sharp peak having a width of two PN chips and an amplitude of

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20log10(m) above the correlation noise (see [Jer92]). The receiver can implement a correlator to

detect relative delays and amplitudes of individual multipath components that arrive at the

receiver16.

Figure 3-9 illustrates a block diagram of the software algorithm used to measure power-delay

profiles, which are plots of amplitude versus delay that represent channel impulse responses.

This design improves upon analog sliding correlator measurement systems, which are limited in

their ability to measure rapidly changing channels because of non-instantaneous sliding of PN

codes [New97]. A problem arises when measuring dynamic channels where channel impulse

responses change rapidly. Such is the case when the receiver or transmitter is moving quickly,

when objects in the environment are in motion, or when the transmitter or receiver are moved

through regions of intermittent shadowing. Errors in measurements result when the channel

changes during a sweep of the analog sliding correlator, producing a power-delay profile that

represents one channel at the beginning of the power-delay profile (short delays) and another

channel at the end of that same profile (long delays). The system illustrated in Figure 3-9

performs a correlation on very short snapshots of signals (15 microseconds or less), and therefore

does not suffer from this problem.

For each of the four receiver channels, the signal acquired from the ADC is filtered in software

and split into two signals. Both signals are translated in frequency using a 150 MHz local

oscillator (LO), with one of the LO signals shifted by 90 degrees. The translated signals are low-

pass filtered and decimated to produce I and Q channel (quadrature) signals. The correlator

correlates the received I and Q signals with the known PN sequence. From these two quadrature

signals, profiles of the magnitude and phase representing the channel impulse response are

produced. An example power-delay profile plot is shown in Figure 3-10. The phase plot must

be interpreted to be valid only at points where multipath components exist17, and the phase

values represent the phase of the multipath carrier relative to other arriving multipath

components.

16 For detailed information on multipath channel measurements and channel measurement systems, see [New97]. 17 The phase values indicated on the plot between the multipath components is simply the phase of the composite noise between the components.

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IFFilter

X

LO

90o

X

150MHz

LowpassFilter

LowpassFilter

I

Q

Decimate Correlator

Sqrt(I2+Q2)

ATAN2(Q,I)

Decimate Correlator

PN SequenceGenerator

PowerDelayProfile

MultipathComponentPhase

IF infromCh n

IFFilter

X

LO

90o

X

150MHz

LowpassFilter

LowpassFilter

I

Q

Decimate Correlator

Sqrt(I2+Q2)

ATAN2(Q,I)

Decimate Correlator

PN SequenceGenerator

PowerDelayProfile

MultipathComponentPhase

IF infromCh n

Figure 3-9. Block diagram of the software module that measures the strength, delay, and phase of multipath components arriving at the receiver.

Figure 3-10. Power-delay profile (amplitude and phase) computed by measurement receiver.

The channel characterization software can run simultaneously with other processing modules,

allowing comparison of receiver performance with radio channel conditions. By having a

power-delay profile recorded at the time of an algorithm anomaly or failure (running in another

processing object), the offending channel conditions that caused the failure can be observed.

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3.8 FPGA-Based Transmitter

The measurement system transmitter produces a programmable test signal appropriate for the

wideband propagation experiment being performed. The transmitter information source is based

on a PLD (programmable logic device), and the transmitted data signal is programming on a PC

and downloaded to the PLD. The output of the PLD modulates a 2050 MHz carrier; the

amplified signal is transmitted by a single antenna. The transmitter transmits symbol at rates up

to 80 Mbps.

3.8.1 Transmitter Hardware

The transmitter configuration illustrated in Figure 3-11 and Figure 3-12 produces a BPSK signal

for channel characterization. The modulating signal is a pseudorandom binary sequence (PN

sequence) having autocorrelation properties suitable for detection of individual multipath

components occurring in radio channels [Jer92].

BasebandData

PLD/FPGA

X GOscillatorSignal Generator

BPF

fo = 2050 MHzBW = 100 MHz

80 Mbps (Mcps)

fc = 2050 MHz

Monopole/DipoleG = 30 dB

Pout = 28 dBm

BasebandData

PLD/FPGA

X GOscillatorSignal Generator

BPF

fo = 2050 MHzBW = 100 MHz

80 Mbps (Mcps)

fc = 2050 MHz

Monopole/DipoleG = 30 dB

Pout = 28 dBm

Figure 3-11. Block diagram of the measurement system transmitter, including a PLD that is programmable to produce the data required for the particular experiment.

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Figure 3-12. Wideband transmitter used for generating BPSK-modulated signal.

3.8.2 Transmitter Verification

The plots in Figure 3-13 show a processed snapshot of the signal produced by the wideband

transmitter; this plot is used to verify the modulation and data sequence content of the signal.

The snapshot was acquired and demodulated using the measurement receiver. To produce the

plots of in-phase and quadrature components, the measurement receiver performed a complex

baseband down-conversion on the received signal. The plot of phase was produced using the I

and Q components.

Symbol timing was acquired by detecting the edge transitions of the baseband signals. The

constellation plot in Figure 3-14 shows the symbols and the decision boundary. The amplitudes

of the I and Q channels were normalized using the same multiplier for each channel. The plot

clearly shows that the transmitter is producing a BPSK signal. The phase rotation is simply due

to the offset in phase between the transmitter local oscillator and the software receiver local

oscillator and is of no significant consequence because that phase rotation can be detected and

applied to either the decision boundary or the symbols. The plot in Figure 3-15 shows the

received signal after symbol decisions have been made; the phase offset was applied to the

decision boundary in this case.

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0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-6

-1

-0.5

0

0.5

1I Component Relative Magnitude

Mag

(V

)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-6

-1

-0.5

0

0.5

1Q Component Relative Magnitude

Mag

(V

)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-6

-4

-2

0

2

4Relative Phase of Received Signal

Time (sec)

Pha

se (

rad)

Figure 3-13. Output of transmitter acquired with measurement receiver (in-phase component, quadrature component, and relative phase shown).

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Received Symbol Constellation

I component

Q c

ompo

nent

Figure 3-14. Signal constellation as demodulated by measurement receiver (phase rotation of constellation has not been applied for illustration purposes; the diagonal dashed line indicates the decision boundary).

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0.5 1 1.5 2 2.5 3 3.5 4 4.5

x 10-6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2Regenerated Signal Produced by Transmitter

Time (sec)

Sym

bol V

alue

Figure 3-15. Transmitter signal acquired with measurement receiver after symbol decisions have been made.

The transmitter discussed here has been used for several channel measurement campaigns. A

variety of PN sequences and chip rates in addition to those employed here for validation have

been programmed into the transmitter during measurements. Chapter 5 presents a description

and results of measurements.

3.9 Summary

This chapter has described the design and development of a wideband, multi-channel, real-time,

software-defined measurement receiver. The measurement receiver has been successfully built,

demonstrated, and used in the field for RF channel measurements. The measurement receiver

has also served as a test bed for smart antenna algorithms and a wideband signal data collection

system.

The measurement receiver can be programmed using MATLAB or C++. Since MATLAB is a

widely used tool for simulating communication systems, the MATLAB interface capability of

the measurement receiver provides a way to turn simulated processing algorithms into functional

software radio modules to process actual received radio signals in real time. The modularity of

the software facilitates managing the code for expansion to future software radio applications.

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The minimization of functionality performed by the RF hardware permits the measurement

receiver to be alterable for other frequency bands of interest. The receiver can process RF

bandwidths up to 400 MHz, and center frequencies can be processed by modifying the mixer and

RF filter in the single down-conversion stage.

The successful development and use of this measurement receiver validates its architecture for

propagation measurement and radio test bed applications. The actual implementation of new

software modules beyond the original design of the receiver and created by researchers in

addition to the original developer supports the motivation for using an object-oriented, multi-

threaded methodology.

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Chapter 4 Multipath Channel Models for Antenna Arrays

This chapter presents research in the area of channel models for use in antenna array simulation

and analysis. The chapter first reviews the purpose and methods of existing channel models, and

then presents the development of new channel models. The channel models considered here

provide information on delay, strength, and direction of multipath components. Sections 4.1 and

4.2 review the purpose and classification of channel models. Section 4.3 describes selected

channel models that are widely accepted. In section 4.4, the general form of an ellipsoidal

channel model is described.

Section 4.5 describes a new air-to-ground channel model in detail. First, equations that specify

the air-to-ground model geometry are derived. Next, a theoretical probability density function

for direction of arrival of multipath components is analytically derived. Finally, joint DOA-

propagation time delay probability density functions are presented, and their implications are

discussed.

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4.1 The Purpose of Radio Channel Models

Channel models provide a means of simulating and analyzing radio channels. A channel model

may perform the function of producing raw channel output, such as multipath strengths and

delays, narrowband fading envelopes, and signal direction of arrival. A channel model may also

be used as a component of a system simulation. In this case, statistics of the channel itself are

not necessarily of interest, but a measure of the impact on the output of the system simulation is

desired. Figure 4-1 illustrates the use of radio channel models.

ChannelModel

Measurements,Geometry,Statistics,…

Mean path loss,Fading envelope,Multipath delays,Direction of arrival,Analytical expression,…

Channel Model

Functional View

System View

Transmitter Receiver

Channel simulator

N M

ChannelModel

Measurements,Geometry,Statistics,…

Mean path loss,Fading envelope,Multipath delays,Direction of arrival,Analytical expression,…

Channel Model

Functional View

System View

Transmitter Receiver

Channel simulator

N M

Figure 4-1. Uses for channel models shown from the standpoints of functionality and system implementation.

As shown in Figure 4-1, the input to the channel model may consist of measurement results,

geometry specifications, or signal statistics. The model may actually represent multiple,

statistically correlated radio channels consisting of N channel inputs and M channel outputs.

Such a channel model is called a vector channel model and describes the spatial and temporal

characteristics of the radio channel [Ree02].

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Table 4-1. Requirements of channel models versus radio access technology.

Receivedpower

Multipathdelay

Directionof Arrival

NarrowbandSystems (e.g., AMPS)

WidebandSystems (e.g., IS-95)

Antenna ArraySystems (e.g., GSM with antenna array)

Wideband AntennaArray Systems (e.g., IS-2000 with ant. array)

Other technologies,New receiver architectures (4G+)

Multiple-InputMultiple-OutputSystems

Receivedpower

Multipathdelay

Directionof Arrival

NarrowbandSystems (e.g., AMPS)NarrowbandSystems (e.g., AMPS)

WidebandSystems (e.g., IS-95)WidebandSystems (e.g., IS-95)

Antenna ArraySystems (e.g., GSM with antenna array)Antenna ArraySystems (e.g., GSM with antenna array)

Wideband AntennaArray Systems (e.g., IS-2000 with ant. array)Wideband AntennaArray Systems (e.g., IS-2000 with ant. array)

Other technologies,New receiver architectures (4G+)Other technologies,New receiver architectures (4G+)

Multiple-InputMultiple-OutputSystems

Multiple-InputMultiple-OutputSystems

Since the deployment of the analog AMPS cellular phone network in the early 1980s,

modulation and signal processing techniques have become increasingly complex, and the

transmitted bandpass signals have become wider in bandwidth. In addition, antenna array

technology is finding its way into commercial wireless communications networks. Channel

models need to accommodate these changes in radio access technologies. Table 4-1 lists a set of

wireless technologies and the associated requirements placed on channel models. In the early

days of cellular, modeling a received power using fading envelope provided much of the

information required to simulate the 25 KHz-wide radio channel. With the introduction of IS-95

CDMA networks, which used rake receivers in base stations and mobile stations, channel models

needed to provide information on the strength and delay of multipath components (temporal

characteristics). As antenna arrays are incorporated into wireless systems, models must provide

direction of arrival information (spatial characteristics). In order to simulate spatial filtering

systems, a multipath radio channel model must not only produce multipath channel parameters18

but also direction of arrival information [Lib95]. Although an assumption can be made that 18 Multipath channel parameters include the strengths and delays of the individual multipath components that form a channel impulse response.

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multipath components arrive along paths that are uniformly distributed in angle from 0 to 2π

around the receiver [Par92], a model that accounts for the physical environment will produce

more realistic results because the model is tied to the physical propagation processes in the

environment. It is historically evident, through decades of publications, that the evolution of

wireless systems requires the evolution of radio channel models.

4.2 Channel Model Classification

Channel models can be developed based on factors of measured data, propagation environment

geometry, and analytical electromagnetic theory. Channel models can be placed into

classifications of geometric and statistical [Ert99]:

• Geometric channel models are developed by characterizing a propagation environment

with a particular geometrical layout. Geometric channel models define a particular

region within which objects act as scatterers, causing multipath within the channel. Time

delay and strength of multipath components are derived using the distances that multipath

signals travel through the environment; properties of the scattering objects may also be

considered. Geometric models may begin based entirely on geometry, and they may be

tuned with measured data so that the models more accurately represent a particular

environment.

• Statistical channel models use a statistical distribution of channel characteristics to

represent the radio channel rather than using the physical geometry of the environment.

Measurements may be used to characterize received power, propagation delay, and

direction of arrival in order to produce the statistical distributions. Measurements can be

made in new environments and frequency bands to determine the statistical

characteristics of signal propagation, or else measurements in similar environments or

nearby frequency bands may be used. In the absence of measurement data, statistical

distributions are sometimes estimated or assumed.

Geometric channel models have the advantage of a physical tie to the channel environment;

because of this, it may be easier to verify and understand the results and implications of channel

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simulations. Geometric channel models are beneficial for producing results that do not tie the

channel to any actual physical environment; for example, measurements made in an urban region

to produce a statistical model may bind the results to the particular region in which the

measurements were performed. Statistical models based on measurements are good if this

environmental binding is desired, and measurements can be performed in multiple sub-

environments to more accurately represent the entire propagation channel.

4.3 Existing Geometric Channel Models

This research focuses on geometric channel models because of their ability to produce spatial

channel characteristics that are tied to the physical propagation environment. Simulations that

represent the physical environment and that implement the geometry of the channel models are

used to verify some of the analytical results derived in this chapter.

4.3.1 Multipath Channel Impulse Response

Multipath channels can be represented by the impulse response h(t) given in ( 4.1 ). The impulse

response represents multiple paths within the radio channel with δ(t) functions, and each

multipath has an associated amplitude αi and delay τi. The parameter L is the number of signal

components, including the LOS component (if one exists), in a given impulse response.

( ) ( )∑−

=

−=1

0

L

iii tth τδα ( 4.1 )

Equation ( 4.1 ) is a bandpass model, which accounts for multipath delays solely in terms of

absolute time. Although phases shifts are in fact minute time delays, a more appropriate model

that explicitly accounts for phase shifts and that is used as a complex baseband model is given in

equation ( 4.2 ). In ( 4.2 ), the parameter φi represents the phase shift of individual multipath

components due to the channel.

( ) ( )∑−

=

−=1

0

L

ii

ji teth i τδα φ ( 4.2 )

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The effect of direction of arrival of signal components and the receiving antenna radiation

pattern can be taken into account with a slight variation of this model. In [Lu97], the radiation

pattern is multiplied by the signal component amplitude coefficient, yielding

( ) ( ) ( )iir

L

ii

ji Fteath i φθτδφ ,−= ∑

=

1

0

( 4.3 )

where the signal component amplitude coefficients ai are the strengths that would be received if

an isotropic antenna were used. The normalized field strength of the receiver antenna in the

direction of θi and φi (azimuth and elevation angles) is specified by ( )iirF φθ , . The relationship

between the amplitude coefficients is given by

( )iirii Fa φθα ,= ( 4.4 )

However, it must be understood that this expression implies that the antenna is part of the radio

channel. In general, it is probably less confusing to separate channel effects from antenna

effects.

Directionality of multipath components can also be taken into account using the following form

of the baseband multipath channel impulse response (taken from [Oda00] with phase term

iφ appended),

( ) ( ) ( )∑−

=

−−=1

0

,L

iii

ji teth i τδθθδαθ φ ( 4.5 )

where iθ represents the direction of arrival of the ith signal component.

The impulse response accurately models a wireless channel but gives no means to statistically or

analytically compute the parameters that determine the strengths, delays, and number of

multipath components. Models discussed in the following sections are used to produce values

for these channel defining parameters.

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4.3.2 Geometrically Based Single-Bounce Elliptical Model

The geometrically based single-bounce elliptical (GBSBE) model is based entirely on geometry

and provides a method of producing values of propagation delay, strength, and direction of

arrival of multipath components [Lib95]. The model assumes that all multipath components

arriving at the receiver undergo a single bounce between the transmitter and receiver. An object

in the environment that caused the bounce is generically called a scatterer19. Because direction

of arrival and direction of departure are modeled using GBSBE, the model can account for

antenna radiation patterns at the transmitter and receiver.

The geometry for the GBSBE model is shown in Figure 4-2. In terrestrial wireless networks

with relatively large transmitter-receiver separations, the vertical distribution of direction of

arrival shows that multipath components arrive primarily along a horizontal plane oriented with

the horizon [Par92]. As such, the GBSBE model uses a planar surface to model the propagation

environment. The transmitter and receiver are located at points T(-f,0) and R(f,0), respectively.

The transmitter-receiver separation is therefore do = 2f, and the line-of-sight propagation delay is

τo = do/c where c is the speed of light (3x108 m/s). A multipath component that arrives with

propagation delay τi equal to a constant value (greater than the LOS delay) and resulting from a

single bounce must have been produced by a scatterer S(xs,ys) located on an ellipse [Par89]. The

defining parameters of the ellipse are

2ic

= ( 4.6 )

22 fab −= ( 4.7 )

where a defines the major axis of the ellipse and b defines the minor axis, and the scatterer

S(xs,ys) lies on the ellipse defined by

12

2

2

2

=+by

ax ss ( 4.8 )

19 Although the object that caused the multipath is called a scatterer, the actual mechanism causing the multipath may be reflection, refraction, or scattering.

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T(-f,0) R(f,0)

S(xs,ys)

-f f

x

y

-b

b

-a a

do = 2f

T(-f,0) R(f,0)

S(xs,ys)

-f f

x

y

-b

b

-a a

do = 2f

Figure 4-2. Physical layout of the geometrically based single-bounce model.

If scatterers are uniformly distributed in space around the transmitter and receiver, then the

single-bounce scatterers that induce a multipath delay between τ and ττ ∆+ would be bounded

by the ellipses E1 and E2 defined by

21τc

a = ( 4.9 )

2211 fab −= ( 4.10 )

for ellipse E1, and

( )22

ττ ∆+=

ca ( 4.11 )

2212 fab −= ( 4.12 )

for ellipse E2. The terms scattering region and scattering surface are herein used to describe the

locus of scatterers that induce multipath components for a particular condition or constraint. In

the case of GBSBE, the scattering surface for delays between τ and ττ ∆+ is the two-

dimensional region outside of E1 and inside of E2. Note for a later discussion that both ellipses

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E1 and E2 used in the derivation of the GBSBE model share common foci at fx ±= . Figure 4-3

illustrates these two ellipses.

T(-f,0) R(f,0)

-f f

x

y

-b1

b1

-a1 a1

do = 2f

-a2 a2

b2

-b2

φ

Scattering Region

ττ ∆+

τE1:

E2:

T(-f,0) R(f,0)

-f f

x

y

-b1

b1

-a1 a1

do = 2f

-a2 a2

b2

-b2

φ

Scattering Region

ττ ∆+

τE1:

E2:

Figure 4-3. Ellipses E1 and E2 that define scattering region between delays τ and τ+∆τ for the GBSBE model.

As shown in Figure 4-3, the angle represented by φ is defined such that 0=φ is in the direction

from the receiver to the transmitter, and clockwise rotation about the receiver is a positive angle

change. The range of φ is defined to be πφπ ≤≤− . To simplify expressions, a parameter for

normalized multipath delay is introduced, ri, given by

o

i

o

ii d

cr

τττ

== ( 4.13 )

where τo is the LOS propagation delay over distance do. For a particular multipath component i,

the parameter ri is the ratio of the propagation time for that multipath component to the line-of-

sight propagation time.

Using the geometry described by equations ( 4.6 ) through ( 4.12 ), the cumulative distribution

function (CDF) for iφ conditioned on the normalized multipath delay ri was shown in [Lib95] to

be

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( )

( )( )( )( )

( )( )( )

−−

−Φ−+

−−

−−

−−−−

=

22

21

22

21

cos12

cos1sin1

coscos1

cos21

1

cos12

cos1sin1

coscos1

cos21

φπ

φ

φφ

π

φπ

φφ

φφ

πφφ

ii

ii

i

i

ii

ii

i

i

ir

rr

rr

rr

rr

rr

rr

rF πφ

φπ

≤≤

≤≤−

0

0 ( 4.14 )

Equation ( 4.14 ) gives the probability that a multipath component i arrives along direction of

arrival between 0 and φ .

By differentiating ( 4.14 ) with respect to φ , the conditional probability density function (PDF)

for direction of arrival was shown to be

( ) ( ) ( )( )( )32

22/32

cos12

1cos21

φπ

φφφ −−

+−−=

ii

iiiir rr

rrrrf πφπ ≤≤− ( 4.15 )

The PDF for the normalized multipath delay is

( )1

122

2

−=

r

rrf r

β mrr <≤1 ( 4.16 )

where the parameter β is given by

12 −= mm rrβ ( 4.17 )

and the parameter rm is the maximum value of the normalized multipath component delay given

by

o

mmr τ

τ= ( 4.18 )

The parameter τm is chosen to be the largest expected detectable multipath delay. The marginal

PDF for the direction of arrival, without regard to time delay or multipath component strength, is

given by

( ) ( )( )2

22

cos

12

1φπβ

φφ−

−=

m

m

r

rf πφπ ≤≤− ( 4.19 )

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Finally, the joint PDF for direction of arrival and normalized multipath delay is

( ) ( )( )( )3

22

,cos

1cos212,

φπβφ

φφ−

+−−=

rrrr

rf r mrr <≤

≤≤−1

πφπ ( 4.20 )

To simulate the impulse response of a multipath channel using the GBSBE model, the CDF for r

is calculated by integrating equation ( 4.16 ), resulting in

( )β

12 −=

rrrFr mrr <≤1 ( 4.21 )

In order to use a uniformly distributed random variable u to produce values of r, the random

value u is set equal to ( )rFr , and the equation is solved for r. The result is

224121

21

ii ur β++= 10 ≤≤ iu ( 4.22 )

Using a uniformly distributed random number generator U(0,1) to produce iu , values of the

normalized multipath delay ri can be produced with ( 4.22 ).

Given ri, the CDF for angle of arrival in equation ( 4.14 ) can be used to calculate a value for iφ .

A uniformly distributed random variable u is set equal to ( )ir rF φφ , and φ is determined as a

function of u. Unlike equation ( 4.21 ), whose functional inverse was easily obtainable, the

functional inverse of ( 4.14 ) needs to be computed numerically. In [Lib95], numerical values

were computed using a lookup table and linear interpolation.

In summary, the GBSBE model provides a way to produce channel impulse responses based on

the geometry of the transmitter, receiver, and statistical location and number of scatterers in the

propagation environment. As discussed in section 4.4, this model can be shown to be a special

case of a constrained ellipsoidal model.

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4.3.3 Geometrically Based Single-Bounce Circular Model

The geometrically based single-bounce circular (GBSBC) model was developed for application

to the reverse link (mobile transmitter to base station receiver) of macro-cellular systems [Pet97].

It is assumed that plane waves arrive in the horizontal direction from scatterers in the cellular

environment, and therefore DOA statistics are calculated only in azimuth. The scatterers in the

environment are assumed to surround the mobile station within a circular boundary as shown in

Figure 4-4.

S

T

ScatteringRegion

Rrθmax

d

(BS) (MS)

S

T

ScatteringRegion

Rrθmax

d

(BS) (MS)

Figure 4-4. Geometry for the geometrically based single-bounce circular model.

In Figure 4-4, the transmitter T (a mobile station) and receiver R (a base station) are separated by

distance d. The circle of radius r defines the scattering region, which circumscribes all of the

uniformly distributed scatterers. Each scatterer is assumed to be an omnidirectional re-radiating

element, and each re-radiated plane wave is only influenced by one scatterer (i.e., single bounce).

The parameter θmax defines the largest deviation of direction of arrival from the line-of-sight

direction; therefore, the spread of direction of arrival is confined to a range of 2θmax, and θmax is

given by

= −

dr1

max sinθ ( 4.23 )

The probability density function was derived in [Pet97] to be

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( )

( ) ( )

+−

=0

coscos22

2222

rrddd

θθ

θθ , otherwise

dr

dr

≤≤

− −− 11 sinsin θ

( 4.24 )

Figure 4-5 illustrates the probability density function for direction of arrival for three different

radii of the scattering region.

-15 -10 -5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

T-R Separation d = 5 kmr = 100 m

r = 300 m

r = 1000 m

Direction of Arrival (deg)

pdf

Probability density function for DOA for GBSB macrocell model

-15 -10 -5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

T-R Separation d = 5 kmr = 100 m

r = 300 m

r = 1000 m

-15 -10 -5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

T-R Separation d = 5 kmr = 100 m

r = 300 m

r = 1000 m

Direction of Arrival (deg)

pdf

Probability density function for DOA for GBSB macrocell model

Figure 4-5. Probability density function for direction of arrival for the GBSB macrocell model with d=5 km and r=100, 300, 1000 m.

Because this model is applied to macro-cellular environments, the distance d is typically large.

For rd >> , where scatterers surround the mobile in close proximity, the spread of angles about

the LOS direction (whether or not an actual propagation path exists) is confined to small angles.

For small scattering regions, when the scattering region is only 2% of the T-R separation,

multipath arrives along directions within a few degrees of the LOS direction. For scattering

regions with a radius of 20% of the T-R separation, which is large for a macro-cellular

environment, the spread of DOA is still within approximately 12 degrees of the LOS direction.

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To simulate a channel with the GBSBC macrocell model, the location of L scatterers is generated

within the scattering region. The power of the LOS component is computed using the log-

distance path loss formula given by

( ) )0(0log10 trref

orefo GG

dd

nPP ++

−= ( 4.25 )

where Pref is the reference power at distance do, n is the path loss exponent, and Gr and Gt are the

receiver and transmitter antenna gains, which are a function of directions of arrival and

departure, respectively. For each multipath component, the excess propagation delay is

calculated based on the excess distance traveled compared to the LOS component. The path loss

for each multipath component is computed using

( ) ( ) ( ) ( )00log10 tdtrarro

ioi GGGGL

dd

nPP −+−+−

−= θθ ( 4.26 )

where di is the distance traveled by the ith multipath component, Lr is the reflection loss of each

scatterer, and θa and θd are the directions of arrival and departure of each multipath component,

respectively. Using this technique, the propagation delay, path loss, and DOA for multipath

components between the mobile station transmitter and the base station receiver can be

computed for each channel, and the process can be repeated for a plurality of multipath channels.

4.3.4 Elliptical Sub-Regions Model

Like the GBSBE model, the elliptical sub-regions model was developed based on physical

propagation processes for testing and validating antenna array systems in multipath

environments [Lu97]. The model is used to simulate multipath vector channels and accounts for

large-scale and small-scale fading.

The elliptical sub-regions model uses the single-bounce assumption for scatterers, implying that

each multipath component arriving at the receiver is reflected by a single scatterer. Instead of

randomly distributing scatterers throughout a single bounding ellipse, where the transmitter and

receiver are located at the foci, this model uses several, co-focused elliptical regions that

correspond to intervals of excess delay. A maximum multipath excess delay τm is defined, and

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the corresponding maximum-delay ellipse is formed. The area is then delimited into M sub-

regions, and the ith sub-region corresponds to excess delays in the intervals of

mm Mi

Mi

ττ ,1

, { }Mi ,,2,1 L∈ ( 4.27 )

The excess delay of each interval is given by

ms Mττ

1=∆ ( 4.28 )

Figure 4-6 illustrates the model geometry. The transmitter and receiver are located at points

( )0,fT − and ( )0,fR , respectively. The outermost ellipse is the boundary within which all

scatterers must lie. A compound Poisson distribution is used to determine the number of

scatterers within each of the M elliptical sub-regions. If pi is defined to be the probability that a

multipath component results from a scatterer in the ith sub-region, causing an excess delay

between ( ) si ττ ∆−= 1 and si ττ ∆= , then pi is given by

( )( )∫

∆−= s

s

i

ii dppτ

τττ

1 ( 4.29 )

where ( )τp is the probability density function for excess delay. If Λ is the Poisson parameter

for the total number of scatterers, then the Poisson parameter for the ith sub-region is given by

Λ=Λ ii p ( 4.30 )

Once the number of scatterers is determined for each sub-region, the scatterers are uniformly

distributed within each sub-region.

The arrival times of signal components are computed in [Lu97] using position vectors for the

transmitter, receiver, and scatterers. The position vectors for the transmitter and receiver are Tx

and Rx , and the position vector for the ith scatterer is ix . The propagation delay due to the ith

scatterer is then given by

( )TiiRi cxxxx −+−=

1τ ( 4.31 )

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x

y

-b

b

-a aT(-f,0) R(f,0)

do = 2f

i=1

i=M

x

y

-b

b

-a aT(-f,0) R(f,0)

do = 2f

i=1

i=M

Figure 4-6. Geometry for the elliptical sub-regions channel model.

If each scatterer is assumed to be a cluster of Ki reflecting points, then the composite signal

component arriving at the receiver from the scatterer will be a sum of reflected signals. This

provision allows a receiver to experience fading signal components in a mobile channel, which

would be the case if the scattering cluster consists of reflecting points that produce signal

components within the multipath delay resolution of the receiver. The delay time of the kth

reflection within the ith scattering cluster is described by the inter-arrival exponential probability

density function, given by

( )( ) ( )

−−= −

− τ

ττ

τττ 1,,

1,, exp1 kiki

kikip , { }iKk ,,2,1 K∈ ( 4.32 )

where τ is the mean inter-arrival time, which is estimated using the spatial extent of the

reflections within the scattering cluster. The value ii ττ =0, is given by equation ( 4.31 ).

The CDF for direction of arrival iθ (for the center of each cluster) is dependent upon the

ellipticity of each bounding ellipse, given by

τ∆+=

icdd

ei , { }Mi ,,1,0 L∈ ( 4.33 )

The CDF is expressed in [Lu97] as

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( ) ( ) ( )∫−+−

−−

=i

dtetetee

eeC

eF i

θ

πθ 2

2

2

cos21cos12

11 ( 4.34 )

The factor ( )eC is chosen so that ( ) 1=eF iθ when πθ =i .

Large-scale fading of multipath components is determined using the location of each scatterer.

The total received power of the multipath component caused by the ith scatterer is given by

( ) ( )nTiiR

tTRiii

PGGP

xxxx −+−=

2

24π

λρη ( 4.35 )

where iη is the effect of shadowing, GT and GR are the transmitter and receiver antenna gains, Pt

is the transmit power, λ is the wavelength, n is the path loss exponent (for the log-distance path

loss model), and iρ is the scattering coefficient ( 1=iρ for an ideal, lossless reflection). The

shadowing factor iη and the scattering coefficient iρ are assumed to follow log-normal

distributions.

Small-scale fading of multipath is determined by summing the signal components arriving from

the ith cluster. In [Lu97], the components from all reflectors within a cluster are assumed to have

the same amplitude. In this case, the (corrected) expression for each reflected component’s

amplitude is

i

iki K

P=,α , { }iKk ,,2,1 K∈ ( 4.36 )

Finally, the impulse response of the channel as represented by the elliptical sub-regions model is

given by

( ) ( )( ) ( )( ) ( ) ( )∑ ∑= =

−+−=L

i

K

kiRkikiokiik

TiTo

i

FttfjFtth1 0

,,,, 2exp; θτδφπαθ ( 4.37 )

Note that this impulse response includes antenna pattern effects of the transmitter ( )( )TiTF θ and

the receiver ( )iRF θ , and ( )Tiθ is the angle from the transmitter to the ith scattering cluster. The

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frequency kif , provides for any Doppler frequency due to the motion of the scatterers,

transmitter, or receiver; with a Doppler frequency given, the observation time is specified by to.

In conclusion, the elliptical sub-regions model provides another way to simulate multipath radio

channels in a cluttered, micro-cellular environment where the transmitter and receiver are

surrounded by multipath-causing scatterers.

4.3.5 Other Channel Models

Some geometric channel models that have been designed to fulfill a particular purpose are worth

mentioning. Lee’s channel model was used to predict signal component correlation at an

antenna array in a macro-cellular environment [Lee82]. The model uses N effective scatterers

uniformly spaced around a ring about a mobile station (see Figure 4-7). Each effective scatterer

represents the effect of several reflections from that scatterer.

MSBS MSBS

Figure 4-7. Base station and mobile station orientation for Lee's geometric model.

The signals reflected by each effective scatterer are summed at the base station and the

correlation coefficient of signal envelopes is determined at pairs of antenna elements.

Extensions to this model have been made, such as the one placing the ring of scatterers in

angular motion about the mobile station to account for Doppler effects [Sta94].

Other models have been developed for the purpose of simulating urban environments, including

the typical urban (TU) model and the bad urban (BU) model [Ert99]. The TU model simulates

scatterers surrounding a mobile station as shown in Figure 4-8. Within 1 km of the mobile

station, 120 scatterers are randomly distributed, and the mobile is moved along a distance of five

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meters. Then the scatterers are oriented back in their initial position about the mobile, and a

random phase is defined for each scatterer. The process repeats to simulate a mobile moving

throughout an urban environment. Path loss is computed using the log-distance path loss model,

and shadowing is computed using a log-normal distribution with standard deviations between 5

dB and 10 dB.

S

ScatteringRegion

1 kmθmax

d

BS MSS

S

MSMotion

5 m

S

ScatteringRegion

1 kmθmax

d

BS MSS

S

MSMotion

5 m

Figure 4-8. Geometry of base station, mobile station, and scatterers for the typical urban model.

BS

S

ScatteringRegion

1 kmMSS

S

MSMotion

5 m

S

SecondaryScattering

Region

S

S

S

BS

S

ScatteringRegion

1 kmMSS

S

MSMotion

5 m

S

ScatteringRegion

1 kmMSS

S

MSMotion

5 m

S

SecondaryScattering

Region

S

S

SS

SecondaryScattering

Region

S

S

S

Figure 4-9. Geometry of base station, mobile station, and two scattering regions for the bad urban model.

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The bad urban model augments a secondary scattering region to the typical urban model. The

secondary scattering region is offset from the first by 45 degrees as shown in Figure 4-9. This

secondary region provides for a harsher propagation environment: increased delay spread, wider

angle spread, and lower signal covariance among antenna array elements.

Another urban channel model is presented in [Oda00] that adds the layout of streets and

structures to a geometric channel model. The mobile is assumed to be at street level in an urban

environment, as shown in Figure 4-10, and the model is used to analyze time of arrival and

direction of arrival of multipath components. The model accounts for three types of propagation

characteristics: 1) street-microcell propagation in the vicinity of the mobile station; 2) reflection

and scattering in isolated areas; 3) macrocell propagation between the reflection areas and the

base station.

MS

BS

Urban StreetsReflection

Area

Mac

roce

llPr

opag

atio

n

Street MicrocellPropagation

MS

BS

Urban StreetsReflection

Area

Mac

roce

llPr

opag

atio

n

Street MicrocellPropagation

Figure 4-10. Orientation of mobile station and base station among city streets for the urban street geometric model, indicating types of propagation.

The path loss for each type of propagation is computed and summed to obtain a composite path

loss. Between the mobile station and the reflection area, LOS or non-LOS propagation may

occur, and the loss is represented by Lp1. The reflection loss experienced in the reflection area is

assigned Lp2; this is the difference in power that leaves the reflection area compared to that which

entered the reflection area. Along the macrocell propagation leg, Lp3 may be calculated using a

model such as the early Hata model [Hat80]. Then, the overall path loss between the mobile

station and base station is computed with

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321 pppp LLLL ++= (dB) ( 4.38 )

The requirement for street geometry is both an advantage and a disadvantage. If the specific

locations of stations are specified, the model will more accurately account for the physical

propagation environment compared to the GBSBE model. If a more statistical result is desired,

rather than results based on specific station locations, then the use of this model becomes more

cumbersome because of the requirements of defining street geometry and specifying

characteristics of the three types of propagation.

4.4 Three-Dimensional Ellipsoidal Channel Model

In macro-cellular systems, multipath components arrive primarily in the direction of the horizon

[Par92] as stated earlier. However, for smaller cell sizes (micro- or pico-cellular systems) or for

communication geometries other than terrestrial communications, a three-dimensional model

provides results based on a more accurate representation of the physical environment. The

GBSBE model relies on the fact that single-bounce multipath components with delays of a

particular value must be caused by scatterers located on an ellipse. This premise, however, is

valid when the transmitter, receiver, and scatterers lie on a common plane.

4.4.1 The Ellipsoidal Scattering Region

Now consider the general case where scatterers can lie anywhere in space around the transmitter

and receiver. The geometric shape that describes the location of scatterers producing a constant

multipath delay is now defined by an ellipsoid. A general ellipsoid surface, centered at the origin

of a Cartesian axis, is defined by

12

2

2

2

2

2

=++cx

by

az

( 4.39 )

The general ellipsoid has axis lengths of 2a, 2b, and 2c. The ellipsoid that defines a constant-

delay surface for multipath components has two equal axis lengths because of rotational

symmetry about a line between the transmitter and receiver. Therefore, the ellipsoid equation

becomes

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12

2

2

2

2

2

=++bx

by

az

( 4.40 )

with a and b completely defining the ellipsoid. This ellipsoid is oriented so that the major axis

on which the transmitter and receiver lie is oriented on the z-axis. The coordinates fz ±=

where the transmitter and receiver are located are defined by

22 baf −= ( 4.41 )

The geometry is illustrated in Figure 4-11. Because of the two common axis lengths, the cross

section of the ellipsoid in the x-y plane is exactly circular.

In the simplest form, the ellipsoidal surface can be used as a boundary within which all scatterers

that produce multipath components less than a particular delay must lie. In the absence of other

scatterer location information, scatterers may be uniformly distributed within the ellipsoidal

scattering volume and around the transmitter and receiver, as shown in Figure 4-12. The scatter

locations can be assumed to be individual scatterers or clusters of scatterers, and signal

component delay, strength, and direction of arrival at the receiver can be computed.

Without further refinement, the utility of this model is questionable because scatterers typically

do not exist uniformly throughout all space surrounding a transmitter and receiver. However, by

placing constraints on the allowable locations of scatterers within the ellipsoid, the model has the

ability to represent real-world propagation geometries more accurately than two-dimensional

geometric models.

4.4.2 Applications of the Bounded Ellipsoid

One application of this model is the simulation of air-to-ground radio channels, discussed in

depth in section 4.5. For this case, the ellipsoid would be oriented such that one focus is located

at the ground station, and the other focus is located at the airborne station. Clearly, the entire

ellipsoid would not be filled with scatterers. Instead, the scatterers would lie on the intersection

of the ground plane (on which the ground station is located) with the ellipsoidal volume. In the

real world, the height of buildings may be considered negligible compared to the altitude of the

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airborne station, and hence scatterers are located on a two-dimensional planar surface20. (Note

that for low-altitude operations, building height could be taken into account by applying a finite

thickness.)

z

(a)

(b)

(c)x y

x

x

z

yz

(a)

(b)

(c)x y

x

x

z

y

Figure 4-11. Geometry of the ellipsoid (a=2, b=1) bounding surface for maximum multipath delay: (a) three-dimensional view, (b) top view, (c) side view.

Another application is the modeling of a cluttered urban environment consisting of tall

structures, a street-level station, and an elevated base station. Consider Figure 4-13, where a

base station antenna is located on a building or other structure. To model this case, the

ellipsoidal scattering volume is truncated by upper and lower planar boundaries. The lower

planar boundary is defined by the street level, and the upper planar boundary is defined by the 20 This planar assumption would be appropriate, for example, for aircraft flying at 7,500 feet when the tallest buildings are 500 feet. One could conceive of situations where the urban ellipsoidal model, discussed shortly, is more appropriate, such as when an aircraft flying along a low-altitude VFR corridor near an urban center at approximately building-top altitudes.

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maximum building height (which may be higher or lower than the height of the elevated station).

In this case, signal component direction of arrival at the receiver cannot be described simply by

an azimuth angle; an elevation angle must also be used. The truncated ellipsoid model provides

for this by allowing scatterers to lie throughout all possible locations of true scattering objects.

This model would be useful for building-mounted, pole-top, or distributed antenna transceivers

used in urban environments, where benefits of smart antennas could be used to solve the

concerns of achieving large capacity, high data rates, and wide bandwidths in an environment

cluttered in three dimensions.

-1

0

1

-1-0.5

00.5

1

-1.5

-1

-0.5

0

0.5

1

1.5

xy

z

-1

0

1

-1-0.5

00.5

1

-1.5

-1

-0.5

0

0.5

1

1.5

xy

z

Figure 4-12. Locations of uniformly distributed scatterers throughout the ellipsoide bounding surface; transmitter and receiver are located at foci.

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Maximum Building Height (Upper Planar Boundary)

Street Level (Lower Planar Boundary)

Ellipsoi

d Boun

dary

Buildings, etc.

Street-LevelStation

ElevatedStation

Buildings, etc.

Maximum Building Height (Upper Planar Boundary)

Street Level (Lower Planar Boundary)

Ellipsoi

d Boun

dary

Buildings, etc.

Street-LevelStation

ElevatedStation

Buildings, etc.

Figure 4-13. An urban model based on the ellipsoidal geometry useful for three-dimensional direction of arrival simulation and analysis.

4.4.3 Axis Lengths and Normalized Excess Delay

The elliptical axis dimensions define the elliptical (two-dimensional) and ellipsoidal (three-

dimensional) boundaries for the geometric channel models that use them, and they have a

significant effect on the probability density function for direction of arrival. For example, if the

axis dimensions are specified such that the ellipse or ellipsoid is largely circular or spherical,

respectively, then the probability of components arriving from any particular direction is roughly

equal when the bounding shape itself is very large. Such would be the case when the maximum

excess delay is very large compared to the LOS propagation time between the transmitter and

receiver.

A quantity called normalized excess delay is now defined to be the ratio of excess delay τ∆ to

theoretical transmitter-receiver LOS propagation time TRτ . The values of TRττ/∆ range from 0

(corresponding to the LOS path) to infinity (or the maximum value detectable by the receiver

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due to path loss over the excess propagation distance). A TRττ/∆ value of 0.25 approximately

corresponds to an excess delay of 1300 ns for a transmitter-receiver separation of 1 mile; values

of this order were observed during the measurements presented in Chapter 5. Larger or smaller

TRττ/∆ values may be used for more sensitive or less sensitive receivers, respectively. Ellipses

for TRττ/∆ equal to 0.05, 0.30, and 0.90 are shown in Figure 4-14. Note that larger TRττ/∆

values correspond to more circular ellipses.

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TRττ∆

= 0.90

0.05

0.30

T R

Ellipses for excess delay ratios 0.05, 0.3, and 0.9

Min

or A

xis

Major axis-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

TRττ∆

= 0.90TRττ∆

= 0.90

0.05

0.30

T R

Ellipses for excess delay ratios 0.05, 0.3, and 0.9

Min

or A

xis

Major axis

Figure 4-14. Scatterer distribution boundaries around transmitter and receiver for normalized excess delay of 0.05, 0.3, and 0.9.

The ratio of minor axis length to major axis length is related to normalized excess delay by

1

112

+∆

+

=

TR

TR

ab

ττ

ττ

( 4.42 )

This relationship is plotted in Figure 4-15 for TRττ/∆ ranging from 0 to 1. As TRττ/∆

approaches and exceeds unity (excess delay equal to LOS delay), the minor axis length

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approaches the major axis length and the ellipse approaches circular. As TRττ/∆ further

increases, the receiver approaches the center of the ellipse (relative to the size of the ellipse) and

the probability of components arriving in any sector around the receiver becomes approximately

equal.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Ellipse minor/major axis ratio versus excess/absolute delay ratio

Excess delay / absolute delay (∆τ/τTR) (sec/sec)

Min

or a

xis

leng

th /

maj

or a

xis

leng

th (b

/a) (

met

ers/

met

er)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Ellipse minor/major axis ratio versus excess/absolute delay ratio

Excess delay / absolute delay (∆τ/τTR) (sec/sec)

Min

or a

xis

leng

th /

maj

or a

xis

leng

th (b

/a) (

met

ers/

met

er)

Figure 4-15. Ratio of minor to major axis of elliptical scatterer boundary versus normalized excess delay.

This ellipsoidal channel model may be applied to a variety of three-dimensional, single-bounce

propagation environments. Two scenarios have been demonstrated here, but others can be

conceived, possibly involving indoor channels which have attenuation functions that vary

depending upon the direction vector of multipath component propagation. A specific case of the

ellipsoidal channel model is presented in the next section, where the development of an air-to-

ground channel model using the ellipsoidal geometry is discussed.

4.5 Geometric Air-to-Ground Ellipsoidal Channel Model

In this section a geometric, single-bounce, air-to-ground multipath channel model is developed.

As described earlier, the geometry for the scattering region is the intersection of an ellipsoidal

volume and a horizontal plane. The scatterers lie on the ground surface within this scattering

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region, and all propagation legs between the airborne station and the ground station must be

considered.

Figure 4-16 illustrates the air-to-ground model geometry. The ellipsoid is defined by the

normalized excess delay, and all ground scatterers have negligible height compared to the

aircraft altitude. The elevation angle from the horizon up to the aircraft is El, and the

complementary angle down from the vertical direction is ψ. The distance from the ground

station to a ground point directly under the airborne station is the range (the distance from the

ground station to the airborne station is commonly called the slant range).

Ground Level (Planar Intersection)

Ellipsoi

d Boun

dary

AirborneStation

AircraftAltitude (AGL)

Scattering Region

GroundStation

ψEl

Range

Slant R

ange

Ground Level (Planar Intersection)

Ellipsoi

d Boun

dary

AirborneStation

AircraftAltitude (AGL)

Scattering Region

GroundStation

ψEl

Range

Slant R

ange

Figure 4-16. Geometry, distance, and angle definitions for the geometric air-to-ground ellipsoidal model.

The air-to-ground geometry produces some challenges in modeling the channel. Note that

existing channel models do not accurately represent the air-to-ground propagation environment:

• GBSBE model accounts for a planar scattering region but does not account for the shape

of the scattering region or additional distance caused by airborne transmitter.

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• GBSBC model accounts for the fact that the transmitter is not within the scattering

region, but does not correctly model the scattering region for the air-to-ground

environment. Also, excess distance caused by the airborne transmitter is not considered.

As such, this air-to-ground channel model was developed. First, the scattering region is derived

and discussed. Then, computation of the model geometry and scattering points for simulation is

presented. Finally, direction of arrival and time of arrival statistics are presented.

4.5.1 Analytical Specification of Scattering Region

The expression for a three-dimensional ellipsoid with a circular cross section in the x'-y' plane

and elliptical cross sections in the x'-z' and y'-z' planes is given by equation ( 4.43 ),

( ) ( ) ( )1

2

2

2

2

2

2

=′

+′

+−′

by

bx

azz o ( 4.43 )

where zo is the distance by which the ellipsoid is offset along the z'-axis (see Figure 4-11). The

equation for a plane through the axis origin at an angle ψ to the x'-z' plane is given by

xmz ′=′ ( 4.44 )

where m is the slope of the plane given by

( )ψ1tan −=m ( 4.45 )

By setting zo = f in ( 4.43 ) where f is the focus distance of the ellipse, the plane given in ( 4.44 )

intercepts the ellipsoid through the focus and at angle ψ with respect to the major axis of the

ellipsoid. The intersection of the plane and the ellipsoid projected onto the x-y axis can be

expressed as

( ) ( ) ( )1

2

2

2

2

2

2

=′

+′

+−′

by

bx

afxm

( 4.46 )

This equation can be expressed as a function of x' with

( ) ( )22

22 1 x

afxm

by ′−

−′−±=′ ( 4.47 )

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Now an axis transformation is introduced to facilitate formation of the equation for the surface of

( 4.46 ) projected onto the plane of ( 4.44 ). The z'-axis and x'-axis are rotated about the y'-axis

by angle ψ so that the new x-axis and y-axis lie in the plane of ( 4.44 ). A new y-axis is named

but is equivalent to the old y'-axis. The x-coordinates are transformed to x'-coordinates through

( )ψcosxx =′ ( 4.48 )

The new surface, which exactly represents the intersection surface of the ellipsoid and the plane,

is given by

( ) ( )ψψ 22

2

22 cos

sin1 x

afx

by −

−−±= ( 4.49 )

where a, b, and f are the parameters of the original ellipsoid. The domain of x for the ellipsoid

on the original set of axes was axa ≤′≤− , but the domain of the x-coordinate for the surface

described by ( 4.49 ) is bounded by

( )

( ) ( )( )

( )

( ) ( )( )ψ

ψψ

ψ

ψψ

ψ

ψ

sincos

sin

tan1

sincos

sin

tan1

2

22

22

22

2

22

22

22

ba

bfa

af

x

ba

bfa

af

+

−++

≤≤+

−+−

( 4.50 )

To simplify the analysis of the problem, the surface in ( 4.49 ) is shown to be an ellipse by

expressing ( 4.49 ) in a form similar to that of ( 4.46 ), given by

( ) ( )1

2

2

2

2

2

2

=++−

by

bx

afxm ξξ

( 4.51 )

where the parameter ( )ψξ cos= is introduced for simplification. Equation ( 4.51 ) can then be

rearranged and equivalently expressed as

( ) ( )

( )1

2

2

2

2222

22

2222

22

222

22

=+

+

++

+−

by

mbaba

mbafb

xmba

fmbx

ξ

ξξ ( 4.52 )

It is now desirable to equate the polynomial of x in the numerator of ( 4.52 ) with form shown in

( 4.53 ) to solve for the terms K and R,

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( ) ( ) RKKxxmba

fbx

mbafmb

x ++−=+

++

− 222222

22

222

22 22

ξξ ( 4.53 )

By equating polynomial coefficients, it can be shown that

( )222

2

mbafmb

K+

( 4.54 )

and

( )2

2222

22

Kmba

fbR −

+=

ξ ( 4.55 )

The denominator in ( 4.52 ) is then equated with

( )2222

22

mbaba

D+

( 4.56 )

Using the parameters K, R, and D, the expression in ( 4.52 ) can be written as

( )1

22

22

2

222

=++−

=+++−

by

DRKx

by

DRKKxx

( 4.57 )

Equation ( 4.57 ) can be rearranged into the form of an offset ellipse, given by

( )1

12

22

=

+−

DR

b

yRD

Kx

( 4.58 )

This ellipse must now be expressed with the defining terms of the original ellipsoid (a and b) and

the major axis angle ψ. To do this, the terms K, R, and D are also expressed in terms of a, b, and

ψ, given by

( )( ) ( )ψψ

ψ2222

222

sincossin

babab

K+

−= ( 4.59 )

and

( )( ) ( )

( )( ) ( )

+

−+−

=ψψ

ψψψ 2222

2

2222

222

sincossin

1sincos ba

bbabab

R ( 4.60 )

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and

( ) ( )ψψ 2222

22

sincos baba

D+

= ( 4.61 )

With these parameters defined, the desired results are shown in Table 4-2, giving expressions for

the surface over which randomly distributed scatterers are placed for the geometric air-to-ground

ellipsoidal channel model.

Table 4-2. Equations that describe the intersection of a tilted, three-dimensional excess delay bounding volume and a planar surface containing scatterers.

Expressions for the Scattering Surface

Surface Equation ( )

12

2

2

2

=+−

pp

p

by

a

xx ( 4.62 )

Major Axis ( ) ( )( ) ( )

( ) ( )

+

−+

+=

ψψψ

ψψ 2222

222

2222

42

sincossin

1sincos ba

baba

ba p ( 4.63 )

Minor Axis ( ) ( )

( ) ( )

+

−+=

ψψψ

2222

222

2

42

sincossin

1ba

baab

bp ( 4.64 )

Major Axis Offset ( )

( ) ( )ψψψ

2222

222

sincossin

babab

x p +−

= ( 4.65 )

Focus pppp xbaf =−= 22 ( 4.66 )

It is notable that one focus of the elliptical scattering surface lies on the axis origin; that is,

pp fx = . This can be shown by using the elliptical focus equation to find fp from ap and bp,

222ppp baf −= ( 4.67 )

and performing a substitution of ap and bp with equations ( 4.63 ) and ( 4.64 ). Simplifying the

resulting expression demonstrates that

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( ) ( )( ) ( )

( ) ( )( ) ( )

( ) ( )

+

−+−

+

−+

+=

ψψψ

ψψψ

ψψ 2222

222

2

4

2222

222

2222

42

sincossin

1sincos

sin1

sincos baba

ab

baba

bab

f p

( )( ) ( )

2

2

2222

222

sincossin

pxba

bab=

+−

=ψψ

ψ ( 4.68 )

This equality has the important implication that ellipses that represent the scattering regions for

arbitrary excess delays do not share a common center but do share one common focus. In

contrast, for the GBSBE model, the scattering regions for arbitrary excess delays do share a

common center and two common foci. This makes sense intuitively because for the GBSBE

model, the foci of the planar ellipse correspond to the actual locations of the transmitter and

receiver; however, for the geometric air-to-ground ellipsoidal model, one focus is the location of

the ground station, but the other focus depends upon the shape of the ellipsoid.

4.5.2 Generating the Ellipsoid and Scatterers on the Rotated Axes

It is useful to have the ability to generate the oblique ellipsoidal surface and points on the surface

for simulation of ellipsoidal-based channel models. Numerically producing the surface aids in

generating scatterers for simulation and assists in verification of channel model geometry.

Consider an ellipsoidal surface for a particular normalized multipath delay ri. A given

normalized multipath delay uniquely defines an ellipsoid in three dimensional space whose

major and minor axes are determined using equations ( 4.13 ), ( 4.9 ), and ( 4.10 ). An equation

for that ellipsoid is given by ( 4.43 ), where the ellipsoid is oriented along the z'-axis and whose

one focus lies on the axis origin so that fzo =' . N number of points with coordinates 'nx , 'ny ,

and 'nz can be generated for this ellipsoid and represented by matrix ''' zyxE given by

( )

=

'''

''''''

222

111

'''

NNN

izyx

zyx

zyxzyx

rMMM

E ( 4.69 )

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In order to represent the oblique ellipsoid for the ellipsoid-planar intersection model, the

ellipsoid is effectively rotated about the y'-axis such that (90o-ψ) is the elevation angle for the

ellipsoid major axis. The rotation is used to place the transmitter and receiver in their respective

positions on the x-z plane for the model. The rotation is performed by defining the unit vectors

for a new coordinate system given by

'' ˆsinˆcosˆ zxx uuu ψψ += ( 4.70 )

'ˆˆ yy uu = ( 4.71 )

'' ˆcosˆsinˆ zxz uuu ψψ +−= ( 4.72 )

where ψ defines the angle between the x-axis and the major axis of the ellipsoid, and 'ˆ xu , 'ˆ yu ,

and 'ˆ zu are the orthonormal unit vectors that define the x'-y'-z' coordinate system (before

rotation). The vectors xu , yu , and zu are the orthonormal unit vectors for the coordinate

system rotated by ψ about the y'-axis. Figure 4-17 illustrates the orientation of the axes.

0

0.5

1

0

0.5

1

0

0.5

1

'ˆ xu'ˆ yu

'ˆ zu

xu

yu

zu

ψ

0

0.5

1

0

0.5

1

0

0.5

1

'ˆ xu'ˆ yu

'ˆ zu

xu

yu

zu

ψ

Figure 4-17. Unit vectors that define the axes for the ellipsoid model geometry.

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For convenience, the unit vectors are represented in a matrix form expressed by

−=

=ψψ

ψψ

cos0sin010

sin0cos

)(,)(,)(,

)(,)(,)(,

)(,)(,)(,

zzzyzx

yzyyyx

xzxyxx

uuuuuuuuu

U ( 4.73 )

In this form, the unit vectors can be used to transform the points of given by ( 4.69 ) into the

points on the oblique ellipsoidal surface xyzE using

( )

=

=

)(,)(,)(,

)(,)(,)(,

)(,)(,)(,222

111

222

111

'''

''''''

zzzyzx

yzyyyx

xzxyxx

NNNNNN

ixyz

uuuuuuuuu

zyx

zyxzyx

zyx

zyxzyx

rMMMMMM

E ( 4.74 )

Simply expressed, this rotation of the is performed with

( ) ( )UEE ix'y'z'ixyz rr = ( 4.75 )

Using equation ( 4.13 ), a set of points uniformly spaced along the z'-axis was generated to

represent scatterers falling on an ellipsoid defined by a normalized multipath delays ri = 1.15.

The elevation angle was set to 30o so that ψ = 60o. Using ( 4.73 ) and ( 4.75 ), the constant-delay

scattering points were rotated to produce the ellipsoidal surface illustrated in Figure 4-18. A z=0

plane is also illustrated to show the horizontal ground scattering constraint. The theoretical

scattering region boundary derived in the previous section and expressed by equations ( 4.62 )

through ( 4.66 ) is shown by the dark line on the horizontal plane. The figure demonstrates the

accurate representation of the scattering surface calculated using ( 4.62 ) through ( 4.66 ).

Equations ( 4.70 ) through ( 4.75 ) are useful for transforming scattering regions or simulated

scatterers into locations that fit the configuration of the physical environment. Also, for other

ellipsoidal model applications other than the air-to-ground model, these equations will prove

useful where the scattering region is a volume rather than a planar surface.

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(a) (b)

(c) (d)

(e)

(a) (b)

(c) (d)

(e)

Figure 4-18. Views of the ellipsoid, ground plane, and scattering region: (a) The oblique view shows the overall geometry of the model and the ellipse outlining the scattering region, (b) The end view shows the y-

axis width of the scattering region, (c) The side view shows the x-length of the scattering region which is clearly dependent upon the major axis elevation angle, (d) The top view shows the perfectly elliptical shape of

the scattering region, (e) The ground-bounded view limits the ellipsoid to z<0 to show that the analytical scattering region exactly matches the ground-ellipsoid intersection.

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4.5.3 Direction-of-Arrival Statistics

Using the equations derived in section 4.5.1, expressions that statistically describe the direction

of arrival (DOA) can be derived. One would suspect that since the scattering surface is exactly

elliptical, the results would mimic those derived for the GBSBE model in [Lib95]. Although

some of the elliptical channel model work in [Lib95] can be advantageously used, the overall

geometry of the three-dimensional environment described here is fundamentally different in that

the transmitter and receiver do not lie on the foci of the scattering surface as required by the

GBSBE model. For the GBSBE model to apply directly, the ellipses corresponding to the same

transmitter/receiver locations but different delays must have the same foci locations.

Since the scatterers for this model are uniformly distributed throughout an elliptical, planar

region, the marginal probability density function for direction of arrival will take the same

functional form as that of the GBSBE model21. However, rather than a direct dependency on the

maximum normalized multipath delay rm, the probability density function will be dependent

upon the scattering region parameters, namely ap and bp. The function of ap and bp, defined to be

g(ap,bp), must be determined so that the following equation, which has the form of equation (

4.19 ), is satisfied:

( ) ( )( )( )( )2

22

cos,

1,

21

φπβφφ

−=

pp

pp

bag

bagf πφπ ≤≤− ( 4.76 )

To solve for g(a,b), the maximum normalized multipath delay must be expressed in terms of ap

and bp, as shown in ( 4.77 ).

22pp

p

o

momo

o

mm

ba

a

ddd

dc

r−

=∆+

=∆+

==οτ

τττ ( 4.77 )

Therefore, g(ap,bp) is given by

21 This equivalence between the GBSBE model and the air-to-ground model is only true for direction of arrival since the distance traveled from the transmitter to the receiver does not affect the DOA PDF. Only the locations of the scatterers around the receiver affect the DOA PDF, and given the same dimensions of a ground-level ellipse, the distribution of scatterers around a receiver for the GBSBE model is the same as that for the air-to-ground model.

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( )22

,pp

ppp

ba

abag

−= ( 4.78 )

and from ( 4.17 ) and ( 4.77 ), an expression that relates β to ap and bp is shown to be

( ) ( )21

22

2

22

2 11,,

−−=−=

pp

p

pp

ppppp ba

a

ba

abagbagβ ( 4.79 )

By combining ( 4.76 ) and ( 4.78 ), the marginal probability density function for the distribution

of direction of arrival around the ground-based receiver is shown to be

( )2

22

22

2

cos

1

21

−=

φπβ

φφ

pp

p

pp

p

ba

a

ba

a

f ( 4.80 )

Using ( 4.62 ) through ( 4.66 ), ap and bp can be derived for the particular model geometry and

used as parameters of ( 4.80 ).

This probability density function has been verified using simulation. The receiver is defined to

be the ground station on the intersecting plane and on the lower focus of the tilted ellipsoid, and

the transmitter is defined to be the airborne station on the elevated focus of the ellipsoid. For the

simulation, scatterers were uniformly distributed on the scattering surface, and the direction of

arrival for signals inbound to the receiver was computed for each scatterer. The scattering

surface was calculated using a maximum normalized multipath value of rm = 1.15. A histogram

for direction of arrival was created, and the bin values were normalized so that histogram

contained unit area over angles of –180o to 180o DOA. The points for the normalized histogram

and the probability density function given in ( 4.80 ) computed over angles of –180o to 180o were

both plotted as shown in Figure 4-19.

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-150 -100 -50 0 50 100 1500

0.2

0.4

0.6

0.8

1

ψ = 30o

(El = 60o)

ψ = 80o

(El = 10o)

Marginal PDF of DOA for Ellipsoidal-Plane Intersection Model

Prob

abili

ty D

ensi

ty F

unct

ion

f φ

Direction of arrival φ (deg)-150 -100 -50 0 50 100 150

0

0.2

0.4

0.6

0.8

1

ψ = 30o

(El = 60o)

ψ = 80o

(El = 10o)

-150 -100 -50 0 50 100 1500

0.2

0.4

0.6

0.8

1

ψ = 30o

(El = 60o)

ψ = 80o

(El = 10o)

Marginal PDF of DOA for Ellipsoidal-Plane Intersection Model

Prob

abili

ty D

ensi

ty F

unct

ion

f φ

Direction of arrival φ (deg)

Figure 4-19. Marginal probability density function of direction of arrival for ψ=30 and ψ=80.

The “x” symbols in Figure 4-19 are the normalized histogram points, and the solid lines

represent the analytically derived marginal PDF for DOA. The PDF was computed for the cases

where the ellipsoid tilt angle ψ was 30o and 80o. An elevation angle for the ellipsoid is also

tagged to each curve, where elevation angle is defined by

ψ−= o90El oo 900 ≤≤ El , oo 900 ≤≤ ψ ( 4.81 )

The simulation shows the results of ten-thousand scatterers distributed on the scattering surface.

The results show that the analytical expression in ( 4.80 ) accurately follows the results of the

simulation.

The direction of arrival statistics derived from the model yield insight into the physical channel.

Specific trends are still being investigated, but the following general statements should be noted:

• As tilt angle ψ decreases (or equivalently as elevation angle El increases), the distribution

of DOA approaches a uniform distribution.

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• As tilt angle ψ increases (or equivalently as elevation angle El decreases), the distribution

of DOA shows that significantly more multipath components arrive in the direction of the

transmitter (φ = 0).

• At tilt angle ψ = 90o (or equivalently El = 0o), the marginal PDF for DOA equals that of

the two-dimensional GBSBE model using the same major and minor axis dimensions.

This is an expected result since the GBSBE model is a special case of this ellipsoidal

model with ψ = 90o.

Although the physical geometry and interpretation of results is different, this simulation result

mathematically validates the marginal probability density function for DOA given by the

GBSBE model presented in [Lib95] when ap and bp are used as dimensions of a and b for the

GBSBE input parameters.

4.5.4 Joint Direction-of-Arrival and Time-Delay Statistics

In this section the direction of arrival and propagation time delay joint probability density

function is investigated. Simulation results for the DOA and time delay marginal probability

density functions are also presented. Of particular interest are the trends of DOA and time delay

as elevation angle is varied. In order to begin, the following points in three-dimensional space

have been defined. These definitions facilitate representing the system in simulation.

T = location of transmitter = (xT, 0, zT) = zTxT zx uu ˆˆ + ( 4.82 )

R = location of receiver = (0, 0, 0) = 0 ( 4.83 )

Si = location of ith scatterer = (xS, yS, 0) = ySxS yx uu ˆˆ + ( 4.84 )

T is the location of the transmitter and R is the location of the receiver; the transmitter is located

on the x-z plane and the receiver is located at the origin of the coordinate system. Each scatterer

has coordinates Si and is located on the x-y plane within the scattering surface (i.e., within the

ellipse in the x-y plane). Coordinates of Si, namely xS and yS, are uniformly distributed within

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the bounds of the scattering surface. Using these points, the following spatial vectors are defined

to represent the relative positions of the transmitter, receiver, and scatterer.

TSv TS −= ii ( 4.85 )

ii SRv RS −= ( 4.86 )

The vector iTSv points from the transmitter to scatter i, and the vector RSv i points from scatterer

i to the receiver. Using these vectors, the relative delay of each multipath component can be

calculated using

222 badr ii

o

iii

+=

+= RSTSRSTS vvvv

( 4.87 )

and the direction of arrival can be calculated using

( )xiyii uSuS ˆ,ˆ2arctan ⋅⋅=φ ( 4.88 )

Where arctan2(y, x) is the inverse tangent function that returns the angle in the appropriate

quadrant given the signs of x and y parameter, where the angle ranges from – π to π radians.

Sample joint probability density functions for ir and iφ are shown in Figure 4-20. These joint

PDFs were computed for elevation angles El of 0o (transmitter rotated down to x-axis, on the x-y

plane with the receiver), 12o, 20o, 30o, 60o, and 90o (transmitter rotated up to z-axis, directly

above the receiver). These PDFs correspond to a maximum relative multipath delay of 1.15.

• Low elevation angles – The plots for El = 0o and El = 12o demonstrate the multipath

characteristics for an airborne transmitter on the ground or barely above the horizon in

angle. The joint PDF plots show a spike at low normalized delay and small DOA angles.

This spike indicates that multipath arrives primarily from the direction of the transmitter

and with relatively low normalized multipath delay. For increasing normalized delays,

the distribution shows a tendency for multipath components to arrive along directions on

either side of line-of-sight from the transmitter. As delay increases to the maximum

delay, the distribution flattens in the DOA dimension, indicating that the spread of

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multipath DOA widens and off-LOS angles are more probable. The results for El = 0o

correspond to the special case when the ellipsoid axes a and b are equal to the scattering

surface axes ap and bp, and these results corroborate the analytical results for the joint

DOA-delay statistics plotted in [Lib95].

• Moderate elevation angles – The plots for El = 20o, El = 30o, and El = 60o demonstrate

multipath characteristics from a transmitter at elevation angles significantly above the

horizon and significantly down from vertical. The joint PDF plots show broadening in

the DOA dimension indicating a wider spread of DOA at the receiver. As elevation angle

increases, the probability of longer multipath delays increases relative to that of shorter

delays. This shift of probability corresponds to the scattering surface becoming more

circular as the elevation angle increases for a constant normalized multipath delay.

• High elevation angles – The plot for El = 90o is representative of DOA-delay

distributions when the transmitter is nearly directly overhead the receiver. The flattening

in the DOA dimension indicates that multipath components arrive from all directions

around the receiver with equal probability. The steady increase in the distribution in the

delay dimension is caused by the circular shape of the scattering surface which grows in

all directions with increasing normalized delay for El = 90o.

For further clarity on the multipath component direction and delay statistics, Figure 4-21

illustrates the marginal probability density functions for direction of arrival and time delay of

arrival.

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El = 90o

El = 30o

El = 12oEl = 0o

El = 60o

El = 20o

DOA (deg)DOA (deg)

DOA (deg)DOA (deg)

DOA (deg)DOA (deg)

Normalized Delay r

Normalized Delay r

Normalized Delay r

Normalized Delay r

Normalized Delay r

Normalized Delay r

El = 90o

El = 30o

El = 12oEl = 0o

El = 60o

El = 20o

DOA (deg)DOA (deg)

DOA (deg)DOA (deg)

DOA (deg)DOA (deg)

Normalized Delay r

Normalized Delay r

Normalized Delay r

Normalized Delay r

Normalized Delay r

Normalized Delay r

Figure 4-20. Joint probability density functions for direction of arrival and normalized multipath delay for several elevation angles El.

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-150 -100 -50 0 50 100 1500

0.2

0.4

0.6

0.8

1

Direction of Arrival Marginal P DF

DOA (deg)

1.02 1.04 1.06 1.08 1.1 1.12 1.140

5

10

15

20

25

P ropagation Delay Marginal P DF

Normalized Multipath Delay r

-150 -100 -50 0 50 100 1500

0.2

0.4

0.6

0.8

1

Direction of Arrival Marginal P DF

DOA (deg)

1.02 1.04 1.06 1.08 1.1 1.12 1.140

2

4

6

8P ropagation Delay Marginal P DF

Normalized Multipath Delay r

-150 -100 -50 0 50 100 1500

0.2

0.4

0.6

Direction of Arrival Marginal P DF

DOA (deg)

1.02 1.04 1.06 1.08 1.1 1.12 1.140

2

4

6

8

P ropagation Delay Marginal PDF

Normalized Multipath Delay r

El = 30o

El = 30o

El = 0o

El = 0o

El = 12o

El = 12o

-150 -100 -50 0 50 100 1500

0.05

0.1

0.15

Direction of Arrival Marginal P DF

DOA (deg)

1.02 1.04 1.06 1.08 1.1 1.12 1.140

2

4

6

8

10

P ropagation Delay Marginal P DF

Normalized Multipath Delay r

El = 90o

El = 90o

-150 -100 -50 0 50 100 1500

0.2

0.4

0.6

0.8

1

Direction of Arrival Marginal P DF

DOA (deg)

1.02 1.04 1.06 1.08 1.1 1.12 1.140

5

10

15

20

25

P ropagation Delay Marginal P DF

Normalized Multipath Delay r

-150 -100 -50 0 50 100 1500

0.2

0.4

0.6

0.8

1

Direction of Arrival Marginal P DF

DOA (deg)

1.02 1.04 1.06 1.08 1.1 1.12 1.140

2

4

6

8P ropagation Delay Marginal P DF

Normalized Multipath Delay r

-150 -100 -50 0 50 100 1500

0.2

0.4

0.6

Direction of Arrival Marginal P DF

DOA (deg)

1.02 1.04 1.06 1.08 1.1 1.12 1.140

2

4

6

8

P ropagation Delay Marginal PDF

Normalized Multipath Delay r

El = 30o

El = 30o

El = 0o

El = 0o

El = 12o

El = 12o

-150 -100 -50 0 50 100 1500

0.05

0.1

0.15

Direction of Arrival Marginal P DF

DOA (deg)

1.02 1.04 1.06 1.08 1.1 1.12 1.140

2

4

6

8

10

P ropagation Delay Marginal P DF

Normalized Multipath Delay r

El = 90o

El = 90o

Figure 4-21. Marginal DOA and delay PDFs for the air-to-ground model.

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4.6 Summary

In this chapter, several existing channel models have been reviewed and new channel models

have been developed. The new channel models were developed based on geometric principals

used by the existing models. The general ellipsoidal channel model provides a framework to

develop three-dimensional, single-bounce, channel models to represent channel environments in

which the transmitter and receiver are surrounded by scatterers in three-dimensions. The general

ellipsoidal model was refined and constrained to form an air-to-ground channel model useful for

airborne vehicle communications. These models assist in developing wireless systems that

employ smart antennas by providing multipath strength, delay, and direction of arrival

information.

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Chapter 5 Channel Measurements

This chapter investigates past results and new developments in radio channel measurements.

First, a survey of terrestrial and air-to-ground measurements is presented. The results of the

survey demonstrate direction of and the interest in various types of radio channel measurements.

Next, measurement campaigns performed at Virginia Tech are discussed, including descriptions

of measurement sites, system configurations, and propagation characteristic results relevant to

antenna arrays and channel modeling. New measurement results presented in this chapter serve

as input to channel simulation and channel model evaluation described later

5.1 Survey of Radio Channel Measurements

Section 5.1 provides an overview of results from measurement campaigns reported in

propagation research literature. This section gives examples of measurement results that are of

interest to propagation researchers and outlines the measurement campaigns performed to obtain

the results.

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5.1.1 Terrestrial Measurements

Numerous terrestrial measurements have been performed by researchers to characterize

propagation between base stations and mobile stations. Measurements were performed as early

as 1972 [Cox72] to characterize multipath properties and wideband propagation for digital

communications in a mobile environment. Measurements continue to be performed today to

characterize radio channels in specific ways for new applications of wireless technology (e.g.,

antenna array applications). Measurements performed by Wilson [Wil01] characterized

wideband propagation at 1920 MHz using a four-element antenna array. A mobile transmitting

antenna and a roof-mounted receiving antenna array were used to measure radio channels

throughout a suburban environment. The receiver antenna array used nonlinear inter-element

separations of 2λ, 5λ, and 10λ. A direct-sequence, spread-spectrum measurement system was

used to log power-delay profiles. Table 5-1 summarizes the measurement results.

Table 5-1. Results of a wideband measurement campaign in a suburban environment [Wil01].

Measurement Parameter Result

Site Suburban (Boulder, CO). Mobile transmitter; roof-mounted

receiver 14 m above predominant elevation.

Multipath characteristics RMS delay spread:

CDF 90%: <1.38 µs and <0.65 µs throughout two

sectors

CDF 99%: <3.14 µs and <1.35 µs throughout two

sectors

Path loss exponent 4.1 and 4.9 throughout two sectors.

Diversity Gain Maximal ratio combining 19.6 KHz BW (4-channels)

CDF 90%: 11.2 dB (max)

CDF 99%: 18.3 dB (max)

Maximal ratio combining 10 MHz BW (4-channels)

CDF 90%: 6.9 dB (max)

CDF 99%: 7.8 dB (max)

Observations • Fade depths decrease for increasing bandwidth.

• Increasing bandwidth reduces computed diversity gain.

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Received power within particular bandwidths was determined by integrating the normalized

power spectral density (NPSD) over the desired bandwidth. Using the notation in [Wil01], The

NPSD normalized to a calibration profile was defined to be

( )( )2

2

_ DPCALDFTDPDFT

NPSD = ( 5.1 )

where DP is the delay profile, DFT(.) is the discrete Fourier transform (DFT), and CAL_PD is

the DFT of the system response delay profile. Delay profiles are related to power-delay profiles

using

( ) ( )2ii tDPtPDP = ( 5.2 )

where ( )itPDP is the power-delay profile curve (showing received power versus propagation

delay). The power-delay profiles used for the results in [Wil01] were a subset (approximately

60%) of the total collected. An acceptance criterion was applied to all power-delay profiles in

order to keep poorly measured profiles (low interval of discrimination, noisy, etc.) from

corrupting measurement results.

Measurements in [Lar99] provided results on spatial and temporal characteristics of radio

channels in urban and suburban environments. Wideband measurements were performed using

an antenna array to produce azimuth-delay spectra showing power versus angle and propagation

delay. Results for delay spread, azimuth spread, and coherence bandwidth were reported; results

are summarized in Table 5-2.

Propagation delay results showed a decrease in RMS delay spread as antenna beamwidth was

narrowed. Rician K-factors in the suburban environments were shown to be higher than those in

urban environments, suggesting that stronger LOS components existed in suburban environments

(K = 0 corresponds to Rayleigh fading).

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Table 5-2. Results of a spatial-temporal measurement campaign [Lar99].

Measurement Parameter Result

Site Dense urban and suburban environments.

Multipath characteristics RMS delay spread:

CDF 50%: <70 ns (15 degree antenna beamwidth)

CDF 50%: <90 ns (120 degree antenna beamwidth)

CDF 90%: <200 ns (15 degree antenna beamwidth)

CDF 90%: <230ns (120 degree antenna beamwidth)

Rician K factors Urban environment CDF 70%: K = 2

Suburban environment CDF 70%: K = 10

Coherence bandwidth CDF 50%: 6 MHz (15 degree antenna beamwidth)

CDF 50%: 4 MHz (120 degree antenna beamwidth)

CDF 80%: 23 MHz (15 degree antenna beamwidth)

CDF 80%: 10 MHz (120 degree antenna beamwidth)

Observations • Approximately 20% of measured channels showed K<1

and coherence bandwidth > 4 MHz.

• Approximately 50% of measured channels showed K<1

and coherence bandwidth > 1 MHz.

Receivers that employ rakes can combine resolvable multipath components, and the number of

useful rake fingers l for an ideal rake receiver is expressed in [Lar99] by

1+

=

CBWB

l ss ( 5.3 )

where Bss is the system bandwidth and CBW is the coherence bandwidth of the channel. For

example, if a 4.096 MHz W-CDMA receiver is used in a channel with a coherence bandwidth

exceeding 4.096 MHz, then less than two rake fingers are active. If multipath components

cannot be resolved, then a rake finger will experience fading because of combining of signal

components within the resolution of the system. Therefore, as shown by the measurement

results, in 20% of the measured channels where K<1 (indicating significant multipath content)

and coherence bandwidth greater than 4 MHz (indicating short relative multipath delays), a W-

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CDMA receiver employing a rake receiver would experience severe fading on a single useful

rake finger. For a 1.25 MHz IS-95 receiver employing a rake, a single finger would experience

severe fading more than approximately 50% of the time due to K<1 and CBW>1 MHz more than

50% of the time.

Results for spatial signatures measured in outdoor environments at 1.88 GHz are presented in

[Kav00]. Variations of spatial signatures due to a dynamic propagation environment can be

quantified using a correlation coefficient given by

ji

jHi

jiaa

aa=,ρ ji ≠ ( 5.4 )

where ai and aj are column vectors representing the ith and jth spatial signatures measured for an

array at two different locations. Measurements were performed in a suburban environment using

a mobile transmitter and a base station array consisting of seven elements in a circular pattern

with a radius of 10 cm. The transmitter antenna was a half-wavelength, vertically polarized

dipole.

Table 5-3. Summary of results of campaign to measure correlation of spatial signatures [Kav00].

Measurement Parameter Result

Site Suburban environment; LOS and NLOS channels.

Spatial signature correlation

coefficients

Pedestrian measurement runs:

CCDF 90%: 0.41 (min) – 0.98 (max)

CCDF 50%: 0.82 (min) – 0.99 (max)

Car measurement runs:

CCDF 90%: 0.21 (min) – 0.69 (max)

CCDF 50%: 0.61 (min) – 0.92 (max)

Observations • For NLOS propagation, spatial signatures become less

correlated with small movements due to varying complex

path attenuation.

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An empirical model that best fit the probability density functions of spatial signature correlation

coefficients was found using the beta function given by

( ) ( )( ) ( ) ( )βψ ρρ

βψβψ

βψρ −1+Γ1+Γ

2++Γ=, 1f , 10 ≤≤ ρ , 1−>ψ , 1−>β ( 5.5 )

where ( )⋅Γ is the gamma function defined by

( ) ( )∫∞

−− −==Γ0

1 !1tdxext xt . ( 5.6 )

Values for the parameters of this model and measured PDFs are presented in [Kav00]. The

results for this measurement campaign showed that spatial signatures in LOS environments

exhibited high correlation between pairs of spatial signature vectors when a the transmitter

antenna was moved through the environment. However, the rich multipath environments of

NLOS channels caused lower values of correlation coefficients computed for pairs of spatial

signature vectors.

To summarize, the following observations have been made regarding the reviewed terrestrial

measurements:

• Increasing signal bandwidth reduces fade depth and reduces potential antenna diversity

gain.

• Narrower antenna beamwidth reduces RMS delay spread and increases coherence

bandwidth because of attenuation of multipath components separated in angle.

• Measurements of coherence bandwidth and Rician K-factors show conditions where rake

receivers can become ineffective because of short multipath delays but strong multipath

content. Rakes become more effective where small K-factors and narrow coherence

bandwidths exist simultaneously.

• Spatial signatures vary more rapidly over shorter distances in shadowed, multipath-rich

environments; conversely, spatial signature vectors remain highly correlated in

predominantly LOS channels.

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5.1.2 Air-to-Ground Measurements

Measurements between low-altitude (below 10,000 feet) airborne vehicles and ground stations

can be found in literature for measurement campaigns intended to emulate satellite-to-ground

communications. Measurements at 1636 MHz are presented in [Smi91] were performed using a

transmitter in a light aircraft and a receiver on the ground. The measurement system was a

sliding correlator system that measured power-delay profiles using a 1023-chip PN sequence

clocked at 10.23 Mcps; the plots presented in [Smi91] indicate that the system had an interval of

discrimination of approximately 28 dB. Data was collected for elevation angles between 60

degrees and 80 degrees above the horizon in suburban environments. The results in primarily

LOS channels indicate low delay spread. When the mobile vehicle was located in a canyon of

tall buildings, sample power-delay profiles indicated excess delay at the 25 dB level to be

between 1 µs and 1.5 µs.

Table 5-4. Results of a measurement campaign using a light aircraft to study land mobile satellite communications [Smi91].

Measurement Parameter Result

Site Suburban and rural environments; 60o to 80o elevation angles.

Multipath characteristics Obstructed channel:

Excess delay (25-dB level): 1.0 µs to 1.25 µs

(building obstruction)

LOS channel

Excess delay: minimal

Observations • LOS channels in suburban and urban environments

showed low delay spread for elevation angles of 60o to

80o.

• Transition from LOS condition to shadowing behind

building obstruction showed sharp increase in multipath

components reflected from nearby buildings.

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Measurements in [Jah96] also used an airborne transmitter to characterize multipath propagation

at 1820 MHz for spread-spectrum satellite communications. The measurement data indicated

that multipath components could be divided among three regions in the power-delay profiles:

direct path, near echoes, and far echoes. Note that this division of the delay axis corresponds to

an approach similar to that of the elliptical sub-regions channel model presented in Chapter 4.

The amplitude of the direct-path component was shown to be Rician distributed in LOS

conditions and Rayleigh distributed in shadowed regions22. In the near-echo region, the

amplitude of components decreased exponentially with delay, and the delay of the components

was exponentially distributed. A majority of the multipath components appeared in the near-

echo region. The components that appeared in the far-echo region were distributed uniformly in

delay and showed Rayleigh-distributed amplitude. Detailed results for various elevation angles

are presented in [Jah96].

The measurement system used for the measurements described in [Jah96] is described in [Jah94].

A sliding correlator system used a chip rates of 10 MHz and 30 MHz and PN sequence lengths of

127, 255, and 511 chips. A maximum transmit power of 44 dBm was available, and an

omnidirectional transmitter antenna was mounted on the skin of an aircraft. The receiver used an

experimental antenna for an INMARSAT-P handheld terminal.

In an air-to-ground channel sounding campaign [Dye98] designed to study aircraft

communications, a narrowband measurement system and a sliding correlator system was used to

measure narrowband and wideband channel characteristics in the VHF communications band23 at

135 MHz. The sliding correlator channel sounder was operated at 5 Mcps, resulting in a

multipath time delay resolution of approximately 0.4 µs. The measurements were performed

between the airport terminal area and an airborne aircraft flying standard departure and arrival

procedures. Table 5-6 summarizes the results of the measurement campaign. Because of the

large K factors, indicating a strong LOS component during measurements, the effect of small

scale fading was reported to be insignificant. 22 Strictly speaking, a completely resolved, direct-path component would not fade. The fading of the “direct-path” component in [Jah96] was caused by the combination of signal components that could not be resolved by the measurement system. 23 The aviation communications band in use by civil aircraft in the United States exists between 118 MHz and 136 MHz. For voice communications, amplitude modulation is used.

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Table 5-5. Summary of results for a campaign that measured land mobile satellite channels [Jah96].

Measurement Parameter Result

Site Open, rural, suburban, urban, highway.

Multipath characteristics Direct path

Rician amplitude in LOS conditions (3.2-11.8 dB

carrier to multipath ratio)

Rayleigh/log-normal in shadowed conditions

Near echoes

Exponentially decreasing mean amplitude with delay

Rayleigh-distributed amplitude around mean

Exponentially-distributed delay of components

Poisson-distributed number of components (λ=0.5-

4.0)

Maximum excess delay 400 ns - 600 ns

Far echoes

Rayleigh-distributed amplitude

Poisson-distributed number of components (λ=0.3-

4.1)

Uniformly-distributed delay of components

Maximum excess delay 5 µs - 15 µs

Observations • Multipath components typically attenuated 10 – 30 dB

relative to LOS component.

• Most multipath components lie in 0 – 600 ns delay region.

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Table 5-6. Results of an air-to-ground measurement campaign [Dye98].

Measurement Parameter Result

Site Airport environment

Small scale fading distribution Predominantly Rician with large K factors

Range of Rician K factors 2.6 dB to 19.7 dB

Average Rician K factor 16 dB

Multipath characteristics RMS delay spread: mean στ = 4.0 µs (variance = 1.4 µs)

Delay spread: mean ∆τ = 2.9 µs (variance = 1.3 µs)

Path loss exponent 2 to 4 at large T-R separations

Observations • Surface and low altitude operations resulted in larger

standard deviation of large scale fading (shadowing)

• Small scale fading was insignificant for this particular

measurement setup

In summary, these observations have been made with respect to measurements performed in the

air-to-ground propagation environment:

• The existence of multipath in the air-to-ground channel is dependent upon the

environment surrounding the ground-based receiver. For the flat, non-obstructed airport

environment, weak multipath resulted in Rician fading with large K-factors.

• Small elevation angles resulted in richer multipath content.

• Although large excess delay values may be apparent (over 1 µs), the air-to-ground

channel may remain Rician with large K-factors.

• Rician fading of direct-path components indicates multipath caused by scatterers in close

proximity to receiver (since airborne transmitter is not near any scatterers).

• Large excess delays can be expected in air-to-ground channels; up to 15 µs has been

recorded.

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5.2 Rooftop-Level Measurement Campaign

Rooftop measurements were performed in a manner that emulated radio channels between tower-

mounted and ground-level transceivers. Measurements were processed to produce results

appropriate for geometric channel model simulation and channel characterization.

5.2.1 Measurement Overview

Wideband measurements were performed at Virginia Tech to record experimental data for a

receiver antenna height of approximately 25 meters above ground level and a receiver

approximately 1.5 meters above ground level. The wideband, multi-channel measurement

system described in Chapter 3 was mounted on the roof of Whittemore, a six-story academic

building on the Virginia Tech campus. The transmitter antenna was mounted on the roof of a

vehicle and driven through the parking lots and streets adjacent to the building on which the

receiver was located. Figure 5-1 shows the measurement system location on the roof and the

orientation of the antenna array relative to the surroundings.

Figure 5-1. The measurement system was positioned on the roof of Whittemore near the corner of the building, and the receiver array was mounted on a stand approximately six feet above roof level.

The antenna array used at the receiver was a four-element linear array, using quarter-wavelength

monopole antenna elements with half-wavelength spacing. The antenna array was mounted with

the ground plane above the antenna elements so that the antennas would receive signals from

below the horizontal plane (where the transmitter was located throughout the measurements).

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The automobile with the transmitter was driven at slow speeds (less than 5 MPH) while the

receiver logged signal data. Table 5-7 summarizes the system configuration and site details.

Table 5-7. Details of the measurement system setup and transmitter/receiver locations for the Whittemore roof measurements.

Measurement Parameter Value / Description

Transmit power +26 dBm

Transmitted signal 80 Mcps PN sequence, 1023 chips, register

taps (3,10)

Transmit frequency 2050 MHz (center)

Transmitter antenna Dipole, vertically-polarized

Transmitter antenna height 1.5 m AGL

Receiver antennas Four-element monopole array, half-

wavelength spacing

Receiver antenna array height Approximately 25 m AGL

Receiver location Whittemore Hall, roof

Drive test areas (transmitter driven) 1) Parking lots north of Whittemore (LOS)

2) Parking lots behind Durham (NLOS)

3) Suburban neighborhood north of

Whittemore(LOS/NLOS)

5.2.2 Multipath RMS Delay Spread

Multipath characteristics were computed from measured power-delay profiles. Sample power-

delay profiles from the Whittemore roof measurements are shown in Figure 5-2. Relative axes

units are typically acceptable for producing meaningful multipath delay characterization results.

For example, RMS delay spread statistics rely only on the relative (as opposed to absolute)

strength and delay of multipath components contained in a power-delay profile. Figure 5-2

illustrates power-delay profiles that were recorded simultaneously at two of the four antenna

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elements. Both power-delay profiles were normalized using the same factor. Differences in

signal component strengths due to uncorrelated multipath fading across the antenna array are

noticeable.

Figure 5-2. Sample power-delay profiles recorded at elements 2 and 3 of the antenna array. The solid line is the channel 2 PDP, and the dotted line is the channel 3 PDP.

RMS delay spread is used to quantify the relative time dispersion of a signal due to multipath.

For TDMA systems, a large delay spread may add the requirement for an equalizer in the

receiver to mitigate frequency selected fading caused by the channel. For CDMA systems, a

large delay spread means that a rake receiver may be used to combine multipath components of

different delays to form a more reliable composite signal. Mean multipath delay is computed

using

=

==N

nn

N

nnn

1

2

1

2

α

τατ ( 5.7 )

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where 2nα is the relative power of each signal component and nτ is the corresponding delay of

each component. Note that mean delay is a function of absolute propagation delay between the

transmitter and receiver, not simply a function of relative delay. RMS delay spread is the second

central moment of the power delay profile computed with

( )

=

=

−= N

nn

N

nnn

1

2

1

22

α

ττασ τ . ( 5.8 )

Because the computation involves subtracting the mean delay from individual multipath delays,

RMS delay spread is not a function of absolute propagation delay.

Table 5-8 shows the RMS delay spread results for the Whittemore roof/Whittemore parking lot

measurements. Mean, standard deviation, minimum, and maximum RMS delay spread values

are given for each element of the antenna array. Figure 5-3 shows the complimentary CDF for

RMS delay spread computed for each antenna element. Results shown on the plot indicate

similar RMS delay spread characteristics across all four elements of the array. This is expected

since all antenna elements received signals through channels in the same propagation

environment.

Table 5-8. RMS delay spread statistics.

Channel 1 Channel 2 Channel 3 Channel 4

Mean RMS Delay

Spread 137.2 ns 106.9 ns 115.1 ns 117.4 ns

Standard Deviation

RMS Delay Spread 186.1 ns 91.6 ns 109.9 ns 107.6 ns

Minimum RMS

Delay Spread 3.2 ns 4.3 ns 14.3 ns 2.4 ns

Maximum RMS

Delay Spread 1186.7 ns 507.0 ns 614.5 ns 633.9 ns

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0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RMS Delay Spread

Pro

babi

lity(

RM

S D

elay

Spr

ead

> A

bsci

ssa

)

RMS Delay Spread Based On Measurements

Channel 1Channel 2Channel 3Channel 4

Figure 5-3. Complementary CDF for RMS delay spread based on measurements.

5.2.3 Distribution of Multipath Components

The histogram in Figure 5-4 was produced to show the distribution of multipath components

across delay in the measured power-delay profiles. All detectable multipath components are

included in the histogram. The results show a decrease in numbers of multipath components

with delay. The specific values of component count can serve as input for simulations using

geometric channel models. The average number of components in each delay bin and for the

entire profile are tabulated in Table 5-9.

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0 500 1000 1500 2000 25000

1

2

3

4

5Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

s

Figure 5-4. Number of signal components versus excess propagation delay.

Table 5-9. Distribution of multipath components among delay bins of power-delay profiles.

Bin # Delay Bin (ns) # Components per

Profile

1 0 – 150 4.69

2 150 – 300 3.03

3 300 – 450 2.29

4 450 – 600 2.16

5 600 – 750 1.84

6 750 – 900 1.50

7 900 – 1050 1.34

8 1050 – 1200 1.08

9 1200 – 1350 0.582

10 1350 – 1500 0.310

11 1500 – 1650 0.172

12 1650 – 1800 0.138

13 1800 – 1950 0.0776

14 1950 – 2100 0.0647

15 2100 – 2250 0.0172

16 2250 – 2400 0.0690

ALL 0 – 2400 19.4

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5.2.4 Multipath Strength Correlation Coefficients Versus Delay

This section provides a method of computing correlation coefficients for signal component

magnitude across an antenna array. The purpose of the method and the associated results is to

investigate behavior of signal component fading across the array and for varying ranges of

excess propagation delay.

It is well known that performance gain provided by antenna diversity is dependent upon the

signal envelope correlation among the elements of an antenna array [Jan02]. Traditionally, the

signals are measured using a continuous-wave transmitted signal and a narrowband receiver to

record the fading envelope at each antenna element simultaneously. When fading envelopes are

highly correlated, improvement of system performance through antenna diversity is low

compared to the case when fading envelopes exhibit low correlation coefficients.

For a narrowband system, a fading envelopes are caused by the constructive and destructive

combination of signal components at the receiving antenna when the receiver or transmitter is in

motion24. These signal components are caused by two or more propagation paths of

electromagnetic energy between the transmitter and receiver. Narrowband systems generally

cannot resolve signal components, and the fading envelopes are a result of the summation of all

signal components arriving at the receiver antenna.

Certain wideband systems, such as direct-sequence spread spectrum systems, have the ability to

resolve individual or groups of signal components at the receiver. A rake receiver can

demodulate signal components that are delayed in time with respect to one another. When signal

components are mutually separated in delay by more than a chip period, those signal components

can be uniquely resolved with unfading magnitude. However, when multiple signal components

arrive at the receiver with relative delays less than one chip period, those signal components

combine and appear as a single signal component25 that fades with time as the receiver or

transmitter moves. It is the correlation coefficient of these fading envelopes, caused by signal

components with irresolvable delays, across elements of an antenna array that is of interest here. 24 Fading envelopes are also caused by relative motion of scatterers in the propagation environment. 25 The composite signal component may appear wider in delay, and the shape may not be that of an ideal PN sequence autocorrelation function observed for single-component peaks.

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The measurements reported here are relevant to a receiver that uses a rake receiver at each

antenna element and combines the output of the rake fingers to form a composite received signal.

Similar to the case of combining multiple narrowband signals directly from antenna elements,

the performance of combining signal components with particular delays from multiple antenna

elements will be affected by the correlation coefficient of the envelopes of the signal

components.

A signal component magnitude for a power-delay profile (PDP) is defined to be the maximum

magnitude value detected for a particular cross-correlation peak that exists in the profile. Figure

5-5 illustrates a sample set of power-delay profiles used for the signal component magnitude

correlation processing. The continuous trace (blue) shown for each channel is a plot of all

samples of the power-delay profile. The straight horizontal (yellow) line indicates the noise

threshold below which all PDP samples are considered noise. The circles (red) around each peak

represent the discrete magnitude and delay pairs that were detected for signal components in the

power-delay profiles.

The correlation coefficients for multipath magnitude across an array are defined as follows. A

power-delay profile P(τ), which may be interpreted as relative received power versus relative

propagation delay, can be represented as a set of Ns samples given by

( ) ( )sn nTPP =τ ( 5.9 )

where Ts is the sample period with which the power-delay profile is sampled, and sn nT=τ is the

discrete time value (in seconds) of the propagation delay for sample { }1,,2,1,0 −∈ sNn L . A

measured power-delay profile represents received signal components as a channel impulse

response convolved with the pulse shape determined by the measurement system response. For

the measurements processed here, the pulse shape is approximately triangular and corresponds to

the autocorrelation function of the PN sequence transmitted for the measurements (see [New97]).

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Figure 5-5. One set of power-delay profiles acquired simultaneously at each antenna element for multipath magnitude correlation processing.

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The samples at the peaks of the signal components, as shown in Figure 5-5, are the relative

signal component strengths αk in the impulse response given by

( ) ( ) ( )∑−

=

−=1

0

expcN

kkkk jh ττδφατ ( 5.10 )

where Nc is the number of signal components26, φk is the phase of the kth signal component, and

τk is the delay of the kth signal component corresponding to strength αk. If we consider only the

peaks of ( )nP τ , occurring at times τk where { }1,,2,1,0 −∈ cNk L , then the discrete magnitudes

and phases of the impulse response in equation ( 5.10 ) are related to the power-delay profile

( )nP τ by

( )kk P τα = ( 5.11 )

and

( )kk P τφ ∠= . ( 5.12 )

Power-delay profiles were identified for this measurement campaign with a snapshot number and

a channel number. A channel number { }4,3,2,1∈i identifies which of the four elements was

used to receive the power-delay profile, and each snapshot number { }1,,2,1,0 −∈ snapNj L

identifies a set of four power-delay profiles recorded simultaneously at the four antenna

elements, where Nsnap is the total number of snapshots recorded. Within each power-delay

profile, individual signal component magnitudes are assigned an index ( ){ }1,,2,1,0 −∈ jcNk L ,

where ( )jcN is the number of signal components in each power-delay profile recorded during the

jth snapshot. With this notation defined, individual multipath components can be identified by

26 Technically, Nc is the number of discrete paths between the transmitter and receiver, but if Nc paths exist, then Nc signal components will also exist at a receiver.

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kji ,,α

i = channel (antenna element) number where { }4,3,2,1∈i

j = power-delay profile snapshot number where { }1,,2,1,0 −∈ snapNj L

k = signal component index where ( ){ }1,,2,1,0 −∈ jcNk L

snapN = number of snapshots

( )jcN = number of signal components in each PDP for jth snapshot

( 5.13 )

Since correlation coefficients versus delay are of interest, each power-delay profile is divided

into Mbins evenly spaced delay bins. Delay bins are identified with index { }binsMm ,,3,2,1 L∈ .

The width of each delay bin is determined by dividing the time between the first-arriving and

last-arriving signal components by the number of delay bins M. Figure 5-6 illustrates delay bins

for a measured power-delay profile.

Delay Bins1 2 3 4

Delay Bins1 2 3 4

Figure 5-6. Delay bins evenly divide the delay between the first arriving signal component and the last arriving signal component.

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In order to operate on all signal components in all power-delay profiles for each channel, the

matrix mA was created. This matrix contains all signal component magnitudes found within

delay bin m.

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

=

−−−− −−−−−

−−−−

1111

0000

,1,4,1,3,1,21,1,1

0,1,40,1,30,1,20,1,1

1,0,41,0,31,0,21,0,1

2,0,42,0,32,0,22,0,1

1,0,41,0,31,0,21,0,1

0,0,40,0,30,0,20,0,1

snapNcsnap

snapNcsnap

snapNcsnap

snapNcsnap

cccc

NNNNNNNN

NNNNm

αααα

αααααααα

αααααααααααα

MMMM

MMMMA . ( 5.14 )

Each column of matrix mA contains the magnitudes of all of the multipath components received

at a particular antenna element (column one corresponds to element one, etc.). Each row of

matrix mA contains four multipath components received simultaneously at the antenna elements

during one of the Nsnap power-delay profile snapshots. In order to simplify the notation for the

elements of mA , and since further calculations only depend upon the column and row

organization of the matrix, the matrix mA will be rewritten as

[ ]4321 aaaaA =m ( 5.15 )

where the column vectors ia represent the signal component magnitudes received by antenna

element i.

The correlation coefficient matrix of mA can now be computed. The signal component

magnitude correlation coefficient matrix ρc is defined as

ρc

=

44434241

34333231

24232221

14131211

ρρρρρρρρρρρρρρρρ

. ( 5.16 )

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The elements mnρ of matrix ρc, where m indicates row and n indicates the column of ρc, are

given by

ρmn ( ) ( )

( ) ( ) ( ) ( )nnT

nnmmT

mm

nnT

mm

aaaa

aa

−−−−

−−=

aaaa

aa ( 5.17 )

where ma and na are the means of column vectors ma and na respectively.

Since ρc is symmetric about the diagonal and ρmn = 1 for m = n, which can be deduced from

equation ( 5.17 ), there are six unique quantities that completely describe the correlation of signal

component magnitudes among the four antenna elements. These quantities are the following

elements of ρc: ρ12, ρ13, ρ14, ρ23, ρ24, and ρ34.

The data recorded during the Whittemore roof measurements was used for this processing.

Measurements can be performed over a local area or a wide area. For example, measurements

presented in [Kav00] use a local area approach, during which the transmitter or receiver is

moved throughout an area of a few wavelengths to characterize small-scale changes in signal

properties (in [Kav00], spatial signature correlation across local areas was investigated). The

measurements discussed in this section were performed using a wide area approach, during

which power-delay profiles were recorded while a transmitter was moved randomly throughout a

very large area compared to a wavelength. The area was chosen such that the propagation

environment remained similar at all points throughout the area (e.g., not mixing urban

environments with rural environments throughout the wide area chosen).

Power-delay profiles used for processing were limited to those which had a large enough interval

of discrimination so that signal components could be measured on a consistent basis. Power-

delay profiles were normalized using a common factor. As such, an approximate index of

discrimination was derived for each channel by comparing the strongest signal component across

all channels with the noise floor of the power-delay profile for each channel. The minimum

index of discrimination allowed was called the noise threshold. The noise threshold was chosen

to be 3 dB above the peak power-delay profile sample in a delay region where no signal

components were observed, defined to be the noise region. For the measurements described in

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this section, the noise region was set to be the last 20 percent of each power-delay profile, as

indicated by the straight vertical (yellow) line in the plots in Figure 5-5.

Multipath components were for each power-delay profile were detected by an iterative process

whereby the maximum magnitude value is identified as a signal component and a window of

samples, having a width equal to the resolution of the measurement system, is removed from the

maximum magnitude check for the next iteration. In order to further assure that noise peaks

were not falsely identified as signal components, a minimum signal component level was

defined. Peaks within this dB level of the strongest signal component across all channels were

used during processing. Table 5-10 summarizes the processing details.

Table 5-11, Table 5-12, and Table 5-13 summarize the results for three different delay bin sizes.

The six correlation coefficients are shown for each delay bin, and the number of signal

components that existed in those delay bins is listed. The delay range for each bin and element

spacing is also shown.

Table 5-10. Processing details for signal component correlation processing.

Processing Factor Details

Noise threshold 30 dB below strongest component across all

channels

Noise region Last 20% of 4 µs power-delay profile

Margin between peak noise region and noise

threshold

3 dB above peak sample in noise region

Number of delay bins 4, 8, and 16 bins

Minimum signal component level 27 dB below strongest component across all

channels

Normalization factor All power-delay profiles normalized by

subtracting same dB factor from dB-scale

PDPs. Normalization factor set such that

strongest component across all channels

equaled 0 dB.

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Table 5-11. Correlation coefficients for signal component magnitude across antenna elements (4 delay bins).

Correlation Coefficients Delay

Bin

No.

Delay

Range

(µs) 12ρ 13ρ 14ρ 23ρ 24ρ 34ρ

Number of

Signal

Components*

1 0-0.36 0.91748 0.89406 0.84693 0.92163 0.8629 0.89392 258

2 0.36-0.71 0.30562 0.26789 0.33806 0.63443 0.61436 0.63367 47

3 0.71-1.07 0.84732 0.70833 0.59953 0.65819 0.58294 0.68511 15

4 1.07-1.42 0.34766 0.24449 0.53386 -0.466 -0.5548 0.6808 7

Element Spacing λ/2 λ 3λ/2 λ/2 λ λ/2

* Signal components detected within 208 power-delay profiles.

Table 5-12. Correlation coefficients for signal component magnitude across antenna elements (8 delay bins).

Correlation Coefficients Delay

Bin

No.

Delay

Range

(µs) 12ρ 13ρ 14ρ 23ρ 24ρ 34ρ

Number of

Components

Signal*

1 0-0.18 0.91495 0.90385 0.88074 0.93027 0.89583 0.92894 206

2 0.18-0.36 0.69605 0.46992 0.19446 0.623 0.30935 0.42116 52

3 0.36-0.53 0.23328 0.18571 0.31093 0.65197 0.54222 0.52036 35

4 0.53-0.71 0.51271 0.49939 0.43926 0.60896 0.73837 0.77877 12

5 0.71-0.89 0.84041 0.8304 0.86474 0.84828 0.93369 0.80717 7

6 0.89-1.07 0.86746 0.65001 0.38844 0.67706 0.44905 0.49309 8

7 1.07-1.25 0.11047 0.96931 0.71757 -0.097809 -0.5893 0.81005 4

8 1.25-1.42 0.91521 -0.39596 0.89873 -0.73242 0.64582 0.046811 3

Element Spacing λ/2 λ 3λ/2 λ/2 λ λ/2

* Signal components detected within 208 power-delay profiles.

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Table 5-13. Correlation coefficients for signal component magnitude across antenna elements (16 delay bins).

Correlation Coefficients Delay

Bin

No.

Delay

Range

(µs) 12ρ 13ρ 14ρ 23ρ 24ρ 34ρ

Number of

Components*

1 0-0.09 0.91996 0.93527 0.91201 0.95558 0.91642 0.94838 144

2 0.09-0.18 0.50385 0.35558 0.26853 0.64626 0.55205 0.66376 62

3 0.18-0.27 0.43866 0.31679 -0.07140 0.29552 0.1415 0.31201 26

4 0.27-0.36 0.84455 0.55788 0.63497 0.71643 0.61248 0.74363 26

5 0.36-0.45 0.25178 0.32238 0.49312 0.67144 0.61809 0.65301 28

6 0.45-0.53 0.22744 0.015498 0.1421 0.68934 0.49123 0.44003 27

7 0.53-0.62 0.58598 0.49731 0.46097 0.82369 0.89891 0.80876 8

8 0.62-0.71 -0.11005 0.94608 0.68587 0.12021 0.43351 0.88461 4

9 0.71-0.80 -0.56082 0.38164 -0.83668 0.37923 0.43101 -0.03374 4

10 0.80-0.89 0.99923 0.93717 0.99984 0.92277 0.99977 0.93079 3

11 0.89-0.98 0.94317 0.68902 0.435 0.87489 0.51255 0.72668 4

12 0.98-1.07 0.8719 0.77448 0.4975 0.47402 0.36116 0.85729 4

13 1.07-1.16 0.17749 0.96976 0.61127 -0.06807 -0.6704 0.78594 3

14 1.16-1.25 ** ** ** ** ** ** 1

15 1.25-1.34 ** ** ** ** ** ** 1

16 1.34-1.42 -1 1 1 -1 -1 1 2

Element Spacing λ/2 λ 3λ/2 λ/2 λ λ/2

* Signal components detected within 208 power-delay profiles.

** Only one component in delay bin; correlation coefficient undefined.

Several observations can be made using these results:

• The first bin of multipath components shows consistently high correlation coefficients

(above 0.9). The presence of a dominant line-of-sight signal component would have this

effect. A dominant line-of-sight component indicates that no significant multipath

components exist near the LOS component (in delay) within the resolution of the

measurement system.

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• As the first bin is widened in delay, the correlation coefficients remain approximately the

same for the λ/2-spaced elements; and the correlation coefficients decrease for more

widely spaced (λ and 3λ/2) elements. This makes sense since a larger number of

multipath components with lower correlation is included in the bin as the bin is widened.

• Although significant multipath exists in the power-delay profiles, signal components in

any delay bin can be highly correlated across the antenna elements.

• There is no obvious trend of monotonically increasing or decreasing values of correlation

coefficient versus delay. Bins of signal components with high correlation coefficients

can immediately follow or precede bins of signal components with low correlation

coefficients.

• Additive noise must be considered when comparing correlation coefficients for signal

component magnitudes. When correlation coefficients are low, additive noise may have

caused highly correlated, weak signal components to appear uncorrelated. However,

when signal components appear highly correlated because of large correlation

coefficients, it can be reasoned that these components were impacted very little by noise

and that these components in actuality were highly correlated. This of course relies upon

the noise of the receiver channels being uncorrelated among the channels, which is a

reasonable assumption since four independent receiver chains were used. The

consequence of this observation is that highly correlated signal component magnitudes

can be known to be highly correlated, but signal component strength relative to noise

level must be considered before deeming signal components uncorrelated because of low

correlation coefficients. The effect of noise on the results can be reduced by using a

higher noise threshold when processing the measurements, but this results in fewer

multipath components per power-delay profile in the sample set.

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5.3 Dense Scatterer Measurement Campaign

Measurements were performed with a ground-level transmitter and a ground-level receiver in an

environment with numerous scatterers to emulate channels experienced micro-cellular, LAN, and

ad-hoc networks operated in outdoor, densely obstructed environments. These channels are

appropriate for being modeled by the two-dimensional elliptical geometric channel models

(GBSBE and elliptical sub-regions models). Processed measurements are used to evaluate these

models in Chapter 7.

5.3.1 Measurement Overview

Wideband measurements were performed on the Virginia Tech campus in an plaza densely

populated by outdoor structures. Figure 5-7 shows a map of the plaza, which is bordered by four

buildings of stone construction reaching heights of two to four stories. Figure 5-8 shows a photo

of the measurement environment. The obstructions within the plaza consist of vestibules and

skylights constructed of concrete, metal, and glass. Pedestrian traffic in the area was very low

during measurements.

Two receiver locations and ten transmitter locations were used. The locations were chosen such

that six sets of non-line-of-sight (NLOS) and four sets of line-of-sight (LOS) measurements

could be performed. For NLOS measurements, the path between the transmitter and receiver

was blocked by multiple obstructions. For LOS measurements, the transmitter antenna was in

view of each receiver antenna element. The receiver antenna was a four-element, linear array of

vertical monopoles with half-wavelength spacing. The transmitter antenna was an end-fed

dipole oriented vertically throughout the measurements. Transmitter-receiver separation for each

location is shown in Table 5-14.

Measurements were performed with the receiver array was held stationary. While the receiver

was logging signal data, the transmitter antenna was moved randomly throughout an extent of

approximately five wavelengths around the defined transmitter location. This movement enabled

recording of small-scale fading of multipath at the receiver while excluding large scale

attenuation effects. A sample measured power-delay profile is shown in Figure 5-9. The profile

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shows relative multipath signal strength versus relative propagation delay. This profile was

measured for the NLOS1 transmitter location and shows the typical multipath measurements

taken at the site.

BU

RR

US

S H

ALL

BURKE JOHNSTON STUDENT CENTER

TXTX

NLOS1 NLOS4

NLOS1-7RX

OBSTRUCTED PATH FO

R NLOS1 M

EASUREMENT

TX TX

NLOS2 NLOS3

TXNLOS5

TX

NLOS6

LOS1-4 RX

TX

LOS1

TX

LOS2

TX

LOS3

TX

LOS4

BU

RR

US

S H

ALL

BURKE JOHNSTON STUDENT CENTER

TXTX

NLOS1 NLOS4

NLOS1-7RX

OBSTRUCTED PATH FO

R NLOS1 M

EASUREMENT

TX TX

NLOS2 NLOS3

TXNLOS5

TX

NLOS6

LOS1-4 RX

TX

LOS1

TX

LOS2

TX

LOS3

TX

LOS4

Figure 5-7. Map of the plaza where measurements were performed.

Figure 5-8. Photo of measurement site with transmitter in the foreground at the LOS1 location.

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Table 5-14. Transmitter-receiver separation for each transmitter location.

Location T-R Separation

NLOS1 205 feet 62.5 m

NLOS2 193 feet 58.8 m

NLOS3 190 feet 57.9 m

NLOS4 195 feet 59.4 m

NLOS5 165 feet 50.3 m

NLOS6 135 feet 41.1 m

LOS1 190 feet 57.9 m

LOS2 145 feet 44.2 m

LOS3 110 feet 33.5 m

LOS4 75 feet 22.9 m

-0.2 0 0.2 0.4 0.6 0.8 1-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5Power Delay Profile - Magnitude

Mul

tipat

h S

tren

gth

(dB

)

Delay (us)

Figure 5-9. Sample power-delay profile from dense scatterer measurement site (NLOS1).

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Table 5-15 shows a link budget used for measurement planning purposes. All locations actually

used for measurements fall within the 300 m range assumed in the link budget calculations.

However, as shown later, the path loss exponent computed for the actual path loss experienced

by multipath signal components was much higher than the path loss exponent used for the link

budget.

Table 5-15. Link budget for terrestrial measurements on the VT campus.

Path Loss DataRange m 300Freq Hz 2.05E+09PL exp - 3Ref dist m 10

Ref PL dB 58.7Path Loss dB 102.99

System Gains and LossesTx Power dBm 27Tx Ant Gain dB 0Tx Ant Gain dB 0.0Total Losses dB 0.0Rx Power dBm -76.0Narrowband Received Power MarginRx noise floor dBm -114.0Margin dB 38.0

VT Campus Site

Over 7,500 power-delay profiles were measured and processed to produce discrete channel

impulse response estimates (magnitude, delay, and phase of resolvable multipath components)

and characterization results.

5.3.2 Multipath RMS Delay Spread

RMS delay spread was calculated for each power-delay profile on each channel for every NLOS

location. Table 5-16 provides the mean, standard deviation, minimum, and maximum RMS

delay spreads divided among channels and locations. Statistics for all channels combined are

also provided for each location. Figure 5-10 through Figure 5-15 show complementary

cumulative distribution functions (CCDF) for all NLOS locations. Results for each channel are

shown on each plot.

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Table 5-16. RMS delay spread results for NLOS locations for the dense scatterer measurement campaign.

RMS Delay Spread (ns) Location Channel Mean Std. Dev. Minimum Maximum

NLOS1 1 67.4 10.2 40.2 99.5 2 68.6 9.12 47.0 108 3 70.7 9.78 48.5 97.9 4 63.3 9.67 44.2 94.1 All 67.5 10.1 40.2 108 NLOS2 1 58.5 9.09 34.4 85.3 2 61.7 10.0 34.1 89.0 3 59.1 10.2 35.0 87.1 4 64.1 9.88 0.00 91.0 All 60.9 10.0 0.00 91.0 NLOS3 1 71.0 10.1 45.7 96.7 2 65.2 12.7 35.9 99.3 3 70.0 11.5 39.8 99.4 4 74.7 12.0 42.1 151.9 All 70.2 12.1 35.9 151.9 NLOS4 1 81.2 11.1 57.2 112 2 79.5 10.6 51.6 103 3 74.8 10.2 55.6 108 4 79.3 9.95 54.5 110 All 78.6 10.7 51.6 112 NLOS5 1 74.4 7.38 50.5 95.3 2 68.8 7.30 51.3 89.0 3 71.3 6.74 55.3 87.2 4 68.2 7.85 49.3 89.8 All 70.7 7.70 49.3 95.3 NLOS6 1 73.6 11.1 40.3 106 2 68.3 9.39 41.1 93.9 3 69.2 13.0 45.4 260 4 66.6 17.5 31.3 368 All 69.4 13.3 31.3 368

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0 20 40 60 80 100 1200

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babi

lity(

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elay

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RMS Delay Spread Based On Measurements

Channel 1Channel 2Channel 3Channel 4

Figure 5-10. RMS delay spread CCDF for NLOS1.

0 20 40 60 80 100 1200

0.1

0.2

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Channel 1Channel 2Channel 3Channel 4

Figure 5-11. RMS delay spread CCDF for NLOS2.

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0 20 40 60 80 100 1200

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RMS Delay Spread Based On Measurements

Channel 1Channel 2Channel 3Channel 4

Figure 5-12. RMS delay spread CCDF for NLOS3.

0 20 40 60 80 100 1200

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elay

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ead

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RMS Delay Spread Based On Measurements

Channel 1Channel 2Channel 3Channel 4

Figure 5-13. RMS delay spread CCDF for NLOS4.

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0 20 40 60 80 100 1200

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elay

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RMS Delay Spread Based On Measurements

Channel 1Channel 2Channel 3Channel 4

Figure 5-14. RMS delay spread CCDF for NLOS5.

0 20 40 60 80 100 1200

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RMS Delay Spread Based On Measurements

Channel 1Channel 2Channel 3Channel 4

Figure 5-15. RMS delay spread CCDF for NLOS6.

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Several observations were made for NLOS RMS delay spread results. Mean RMS delay spread

values remain relatively constant throughout all NLOS measurements. RMS delay spread is

typically expected to increase with increasing transmitter-receiver separation; however,

separation only varied between 135 feet and 205 feet. This consistency of RMS delay spread

suggests that the measured region is well characterized by a single RMS delay spread value (e.g.,

the mean value). Single, large RMS delay spread values occurred on a channel when the

strongest, early-arriving multipath components faded simultaneously. Fading of the dominant

components cause weaker, late-arriving components to contain a larger percentage of the

composite signal energy. RMS delay spreads as large as 368 ns were measured, over five times

the average RMS delay spread for NLOS locations.

RMS delay spread values were also computed for each power-delay profile on each channel for

every LOS location. Table 5-18 provides the mean, standard deviation, minimum, and

maximum RMS delay spreads for all channels and locations. Figure 5-16 through Figure 5-19

show CCDF plots of RMS delay spread for all LOS locations.

It was observed that RMS delay spread was smaller for LOS locations compared to NLOS

locations, a result consistent with expectations. Unobstructed LOS signal components are

typically strong compared to components with larger delays, resulting in relatively smaller RMS

delay spreads. Table 5-17 summarizes RMS delay spread for the entire site. The mean LOS

RMS delay spread was shown to be nearly half of that for NLOS locations.

Table 5-17. Summary of RMS delay spread results for dense-scatterer measurement site.

Location Mean RMS Delay Spread

NLOS locations 69.6 ns

LOS locations 36.6 ns

All dense-scatter site locations 53.1 ns

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Table 5-18. RMS delay spread results for LOS locations for the dense-scatterer measurement campaign.

RMS Delay Spread (ns) Location Channel

Mean Std. Dev. Minimum Maximum

LOS1 1 34.5 5.13 23.5 48.8

2 32.7 4.66 21.4 42.0

3 33.2 3.82 24.0 43.9

4 37.4 4.11 28.2 51.2

All 34.4 4.81 21.4 51.2

LOS2 1 36.2 6.49 22.8 54.7

2 36.7 7.07 21.6 53.8

3 39.0 7.26 23.3 63.2

4 43.5 9.96 0.00 73.3

All 38.8 8.31 0.00 73.3

LOS3 1 37.8 10.9 22.2 73.9

2 36.7 12.3 20.1 91.8

3 39.2 12.7 22.5 84.3

4 42.3 12.0 25.7 86.1

All 39.0 12.1 20.1 91.8

LOS4 1 34.6 8.7 16.9 69.9

2 32.9 8.5 17.6 65.1

3 34.7 9.4 19.2 61.9

4 34.6 8.1 19.6 56.9

All 34.2 8.7 16.9 69.9

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0 20 40 60 80 100 1200

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Channel 1Channel 2Channel 3Channel 4

Figure 5-16. RMS delay spread CCDF for LOS1.

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Channel 1Channel 2Channel 3Channel 4

Figure 5-17. RMS delay spread CCDF for LOS2.

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0 20 40 60 80 100 1200

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Channel 1Channel 2Channel 3Channel 4

Figure 5-18. RMS delay spread CCDF for LOS3.

0 20 40 60 80 100 1200

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Channel 1Channel 2Channel 3Channel 4

Figure 5-19. RMS delay spread CCDF for LOS4.

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5.3.3 Multipath Excess Delay Spread

Excess delay spread is defined to be the largest difference in delay between multipath

components that are within a particular dB level below the strongest received multipath

component. Excess delay spread gives insight into the largest excess delay associated with

strong multipath components. Excess delay spread was calculated from the measured power-

delay profiles recorded at NLOS and LOS locations. Table 5-19 and Table 5-20 give excess

delay spread values for NLOS and NLOS measurements for 10 dB, 20 dB, 25 dB, and 30 dB

levels. The means of the values of excess delay spread for NLOS and LOS groups are also

shown.

Table 5-19. Excess delay spread values for NLOS locations.

Excess Delay Spread (ns)

Level 10 dB 20 dB 25 dB 30 dB

Mean Max Mean Max Mean Max Mean Max

NLOS1 200 480 390 1300 549 1300 682 1500

NLOS2 204 447 328 697 440 811 601 1510

NLOS3 272 580 435 775 581 1250 693 1450

NLOS4 252 572 499 776 615 888 712 1380

NLOS5 243 493 380 747 503 909 637 1210

NLOS6 207 478 367 758 471 1365 620 1450

Mean 230 508 400 842 527 1087 658 1417

Table 5-20. Excess delay values for LOS locations.

Excess Delay Spread (ns)

Level 10 dB 20 dB 25 dB 30 dB

Mean Max Mean Max Mean Max Mean Max

LOS1 115 335 196 533 230 725 313 751

LOS2 131 501 233 790 300 790 408 791

LOS3 123 509 222 651 315 835 432 868

LOS4 89.1 421 162 586 263 786 390 861

Mean 115 442 203 640 277 784 386 818

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5.3.4 Distribution of Multipath Components

Distribution of multipath components over excess propagation delay is illustrated in the

following normalized histograms and tables. These results are useful for implementing and

evaluating geometric channel models based on scatterer sub-regions. Results showing average

number of signal components per channel are useful for wideband channel modeling in general.

Figure 5-20 through Figure 5-25 show normalized histograms of the number of multipath signal

components for NLOS locations. The first histogram bin begins at 0 ns excess delay, and the last

bin ends at the largest measured multipath excess delay measured for each location. Each bin

width is approximately 100 ns. The first bar (leftmost bar) in each bin represents the average

number of multipath components per profile in that bin. The following four bars in each bin

correspond to the average number of multipath components per profile for each channel. The

count of multipath components in each bin includes all detectable components above the power-

delay profile noise threshold. Figure 5-26 through Figure 5-29 show normalized histograms of

measured multipath components for LOS locations.

0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

s

All ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-20. Average number of signal components using 16 delay bins for NLOS1.

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0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

sAll ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-21. Average number of signal components using 16 delay bins for NLOS2.

0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

s

All ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-22. Average number of signal components using 16 delay bins for NLOS3.

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0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

sAll ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-23. Average number of signal components using 16 delay bins for NLOS4.

0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

s

All ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-24. Average number of signal components using 16 delay bins for NLOS5.

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0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

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sAll ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-25. Average number of signal components using 16 delay bins for NLOS6.

0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

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of c

ompo

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s

All ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-26. Average number of signal components using 16 delay bins for LOS1.

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0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

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sAll ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-27. Average number of signal components using 16 delay bins for LOS2.

0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

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of c

ompo

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s

All ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-28. Average number of signal components using 16 delay bins for LOS3.

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0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

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sAll ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-29. Average number of signal components using 16 delay bins for LOS4.

0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4NLOS Measurements - Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

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s

All Channels (1 through 4)

Figure 5-30. Average number of signal components using 16 delay bins for all NLOS measurements.

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0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4LOS Measurements - Average number of signal components per delay bin

Excess delay (ns)

Ave

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sAll Channels (1 through 4)

Figure 5-31. Average number of signal components using 16 delay bins for all LOS measurements.

Table 5-21. Average number of signal components per delay bin per profile for NLOS measurements.

Delay Range (ns) Average number of signal components per delay bin per profile

0 – 99 3.54

99 – 199 2.96

199 – 298 2.99

298 – 397 2.90

397 – 496 2.76

496 – 596 2.63

596 – 695 2.07

695 – 794 0.937

794 – 893 0.337

893 – 993 0.259

993 – 1092 0.193

1092 – 1191 0.104

1191 –1290 0.0560

1290 – 1390 0.0480

1390 – 1489 0.0407

1489 – 1588 0.00803

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Table 5-22. Average number of signal components per delay bin per profile for LOS measurements.

Delay Range (ns) Average number of signal components per delay bin per profile

0 – 97 3.59

97 – 194 2.87

194 – 292 2.67

292 – 389 2.39

389 – 487 1.21

487 – 584 1.65

584 – 681 0.430

681 – 779 0.0569

779 – 876 0.0997

876 – 973 0.0596

973 – 1070 0.0401

1070 – 1168 0.0218

1168 –1265 0.0101

1265 – 1363 0.220

1363 – 1460 0.0187

1460 – 1557 0.00312

Measurements for all NLOS locations were combined to form the histogram shown in Figure

5-30 and the results shown in Table 5-21. Figure 5-31 and Table 5-22 show the combined results

for LOS locations. Results for both NLOS and LOS locations suggest a non-uniform distribution

of measurable multipath components that must be handled by channel models. While an

appropriate channel model may still use a uniform distribution of scatterers over a region, the

resulting simulated channel impulse responses must show a decrease of significant components

with increasing delay. Compared to measured NLOS power-delay profiles, LOS power-delay

profiles have the same number of detectable multipath components in the first bin but generally

fewer components in bins representing longer delays. Given the resolution of the measurement

system and the processing technique used, approximately four components is the maximum

number of detectable multipath components in each bin.

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Table 5-23 shows the average number of measured signal components per power-delay profile

over the entire excess delay range. Results for NLOS locations, LOS locations, and the entire

dense-scatterer site are shown.

Table 5-23. Average number of signal components per power-delay profile for LOS and NLOS measurements.

Measurement Type Average number of signal components per profile

NLOS 21.8

LOS 15.3

NLOS and LOS combined 19.6

5.3.5 Strength of Multipath Components Versus Delay

The strengths of multipath components propagating along a path in a geometric channel model

can be related using the log-distance path loss model [Lib95]. In this section, a method of

computing the path loss exponent given measured power-delay profiles is derived.

Using the log-distance path loss model, the received power in dB-units (e.g., dBm or dBW) of a

signal propagating over distance d is given by

Ldd

nPPref

refr −

−= 10log10 ( 5.18 )

where Pref is a reference power measured at distance dref. The factor L is a fixed loss not

experienced during the Pref measurement, such as a reflection loss if the signal is a single-bounce

multipath component,. Distance can be replaced by absolute (not relative) propagation delay

using

Lcc

nPPref

refr −

−=

ττ

10log10 ( 5.19 )

yielding the expression for a log-time model given by

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LnPPref

refr −

−=

ττ

10log10 . ( 5.20 )

This expression is equivalently expressed as

( ) ( ) LnnPP refrefr −+−= ττ 1010 log10log10 . ( 5.21 )

Let 1rP and 2rP be the power of multipath components arriving at a receiver with absolute

propagation delays 1τ and 2τ , respectively, where 1> ττ 2 . The power of each component is

given by

( ) ( ) LnnPP refrefr −+−= 1 ττ 10101 log10log10 ( 5.22 )

and

( ) ( ) LnnPP refrefr −+−= ττ 102102 log10log10 . ( 5.23 )

The difference in power in dB is given by

( ) ( )11021012 log10log10 ττ nnPP rr +−=− ( 5.24 )

simplifying to

( ) ( )( )11021012 log10log10 ττ nnPP rr −−=− ( 5.25 )

and

( ) ( )( )11021012 loglog10 ττ −−=− nPP rr . ( 5.26 )

The ratio of power differences (in dB) to log-delay differences is given by

( ) ( ) nPP rr 10loglog 110210

12 −=−−

ττ ( 5.27 )

The path loss exponent can be isolated in the equation by expressing the relationship as

( ) ( )

−−

−=110210

12

loglog101

ττrr PP

n . ( 5.28 )

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As shown in Figure 5-32, the expression in parentheses is actually the slope of the line

connecting the components on a power (dB) versus ( )τ10log plot.

1τ 2τ

2rP

1rP

Log10(Absolute Propagation Delay [sec])

Rel

ativ

e P

ower

[dB

] ( ) ( )110210

12

loglog ττ −−

== rr PPmslope

1τ 2τ

2rP

1rP

Log10(Absolute Propagation Delay [sec])

Rel

ativ

e P

ower

[dB

] ( ) ( )110210

12

loglog ττ −−

== rr PPmslope

Figure 5-32. Relationship between two multipath components arriving with different delays with all other factors held constant.

This slope, defined as m, is given explicitly by

( ) ( )110210

12

loglog ττ −−

= rr PPm . ( 5.29 )

Therefore, in the ideal case, the path loss exponent n can be related to the slope m of the power

(dB) versus ( )τ10log using the equation

mn101

−= . ( 5.30 )

Since a constant dB value can be added to both multipath components without affecting the

slope, the power axis of the plot can be relative power units (e.g., dB) rather than absolute power

units (e.g., dBm or dBW).

The power versus log-delay line must also be characterized by an intercept point in addition to a

slope. A convenient intercept point to use is the value of the line where ( ) 0log10 =τ . If units of

seconds are used, then the intercept point occurs at 1-second (where ( ) 0log10 =τ ). The value B

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is defined to be the power value at the 1-second intercept. Using this definition, the equation of

the power versus log-delay line is given by

( ) ( ) BmP += ττ 10log . ( 5.31 )

In actual propagation environments, factors such as shadowing, reflection loss differences, and

fading of resolvable components will cause multipath component strengths to deviate from the

theoretical power versus log-delay line. Each factor may impose its own statistical distribution

on signal strength. For example, shadowing may follow a log-normal distribution, and fading

may follow a Rayleigh or Rician distribution. Here, the composite deviation is modeled by a

zero-mean, log-normal random variable σG with variance 2Pσ (or standard deviation Pσ ).

Assuming this distribution, the power (in dB-units) of measured multipath components is given

by

( ) ( ) σττ GBmP ++= 10log . ( 5.32 )

For each location, the slope m and intercept B of the best-fit line (in the least-squares sense)

through signal component powers of each power-delay profile were computed. The standard

deviation Pσ of the component strengths about the corresponding line values was also

computed. Figure 5-33 through Figure 5-44 show three plots for each location NLOS1 through

NLOS6. The first plot in each set shows a scatter plot of magnitudes of all of the detected

multipath components and the best-fit line on a power versus log-delay plot. The second plot

shows a histogram of the deviation of multipath component power from the best-fit line. The

third plot shows a normalized histogram overlaid on a theoretical Gaussian probability density

function, where the zero-mean Gaussian PDF was calculated using the variance computed from

the corresponding measurements of deviation from the best-fit line.

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-30 -20 -10 0 10 20 300

100

200

300

400

500

600

700Histogram of differences between measured multipath strength and best-fit line

Multipath strength difference (dB)

Occ

uren

ces

(a) (b)

Figure 5-33. NLOS1 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

-30 -20 -10 0 10 20 300

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09PDF of differences between measured multipath strength and best-fit line

Multipath strength difference (dB)

PD

F

MeasuredGaussian

Figure 5-34. NLOS1: PDF created using data points and corresponding theoretical Gaussian distribution.

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100

200

300

400

500

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Occ

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(a) (b)

Figure 5-35. NLOS2 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

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0.01

0.02

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0.04

0.05

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PD

F

MeasuredGaussian

Figure 5-36. NLOS2: PDF created using data points and corresponding theoretical Gaussian distribution.

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100

200

300

400

500

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Occ

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(a) (b)

Figure 5-37. NLOS3 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

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0.01

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0.04

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0.07

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PD

F

MeasuredGaussian

Figure 5-38. NLOS3: PDF created using data points and corresponding theoretical Gaussian distribution.

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100

200

300

400

500

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Occ

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(a) (b)

Figure 5-39. NLOS4 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

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0.01

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PD

F

MeasuredGaussian

Figure 5-40. NLOS4: PDF created using data points and corresponding theoretical Gaussian distribution.

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500

600

700

800Histogram of differences between measured multipath strength and best-fit line

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Occ

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Figure 5-41. NLOS5 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

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0.1

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PD

F

MeasuredGaussian

Figure 5-42. NLOS5: PDF created using data points and corresponding theoretical Gaussian distribution.

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500

1000

1500

2000

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Occ

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(a) (b)

Figure 5-43. NLOS6 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

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F

MeasuredGaussian

Figure 5-44. NLOS6: PDF created using data points and corresponding theoretical Gaussian distribution.

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Normalized histogram results for all NLOS measurements visually show a similarity to the

associated Gaussian PDFs. The NLOS measurement location where the largest number of

power-delay profiles were logged, NLOS6, shows the best fit to the Gaussian PDF. Scatter plots

for NLOS1 through NLOS4 show a nonlinear trend of signal component magnitude that deviates

from the best-fit lines for early delays. This trend may be caused by non-uniform distribution of

scatterers or dissimilar distributions of factors such as reflection coefficients among scatterers.

NLOS5 and NLOS6 show a more linear trend of multipath component power versus log-delay.

Table 5-24 shows path loss exponent, standard deviation, and 1-second intercept points

calculated from the measured multipath components at NLOS locations. The path loss

exponents computed from the multipath strengths are large compared to path loss exponents

expected for narrowband measurements in the same environment. A fundamental difference is

that traditional path loss exponents are based on local averages of composite signals comprising

many multipath components. For the case here, however, magnitude measurements at a

particular delay on the plot correspond to a single or possibly small number of multipath

components, which is a different physical scenario.

Table 5-24. Path loss exponent, standard deviation of multipath strength about best-fit line, and intercept of best-fit line for NLOS measurements.

Location Path Loss Exponent

n

Standard deviation

about best-fit line

Pσ (dB)

1-second τ intercept

point B (dB)

NLOS1 5.10 4.72 -341

NLOS2 5.22 5.42 -350

NLOS3 4.79 5.46 -320

NLOS4 4.30 5.46 -287

NLOS5 5.01 4.20 -337

NLOS6 4.55 4.41 -309

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Figure 5-45 through Figure 5-52 show the scatter plots, histograms, and probability density

functions for the LOS measurements. The scatter plots show dense areas of signal components

at discrete times, suggesting that a few multipath components dominated the power delay

profiles throughout the measurements at each location. The LOS histograms follow the Gaussian

distribution less closely than those for the NLOS measurements, but in general the assumption of

a Gaussian distribution still appears valid.

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50

100

150

200

250

300

350Histogram of differences between measured multipath strength and best-fit line

Multipath strength difference (dB)

Occ

uren

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(a) (b)

Figure 5-45. LOS1 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

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PD

F

MeasuredGaussian

Figure 5-46. LOS1: PDF created using data points and corresponding theoretical Gaussian distribution.

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50

100

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250

300

350

400Histogram of differences between measured multipath strength and best-fit line

Multipath strength difference (dB)

Occ

uren

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(a) (b)

Figure 5-47. LOS2 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

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PD

F

MeasuredGaussian

Figure 5-48. LOS2: PDF created using data points and corresponding theoretical Gaussian distribution.

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Occ

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(a) (b)

Figure 5-49. LOS3 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

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0.01

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PD

F

MeasuredGaussian

Figure 5-50. LOS3: PDF created using data points and corresponding theoretical Gaussian distribution.

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400

450

500Histogram of differences between measured multipath strength and best-fit line

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Occ

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(a) (b)

Figure 5-51. LOS4 multipath strength: (a) Multipath strength versus log of propagation delay for measured data and best-fit line. (b) Histogram of difference between data points and best-fit line values.

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PD

F

MeasuredGaussian

Figure 5-52. LOS4: PDF created using data points and corresponding theoretical Gaussian distribution.

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The best-fit line for each location was computed by removing the first-arriving component,

which was assumed to be the LOS component. In order to relate the strength of the LOS

component to the strength of the later-arriving components (for LOS locations), the power of the

LOS component relative to the value of the best-fit line at the LOS delay was calculated. This

parameter can be used in modeling LOS channels based on this measurement data.

Table 5-25 shows the path loss exponent, standard deviation of measured multipath strength

about the best-fit line, 1-second intercept point for the best-fit line, and average strength (in dB)

of the LOS component above the best-fit line for the LOS measurement data.

Table 5-25. Path loss exponent, standard deviation of multipath strength about best-fit line, intercept of best-fit line, and LOS strength above best-fit line for LOS measurements.

Location Path Loss

Exponent n

Standard

deviation about

best-fit line Pσ

(dB)

1-second τ

intercept point

B (dB)

LOS component

dB above best-

fit line (dB)

LOS1 5.16 5.65 -357 10.9

LOS2 4.44 5.29 -313 8.63

LOS3 3.52 5.07 -255 12.5

LOS4 3.27 4.95 -242 9.95

Table 5-26 summarizes the results for all NLOS measurements and LOS measurements,

individually and combined. The results show that LOS measurements exhibited a slightly larger

path loss exponent and standard deviation compared to NLOS measurements. However, because

the values are relatively close, it appears that a single path loss exponent and standard deviation

can be used to characterize the site for both NLOS and LOS propagation, while simulations of

LOS will include an additional signal component, namely the LOS components 10.5 dB higher

than the best-fit line for the other multipath components.

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Table 5-26. Summary of multipath strength results for all measurements at the dense-scatterer site.

Location Path Loss Exponent

n

Standard deviation

about best-fit line

Pσ (dB)

LOS component dB

above best-fit line

(dB)

All NLOS 4.83 4.95 N/A

All LOS 4.10 5.24 10.5

NLOS and LOS 4.54 5.06 N/A

5.3.6 Multipath Strength Correlation Coefficients Versus Delay

The measurements for NLOS6, which had the greatest number of measured power-delay profiles

compared to other locations within the site, were processed to produce the correlation

coefficients using the technique described in section 5.2.4 for 4, 8, and 16 propagation delay

bins. Results are shown in Table 5-27 through Table 5-29. Although the results presented here

seem to suggest decreasing correlation coefficients with increasing delay, measurement results in

section 5.2.4 show that high correlation coefficients can exist in any delay bin, and there is not

necessarily a consistent trend of monotonically increasing or decreasing values of correlation

coefficients versus delay.

Differences in correlation coefficients among antenna pairs may also be affected by mutual

coupling of antenna elements causing a dissimilar pattern of antenna elements across the array,

in effect causing antenna pattern diversity. The measured correlation coefficients can be used to

simulate vector channels for antenna arrays used in wideband systems.

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Table 5-27. NLOS Measurement Results (4 propagation delay bins).

Correlation Coefficients Delay

Bin

No.

Delay

Range (ns) 12ρ 13ρ 14ρ 23ρ 24ρ 34ρ

Number of

Signal

Components*

1 0-210 0.62942 0.62743 0.63907 0.63846 0.64184 0.64700 1657

2 210-421 0.47263 0.46657 0.52647 0.44548 0.45981 0.45714 2290

3 421-632 0.39867 0.36148 0.35690 0.36105 0.40892 0.29867 1136

4 632-843 0.14801 0.17851 0.12146 0.23415 0.18314 0.07175 152

Element Spacing λ/2 λ 3λ/2 λ/2 λ λ/2

Table 5-28. NLOS Measurement Results (8 propagation delay bins).

Correlation Coefficients Delay

Bin

No.

Delay

Range

(ns) 12ρ 13ρ 14ρ 23ρ 24ρ 34ρ

Number of

Components

Signal*

1 0-105 0.73226 0.75130 0.71784 0.75499 0.76941 0.74555 492

2 105-210 0.52076 0.49964 0.55326 0.49363 0.48532 0.52334 1165

3 210-316 0.41198 0.36025 0.46810 0.40410 0.42581 0.41246 1142

4 316-421 0.32740 0.33451 0.33983 0.29788 0.29004 0.26510 1148

5 421-526 0.37857 0.34494 0.30520 0.41893 0.42646 0.32013 742

6 526-632 0.15214 0.17750 0.17262 0.02548 0.09292 0.00701 394

7 632-737 0.10679 0.15660 0.09025 0.20518 0.14112 0.05062 146

8 737-843 0.66539 0.12377 0.80588 -0.06541 0.65434 -0.09817 6

Element Spacing λ/2 λ 3λ/2 λ/2 λ λ/2

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Table 5-29. NLOS Measurement Results (16 propagation delay bins).

Correlation Coefficients Delay

Bin

No.

Delay

Range

(ns) 12ρ 13ρ 14ρ 23ρ 24ρ 34ρ

Number of

Components*

1 0-52 0.73780 0.80110 0.79264 0.75896 0.75246 0.83875 105

2 52-105 0.73068 0.74236 0.69963 0.75611 0.77685 0.72228 387

3 105-158 0.48077 0.43925 0.53715 0.42056 0.46994 0.47399 576

4 158-210 0.41665 0.40293 0.45802 0.46148 0.40721 0.48109 589

5 210-263 0.51223 0.39676 0.49171 0.43342 0.47014 0.43788 558

6 263-316 0.20517 0.21916 0.37548 0.25516 0.26969 0.29113 584

7 316-368 0.23466 0.28203 0.23221 0.22723 0.20330 0.17199 617

8 368-421 0.39035 0.30464 0.39947 0.32989 0.35294 0.30345 531

9 421-474 0.35500 0.34197 0.24475 0.43696 0.42898 0.32293 445

10 474-526 0.21663 0.12871 0.23244 0.16183 0.22856 0.09367 297

11 526-579 0.17773 0.24197 0.24641 0.01270 0.08605 0.05355 228

12 579-632 0.10884 0.10486 0.06676 0.05029 0.10112 -0.05999 166

13 632-684 0.04007 0.14786 0.12432 0.23377 0.08294 0.04031 108

14 684-737 0.24986 0.08046 -0.10462 -0.04656 0.16377 -0.01461 38

15 737-790 0.61112 0.55191 0.82011 0.20992 0.6381 0.73777 5

16 790-843 ** ** ** ** ** ** 1

Element Spacing λ/2 λ 3λ/2 λ/2 λ λ/2

* Signal components detected within 1544 power-delay profiles.

** Only one component in delay bin; correlation coefficient undefined.

5.4 Air-to-Ground Measurement Campaign

An air-to-ground measurement campaign was performed to characterize the wideband air-to-

ground radio channel, to provide parameter input for the geometric air-to-ground channel model,

and to provide measurement data for evaluation of the geometric air-to-ground channel model.

Measurement results presented in this section apply to simulation and analysis of air-to-ground

communications for applications such as UAVs and airborne network nodes.

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Table 5-30. Link budget calculations for each of the four elevation angles measured.

Measurement Pattern 1 Measurement Pattern 2 Locations Data Locations Data Input Param Output Param Units Value Input Param Output Param Units Value Range nm 1.8 Range nm 0.9 Altitude (MSL) ft 3,590 Altitude (MSL) ft 3,620 Ground Elev ft 2,150 Ground Elev ft 2,150 Altitude (AGL) ft 1,440 Altitude (AGL) ft 1,470 Range m 3,333.6 Range m 1,666.8 Altitude m 438.9 Altitude m 448.1 T-R m 3,362.4 T-R m 1,726.0 Elev. Angle deg 7.5 Elev. Angle deg 15.0 Path Loss Data Path Loss Data Freq Hz 2.05E+09 Freq Hz 2.05E+09 PL exp - 2 PL exp - 2 Ref dist m 1 Ref dist m 1 Ref PL dB 38.7 Ref PL dB 38.7 Path Loss dB 109.21 Path Loss dB 103.42 System Gains and Losses System Gains and Losses Tx Power dBm 27 Tx Power dBm 27 Rx Ant Gain dB 0 Rx Ant Gain dB 0 Tx Ant Pattern dB 2.04 Tx Ant Pattern dB 1.71 Total Losses dB 0 Total Losses dB 0 Rx Power dBm -80.2 Rx Power dBm -74.7

Measurement Pattern 3 Measurement Pattern 4 Locations Data Locations Data Input Param Output Param Units Value Input Param Output Param Units Value Range nm 0.9 Range nm 0.9 Altitude (MSL) ft 4,420 Altitude (MSL) ft 5,310 Ground Elev ft 2,150 Ground Elev ft 2,150 Altitude (AGL) ft 2,270 Altitude (AGL) ft 3,160 Range m 1,666.8 Range m 1,666.8 Altitude m 691.9 Altitude m 963.2 T-R m 1,804.7 T-R m 1,925.1 Elev. Angle deg 22.5 Elev. Angle deg 30.0 Path Loss Data Path Loss Data Freq Hz 2.05E+09 Freq Hz 2.05E+09 PL exp - 2 PL exp - 2 Ref dist m 1 Ref dist m 1 Ref PL dB 38.7 Ref PL dB 38.7 Path Loss dB 103.80 Path Loss dB 104.37 System Gains and Losses System Gains and Losses Tx Power dBm 27 Tx Power dBm 27 Rx Ant Gain dB 0 Rx Ant Gain dB 0 Tx Ant Pattern dB 1.16 Tx Ant Pattern dB 0.38 Total Losses dB 0 Total Losses dB 0 Rx Power dBm -75.6 Rx Power dBm -77.0

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5.4.1 Measurement Overview

Measurements were performed for radio channels between the airspace over Blacksburg,

Virginia and a ground location on the Virginia Tech campus. Four different elevation angles

from the receiver were measured, where the elevation angle is defined to be the angle between

the horizon and the aircraft as viewed from the receiver location.

Tx AntennaTx Antenna

Figure 5-53. Location of the transmitter antenna under aircraft fuselage and wing.

Figure 5-54. Ground location of the receiver array for the air-to-ground measurements.

A link budget was used to provide rough estimates of received power and to plan the possible

elevation angles and flight paths. The link budgets for the four elevation angles are shown in

Table 5-30. Constant altitude, circular flight paths around the receiver were chosen such that the

received power of a line-of-sight signal component was equal to or greater than approximately –

80 dBm. A flight altitude above mean sea level (MSL) was chosen based on the altitude above

ground level (AGL) and ground range required for the selected elevation angles.

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Figure 5-53 illustrates the location of the transmitter antenna on the aircraft. A vertically

polarized, monopole antenna was temporarily placed under the fuselage near the right wing for

the measurements, where minimal obstructions and a large ground plane were present. Figure

5-54 illustrates the site of the receiver array among buildings on the Virginia Tech campus.

Buildings up to four stories and automobiles surrounded the receiver location. A GPS waypoint

was recorded at the receiver location, and the aircraft was flown at constant radii around the GPS

waypoint during measurements.

5.4.2 Multipath RMS Delay Spread

RMS delay spread was calculated for all power-delay profiles. RMS delay spread results divided

among channels and elevation angles are shown in Table 5-31. Figure 5-55, Figure 5-56, Figure

5-57, and Figure 5-58 show sample power-delay profiles measured for each elevation angle.

Table 5-31. RMS delay spread results for the air-to-ground measurement campaign.

RMS Delay Spread (ns) Elevation Angle (deg)

Channel Mean Std. Dev. Minimum Maximum

7.5 1 104 90.2 0 485 2 102 83.5 0 498 3 93.2 80.4 0 545 4 92.8 73.5 0 452 All 98.1 82.2 0 545 15 1 55.7 41.8 0 315 2 54.0 36.9 0 288 3 54.9 38.5 4.45 356 4 54.8 44.9 2.51 560 All 54.9 40.6 0 560 22.5 1 24.8 18.9 3.02 216 2 23.8 14.1 3.50 141 3 23.3 15.5 3.50 154 4 25.1 18.0 2.75 206 All 24.3 16.7 2.75 216 30 1 18.7 10.3 2.00 57.4 2 18.2 9.42 2.83 64.9 3 17.1 9.28 1.10 53.8 4 19.4 10.4 3.44 75.0 All 18.3 9.89 1.10 75.0

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-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5Power Delay Profile - Magnitude

Mul

tipat

h S

tren

gth

(dB

)

Delay (us)

Figure 5-55. Sample power-delay profile for 7.5 degree elevation angle.

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5Power Delay Profile - Magnitude

Mul

tipat

h S

tren

gth

(dB

)

Delay (us)

Figure 5-56. Sample power-delay profile for 15 degree elevation angle.

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-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5Power Delay Profile - Magnitude

Mul

tipat

h S

tren

gth

(dB

)

Delay (us)

Figure 5-57. Sample power-delay profile for 22.5 degree elevation angle.

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5Power Delay Profile - Magnitude

Mul

tipat

h S

tren

gth

(dB

)

Delay (us)

Figure 5-58. Sample power-delay profile for 30 degree elevation angle.

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0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RMS Delay Spread (ns)

Pro

babi

lity(

RM

S D

elay

Spr

ead

> A

bsci

ssa

)

RMS Delay Spread Based On Measurements

Channel 1Channel 2Channel 3Channel 4

22.5 deg

15 deg

7.5 deg

30 deg

Figure 5-59. RMS delay spread CCDF for all measured elevation angles.

Figure 5-59 shows CCDF plots of RMS delay spread for elevation angles of 7.5, 15, 22.5, and 30

degrees on a single figure. The measurements show a trend of increasing RMS delay spread as

elevation angle is decreased from 30 degrees to 7.5 degrees. This trend is corroborated by past

air-to-ground measurement results presented in section 5.1.2. RMS delay spreads in excess of

500 ns were observed for the 7.5 and 15 degree elevation angles.

5.4.3 Multipath Excess Delay Spread

Excess delay spread was calculated for each elevation angle using all measured power-delay

profiles. Table 5-32 shows mean and maximum excess delay spread values for 10 dB, 20 dB, 25

dB, and 30 dB levels. The excess delay spread results show that mean excess delay spread

increases with decreasing elevation angle, a trend similar to that of RMS delay spread.

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Table 5-32. Excess delay spread values for air-to-ground measurements.

Excess Delay Spread (ns)

Level 10 dB 20 dB 25 dB 30 dB

Mean Max Mean Max Mean Max Mean Max

7.5 deg 169 1380 431 1490 613 1550 703 1570

15 deg 104 1300 250 1480 407 1480 595 1590

22.5 deg 90.0 1031 127 1294 199 1294 352 1407

30 deg 89.0 256 108 471 157 1290 284 1340

Mean 113 992 229 1180 344 1400 484 1480

5.4.4 Distribution of Multipath Components

The distribution of multipath components over excess propagation delay was examined in a

manner similar to that of section 5.3.4. The histograms in Figure 5-60 through Figure 5-63 show

the average number of signal components per delay bin per profile for each channel and for all

channels combined. One normalized histogram is plotted per elevation angle measured.

Figure 5-64 shows normalized histograms for each elevation angle and combined elevation

angles on the same plot. The largest measured multipath excess delay was 1556 ns. The excess

delay range was divided into 16 bins, resulting in bin widths of approximately 97 ns. Figure

5-65 and Table 5-33 show results for all elevation angles combined. It is interesting to note that

the number of multipath components for a particular excess delay bin does not vary greatly as

elevation angle is changed.

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0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

sAll ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-60. Average number of signal components using 16 delay bins for 7.5 degree elevation angle.

0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

s

All ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-61. Average number of signal components using 16 delay bins for 15 degree elevation angle.

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0 500 1000 15000

0.5

1

1.5

2

2.5

3

3.5Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

sAll ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-62. Average number of signal components using 16 delay bins for 22.5 degree elevation angle.

0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

s

All ChannelsChannel 1 Channel 2 Channel 3 Channel 4

Figure 5-63. Average number of signal components using 16 delay bins for 30 degree elevation angle.

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Excess delay (ns)

Ave

rage

Num

ber

of C

ompo

nent

s

Excess delay (ns)

Ave

rage

Num

ber

of C

ompo

nent

s

Figure 5-64. Average number of signal components using 16 delay bins for each elevation angle.

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0 200 400 600 800 1000 1200 1400 16000

0.5

1

1.5

2

2.5

3

3.5

4Air-to-Ground Measurements - Average number of signal components per delay bin

Excess delay (ns)

Ave

rage

num

ber

of c

ompo

nent

s

All Channels (1 through 4)

Figure 5-65. Average number of signal components using 16 delay bins for all air-to-ground measurements.

Table 5-33. Average number of signal components per delay bin per profile for air-to-ground measurements.

Delay Range (ns) Average number of signal components per delay bin per profile

0 – 97 2.98

97 – 195 1.53

195 – 292 1.19

292 – 389 0.620

389 – 486 0.404

486 – 584 0.253

584 – 681 0.163

681 – 778 0.156

778 – 875 0.167

875 – 973 0.180

973 – 1070 0.107

1070 – 1167 0.0664

1167 –1264 0.0389

1264 – 1362 0.0228

1362 – 1459 0.00265

1459 – 1556 0.00139

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Table 5-34. Average number of signal components per power-delay profile for each elevation angle measured during air-to-ground measurements.

Measurement Type Average number of signal components per profile

7.5 7.54

15 8.61

22.5 7.79

30 7.74

All angles combined 7.88

Table 5-34 summarizes the results for each elevation angle. On average, each power delay

profiles contained 7.88 measurable multipath components. Although measurement results in

section 5.4.2 showed that RMS delay spread generally increases with decreasing elevation angle,

these results show that the number of measured multipath components tends to remain constant

with elevation angle. Since the number of multipath components in each delay bin also tend to

remain constant as elevation angle changes, this suggests that the strengths of multipath

components with long delays become larger as elevation angle decreases.

5.5 Summary

In this chapter, past measurement results and methods have been reviewed, and results and

methods of new measurements have been reported. Measurement campaigns at Virginia Tech

have produced characterizations of terrestrial and air-to-ground communication environments.

RMS delay spread and excess delay spread statistics were reported. The largest RMS delay

spreads (over 1 µ s) were observed for the rooftop measurement campaign. Mean RMS delay

spread for the rooftop measurements was approximately 120 ns. The dense scatterer campaign

showed mean RMS delay spreads of approximately 70 ns for NLOS channels and 37 ns for LOS

channels. Mean excess delay spreads for the 20 dB level ranged from approximately 160 ns to

500 ns for the dense scatterer site. Mean RMS delay spreads for air-to-ground channels ranged

from 18 ns to 98 ns, and RMS delay spread was shown to increase as elevation angle decreased

from 30 degrees to 7.5 degrees. Mean excess delay spread for the 20 dB level for air-to-ground

measurements ranged from 108 ns at a 30 degree elevation angle to 431 ns at a 7.5 degree

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elevation angle. The maximum excess delay at the 20 dB level was 1490 ns at a 7.5 degree

elevation angle.

Distributions of multipath components across excess delay were reported for each campaign.

The average number of measurable multipath components per power-delay profile for the

rooftop measurements and the dense scatterer measurements was approximately 19, nearly equal

for both sites, while RMS delay spread for the rooftop measurements was larger. Fewer

multipath components were found in the air-to-ground power delay profiles, where

approximately 8 existed on average. For air-to-ground channels, the number of components per

power-delay profile was not found to be dependent upon elevation angle.

Correlation coefficients for fading of multipath components across an antenna array were

computed for the rooftop measurements and the dense-scatterer measurements. LOS channels

showed a high correlation in the first delay bins due to a dominant multipath component.

Measurements showed that high correlation could also exist for bins of larger delay.

For the dense scatterer measurements, where measurement data for a number of locations within

one environment was recorded, results on multipath strength versus propagation delay were

produced. A path loss exponent was computed for each location by determining the best-fit line

through measured multipath strengths on a power (dB) versus log-delay axis. The deviation of

measured powers from the best-fit line was shown to be approximately Gaussian. The standard

deviation of the measured distribution about the best-fit line was reported for each location. For

LOS measurements, the mean relative strength of the LOS component compared to the best-fit

line of delayed components was reported.

The results of this chapter are useful for analysis and simulation of radio channels. The results

can be used as input to channel models and provide a basis for evaluation of channel models.

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Chapter 6 Wideband Vector Channel Simulation

This chapter describes a channel simulator that was developed based on channel model research

and propagation measurements presented in this dissertation. This simulator was used to

implement three of the geometric channel models discussed in Chapter 4. An understanding of

the simulator is important for interpreting the channel model evaluation results described in

Chapter 7. The objective of the channel simulator is to provide a means of producing channel

impulse responses for wireless system simulation. The three channel models simulated are the

geometrically based single-bounce elliptical (GBSBE) model, the elliptical sub-regions (ESR)

model, and the geometric air-to-ground ellipsoidal (GAGE) model.

Presented first is an overview of the simulator architecture. All relevant input parameters are

defined and described. Next, geometric relationships between transmitters, receivers, scatterers,

and scattering regions are described and illustrated. The methods of computing multipath

strength, delay, and direction of arrival are then described for each model. Rayleigh fading, log-

normal strength variation, and Poisson distributions for scatterer counts are all used by the

simulator to model as accurately as possible the channel behaviors observed and quantified

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during measurements. The description of the simulator provided in this chapter will aid users of

the simulation and provide guidance for development of new channel simulators.

6.1 Simulation Overview

The wideband vector channel simulator illustrated in Figure 6-1 simulates wideband vector

channels. The simulator uses results of measured signal data as input to produce channel

simulations based on geometric channel models. Channel impulse responses, which are

represented as magnitude and delays of multipath components, are produced at the output.

InitialParameter

CalculationsInpu

tP

aram

eter

s

Add LOSComponentAdd LOS

Component

Apply Log-Normal

Variation

Apply Log-Normal

Variation

Apply ArrayElementPositions

Apply ArrayElementPositions

ApplyRayleighFading

ApplyRayleighFading

ComputeGeometry

ESRESRGBSBEGBSBE

GAGEGAGE

Computations Based on Physical Paths

ComputePath

Attenuation& Delay

ComputePath

Attenuation& Delay

Produce Intermediate Plots

ProduceGeometry

Plot

Cha

nnel

Im

puls

eR

espo

nses

InitialParameter

CalculationsInpu

tP

aram

eter

s

Add LOSComponentAdd LOS

Component

Apply Log-Normal

Variation

Apply Log-Normal

Variation

Apply ArrayElementPositions

Apply ArrayElementPositions

ApplyRayleighFading

ApplyRayleighFading

ComputeGeometry

ESRESRGBSBEGBSBE

GAGEGAGE

Computations Based on Physical Paths

ComputePath

Attenuation& Delay

ComputePath

Attenuation& Delay

Produce Intermediate Plots

ProduceGeometry

Plot

Cha

nnel

Im

puls

eR

espo

nses

Figure 6-1. Block diagram of wideband vector channel simulator.

Figure 6-1 shows all of the major functional components of the channel simulator. The simulator

was programmed using MATLAB (see Appendix C for more information), and functional blocks

of the source code are divided in a manner similar to the blocks shown in the diagram. Input

parameters based on measurements and physical dimensions are used in the “Initial Parameter

Calculations” block to determine preliminary simulation parameters, such as wavelength and

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default correlation coefficient matrices, and to verify the validity of input parameters, such as

comparing the number of Poisson parameters to the number of geometric sub-regions. In the

“Compute Geometry” block, the simulator uses the model specified by the input to generate

scatterers and compute distances and angles required for the subsequent blocks. Once the model

geometry has been generated, the simulator can plot the locations of all entities and sub-regions

in two or three dimensions.

A simulated channel impulse response is produced in stages in the block labeled “Computations

Based on Physical Paths.” Each internal block uses the model geometry to produce or affect the

strength of multipath components. Details of these processes are discussed in the following

sections of this chapter. Several of the blocks can produce intermediate plots of results. This

allows the simulation to be incrementally verified and facilitates tuning of parameters to produce

accurate results.

Table 6-1 lists the input parameters of the simulator. As discussed in Chapter 4, geometric

channel models use the physical configuration of transmitters, receivers, and scatterers to model

radio channels. Physical configurations include transmitter-receiver separation, antenna array

element positions, and distances to scatterers in the environment. While geometric parameters

are the basis for the model, statistical distributions may be used to bind a model to a particular

propagation environment. For example, statistical distribution functions may be used to

determine locations and numbers of reflecting objects in the environment, and these distribution

functions may be linked to measurements performed in a particular environment. Parameters of

type “D” shown in the table are typically known or deterministic. Parameters of type “M” are

derived from measurements. Parameters marked “A” typically must be assumed because of

difficulty in measurement or because exact value for optimum simulation performance is

unknown27.

27 For example, the number of sub-regions that produces the best simulation results is not well studied. A larger number of sub-regions may produce more accurate results but greatly increases the number of measurements and amount of processing required to characterize each sub-region.

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Table 6-1. Input parameters used by the wideband vector channel model simulator.

Input Parameter Parameter Type

Description

Model type D ESR, GBSBE, or GAGE. Frequency D Center frequency of operation in Hertz. Antenna element position D Antenna (x,y) coordinates in meters. Transmitter-receiver separation

D Distance between transmitter and receiver in meters.

Elevation angle D For GAGE model only. Elevation angle (in degrees) toward airborne station as seen from ground station (horizon is 0 degrees and vertical is 90 degrees).

Log-distance path loss exponent

M Path loss exponent for propagation through ground scatterers (n=2 is free space).

Log-distance reference distance

A Reference distance from transmitter within which free-space propagation is assumed.

Reflection loss A Attenuation in dB of multipath signal experienced at each scatterer.

LOS component strength offset

M Offset (in dB) of line-of-sight component above level of multipath components compensated for delay.

Number of sub-regions A Number of elliptically bounded sub-regions within which scatterers are distributed.

Poisson parameters M Mean values of expected number of multipath components in each sub-region.

Standard deviation of log-normal strength variation

M Standard deviation (in dB) of log-normal random variable used to model variations of multipath strength.

Maximum excess delay M Largest multipath delay measured or expected. Rayleigh fading correlation coefficient matrix

M Correlation coefficients that define the correlation of Rayleigh fading of multipath components applied to each antenna element.

Plot parameters D Flags that determine graphical output of the simulation.

D = Parameter is deterministic or a selection chosen by the user. M = Parameter is a measured quantity or based on measurements. A = Parameter is typically assumed or based on assumptions used during measurements.

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6.2 Simulation Geometries

The type of geometry used, namely ESR, GBSBE, or GAGE, is specified as an input to the

simulation. Regardless of model type, the purpose of simulating the geometry is to produce

coordinates of scatterers relative to the coordinates of the transmitters and receivers. For each

scatterer location, a vector from the transmitter to the scatter and a vector from the scatterer to

receiver are calculated. The magnitudes of both vectors are used to generate mean multipath

strength and delay at the center of the receiver array. The latter vector is used to generate

direction off arrival for the receiver array.

6.2.1 Simulating the ESR Model Geometry

For the ESR model, the transmitter and receiver are located on the x-axis (y=0) and fx ±= on a

two-dimensional coordinate plane, as shown in Figure 6-2, where f is the focus distance from the

center of the ellipses that define the sub-regions. Line-of-sight propagation time is calculated

using the specified transmitter-receiver separation and is added to the specified maximum excess

delay to obtain the maximum multipath delay (absolute delay between transmitter and receiver

along the longest possible single-bounce path). The maximum excess delay is divided equally

into the input number of sub-regions. For M sub-regions, there are M+1 bounding ellipses,

where the innermost ellipse corresponds to a propagation delay equal to the line-of-sight

propagation delay. This first ellipse has a minor axis length of zero, which forms a straight line

between the transmitter and receiver and circumscribes zero area, and the outermost ellipse

corresponds to the boundary for all scatterers that cause delays less than or equal to the

maximum multipath delay. The ellipse major and minor axis parameters (a and b) for each are

calculated from the delay of each boundary as described by the equations in section 4.3.2 and

section 4.3.4.

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-30 -20 -10 0 10 20 30-25

-20

-15

-10

-5

0

5

10

15

20

25Top View of Propagation Environment

x-coordinate (m)

y-co

ordi

nate

(m

)

Figure 6-2. Geometry plot produced by the simulator for the ESR model showing a top view of transmitter (+) and receiver (o) locations, elliptical boundaries, scatterer locations, and propagation paths.

-30 -20 -10 0 10 20 30-25

-20

-15

-10

-5

0

5

10

15

20

25Top View of Propagation Environment

x-coordinate (m)

y-co

ordi

nate

(m

)

Figure 6-3. Geometry plot produced by the simulator for the GBSBE model showing a top view of transmitter (+) and receiver (o) locations, elliptical boundary, scatterer locations, and propagation paths.

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6.2.2 Simulating the GBSBE Model Geometry

The GBSBE geometry is similar to the ESR geometry except that only one region is defined as

shown in Figure 6-3. The region is bounded by an outer ellipse corresponding to the maximum

multipath delay; scatterers may fall uniformly throughout this region. The simulator uses the

ESR software routines to generate the GBSBE geometry by specifying one region for the input.

While the GBSBE model seems to be only a special case of the ESR model, the value in

evaluating the GBSBE model comes from determining the degradation in performance, if any, of

a lower complexity model.

6.2.3 Simulating the GAGE Model Geometry

The GAGE model represents three-dimensional air-to-ground channels rather than two-

dimensional terrestrial channels, and while the geometry of the GAGE model is intuitively

simple, the calculations of the model geometry are intrinsically more complex than those for the

ESR and GBSBE models. As described in section 4.5 beginning on page 101, the model

involves using three-dimensional ellipsoids to represent bounding surfaces of constant delay and

two-dimensional ellipses to represent bounding lines for ground scatterers. In addition to

transmitter-receiver separation and maximum multipath delay, the geometric calculations also

require as input an elevation angle from the ground station to the airborne station, where the

elevation angle from the ground station to the horizon is zero degrees, and the elevation angle

from the ground station straight up is 90 degrees28.

Using methods similar to those of the ESR model, ellipsoidal surfaces that bound sub-regions of

scatterers are calculated by dividing the ellipsoidal volume into ellipsoidal sub-volumes. Each

one of the ellipsoidal bounding surfaces corresponds to a constant multipath delay. The

parameters defining the bounding surfaces are used to compute the parameters of the

corresponding ground-level bounding ellipses using the equations derived in section 4.5.

Ground-level regions are thereby defined, within which ground-level scatterers are distributed

for simulation of the air-to-ground channel.

28 Note that GAGE equations use a variable ψ, which is the complement of elevation angle, so that El = 90o – ψ.

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-2000

200400

600800

10001200 -500

0

5000

200

400

600

800

1000

1200

y-coordinate (m)

Propagation Environment

x-coordinate (m)

z-co

ordi

nate

(m

)

Figure 6-4. Geometry plot produced by the simulator for the GAGE model showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and

propagation paths. Elevation angle in this case is 45 degrees.

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-400-200

0200

400-400

-200

0

200

400

0

200

400

600

800

1000

1200

1400

1600

1800

y-coordinate (m)

Propagation Environment

x-coordinate (m)

z-co

ordi

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(m

)

Figure 6-5. Geometry plot produced by the simulator for the GAGE model, showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and

propagation paths. Elevation angle in this case is 90 degrees.

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0

500

1000

1500

2000-600

-400

-200

0

200

400

600

x-coordinate (m)

y-coordinate (m)

z-co

ordi

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(m

)

Propagation Environment

Figure 6-6. Geometry plot produced by the simulator for the GAGE model, showing a diagonal view of transmitter (+) and receiver (o) locations, ground-level elliptical boundaries, scatterer locations, and

propagation paths. Elevation angle in this case is 0 degrees.

Unlike the ESR model, the receiver in the GAGE model is located at x=0 and y=0 on the x-y

plane; it is also at z=0 in the three-dimensional coordinate system. As shown in Figure 6-4, the

transmitter location falls on the y=0 plane at x and z coordinates determined by the transmitter-

receiver separation and elevation angle provided as input. The ground-level elliptical sub-

regions, whose parameters were derived from the ellipsoidal bounding surfaces, are depicted in

Figure 6-4 on the x-z plane. All bounding ellipses share a common focus at the receiver, but the

other focus of each bounding ellipse varies in position depending upon the delay represented by

that ellipse29.

Figure 6-4 shows the geometry plot produced by the simulator for an elevation angle of 45

degrees. The limits of elevation angle and the corresponding geometry plots are shown in Figure

29 There is actually one case where ellipses share both foci, which happens when the elevation angle is set to zero degrees. As elevation angle decreases to very small values, the GAGE model converges to the GBSBE (or ESR) model.

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6-5 and Figure 6-6. Figure 6-5 shows the case where the airborne station is directly overhead the

ground station at an elevation angle of 90 degrees. In this case, the ground-level boundaries

become circular. In Figure 6-6, the elevation angle is zero degrees (i.e., the airborne station is on

the ground). The simulation using the geometry in Figure 6-6 produces the same results as the

simulation for the GBSBE model (or ESR, depending whether sub-regions are defined) given the

same input parameters.

6.3 Multipath Component Distribution, Strength, and Delay

Delay for each propagation path is computed using the propagation distance of each path and the

speed of propagation in free space (3x108 m/s). Attenuations for each path are determined using

the log-distance path loss model for the specified path loss exponent and reference distance given

as input. The details are as follows.

6.3.1 Distribution of Multipath Components in Delay

Within each propagation delay range that defines a scattering region (or sub-region), the

distribution of multipath components versus delay is a function of the locations of the scatterers

that fall in each region. The number of scatterers generated in each region is based on

measurements performed in the type of environment being modeled. The mean value of the

number of multipath components measured in a particular region is used as the parameter of a

Poisson distribution. A Poisson random number generator is used to produce the number of

scatterers that are uniformly distributed throughout each region that has been characterized by

measurements. For example, if sixteen regions have been defined for an ESR model, then

sixteen measured mean values of multipath component count will be required by the channel

simulation.

Uniform distribution of scatterers in each elliptical region is performed by computing a uniform

distribution of points within a rectangle that circumscribes the ellipse and eliminating points that

fall outside of the elliptical region. Two independent random variables are used to generate the x

and y positions of each scatterer. Then, the x-versus-y equation of the ellipse is used to check the

position of the scatterer relative to the ellipse. For sub-regions consisting of an inner and outer

ellipse, points outside the outer ellipse points inside the inner ellipse eliminated from the

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generated set. Figure 6-7 illustrates a dense distribution of scatterers in the seventh (non-zero

area) elliptical region for the GAGE model. Several checks like this were performed to verify

correct distribution of scatterers for all models simulated.

0

500

1000

1500 -500

0

5000

200

400

600

800

y-coordinate (m)

Propagation Environment

x-coordinate (m)

z-co

ordi

nate

(m

)

Figure 6-7. Dense uniform distribution of scatterers in the seventh scattering region for the GAGE model.

6.3.2 Multipath Delay

Absolute propagation delay for each simulated multipath component is calculated in two stages.

In the first stage, the delay along the two legs of propagation from the transmitter to the center of

the receiver array by way of each scatterer is calculated for each scatterer30. The center of the

receiver array is defined by the encircled ‘R’ as shown in Figure 6-8(b) for the GBSBE and ESR

models, where the origin of the array element axis xe-ye is located at the focus of the elliptical

boundary. Figure 6-9(b) shows the location of the center of the receiver array for the GAGE

model, where the origin of the array element axis xe-ye is located at the origin of the x-y axis. In

the second stage of multipath delay calculation, the extra delay imposed by the offset of the array 30 Free-space propagation is assumed, and the delay in seconds is simply the distance in meters divided by 3x108 m/s.

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element from the center of the array is determined. The extra distance is calculated using the

vector from the receiver array center to the array element by computing the component of the

vector parallel to the propagation path.

It is sometimes necessary to use a measure of phase along with absolute propagation delay. The

simulation provides phase for each simulated multipath, which can be calculated using

−=

λτ

λτ

πφ absabs cc2 radians ( 6.1 )

where absτ is the absolute propagation delay and λ is the wavelength.

Transmitter

S

x

yb

a

ye

xe

ReceiverArray

Transmitter

S

x

yb

a

ye

xe

ye

xe

ReceiverArray

Additio

nal delay

due to

array ele

ment position

Incident multipath

component

ye

xeR

Antenna array

element

Additional d

elay due to

array ele

ment position

Incident multipath

component

ye

xeR

Antenna array

element

(a) (b)

Figure 6-8. Absolute propagation delay for the GBSBE and ESR models is calculated using (a) the distance from the transmitter to the center of the receiver array by way of the scatterer and (b) the distance between

parallel lines through the receiver array center and the array element drawn orthogonally to the propagation path.

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T

S

x

y

AirborneTransmitter

GroundReceiver Top View

(View down from positive z-axis)

ye

xe T

S

x

y

AirborneTransmitter

GroundReceiver Top View

(View down from positive z-axis)

ye

xe

Additional delay due to

array element position

Inciden

t multi

path

compon

entye

xeR

Antenna array

element

Additional delay due to

array element position

Inciden

t multi

path

compon

entye

xeR

Antenna array

element

(a) (b)

Figure 6-9. Absolute propagation delay for the GAGE model is calculated using (a) the distance from the transmitter to the center of the receiver array by way of the scatterer and (b) the distance between parallel lines through the receiver array center and the array element drawn orthogonally to the propagation path.

6.3.3 Strength Modeling for ESR and GBSBE

Multipath component strength is simulated based on the distances between the transmitter,

scatterers, and receiver and is influenced by reflection loss of the scatterers. A log-distance path

loss exponent defines the characteristic of strength versus path distance for each multipath

component. Path loss exponent for simulating an environment can be determined from

measurements or by comparing the environment to well studied environments for which the path

loss exponent is known. Reflection loss is the strength of a multipath component just after

reflection relative to the strength of the component just prior to reflection expressed in dB.

Figure 6-10 illustrates the relative strength of multipath components versus delay influenced only

by log-distance path loss and reflection loss for a non-line-of-sight channel. Results are shown

on both dB-versus-delay and dB-versus-log-delay31 axes. The dB axis shows values of negative

path loss to depict relative multipath component power. The dB-versus-delay plot shows a

smooth decrease of multipath strength with delay. In the dB versus-log-delay plot, there is an

obvious linear trend of multipath component strength, which supports the strength and path loss

exponent equations discussed in section 5.3.5. As discussed in section 5.3.5, the slope of the line

shown on the plot is a function of the path loss exponent.

31 The log-delay axis values represent absolute propagation delay, not relative delay.

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As in all applications of the log-distance path loss model, the reference distance for a reference

path loss must be assumed. Free space propagation (n=2) is assumed between the transmitter

and the reference path loss distance; at this distance a breakpoint occurs, and the path loss trend

changes to the path loss exponent specified for the model. Reference distances approximately

equal to the mean distance between the transmitter and the closest scatterers surrounding the

transmitter are appropriate. Reference distances should be larger than the far-field distance,

which is a function of physical antenna extent and wavelength.

Reflection loss affects all reflected multipath components equally since all reflected multipath

components experience a single bounce by a scatterer assumed to have the same reflection loss

exhibited by all other scatterers. As such, changing the reflection coefficient has the effect of

adding or subtracting a single dB value from all components shown on the plot, simply

translating all components up or down on the plot.

200 400 600 800 1000 1200 1400 1600 1800-180

-170

-160

-150

-140

-130Relative Multipath Strength Versus Delay

Absolute Propagation Delay (ns)

(Neg

ativ

e) P

ath

Loss

(dB

)

-6.7 -6.6 -6.5 -6.4 -6.3 -6.2 -6.1 -6 -5.9 -5.8 -5.7-180

-170

-160

-150

-140

-130

log10(Absolute Propagation Delay [sec])

Mag

nitu

de (

dB)

Figure 6-10. Typical strength-versus-delay plot (ESR model) for a channel impulse response affected only by log-distance path loss and reflection loss (non-line-of-sight channel).

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6.3.4 Strength Modeling for GAGE

The propagation environment for air-to-ground channels causes multipath attenuation to occur

differently compared to terrestrial channels because of distance differences in free-space

propagation legs. Figure 6-11 illustrates the air-to-ground propagation environment with two

scatterers. The first multipath component follows a path from the transmitter to Scatterer 1 to

the ground receiver. The second multipath component follows a path that reflects off of

Scatterer 2 to the receiver. Each reflected propagation path experiences the same reflection loss

at the scatterers for this explanation. Both Scatterer 1 and Scatterer 2 lie on the ground-level

constant-delay ellipse32, which means that both multipath components have the same propagation

delay. While the line-of-sight component (if it is not obstructed) experiences a single leg of free-

space propagation, each reflected multipath component experiences an air leg and a ground leg.

Air legs experience free-space propagation, but ground legs can be modeled by the log-distance

path loss model because of the presence of ground-level obstructions.

For ESR and GBSBE terrestrial models, the influence of log-distance path loss and uniform

reflection loss causes two multipath components with the same delay to experience the same

attenuation because the same distance through 2≠n obstructed regions is traversed by both

multipath components. In the air-to-ground environment, however, the distances through the

2≠n obstructed regions are different depending upon the azimuthal radial from the receiver on

which the scatterer lies. Because of the difference in distances of these legs and the 2=n air

legs, multipath components with the same delay can experience different magnitudes of

attenuation even though log-distance path loss and reflection loss are the only attenuation factors

applied.

A sample channel impulse response produced by the GAGE model simulation is shown in Figure

6-12. Multipath strength is plotted on dB-versus-delay and dB-versus-log-delay axes. Unlike

the ESR and GBSBE simulations, multipath component strengths on the dB-versus-log-delay

plot do not fall on a straight line because of the differences in ground-leg propagation distances.

This fact provides insight into the air-to-ground channel in that strength of multipath components

32 In the side view of the propagation environment, the scatterers do not appear on the edge boundary of the ellipsoid because they lie on the surface at positions in front of or behind the x-z plane.

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for particular delays are a function of direction of arrival, which directly relates to the ground-

level propagation distance.

Ground Level

Ellipsoi

d Boun

dary

AirborneTransmitter

Scattering RegionGroundReceiver

Scatterer1

x

y

Top

Vie

w(V

iew

dow

n fr

om p

osit

ive

z-ax

is)

Ground-LevelConstant-Delay Ellipse

Scatterer1

z

Side

Vie

w(V

iew

alo

ng y

-axi

s)

xLOS Prop

agation

Path (n=2)

Mult

ipath

2 Air

Leg (

n=2)

Multipath 2Air Leg (n=2)

Multipath 2

Ground Leg (n≠2)

Multipath 1 Air L

eg (n=2)

Multipath 1

Air Leg (n=2)

Mul

tipat

h 1

Gro

und

Leg (

n≠2

)

AirborneTransmitter

GroundReceiver

Scatterer2

Scatterer2

Ground Level

Ellipsoi

d Boun

dary

AirborneTransmitter

Scattering RegionGroundReceiver

Scatterer1

x

y

Top

Vie

w(V

iew

dow

n fr

om p

osit

ive

z-ax

is)

Ground-LevelConstant-Delay Ellipse

Scatterer1

z

Side

Vie

w(V

iew

alo

ng y

-axi

s)

xLOS Prop

agation

Path (n=2)

Mult

ipath

2 Air

Leg (

n=2)

Multipath 2Air Leg (n=2)

Multipath 2

Ground Leg (n≠2)

Multipath 1 Air L

eg (n=2)

Multipath 1

Air Leg (n=2)

Mul

tipat

h 1

Gro

und

Leg (

n≠2

)

AirborneTransmitter

GroundReceiver

Scatterer2

Scatterer2

Figure 6-11. Top and side view of propagation environment for air-to-ground radio channels.

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6400 6600 6800 7000 7200 7400 7600 7800 8000-135

-130

-125

-120

-115Relative Multipath Strength Versus Delay

Absolute Propagation Delay (ns)

(Neg

ativ

e) P

ath

Loss

(dB

)

-5.2 -5.19 -5.18 -5.17 -5.16 -5.15 -5.14 -5.13 -5.12 -5.11 -5.1-135

-130

-125

-120

-115

log10(Absolute Propagation Delay [sec])

Mag

nitu

de (

dB)

Figure 6-12. Example strength-versus-delay plot (GAGE model) for a channel impulse response affected only by log-distance path loss and reflection loss.

6.3.5 Line of Sight Components

Line-of-sight (LOS) path signal components are treated differently than reflected components for

strength modeling for ESR, GBSBE, and GAGE models. After the model geometry has been

used to produce reflected component strengths and delays, the LOS component is added to the

channel impulse response. The delay of the LOS component at the receiver array center is

determined from the straight-line distance between the transmitter and receiver. Variations in

delay due to array element positions are then managed as described in section 6.3.2. The

strength of the LOS component for the ESR and GBSBE models can be treated as partially

obstructed so that 2≠n propagation occurs.

Figure 6-13 illustrates a simulated channel impulse response using the ESR model where the

LOS component has been added. The strength of the LOS component relative to the reflected

components can be controlled using the LOS component strength offset input parameter, which

can be determined from measurements. The LOS component is not attenuated by reflection loss

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and therefore is not affected by the reflection loss input parameter. As shown in Figure 6-13 in

the dB-versus-log-delay plot, the strength of the LOS component rises above the trend of the

reflected components based on the input reflection loss and LOS offset parameters.

0 200 400 600 800 1000 1200 1400 1600 1800-180

-160

-140

-120

-100Relative Multipath Strength Versus Delay

Absolute Propagation Delay (ns)

(Neg

ativ

e) P

ath

Loss

(dB

)

-7 -6.5 -6 -5.5-200

-180

-160

-140

-120

-100

log10(Absolute Propagation Delay [sec])

Mag

nitu

de (

dB)

Figure 6-13. Simulated channel impulse response for the ESR model after the LOS component is added.

6.3.6 Log-Normal Multipath Strength Variation

Measurements indicated a log-normal distribution of multipath component strength about the

best-fit line through the strength values on a dB-versus-log-delay plot. A Gaussian random

variable was included in the simulator to account for this log-normal variation. The standard

deviation (in dB) of the strength variation is an input parameter to the simulator. The strength

variation is applied to the reflected components and optionally to the LOS component. Log-

normal variations are applied to reflected components to account for strength variations observed

in actual channels due to shadowing, variable reflection coefficients, and combination of

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multipath components with the resolution of the measurement system33. Log-normal variations

are applied to LOS components to account for shadowing and combination of multipath

components within the resolution of the measurement system34.

Figure 6-14 illustrates a channel impulse response simulated with the ESR model after the log-

normal strength variation has been applied. The characteristics of multipath strengths appear to

more closely resemble those of measured power-delay profiles compared to simulated results

produced up until this point in the process (e.g., compared to Figure 6-13).

0 200 400 600 800 1000 1200 1400 1600 1800-200

-180

-160

-140

-120

-100Relative Multipath Strength Versus Delay

Absolute Propagation Delay (ns)

(Neg

ativ

e) P

ath

Loss

(dB

)

-7 -6.5 -6 -5.5-200

-180

-160

-140

-120

-100

log10(Absolute Propagation Delay [sec])

Mag

nitu

de (

dB)

Figure 6-14. Simulated channel impulse response for the ESR model after the log-normal strength variation has been applied.

33 This contribution to strength variation due to measurement system resolution is appropriate for comparing simulated channel impulse responses with measured power-delay profiles. 34 While true LOS components do not experience shadowing, this simulator makes provisions for components that follow LOS paths but are attenuated by obstructions and are not attenuated by reflection loss.

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6.3.7 Rayleigh Fading

A provision for correlated Rayleigh fading among antenna array elements is included in the

simulation. When multipath components are assumed to be diffuse or multiple specular

components shorter than the multipath resolution of the receiver, those multipath components

will fade across the array. The simulator generates correlated Rayleigh random variables, one

for each antenna element, that affect multipath strength received by each element.

Correlated Rayleigh values are produced by first generating independent Gaussian random

values to serve as in-phase and quadrature components, which are combined to form complex

Gaussian values. The independent complex Gaussian values are made into correlated complex

Gaussian values using a Cholesky matrix. The correlation coefficient matrix for the complex

Gaussian values is calculated from the desired Rayleigh correlation coefficient matrix. As

described in [Goz02], let the correlation coefficient matrix for Gaussian random variables be

given by

=

1

11

~

21

221

112

LMOMM

LL

NN

N

N

C

ρρ

ρρρρ

( 6.2 )

Let the desired correlation coefficient matrix for the Rayleigh random variables be defined by

=

1~~

~1~~~1

21

221

112

LMOMM

LL

NN

N

N

C

ρρ

ρρρρ

( 6.3 )

The relationship between the Rayleigh correlation coefficients ijρ and the Gaussian correlation

coefficients ijρ~ is given by

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( )

2−

2−

++

πρ

ρρ

ρ2

~1

~2~1ij

ij

iij

ij

E

( 6.4 )

The function ( )ηiE is the complete elliptical integral of the second kind with modulus η , which

does not have a closed form solution. Lookup tables have been produced using numerical

methods to solve the expression. Table 6-2 lists correlation coefficients for Gaussian random

variables and corresponding correlation coefficients for Rayleigh random variables based on the

equation ( 6.4 ) [Goz02].

Table 6-2. Relationship between correlation coefficients of Gaussian random variables and correlation coefficients of Rayleigh random variables computed from the envelope of the Gaussian random variables.

Rayleigh

Correlation

Coefficient

Gaussian

Correlation

Coefficient

Rayleigh

Correlation

Coefficient

Gaussian

Correlation

Coefficient

Rayleigh

Correlation

Coefficient

Gaussian

Correlation

Coefficient

Rayleigh

Correlation

Coefficient

Gaussian

Correlation

Coefficient

ijρ ijρ~ ijρ ijρ~ ijρ ijρ~ ijρ ijρ~

0.00 0.0000 0.25 0.0559 0.50 0.2227 0.75 0.5410

0.05 0.0047 0.30 0.0737 0.55 0.2752 0.80 0.6073

0.10 0.0056 0.35 0.0965 0.60 0.3327 0.85 0.6974

0.15 0.0243 0.40 0.1494 0.65 0.4133 0.90 0.7913

0.20 0.0337 0.45 0.1836 0.70 0.4562 0.95 0.9005

Using values in Table 6-2 and through interpolation, the channel simulator calculates a

correlation coefficient matrix for the Gaussian random variables based on the desired Rayleigh

random variable correlation coefficient matrix. Then, independent complex Gaussian random

values are generated for each antenna element. These independent Gaussian random values are

transformed into correlated Gaussian random values using a Cholesky decomposition of the

Gaussian correlation coefficient matrix. Let W be an N-by-l matrix with zero-mean, complex

Gaussian values stored in the rows of W, where l is the length of the rows of Gaussian values and

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the rows are independent. A matrix X is desired that contains rows of zero-mean, complex

Gaussian values, where the correlation among rows is specified by correlation coefficient matrix

C~

. A lower triangular coloring matrix L is calculated using a Cholesky decomposition35 such

that

CLLH ~= ( 6.5 )

Then, let

LWX = ( 6.6 )

It can be shown that the matrix multiplication of L by W produces matrix X that contains N rows

of l complex Gaussian values, wherein the correlation of rows is determined by matrix C~

, using

the expression

{ } { } CLLLLWWEXXE HHHH ~=== ( 6.7 )

Calculating the envelope of the rows of X results in N vectors of Rayleigh-distributed random

values having correlation coefficients defined in C .

An example of Rayleigh faded multipath components is illustrated in Figure 6-15. Channel

impulse responses for four antenna array elements are superimposed on the plot. Large

differences in delay among multipath components are caused by different propagation paths.

Very small differences in delay are caused by excess delay due to array element position.

35 When using the MATLAB function chol(.), the resulting matrix must be transposed before it is used by these equations because chol(.) produces an upper triangular matrix.

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0 200 400 600 800 1000 1200 1400 1600 1800-210

-200

-190

-180

-170

-160

-150

-140

-130

-120

-110Relative Multipath Strength Versus Delay

Absolute Propagation Delay (ns)

(Neg

ativ

e) P

ath

Loss

(dB

)

Figure 6-15. Channel impulse response of four array element superimposed on one plot after correlated Rayleigh fading has been applied.

6.4 Direction of Arrival

The ESR, GBSBE, and GAGE models directly produce direction of arrival (DOA) information

since the simulated positions of scatterers are known. The channel model simulator makes the

assumption that the size of the array is small compared to the distances traversed by multipath

components. Using this assumption, the DOA for a particular multipath component is the same

for each antenna element of the array.

6.4.1 Direction of Arrival for ESR and GBSBE

The ESR and GBSBE models define direction of arrival as shown in Figure 6-16. The receiver

array is located at the right focus of the ellipse. The array element axis origin (xe-ye) is located at

the center of the receiver array. Direction of arrival is defined as the angle between the x-axis

and the vector connecting the scatterer to the center of the receiver array. DOA ranges from π−

to π radians (-180 to 180 degrees). The simulator defines a positive DOA to be a rotation from

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the negative direction of the x-axis clockwise; the scatterer shown in Figure 6-16 produces a

multipath component with a positive DOA.

Transmitter

S

x

yb

a

DOAye

xe

ReceiverArray

Transmitter

S

x

yb

a

DOAye

xe

ye

xe

ReceiverArray

Figure 6-16. Definition of direction of arrival for the ESR and GBSBE models.

T

S

x

y

DOA

AirborneTransmitter

GroundReceiver Top View

(View down from positive z-axis)

ye

xe T

S

x

y

DOA

AirborneTransmitter

GroundReceiver Top View

(View down from positive z-axis)

ye

xe

Figure 6-17. Definition of direction of arrival for the GAGE model.

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6.4.2 Direction of Arrival for GAGE

The GAGE model defines direction of arrival as shown in Figure 6-17. The receiver antenna

array is located at the axis origin. Direction of arrival is defined to be angle between the

projection of the line-of-sight path onto the x-y plane (which falls on the x-axis) and the vector

connecting the scatterer to the receiver array center. A positive DOA is defined to be a rotation

from the positive x-axis counterclockwise, as illustrated in Figure 6-17.

6.5 Summary

This chapter has presented a detailed description of the simulator used to implement the

geometrically based single-bounce elliptical (GBSBE) model, the elliptical sub-regions (ESR)

model, and the geometric air-to-ground ellipsoidal (GAGE) model. The simulator produces

output based on physical dimensions and parameters derived from measurements. Channels are

simulated based on locations of scatterers in the environment and relative positions of the

transmitter and receiver. Statistical distributions (Gaussian, Rayleigh, and Poisson) are used to

model strength variations and counts of multipath components in the propagation environment.

At the output, the simulator produces channel impulse responses, which include multipath

strength, delay, phase, and direction of arrival at each element of an antenna array. This

simulator was used as a vehicle to evaluate geometric channel models as discussed in Chapter 7.

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229

Chapter 7 Channel Model Evaluation

Geometric channel models are often used for simulation because of their intuitive link to

physical characteristics of propagation environments. This chapter provides an evaluation of

three geometric channel models with respect to their ability to produce channel impulse

responses that accurately represent characteristics of measured radio channels. This evaluation

provides validation not only for the channel models themselves but also for wireless system

simulations whose results are influenced by the realism of the channel models employed.

The evaluation approach used here is to compare results derived from channel impulse responses

produced by a channel model with results derived from measured power-delay profiles. These

results derived from measured and simulated channels may be as simple as RMS delay spread or

as complex as effective gain achieved through the use of a two-dimensional rake receiver. By

establishing criteria that are of importance to a wide range of old and new wireless system

technologies, the evaluation can have the most relevance to the wireless field.

The specific criteria used for this evaluation include multipath signal strength characteristics,

RMS delay spread, excess delay spread, multipath fading statistics, antenna diversity gain, and

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two-dimensional rake receiver gain. Comparisons between results derived from modeled and

measured channels are performed for three channel models, namely the elliptical sub-regions

(ESR) model, the geometrically based single-bounce elliptical (GBSBE) model, and the

geometric air-to-ground (GAGE) model, which are theoretically defined in Chapter 4.

Measurements

Transmitter

Channel

Receiver

System Simulation

Transmitter

Channel

Receiver

ChannelModel

System Simulation

StatisticalResults

StatisticalResults

Comparison

ModelEvaluation

Measurements

Transmitter

Channel

Receiver

System Simulation

Transmitter

Channel

Receiver

ChannelModel

System Simulation

StatisticalResults

StatisticalResults

Comparison

ModelEvaluation

Figure 7-1. A block diagram of the process for evaluating channel models.

The method for channel model evaluation is shown schematically in Figure 7-1. For each

criterion, two identical signal processes were executed to represent each branch illustrated in

Figure 7-1. In one process, the channel was based solely on channel measurements; in the

second process, the channel was based on the output from a channel model. The channel model

itself may use information from the channel measurements as input, which allows a best-case

comparison of modeled channels with their associated measured channels. The output of each

process is statistically summarized (e.g., mean values, standard deviations, cumulative

distribution functions) and then compared.

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CHAPTER 7 – CHANNEL MODEL EVALUATION

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7.1 Elliptical Sub-Regions Channel Model

The elliptical sub-regions (ESR) model was a good candidate for evaluation because of its ability

to accept multiple sets of input parameters for multiple geometric regions rather than assuming a

single set of parameters applied uniformly across a single geometric region. The results are

especially of interest in relation to the geometrically based single-bounce elliptical model, whose

evaluation is presented in section 7.2.

The ESR model was evaluated using measurements performed for the dense-scatterer

measurement campaign discussed in section 5.3. This measurement site characterized line-of-

sight (LOS) and non-line-of-sight (NLOS) channels. As a consequence, the ESR model is

evaluated using measured and modeled signal data for both LOS and NLOS sites. LOS and

NLOS simulations were performed separately and used different input channel parameters as

required by measurement results.

7.1.1 Simulation Parameters

Table 7-1 lists the input parameters for the ESR model used to simulate the NLOS measurement

site. The number of regions (16) was chosen based on the delay ranges characterized during

measurements, ranges which achieve a balance between model resolution and amount of

measurement data required. Element locations were chosen to match the array that was used for

dense-scatterer measurements. Parameters of frequency, path loss exponent, standard deviation

of strength variation, maximum excess delay, and transmitter-receiver separation were chosen

equal to those used for or derived from measurements. Parameters of log-distance path loss

reference distance and reflection loss are assumed values36.

Table 7-2 lists the input parameters for the LOS simulations of the dense-scatterer site. Several

values are largely similar to those for NLOS locations, but exact values based on LOS

measurements that were different than NLOS measurement values were used to provide a more

meaningful evaluation.

36 Reflection loss affects the absolute strength of received multipath components rather than their relative values. Since the models are evaluated using relative strength values, the selection of reflection loss is not critical for NLOS channels.

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Table 7-1. Major simulation parameters for elliptical sub-regions model for NLOS channels.

Parameter Value Number of sub-regions 16 Poisson parameters Equal to measured values for combined NLOS

locations (see Table 5-21 on page 167) Frequency 2050 MHz Path loss exponent 4.83 Log-distance path loss reference distance 1 m Standard deviation of log-normal strength variation

4.95 dB

Reflection loss 10 dB Maximum excess delay 1588 ns Transmitter-receiver separation Equal to values for NLOS locations (see Table

5-14 on page 150) Element locations (xe, ye) coordinates: (0, 4/3λ ); (0, 4/1λ );

(0, – 4/1λ ); (0, – 4/3λ ) in meters

Table 7-2. Major simulation parameters for elliptical sub-regions model for LOS channels.

Parameter Value Number of sub-regions 16 Poisson parameters Equal to measured values for combined NLOS

locations (see Table 5-22 on page 168) Frequency 2050 MHz Path loss exponent 4.10 Log-distance path loss reference distance (for single-bounce multipath components)

1 m

Standard deviation of log-normal strength variation

5.24 dB

Reflection loss 10 dB LOS component dB above best-fit line 10.5 dB (includes reflection loss in simulator) Maximum excess delay 1557 ns Transmitter-receiver separation Equal to values for LOS locations (see Table

5-14 on page 150) Element locations (xe, ye) coordinates: (0, 4/3λ ); (0, 4/1λ );

(0, – 4/1λ ); (0, – 4/3λ ) in meters

Figure 7-2 shows the modeled propagation environment appropriate for the parameters given in

Table 7-1 and Table 7-2. Elliptical boundaries correspond to excess multipath delay divided into

equal delay intervals. The transmitter is located at the plus symbol, and the receiver is located at

the circle. Randomly generated scatterer positions, whose count in each region depends upon a

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CHAPTER 7 – CHANNEL MODEL EVALUATION

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specified Poisson parameter, are shown as dots. Lines connecting the transmitter and receiver by

way of each scatterer are single-bounce propagation paths. From this geometry (and other input

parameters), the strength, delay, and direction of arrival of multipath components in channel

impulse response are computed.

-300 -200 -100 0 100 200 300-250

-200

-150

-100

-50

0

50

100

150

200

250

x-coordinate (m)

y-co

ordi

nate

(m

)

Top View of Propagation Environment

Figure 7-2. Example of geometric channel simulation (elliptical sub-regions model) showing transmitter location (plus symbol at focus), receiver location (circle at other focus), scatterers (dots), propagation paths

(yellow lines), and elliptical sub-region boundaries.

7.1.2 Multipath Signal Strength

Relative strength and delay of multipath components in channel impulse responses affect

performance of radio systems. For narrowband systems, multipath strengths and delays in the

channel are associated with the fading depth of signal envelopes and relate to the requirement for

an equalizer to mitigate inter-symbol interference (ISI). For wideband direct-sequence spread-

spectrum (DS-SS) systems, multipath strengths and delays relate to rake receiver requirements

(e.g., number of fingers, searcher window size, gains achieved). For these reasons, multipath

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strength scatter plots and strength distribution plots were produced by the simulator for

comparison to measured results.

Figure 7-3 through Figure 7-8 depict strength information output by simulations of the ESR

model for the NLOS locations (NLOS1-NLOS6) at the dense-scatterer site. One pair of plots is

given for each location. The plot labeled (a) in each figure is a scatter plot of multipath strength

versus log-delay. The plot labeled (b) in each figure shows a normalized histogram of multipath

component strength along with a theoretical Gaussian probability density function for

comparison.

The simulated NLOS strength results37 can be compared to the measurement results provided in

section 5.3.5 starting on page 169. The histograms of multipath strength for simulated channels

is very similar to those for measured channels, as expected since the Gaussian strength variation

trend was designed into the channel simulator. Strength-versus-log-time scatter plots differ

slightly between simulated and measured channels. Scatter plots for simulated channels show

approximately equal distribution on either side of and along the best-fit line, while measured

channels contain ranges of delay where multipath strength points moderately deviate from the

best-fit line in clusters. Differences early in the profile where measurements fall below the best-

fit line are likely due to obstructions shadowing multipath with short delays. Sporadic deviations

in later delays are likely due to differences in reflection coefficients and path loss exponents,

which the simulator treats as constants over the entire environment. In general, the strength

characteristics of channel impulse responses produced by the ESR model appear to be

satisfactory.

37 Simulations and measurements were processed to provide relative multipath strength data for comparison.

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Figure 7-3. NLOS 1 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

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Figure 7-4. NLOS 2 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-5. NLOS 3 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-6. NLOS 4 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-7. NLOS 5 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-8. NLOS 6 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

best-fit line values; theoretical Gaussian PDF also shown.

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The simulations of the ESR model used for Figure 7-3 through Figure 7-8 include Gaussian

strength variation but not Rayleigh fading of multipath components. In order to compare

multipath strength distributions with and without Rayleigh fading, the plots in Figure 7-9 and

Figure 7-10 were produced. Figure 7-9 is the output of the ESR simulation using 1000 simulated

channel impulse responses for NLOS6 with Gaussian strength variation but not Rayleigh fading.

Figure 7-10 was produced by the ESR simulation with both Gaussian strength variation and

Rayleigh fading, where the Gaussian standard deviation for Figure 7-10 was adjusted such that

the standard deviation of the strength variation for the combined effect of Gaussian and Rayleigh

distributions equals that when only Gaussian variations were applied. The comparison between

the plots show that when all multipath components are truly Rayleigh faded, the distribution

skews away from the Gaussian PDF. This suggests that the multipath strength characteristics of

the measured channels, which are better represented by the Gaussian PDF, can be modeled more

accurately using only Gaussian variation of strength. This is evidence that multipath components

in the measured channels were not all affected by Rayleigh fading.

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Figure 7-9. NLOS 6 simulated multipath strength (ESR) for 1000 impulse responses (without Rayleigh fading): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b)

Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-10. NLOS 6 simulated multipath strength (ESR) for 1000 impulse responses (Rayleigh fading, no log-normal deviation): (a) Multipath strength versus log of propagation delay for simulated data and best-fit

line. (b) Normalized histogram of difference between data points and best-fit line values; theoretical Gaussian PDF also shown. Standard deviation about best-fit line of 5.4 dB results

Figure 7-11 through Figure 7-14 show ESR simulation results for the LOS locations at the dense-

scatterer site. These plots can be compared to the measurement results presented in section 5.3.5

starting on page 169. Except for later delays, where small Poisson parameters resulted in sparse

multipath components, scatter plots for simulations appear to have a regular spreading of

multipath components across delay. Measurements of LOS locations, however, showed short

delay ranges containing strong clusters of multipath components. This suggests that a few

multipath components at particular delays dominated measurements at each LOS location. The

methods used by the ESR model do not directly provide a way to allow persistent multipath

components that remain dominant in all generated channel impulse responses. While the model

may work well for data combined for all measurement locations, it falls somewhat short of

accurately modeling strength for individual LOS locations because of its inability to include

concentrations of dominant multipath components.

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Figure 7-11. LOS 1 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-12. LOS 2 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-13. LOS 3 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-14. LOS 4 simulated multipath strength (ESR): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data points and

best-fit line values; theoretical Gaussian PDF also shown.

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7.1.3 RMS Delay Spread

RMS delay spread was calculated for each channel impulse response generated by the ESR

simulator. A summary of RMS delay spread, divided among NLOS locations, is shown in Table

7-3. The table also includes results of measured channels for comparison of mean, standard

deviation, minimum, and maximum RMS delay spread.

Table 7-3. RMS delay spread results for simulations (ESR) and measurements of NLOS dense scatterer locations.

RMS Delay Spread (ns) Location

Mean Std. Dev. Minimum Maximum

Sim Meas Sim Meas Sim Meas Sim Meas

NLOS1 87.4 67.5 28.4 10.1 16.9 40.2 169 108

NLOS2 84.8 60.9 26.6 10.0 26.4 0.00 176 91.0

NLOS3 79.1 70.2 26.1 12.1 25.5 35.9 198 152

NLOS4 82.5 78.6 25.8 10.7 28.4 51.6 162 112

NLOS5 72.8 70.7 25.6 7.70 24.1 49.3 170 95.3

NLOS6 64.4 69.4 24.3 13.3 19.8 31.3 142 368

Results show that the simulator generally produces channel impulse responses with mean RMS

delay spreads larger that those for measured channels. Standard deviations of RMS delay spread

were also larger for simulated channels. This overestimation of mean RMS delay spread is likely

due to measured channels containing strong multipath components early in their power-delay

profiles. Strong multipath components early in the profiles reduce RMS delay spread because

weaker, long-delay components become less significant.

Complementary cumulative distribution functions (CCDF) were produced for simulated NLOS

locations for comparison to CCDFs of measurement data shown in section 5.3.2 beginning on

page 151. These CCDFs show again that RMS delay spread is overestimated by the ESR model.

In order to force the ESR model to simulate RMS delay spread more accurately for NLOS

channels, the maximum excess delay could be reduced or the path loss exponent could be

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increased. While this will affect other characteristics of the simulated channel impulse

responses, such a compensation is appropriate if RMS delay spread is the most important

characteristic of the responses required by certain wireless system simulations.

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Figure 7-15. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS1 (b) NLOS2.

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Figure 7-16. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS3 (b) NLOS4.

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Figure 7-17. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS5 (b) NLOS6.

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Figure 7-18. RMS delay spread CCDF for simulated (ESR) channels (a) NLOS6 simulated using log-normal variation about best-fit power (dB) versus log-delay line, and (b) NLOS6 simulated using log-normal

variation and Rayleigh fading for multipath components.

Results using solely a log-normal distribution of multipath strength variation and results using

both Gaussian and Rayleigh distributions for multipath strength were produced and compared.

Figure 7-18 shows CCDF plots of RMS delay spread for NLOS6 based on 1000 simulated

channel impulse responses. Plot (a) in the figure summarizes RMS delay spread for simulations

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using only log-normal variation of multipath strength. Plot (b) in the figure uses log-normal

variation and Rayleigh fading, where the standard deviation of the Gaussian variation was

adjusted so that the combination effects of the Gaussian and Rayleigh distributions produced an

overall standard deviation equal to that used for plot (a) in the figure. These simulations resulted

in mean RMS delay spreads of (a) 62.8 ns and (b) 61.7 ns, respectively. This insignificant

difference in mean RMS delay spreads suggests that Rayleigh fading may be used in the ESR

simulation without significantly affecting RMS spread of the output responses.

Table 7-4 shows RMS delay spread for each LOS channel impulse response simulated using the

ESR model, divided among NLOS locations. The table includes results of measured channels

for comparison of mean, standard deviation, minimum, and maximum RMS delay spread. Figure

7-19 and Figure 7-20 depict CCDFs for RMS delay spread for each LOS location. The results

show that the simulation can overestimate or underestimate the RMS delay spread compared to

measurements. The simulations show an increase in RMS delay spread with transmitter-receiver

separation (see for T-R separation values for LOS locations in Table 5-14 on page 150).

Measurements, however, show RMS delay spread remaining relatively constant over all

locations.

Table 7-4. RMS delay spread results for simulations (ESR) and measurements of LOS dense scatterer locations.

RMS Delay Spread (ns) Location

Mean Std. Dev. Minimum Maximum

Sim Meas Sim Meas Sim Meas Sim Meas

LOS1 50.1 34.4 12.3 4.81 27.1 21.4 103 51.2

LOS2 39.0 38.8 10.3 8.31 15.3 0.00 77.6 73.3

LOS3 28.8 39.0 6.87 12.1 13.7 20.1 51.7 91.8

LOS4 18.7 34.2 50.3 8.7 7.39 16.9 34.9 69.9

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Figure 7-19. RMS delay spread CCDF for simulated (ESR) channels (a) LOS1 (b) LOS2.

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Figure 7-20. RMS delay spread CCDF for simulated (ESR) channels (a) LOS3 (b) LOS4.

7.1.4 Excess Delay Spread

Excess delay spread results for simulated and measured channels for the NLOS dense-scatterer

locations are shown in Table 7-5. Means of excess delay spread results at the 10 dB level for

measurements exceed those for simulation. This is explained by the tendency of the measured

power delay profiles to have strong components at early delays. For 20 dB levels and higher, the

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simulated results approach the values of the measured results, where weaker measured and

simulated multipath components at longer delays tend to have the same strength.

Table 7-6 lists excess delay spread results for simulated and measured LOS channels. As with

the simulated RMS delay spread results, excess delay spread based on simulated channel impulse

responses tends to increase with increasing transmitter-receiver separation. Measured excess

delay spread means do not follow this trend for the dense-scatterer site.

Table 7-5. Excess delay spread values for simulated (ESR) and measured NLOS channel impulse responses.

Excess Delay Spread (ns)

10 dB Level 20 dB Level 25 dB Level 30 dB Level

Mean Max Mean Max Mean Max Mean Max Location

Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas

NLOS1 155 200 537 480 389 390 743 1300 516 549 1009 1300 635 682 1029 1500

NLOS2 143 204 466 447 372 328 875 697 510 440 889 811 621 601 1199 1510

NLOS3 125 272 479 580 351 435 775 775 487 581 1228 1250 606 693 1228 1450

NLOS4 141 252 460 572 378 499 868 776 505 615 981 888 630 712 1250 1380

NLOS5 104 243 407 493 311 380 840 747 434 503 864 909 556 637 971 1210

NLOS6 96 207 379 478 269 367 711 758 379 471 830 1365 508 620 1165 1450

Table 7-6. Excess delay spread values for simulated (ESR) and measured LOS channel impulse responses.

Excess Delay Spread (ns)

10 dB Level 20 dB Level 25 dB Level 30 dB Level

Mean Max Mean Max Mean Max Mean Max Location

Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas

LOS1 29.1 115 209 335 194 196 458 533 316 230 591 725 424 313 1003 751

LOS2 19.0 131 173 501 138 233 374 790 237 300 566 790 364 408 659 791

LOS3 11.3 123 131 509 95.5 222 338 651 165 315 358 835 264 432 568 868

LOS4 5.53 89.1 60.7 421 55.3 162 196 586 107 263 275 786 177 390 384 861

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7.1.5 Multipath Fading

Impulse response data from the dense-scatterer measurements and ESR model simulations was

used to generate fading envelopes for comparison. Signal envelopes were formed by performing

a vector sum of all signal components in each channel impulse response and taking the

magnitude of the result. Envelope magnitude data from all antenna elements was combined to

increase the number of samples available.

Cumulative distribution functions (CDF) of signal envelope strength for simulated and measured

fading are shown in Figure 7-21 and Figure 7-22. Signal levels were normalize so that the CDFs

show envelope strength relative to the median for each signal. A theoretical CDF for Rayleigh

fading, which was also normalized to its median value, is also shown on each plot.

Results shown in Figure 7-21 indicate that CDFs for measurements at all NLOS locations fall

very close to the theoretical Rayleigh CDF. Simulated channels also show a Rayleigh trend.

Note that Rayleigh fading of the signal envelope discussed here is not the same as Rayleigh

fading of individual multipath components. Multipath components at a receiver site can exhibit

no fading, while the signal envelope formed by the vector sum of all multipath components may

be very Rayleigh in nature. Rayleigh fading of multipath components requires multipath having

the same delay or close delays within the resolution of the receiver to be combined at the

receiver. Signal envelopes, however, are a combination of all multipath components in the

channel impulse response.

LOS results in Figure 7-22 indicate a Rician fading characteristic (with a non-zero K value) for

simulated channels and measured channels. Strong line-of-sight components in the measured

and simulated channels cause the probability of deep fades to be lower compared to Rayleigh

fading. This suggests that the strength of the line-of-sight component relative to the strengths of

the multipath components is modeled accurately for the purposes of multipath fading.

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Figure 7-21. Signal strength CDF for each NLOS location derived from (a) channel impulse response simulations (ESR) and (b) measured channels.

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Figure 7-22. Signal strength CDF for each LOS location derived from (a) channel impulse response simulations (ESR) and (b) measured channels.

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7.1.6 Antenna Diversity

Gains achieved through antenna diversity applied to measured and simulated channels were

computed for comparison. Maximal ratio combining (MRC) was selected because it enables the

best fading mitigation (statistically) compared to other types of linear diversity combiners

[Ree02]. Since the highest amount of diversity gain is achieved for narrowband signals,

continuous-wave signals are assumed for this comparison. An antenna element separation of

2/λ was used. Figure 7-23 through Figure 7-28 show CDFs of signal envelope strengths for

NLOS dense-scatterer site simulations and measurements. Each plot shows two CDFs of relative

signal envelope power, one CDF corresponding to a receiver using single-element and one CDF

corresponding to the output of MRC diversity combining.

Table 7-7 lists approximate diversity gains for simulated and measured NLOS locations for the

1% and 10% CDF levels. These results show that simulated and measured diversity gain at the

10% level are approximately equal within one dB. At the 1% level, diversity gain for measured

channels is slightly larger (about 2.3 dB on average) than the diversity gain for simulated

channels. It appears that this is due to measured channels experiencing deeper fades a lower

percentage of the time.

Figure 7-29 through Figure 7-32 are CDF plots of simulations and measurements for LOS

locations at the dense-scatterer site. CDFs of relative envelope power for a single-element and

for MRC-diversity output are shown on each plot. Table 7-8 lists diversity gain for the 10% and

1% CDF levels for LOS simulations and measurements. While at three of the LOS locations

diversity gain at the 10% level differs by 1 dB or less between measured and simulated results,

diversity gain differences of up to 6 dB at the 1% CDF level were observed. This suggests that

simulated channels may have gone into deeper fades or simulated channels exhibited lower

envelope correlation coefficients among elements.

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Figure 7-23. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

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Figure 7-24. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

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Figure 7-25. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

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Figure 7-26. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

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Figure 7-27. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS5 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

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Figure 7-28. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS6 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

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Table 7-7. Approximate diversity gain for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels.

Diversity Gain (dB)

10% CDF Level 1% CDF Level Location

Simulated Measured Simulated Measured

NLOS1 3 2 6 4

NLOS2 2 4 4 8

NLOS3 2 3 3 7

NLOS4 3 3 4 9

NLOS5 3 4 4 7

NLOS6 2 3 5 5

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Figure 7-29. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS1 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

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Figure 7-30. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS2 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

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Figure 7-31. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS3 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

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Figure 7-32. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS4 for (a) simulated (ESR) channel impulse responses and (b) measured channels.

Table 7-8. Approximate diversity gain for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels.

Diversity Gain (dB)

10% CDF Level 1% CDF Level Location

Simulated Measured Simulated Measured

LOS1 1.5 0.5 8 2

LOS2 1.5 2 5 3

LOS3 1.5 0.5 5 2

LOS4 1 1 5.5 5

7.1.7 Two-Dimensional Rake Receiver

A two-dimensional rake receiver is a space-time signal processing architecture that joins a

traditional rake receiver with smart antenna capabilities. A two-dimensional rake combines

resolvable multipath components in the temporal domain as well as combining or beamforming

on multipath components in the spatial domain. Processing used for evaluation here temporally

and spatially combines multipath components from four antenna array elements using four rake

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fingers per antenna element. The four strongest multipath components are used for temporal

rake combining, and co-phased rake output signals are summed to produce the composite output

signal.

Figure 7-33 through Figure 7-38 show CDFs of the received signal envelope with and without

the use of a two-dimensional rake receiver for NLOS locations. Table 7-9 provides approximate

gains achieved through the use of the two-dimensional rake for simulated and measured

channels. Gains for 10% and 1% CDF levels are shown. Mitigation of fading was generally

better for measured channels compared to simulated channels. Simulated channels showed gains

up to 10 dB at the 1% CDF level, while measured channel gains of up to 20 dB were observed.

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Figure 7-33. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS1 for (a) simulated (ESR) channel impulse

responses and (b) measured channels.

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Figure 7-34. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS2 for (a) simulated (ESR) channel impulse

responses and (b) measured channels.

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Figure 7-35. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS3 for (a) simulated (ESR) channel impulse

responses and (b) measured channels.

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Figure 7-36. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS4 for (a) simulated (ESR) channel impulse

responses and (b) measured channels.

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Figure 7-37. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS5 for (a) simulated (ESR) channel impulse

responses and (b) measured channels.

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Figure 7-38. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS6 for (a) simulated (ESR) channel impulse

responses and (b) measured channels.

Table 7-9. Approximate fading levels differences between 2-D rake output and single channel output for NLOS locations computed from simulated (ESR) channel impulse responses and measured channels.

Fading Level Relative to Mean Signal Strength –

2-D Rake Output Minus Single Channel Output

(dB)

10% CDF Level 1% CDF Level

Location

Simulated Measured Simulated Measured

NLOS1 4 5 10 14

NLOS2 6 7.5 10 20

NLOS3 3.5 5 5 16

NLOS4 5.5 8 9 16

NLOS5 5.5 7 7 15

NLOS6 4 8.5 8 16

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Figure 7-39 through Figure 7-42 were created from LOS location simulations and measurements,

showing CDFs of relative signal envelope strengths with and without the application of a two-

dimensional rake. Table 7-10 shows the approximate gains achieved using the two-dimensional

rake for both simulated and measured channels. Gains for 10% and 1% CDF levels show

slightly larger gains for simulated channels compared to measured channels. Gains for simulated

channels up to 10 dB at the 1% CDF level where achieved, while measured channel reached

gains of 6 dB at the 1% level. Unlike simulations of the NLOS locations, LOS simulations of

the dense-scatterer site tend to overestimate achievable gains using a two-dimensional rake

receiver.

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Figure 7-39. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS1 for (a) simulated (ESR) channel impulse responses

and (b) measured channels.

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Figure 7-40. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS2 for (a) simulated (ESR) channel impulse responses

and (b) measured channels.

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Figure 7-41. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS3 for (a) simulated (ESR) channel impulse responses

and (b) measured channels.

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Figure 7-42. CDF of received signal strength relative to mean strength using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS4 for (a) simulated (ESR) channel impulse responses

and (b) measured channels.

Table 7-10. Approximate fading levels differences between 2-D rake output and single channel output for LOS locations computed from simulated (ESR) channel impulse responses and measured channels.

Fading Level Relative to Mean Signal Strength –

2-D Rake Output Minus Single Channel Output

(dB)

10% CDF Level 1% CDF Level

Location

Simulated Measured Simulated Measured

LOS1 3.5 2 8 6

LOS2 2.5 2 8 5

LOS3 3 1.5 7.5 4

LOS4 1.5 2 10 5

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7.1.8 ESR Comparison Summary

Results of the evaluation of the ESR channel model through comparison of simulated ESR

channel impulse responses and actual channel measurements are summarized by the following

points:

• In general, the ESR model provides a reasonable representation of the channel but should

be tuned to achieve the desired channel characteristics. For example, for the simulation

of wireless systems employing diversity or two dimensional rake receivers in LOS

channels, the strength of LOS component strength could be adjusted to meet a desired

Rician distribution K-factor.

• The ESR model as implemented produces largely accurate Gaussian distributions of

multipath strength about a dB-versus-log-delay straight-line trend for NLOS channels.

Gaussian distributions of strength produced by the model can be made to match the

measured multipath strength distributions by using the standard deviation from

measurements as an input to the channel model simulator. Visual differences between

the dB-versus-log-time scatter plots are apparent, such as deeper fades for a few

multipath components, indicating that these multipath components may be Rayleigh

faded. The channel model simulator can be set to use Rayleigh fading for all multipath

components in the channel, but this causes a skewing of the strength distribution away

from Gaussian.

• The ESR model does not accurately represent clustering of multipath at particular delays

as observed in measured NLOS and LOS power-delay profiles. Rather, as it was

simulated for this research, the ESR model produces smooth distributions of multipath

components across propagation delay in the channel impulse response. Adjustments

could be made to the model input to account for clustering, such as significantly

increasing the Poisson parameter for a scattering sub-region corresponding to the delay

bin in which the cluster occurs. Strength adjustment factors could also be used to

increase the strength of clusters above the strength trend of other multipath components

in the channel impulse response.

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• NLOS channel impulse responses produced by the ESR model simulation exhibited

higher RMS delay spread than the measurements the model was intended to represent.

The larger simulated RMS delay spreads are likely due to comparatively larger multipath

components at small propagation delays in measured profiles. In general, strong clusters

early in the profile reduce RMS delay spread, and strong clusters late in the profile

increase RMS delay spread. A provision for stronger (or even weaker) clusters that

deviate from the strength trend of other multipath components could resolve this

discrepancy. Simulated LOS channels show increasing RMS delay spread with distance,

but measured LOS channels do not show a similar trend. While larger RMS delay spread

is expected with larger distance, additional multipath components for measured LOS

channels late in delay may have been considerably weaker than dominant early delays,

causing a loss of this trend due to dynamic range limitations of the measurement receiver.

• ESR NLOS excess delay spread results for the 10 dB level tend to be overestimates

compared to measured results. For larger levels (20 dB, 25 dB, and 30 dB), simulation

results seem to better represent measurements. This is expected since relative strengths

of simulated multipath components in later delays, where weaker multipath components

exist, are more accurately modeled compared to those of early delays.

• The ESR model produces vector channel impulse responses that result in reasonable

MRC antenna diversity characteristics for NLOS channels. For NLOS channels,

measurements resulted in slightly lower achievable diversity gain compared to

simulation. Simulations of LOS channels produced an optimistic estimate of achievable

diversity gain.

• Mitigation of fading in NLOS channels using a two-dimensional rake receiver was

generally better for measured vector channels compared to simulated channels. Gains for

simulated channels were up to 10 dB at the 1% CDF level, while gains for measured

channels up to 20 dB were computed. Simulations of LOS channels produced an

optimistic estimate of achievable gains using spatial-temporal combining of multipath

components.

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7.2 Geometrically Based Single-Bounce Elliptical Channel Model

The geometrically based single-bounce (GBSBE) channel model is similar to the elliptical sub-

regions model except that it uses a single geometric region in which to distribute scatterers.

Therefore, through comparing the evaluation of the GBSBE model with the evaluation of the

ESR model, the value of using the additional regions and the associated increase in complexity

of the ESR model can be judged.

Like the ESR model, the GBSBE model was evaluated using measurements taken at the dense-

scatterer measurement site discussed in section 5.3. Line-of-sight (LOS) and non-line-of-sight

(NLOS) measurements are used in the evaluation. LOS and NLOS simulations were performed

separately and used different input channel parameters corresponding to LOS and NLOS

measurement results.

7.2.1 Simulation Parameters

Table 7-11 details the GBSBE input parameters used to simulate the NLOS measurement site.

Element locations were chosen to match the array that was used for dense-scatterer

measurements and the simulations of the ESR model. Frequency, path loss exponent, standard

deviation of strength variation, maximum excess delay, and transmitter-receiver separation are

equal to those parameters used for or computed from measurements. Log-distance path loss

reference distance and reflection loss are still assumed values38, but these values were chosen to

be the same as those used for the ESR model simulations.

Table 7-12 lists the input parameters used for the GBSBE LOS simulations of the dense-scatterer

site. Some values are different than those for NLOS GBSBE parameters because of

measurement result differences between LOS and NLOS locations at the site.

38 Again, these parameters affect the absolute strength of received multipath components rather than their relative values. Since GBSBE and ESR models are using the same values here, absolute strength of components produced by these models could actually be compared, but relative strengths are of interest here so that evaluations of both models with respect to measurements can be compared using the same criteria.

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Table 7-11. Major simulation parameters for GBSBE model for NLOS channels.

Parameter Value Number of regions 1 (equivalent to sub-regions model with one

region) Poisson parameter (average number of scatterers)

21.8 (from Table 5-23 on page 169)

Frequency 2050 MHz Path loss exponent 4.83 (from Table 5-26 on page 186) Log-distance path loss reference distance 1 m Standard deviation of log-normal strength variation

4.95 dB

Reflection loss 10 dB Maximum excess delay 1588 ns Transmitter-receiver separation Equal to values for NLOS locations (see Table

5-14 on page 150) Element locations (xe, ye) coordinates: (0, 4/3λ ); (0, 4/1λ );

(0, – 4/1λ ); (0, – 4/3λ ) in meters

Table 7-12. Major simulation parameters for GBSBE model for LOS channels.

Parameter Value Number of regions 1 (equivalent to sub-regions model with one

region) Poisson parameters 15.3 (from Table 5-23 on page 169) Frequency 2050 MHz Path loss exponent 4.10 (from Table 5-26 on page 186) Log-distance path loss reference distance 1 m Standard deviation of log-normal strength variation

5.24 dB

Reflection loss 10 dB LOS component dB above best-fit line 10.5 dB (includes reflection loss in simulation) Maximum excess delay 1557 ns Transmitter-receiver separation Equal to values for LOS locations (see Table

5-14 on page 150) Element locations (xe, ye) coordinates: (0, 4/3λ ); (0, 4/1λ );

(0, – 4/1λ ); (0, – 4/3λ ) in meters

The propagation environment simulated for the GBSBE model is shown in Figure 7-43. A single

elliptical boundary that represents the largest single-bounce multipath delay is shown. The plus

symbol and circle on the plot indicate the transmitter and receiver locations, respectively. The

dots on the plot indicate locations of randomly generated scatterer positions, whose count within

the entire elliptical region depends upon the input Poisson parameter. Single-bounce

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propagation paths are shown as lines that connect the transmitter, each scatterer, and the receiver.

This geometry was used to produce channel impulse responses for comparison to measured

channels at the modeled site.

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Figure 7-43. Example of geometric channel simulation (GBSBE model) showing transmitter location (plus symbol at focus), receiver location (circle at other focus), scatterers (dots), propagation paths (yellow lines),

and elliptical boundary for uniformly distributed scatterers.

7.2.2 Multipath Signal Strength

Figure 7-44 through Figure 7-49 illustrate the characteristics of multipath strength produced by

simulations of the GBSBE model for the NLOS locations (NLOS1-NLOS6). A pair of strength

plots was produced for each of the locations NLOS1 through NLOS6. The (a) plot in each figure

is a scatter plot of multipath strength versus log-delay, and the (b) plot in each figure illustrates a

normalized histogram of multipath component relative strength and an overlaid Gaussian

probability density function.

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Measurement results in section 5.3.5 starting on page 169 can be used for comparison to the

multipath strength plots in this section. Multipath strength histograms for simulated channels

and measured channels are similar, as expected because of the Gaussian strength variation of the

simulator that is based on measurements. Strength-versus-log-delay scatter plots for simulated

channels are different than those for measured channels in two respects. First, like the results of

the ESR model, scatter plots for simulated channels show approximately equal distribution on

either side of the best-fit line; measured channels, however, contain clusters of multipath whose

strength deviates from the best-fit line. Obstructions causing shadowing of multipath with short

delays is likely the cause of multipath falling below the best-fit line for early delays as shown by

measurements. Differences in reflection coefficients and path loss exponents experienced during

measurements are likely the cause of deviations for later delays. The second difference between

measured and simulated scatter plots is the density of multipath occurrences versus propagation

delay. On the dB-versus-log-time plot, simulations show a clear trend of increasing density as

delay increases, unlike the trend of measurements and the ESR model. This difference is due to

the uniform distribution of scatterers throughout the elliptical region. Because the ESR model

specifies placement of scatterers more densely in sub-regions corresponding to shorter delays,

multipath components appear more evenly distributed on a log-delay plot.

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Figure 7-44. NLOS1 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-45. NLOS2 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-46. NLOS3 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-47. NLOS4 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-48. NLOS5 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-49. NLOS6 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

Figure 7-50 through Figure 7-53 illustrate GBSBE channel model simulation results for the LOS

locations at the dense-scatterer site. Measurement results presented in section 5.3.5 starting on

page 169 can be compared to these plots of results. In addition to a steady increase in multipath

component density as delay increases on the log-delay plot, simulated LOS channel impulse

responses do not contain the dense clusters of components shown in plots of LOS measurement

results. Like the shortfall of the ESR model, the GBSBE does not accurately model the few

multipath components at particular delays that dominated responses measured at each LOS

location. The GBSBE model does not provide a way to allow persistent, dominant multipath

components for a series of simulations. It appears that the model may perform satisfactorily for

data combined for several LOS measurement locations, but it does not accurately model

multipath strength for individual LOS locations because of its inability to include clusters of

dominant multipath components.

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Figure 7-50. LOS1 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-51. LOS2 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-52. LOS3 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

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Figure 7-53. LOS4 simulated multipath strength (GBSBE model): (a) Multipath strength versus log of propagation delay for simulated data and best-fit line. (b) Normalized histogram of difference between data

points and best-fit line values; theoretical Gaussian PDF also shown.

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7.2.3 RMS Delay Spread

RMS delay spread was calculated for channel impulse responses produced by the GBSBE

channel model simulator. RMS delay spread statistics for simulated and measured channels for

each NLOS location at the dense-scatterer site are shown in Table 7-13.

Table 7-13. RMS delay spread results for simulations (GBSBE) and measurements of NLOS dense scatterer locations.

RMS Delay Spread (ns) Location

Mean Std. Dev. Minimum Maximum

Sim Meas Sim Meas Sim Meas Sim Meas

NLOS1 172 67.5 72.4 10.1 20.5 40.2 352 108

NLOS2 167 60.9 76.5 10.0 25.4 0.00 356 91.0

NLOS3 167 70.2 76.9 12.1 33.2 35.9 385 152

NLOS4 168 78.6 80.1 10.7 17.1 51.6 391 112

NLOS5 179 70.7 76.9 7.70 26.0 49.3 430 95.3

NLOS6 150 69.4 76.3 13.3 12.2 31.3 409 368

Table 7-13 shows that the GBSBE model simulator produces channel impulse responses with

large RMS delay spreads and large standard deviation of RMS delay spreads compared to those

for measured channel responses. Two explanations support the high RMS delay spread of

simulations. First, the existence of strong multipath components early in the measured power-

delay profiles cause late multipath, which normally increases RMS delay spread, to affect RMS

delay spread less significantly. Second, the uniform distribution of scatterers over the entire

elliptical region in the simulation causes a relatively large number of multipath components to

exist late in delay, where few multipath components normally exist as seen during

measurements. This has the effect of increasing RMS delay spread for GBSBE simulations.

Complementary cumulative distribution functions (CCDF) of RMS delay spread for simulated

NLOS locations are shown in Figure 7-54 through Figure 7-56. These results can be compared

to the RMS delay spread results shown in section 5.3.2 beginning on page 151. The CCDFs

support that RMS delay spread is overestimated by the GBSBE model to a greater degree than

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the ESR model. This suggests that either the number of scatterers needs to be reduced or the

path loss exponent needs to be increased in order to simulate channels with a specified RMS

delay spread using the GBSBE model. Also, a restriction could be placed on maximum

multipath delay to shorten RMS delay spread, but weak, long-delay multipath components would

fail to be modeled accurately.

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Figure 7-54. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS1 (b) NLOS2.

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Figure 7-55. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS3 (b) NLOS4.

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Figure 7-56. RMS delay spread CCDF for simulated (GBSBE) channels (a) NLOS5 (b) NLOS6.

Simulated channel impulse responses were also simulated using the GBSBE model for locations

LOS1 through LOS4. Table 7-14 statistically summarizes the results. CCDFs of RMS delay

spread for each location are shown in Figure 7-57 and Figure 7-58. Like the ESR model, the

results show that simulations can overestimate or underestimate the RMS delay spread compared

to measurements. A trend of increasing RMS delay spread with transmitter-receiver separation

is again noted, as opposed to measurements that show RMS delay spread remaining relatively

constant over all locations.

Table 7-14. RMS delay spread results for simulations (GBSBE) and measurements of LOS dense scatterer locations.

RMS Delay Spread (ns) Location

Mean Std. Dev. Minimum Maximum

Sim Meas Sim Meas Sim Meas Sim Meas

LOS1 42.3 34.4 11.5 4.81 20.4 21.4 84.6 51.2

LOS2 27.3 38.8 8.84 8.31 12.2 0.00 58.9 73.3

LOS3 17.4 39.0 6.64 12.1 6.46 20.1 72.1 91.8

LOS4 9.31 34.2 3.70 8.7 3.15 16.9 29.8 69.9

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Figure 7-57. RMS delay spread CCDF for simulated (GBSBE) channels (a) LOS1 (b) LOS2.

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Figure 7-58. RMS delay spread CCDF for simulated (GBSBE) channels (a) LOS3 (b) LOS4.

7.2.4 Excess Delay Spread

Results of excess delay spread using the GBSBE model for simulated channels and for measured

channels are shown in Table 7-15 for NLOS locations. Means of excess delay spread at the 10

dB level for simulations are close to those for measurement data. For 20 dB levels and higher,

the simulated excess delay spread results exceed those for measured channels. This is likely due

to the use of uniform distribution of scatterers over the entire elliptical region, causing the

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probability of scatterers that produce longer delays to be higher than that for measurements

where the count of multipath components at long delays is lower. The existence of even one

large delay multipath component within 20 dB to 30 dB of the strong components causes excess

delay spread at these levels to be large.

Excess delay spread results for simulated and measured LOS channels are shown in Table 7-16.

As with the simulated RMS delay spread results, increasing excess delay spread based on

simulated channel impulse responses has a strong correlation with increasing transmitter-receiver

separation. Means of measured excess delay spread do not strictly adhere to this trend.

Table 7-15. Excess delay spread values for simulated (GBSBE) and measured NLOS channel impulse responses.

Excess Delay Spread (ns)

10 dB Level 20 dB Level 25 dB Level 30 dB Level

Mean Max Mean Max Mean Max Mean Max Location

Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas

NLOS1 222 200 1081 480 696 390 1432 1300 884 549 1432 1300 1103 682 1520 1500

NLOS2 222 204 1092 447 627 328 1468 697 872 440 1468 811 1047 601 1492 1510

NLOS3 243 272 1142 580 640 435 1402 775 869 581 1418 1250 1052 693 1496 1450

NLOS4 225 252 1135 572 648 499 1416 776 854 615 1512 888 1064 712 1537 1380

NLOS5 231 243 1418 493 626 380 1418 747 856 503 1432 909 1060 637 1531 1210

NLOS6 202 207 1107 478 571 367 1352 758 784 471 1430 1365 979 620 1441 1450

Table 7-16. Excess delay spread values for simulated (GBSBE) and measured LOS channel impulse responses.

Excess Delay Spread (ns)

10 dB Level 20 dB Level 25 dB Level 30 dB Level

Mean Max Mean Max Mean Max Mean Max Location

Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas Sim Meas

LOS1 3.75 115 206 335 55.8 196 356 533 152 230 836 725 353 313 1458 751

LOS2 2.95 131 166 501 22.8 233 414 790 76.4 300 497 790 186 408 855 791

LOS3 0.623 123 61.3 509 11.7 222 438 651 40.3 315 490 835 100 432 566 868

LOS4 0.027 89.1 5.40 421 6.45 162 150 586 16.9 263 201 786 33.4 390 331 861

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7.2.5 Multipath Fading

Fading envelopes generated from GBSBE simulations of impulse responses were compared to

fading envelopes generated from measured power-delay profiles. As with the ESR model

evaluation, signal envelopes were formed by performing a vector sum of all signal components

in each channel impulse response and taking the magnitude of the result. Envelope information

from all antenna elements was used.

Figure 7-59 and Figure 7-60 show cumulative distribution functions (CDF) of signal envelope

strength for fading resulting from simulated and measured channels. Signal levels were

normalized to the median of signal strength for the CDF. A theoretical, median-normalized CDF

for Rayleigh fading is also shown on each plot. Figure 7-59 shows that CDFs for measurements

at all NLOS locations fall very close to the theoretical Rayleigh CDF, as demonstrated

previously. For simulated channels, however, the CDF deviates from the Rayleigh characteristic

such that deeper fades are more probable. For LOS channels, Figure 7-60 shows that fading

calculated from measured responses exhibits a Rician characteristic. Simulation results also

show a Rician characteristic but with a larger K-factor. The difference in the LOS CDFs

suggests that the GBSBE model produces multipath components with a weaker combined power

relative to the LOS component power in comparison to measured channels.

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Figure 7-59. Signal strength CDF for each NLOS location derived from (a) channel impulse response simulations (GBSBE) and (b) measured channels.

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Figure 7-60. Signal strength CDF for each LOS location derived from (a) channel impulse response simulations (GBSBE) and (b) measured channels.

7.2.6 Antenna Diversity

Maximal ratio combining (MRC) with an antenna element separation of 2/λ was used to

compare diversity gains achieved for simulated and measured channels. Figure 7-61 through

Figure 7-66 show signal strength envelope CDFs for simulations and measurements of NLOS

locations. A CDF of strength for a receiver using single antenna element and a CDF for a

receiver using MRC diversity combining are shown on each plot.

Approximate diversity gains for simulated and measured NLOS locations for the 1% and 10%

CDF levels are shown in Table 7-17. These results show that measured channel diversity gains

at the 10% level are 0.5 dB to 3 dB higher than diversity gains for simulated channels. At the

1% level, differences in diversity gain range from 1.5 dB to 4 dB.

Figure 7-67 through Figure 7-70 show single-element and MRC diversity CDF plots for LOS

locations. Approximate diversity gain for the 10% and 1% CDF levels for LOS simulations and

measurements are tabulated in Table 7-18. Diversity gains at 10% and 1% levels for measured

and simulated channels are similar but relatively small. Differences between diversity gains for

measured and simulated channels are 2 dB or less.

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Figure 7-61. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

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Figure 7-62. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

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Figure 7-63. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

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Figure 7-64. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

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Figure 7-65. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS5 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

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Figure 7-66. CDF of received signal strength using maximal ratio combining and using a single antenna for NLOS6 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

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Table 7-17. Approximate diversity gain for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels.

Diversity Gain (dB)

10% CDF Level 1% CDF Level Location

Simulated Measured Simulated Measured

NLOS1 1.5 2 6.5 4

NLOS2 1 4 6 8

NLOS3 1.5 3 3 7

NLOS4 1.5 3 6.5 9

NLOS5 1.5 4 5 7

NLOS6 1.5 3 5 5

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Figure 7-67. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS1 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

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Figure 7-68. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS2 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

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Figure 7-69. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS3 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

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Figure 7-70. CDF of received signal strength using maximal ratio combining and using a single antenna for LOS4 for (a) simulated (GBSBE) channel impulse responses and (b) measured channels.

Table 7-18. Approximate diversity gain for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels.

Diversity Gain (dB)

10% CDF Level 1% CDF Level Location

Simulated Measured Simulated Measured

LOS1 1 0.5 1.5 2

LOS2 0.5 2 1.5 3

LOS3 0.25 0.5 0.5 2

LOS4 <0.25 1 <0.25 2

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7.2.7 Two-Dimensional Rake Receiver

The two-dimensional rake receiver processing used for simulated and measured channels

temporally and spatially combines multipath components from four antenna array elements using

four rake fingers per element. One-dimensional rake receivers temporally combine the four

strongest multipath components, and co-phased rake output signals are combined to produce the

two-dimensional rake output signal.

CDFs of the received signal envelope with and without the use of a two-dimensional rake

receiver for NLOS locations are shown in Figure 7-71 through Figure 7-76. Approximate gains

achieved using the two-dimensional rake for simulated and measured channels are shown in

Table 7-19. Similar to ESR model results, mitigation of fading using the two-dimensional rake

was generally better for measured channels compared to simulated channels. Gains for

simulated channels up to 12 dB were achieved at the 1% CDF level, while gains for measured

channels up to 20 dB were observed.

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Figure 7-71. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS1 for (a) simulated (GBSBE) channel impulse

responses and (b) measured channels.

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Figure 7-72. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS2 for (a) simulated (GBSBE) channel impulse

responses and (b) measured channels.

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Figure 7-73. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS3 for (a) simulated (GBSBE) channel impulse

responses and (b) measured channels.

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Figure 7-74. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS4 for (a) simulated (GBSBE) channel impulse

responses and (b) measured channels.

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Figure 7-75. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS5 for (a) simulated (GBSBE) channel impulse

responses and (b) measured channels.

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Figure 7-76. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for NLOS6 for (a) simulated (GBSBE) channel impulse

responses and (b) measured channels.

Table 7-19. Approximate fading levels differences between 2-D rake output and single channel output for NLOS locations computed from simulated (GBSBE) channel impulse responses and measured channels.

Fading Level Relative to Mean Signal Strength –

2-D Rake Output Minus Single Channel Output

(dB)

10% CDF Level 1% CDF Level

Location

Simulated Measured Simulated Measured

NLOS1 4 5 12 14

NLOS2 3 7.5 6 20

NLOS3 4 5 8.5 16

NLOS4 4.5 8 12 16

NLOS5 3 7 12 15

NLOS6 6 8.5 10 16

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For LOS locations at the dense-scatterer site, Figure 7-77 through Figure 7-80 show CDFs of

relative signal envelope strengths with and without the application of a two-dimensional rake.

Approximate gains achieved using the two-dimensional rake for both simulated and measured

channels are shown in Table 7-20. Gains for 10% and 1% CDF levels show larger gains for

measured channels compared to simulated channels. In fact, gains for the simulated channels are

virtually nonexistent. Gains for measured channels up to 6 dB at the 1% CDF level where

achieved. When gains are relatively small, such as in this case for the 10% CDF level,

evaluation of model performance based on achievable gains becomes less meaningful based on

the resulting small differences between measured and simulated gains.

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Figure 7-77. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS1 for (a) simulated (GBSBE) channel impulse responses

and (b) measured channels.

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Figure 7-78. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS2 for (a) simulated (GBSBE) channel impulse responses

and (b) measured channels.

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Figure 7-79. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS3 for (a) simulated (GBSBE) channel impulse responses

and (b) measured channels.

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100CDF of Single Element Signal Strength & 2-D Rake Output

Strength Relative to Mean (dB)

Pro

babi

lity

( S

tren

gth

< A

bsci

ssa

)

Single Element (Channel 1) 2-D Rake (4 fingers per chan)

(a) (b)

Figure 7-80. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for LOS4 for (a) simulated (GBSBE) channel impulse responses

and (b) measured channels.

Table 7-20. Approximate fading levels differences between 2-D rake output and single channel output for LOS locations computed from simulated (GBSBE) channel impulse responses and measured channels.

Fading Level Relative to Mean Signal Strength –

2-D Rake Output Minus Single Channel Output

(dB)

10% CDF Level 1% CDF Level

Location

Simulated Measured Simulated Measured

LOS1 0.25 2 <0.25 6

LOS2 <0.25 2 <0.25 5

LOS3 <0.25 1.5 <0.25 4

LOS4 <0.25 2 <0.25 5

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7.2.8 GBSBE Comparison Summary

In comparing measured channel characteristics with results produced by simulations of the

GBSBE model, the following observations were made:

• In general, the GBSBE model appears to produce realistic simulations of NLOS and LOS

radio channels. To accurately represent specific characteristics of radio channels, the

model needs to be tuned using the input parameters. The model appears to be less

accurate compared to the ESR model.

• The GBSBE model produces Gaussian distributions of multipath strength (about a dB-

versus-log-delay straight line) that generally match those of NLOS measurements. This

is expected since the Gaussian trend was designed into the model using measurements.

Discrete clustering of multipath components in NLOS and LOS measured channels is not

handled by the GBSBE model. Unlike the ESR model, the GBSBE model does not

provide a way of increasing multipath count in a particular range of delay by increasing

the Poisson parameter for the corresponding scattering region. For NLOS channels,

occasional deviations of strength above the straight-line trend for early delay ranges are

not handled by the GBSBE model.

• Mean RMS delay spread for NLOS channels was higher for simulated channels

compared to measured channels. This is likely related to two causes. First, measured

NLOS channels showed relatively strong multipath early in delay, which was not

accurately managed by the GBSBE model. Second, the GBSBE model does not have the

ability to account for fewer scatterers that cause multipath for long delays compared to

the count of scatterers that cause multipath with short delays. For LOS channels,

simulated result showed a correlation of increasing mean RMS delay spread with

increasing distance, while measurements did not show this trend.

• For NLOS channels, mean excess delay spreads at the 10 dB level for simulated and

measured channels were similar. For 20 dB, 25 dB, and 30 dB levels, excess delay

spread means for simulated channels exceeded those for measured channels. For LOS

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channels, simulated results showed a strong trend between mean excess delay spread and

transmitter-receiver separation. Measured results did not necessarily follow this trend.

• Fading for simulated channels is shown to be similar to measured channels with respect

to cumulative distribution functions. Fading was Rayleigh for NLOS channels and

Rician for LOS channels. Rician K-factors were slightly larger for simulated channels.

• The GBSBE model appears to produce channel impulse responses appropriate for

reasonably simulating MRC antenna diversity. For 1% CDF levels, diversity gains of

measured NLOS channels were shown to exceed those for simulated channels, but gain

differences were 4 dB or less. For measured and simulated LOS channels, gains were

similar but small, making the comparison difficult to definitively judge.

• Performance of a two-dimensional rake receiver was shown to be better for measured

channels. Gain differences at the 1% CDF level ranged from 2 dB to 14 dB between

NLOS simulations and measurements. At the 10% level, gain differences of 4 dB or less

were observed.

Despite some shortcomings of the GBSBE model, the model is useful for generating channel

impulse responses where characterizations of input parameters for the ESR model are not

available. Differences between simulated and measured channel characteristics, such as RMS

delay spread, can be reduced by adjusting GBSBE input parameters to achieve results that better

match desired characteristics (if known). The tuned model can then be used for system

simulations.

7.3 Geometric Air-to-Ground Ellipsoidal Channel Model

The geometric air-to-ground channel model was first developed for this dissertation, and

therefore this is its first test of ability to represent the actual air-to-ground channel. The air-to-

ground measurements presented in Chapter 5 serve to provide the measurement parameter input

for the GAGE model and act as the source of measurement characteristic comparison. Air-to-

ground measurements were performed for four elevation angles, and results from several

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hundred power-delay profiles were used for evaluation of each elevation angle. Simulation

results for all measured elevation angles are presented here, allowing a comparison of results for

a variety of conditions.

7.3.1 Simulation Parameters

Details of the GAGE input parameters used to simulate the air-to-ground channel are shown in

Table 7-21. Antenna element locations, frequency, transmitter-receiver separation, and elevation

angles mimic those used for measurements. Since propagation distance through ground regions

depends upon azimuthal angle, log-distance path loss parameters could not be calculated from

measured data. However, the measured air-to-ground measurements were performed largely for

line-of-sight channels, and terrestrial measurements have been performed to characterize the

ground region near where the ground station was located; therefore, results from the LOS

locations at the dense-scatterer site were used to define the GAGE input parameters of path loss

exponent and standard deviation of strength variation. Maximum excess delay was set to the

largest excess delay logged during air-to-ground measurements. As in the evaluation of the ESR

and GBSBE models, log-distance path loss reference distance remains an assumed value, which

was chosen equal to that used for ESR and GBSBE model simulations. Reflection loss was

selected as a function of elevation angle as described in section 7.3.2.

Because of the non-uniform distribution of measured multipath component count versus delay

(see section 5.4.4), a sub-regions approach was taken with the GAGE model. Equal intervals of

multipath excess delay were used. The delays correspond to concentric ellipsoids in three

dimensional space that form elliptical intersections with the ground plane; these elliptical

intersections share one common focus at the ground-based receiver location. The simulated air-

to-ground propagation environment for the GAGE model is shown in Figure 7-81. The ground-

level elliptical boundaries depicted represent equal intervals of excess multipath delay. The

transmitter and receiver are located at the elevated plus symbol and ground-level circle,

respectively. Ground-level dots correspond to randomly generated scatterer positions, the counts

of which depend upon specified Poisson parameters. Lines connecting the transmitter, scatterer,

and receiver are the single-bounce propagation paths.

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Table 7-21. Major simulation parameters for geometric air-to-ground ellipsoidal channel model.

Parameter Value Number of sub-regions 16 Poisson parameters Equal to values measured during air-to-ground

measurements (see Table 5-33 on page 199) Frequency 2050 MHz Path loss exponent 4.10 Standard deviation of strength variation 5.24 dB Reflection loss Varies based on elevation angle (see section

7.3.2) Maximum excess delay 1556 ns Transmitter-receiver separation Equal to values used for measurements (see

Table 5-30 on page 189)

0

500

1000

1500 -500

0

5000

200

400

600

y-coordinate (m)

Propagation Environment

x-coordinate (m)

z-co

ordi

nate

(m

)

Figure 7-81. Example of geometric air-to-ground channel model simulation showing transmitter location (plus symbol at elevated ellipsoid focus), receiver location (circle at ellipsoid and ground ellipse shared focus), scatterers (dots), propagation paths (green lines), and sub-region boundaries of constant propagation delay.

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7.3.2 RMS Delay Spread

Measured RMS delay spread results showed a strong correlation with elevation angle, a trend

which was anticipated for simulated channels. However, initial RMS delay spread results did not

show the expected elevation angle dependency. Figure 7-82 shows CCDFs of RMS delay spread

for a constant reflection coefficient of 10 dB. The plot labeled (a) shows simulation results, and

the plot labeled (b) shows results derived from measurements of the channel. The measured

results illustrate the dependency of RMS delay spread distribution on elevation angle. However,

the results based on simulated channel impulse responses clearly fail to follow a similar trend.

As a result of the RMS delay spread distribution discrepancy, it was hypothesized that the

elevation angle dependency was a result of reflection loss being a function of elevation angle.

Although varying the number of multipath components as a function of elevation angle could

also be used to increase or reduce RMS delay spread as needed to match measurements, air-to-

ground measurement results described in section 5.4.4 showed that the number of multipath

components in each of 16 delay bins did not vary significantly with changes in elevation angle.

Therefore, a variable reflection loss was used and the hypothesis tested.

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RMS Delay Spread (ns)

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RMS Delay Spread Based On Simulated Channels

Elevation angle 7.5 deg Elevation angle 15 deg Elevation angle 22.5 degElevation angle 30 deg

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

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0.8

0.9

1

RMS Delay Spread (ns)

Pro

babi

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RM

S D

elay

Spr

ead

> A

bsci

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)

RMS Delay Spread Based On Measurements

Channel 1Channel 2Channel 3Channel 4

7.5 deg

15 deg

22.5 deg

30 deg

(a) (b)

Figure 7-82. CDF of RMS delay spread for four elevation angles for (a) simulated (GAGE) channel impulse responses and (b) measured channels. A constant reflection loss was used.

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RMS delay spread results using a variable reflection loss are shown in Figure 7-83. Plot (a) is an

RMS delay spread CCDF based on simulated channels, and plot (b) is an RMS delay spread

CCDF base on measured channels. Reflection loss values used to produce these CCDFs of RMS

delay spread results are shown in Table 7-22. The CCDF plots show that a variable refection

loss can be used to produce accurate modeling of RMS delay spread distributions. Mean and

standard deviation of RMS delay spread results for simulated and modeled channels are shown in

Table 7-23. The table shows good agreement between simulated and measured values for all

elevation angles. For the remaining GAGE channel model discussions, simulations use the

reflection losses set forth in Table 7-22.

Table 7-22. Reflection losses as a function of elevation angle used to produce the most accurate RMS delay spread results for the GAGE model.

Elevation Angle Reflection Loss

7.5 14

15 21

22.5 30

30 33

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RMS Delay Spread (ns)

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elay

Spr

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> A

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ssa

)

RMS Delay Spread Based On Simulated Channels

Elevation angle 7.5 deg Elevation angle 15 deg Elevation angle 22.5 degElevation angle 30 deg

0 20 40 60 80 100 120 140 160 180 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

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0.9

1

RMS Delay Spread (ns)

Pro

babi

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RM

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elay

Spr

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> A

bsci

ssa

)

RMS Delay Spread Based On Measurements

Channel 1Channel 2Channel 3Channel 4

7.5 deg

15 deg

22.5 deg

30 deg

(a) (b)

Figure 7-83. CCDF of RMS delay spread for four elevation angles for (a) simulated (GAGE) channel impulse responses and (b) measured channels. Reflection loss was defined to be a function of elevation angle.

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Table 7-23. RMS delay spread results for air-to-ground simulations using the GAGE model versus measurements.

RMS Delay Spread (ns) Elevation

Angle (deg) Mean Standard Deviation

Simulated Measured Simulated Measured

7.5 104 98.1 65.8 82.2

15 55.5 54.9 36.4 40.6

22.5 23.0 24.3 12.6 16.7

30 18.7 18.3 10.7 9.89

7.3.3 Multipath Signal Strength

As discussed earlier, path loss for the GAGE model is fundamentally different than path loss for

the ESR and GBSBE models because the distance traversed by multipath components through

the scattering region is dependent upon direction of arrival. Notwithstanding that fact, scatter

plots of multipath strength versus log-delay were produced for comparison of the GAGE model

to measurements. Figure 7-84 through Figure 7-87 illustrate scatter plots based on simulated and

measured channels. In comparing these figures, it can be noted that the measured plots show

sporadic delay intervals where strong multipath components exist. These clusters of strong

multipath are likely due to dominant scatterers in the environment that reflected energy

effectively. The GAGE model has no provision for directly modeling these clusters; however,

Poisson parameters for each sub-region could be adjusted to produce clusters of multipath

components.

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(a) (b)

Figure 7-84. Scatter plot of multipath strength versus log of propagation delay for the 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles.

(a) (b)

Figure 7-85. Scatter plot of multipath strength versus log of propagation delay for the 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles.

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(a) (b)

Figure 7-86. Scatter plot of multipath strength versus log of propagation delay for the 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles.

(a) (b)

Figure 7-87. Scatter plot of multipath strength versus log of propagation delay for the 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured power-delay profiles.

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7.3.4 Excess Delay Spread

Excess delay spread results for simulated and measured air-to-ground channels are shown in

Table 7-24. For all excess delay spread levels, nearly all means of excess delay spread for

measurements exceed those for simulation. Both simulations and measurements show a decrease

in mean excess delay spread as elevation angle increases. Discrepancies between simulated and

measured mean excess delay spread become smaller in terms of percentages as excess delay

spread level increases. Differences such as these can be caused by errors in selection multipath

strength distribution parameters, errors in selection of log-distance path loss exponents for the

ground propagation leg, or the variability of model parameters with propagation distance or

azimuthal angle39.

Table 7-24. Excess delay spread values for simulated and measured air-to-ground channel impulse responses.

Excess Delay Spread (ns)

10 dB Level 20 dB Level

Mean Max Mean Max

Elevation

Angle

Sim Meas Sim Meas Sim Meas Sim Meas

7.5 94.8 169 1185 1380 460 431 1358 1490

15 3.40 104 673 1300 206 250 1335 1480

22.5 0 90.0 0 1031 11.9 127 588 1294

30 0 89.0 0 256 3.57 108 574 471

Excess Delay Spread (ns)

25 dB Level 30 dB Level

Mean Max Mean Max

Elevation

Angle

Sim Meas Sim Meas Sim Meas Sim Meas

7.5 589 613 1509 1550 656 703 1509 1570

15 400 407 1359 1480 567 595 1361 1590

22.5 96.0 199 1197 1294 290 352 1318 1407

30 47.7 157 992 1290 196 284 1257 1340

39 The model assumes constant input parameters as the aircraft circles the receiver location. In practice, however, the environmental characteristics may not be uniform in azimuthal angle around the receiver.

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7.3.5 Multipath Fading

Fading envelopes for the air-to-ground channel were computed by vector sum of multipath

components in measured power-delay profiles and simulated channel impulse responses. CDFs

of signal envelopes, normalized to median values, are shown in Figure 7-88. For comparison of

measured data, simulated data, and theory, CDFs for Rayleigh fading are also shown in the plots.

Figure 7-89 indicates that air-to-ground CDFs for simulations and measurements exhibit Rician

characteristics. Simulated channels show a slightly larger Rician K-factor.

-25 -20 -15 -10 -5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1CDF of Received Signal Strength for Simulated Air-to-Ground Channels

Signal Strength Relative to Median (dB)

Pro

babi

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( S

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< A

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)

Elevation angle 7.5 deg Elevation angle 15 deg Elevation angle 22.5 degElevation angle 30 deg Rayleigh

-25 -20 -15 -10 -5 0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1CDF of Received Signal Strength for Measured Air-to-Ground Channels

Signal Strength Relative to Median (dB)

Pro

babi

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( S

tren

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< A

bsci

ssa

)

Elevation angle 7.5 deg Elevation angle 15 deg Elevation angle 22.5 degElevation angle 30 deg Rayleigh

(a) (b)

Figure 7-88. Signal strength CDF for each air-to-ground elevation angle derived from (a) channel impulse response simulations and (b) measured channels.

7.3.6 Antenna Diversity

Maximal ratio combining (MRC) was applied to the simulated and measured air-to-ground

channels using an antenna element separation of 2/λ . Figure 7-89 through Figure 7-92 show

CDFs of relative signal envelope power. One CDF in each plot corresponds to a receiver using

single antenna element, and the other CDF on each plot corresponds to the output of MRC

diversity combining.

Shown in Table 2-1 are approximate diversity gains for simulated and measured air-to-ground

channels for the 1% and 10% CDF levels. These results show that only modest diversity gains of

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2.5 dB or less are achievable for measured channels. Diversity gains for simulated channels are

close to those for measured channels, where differences for the 10% level are less than 0.5 dB

and differences for the 1% level are less than 1.5 dB.

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10-2

10-1

100

CDF of Single Element Signal Strength & Diversity Combiner Output

Strength Relative to Mean (dB)

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Single ElementMRC Diversity

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-3

10-2

10-1

100CDF of Single Element Signal Strength & Diversity Combiner Output

Strength Relative to Mean (dB)P

roba

bilit

y (

Str

engt

h <

Abs

ciss

a ) Single Element

MRC Diversity

(a) (b)

Figure 7-89. CDF of received signal strength using maximal ratio combining and using a single antenna for 7.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

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-3

10-2

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100

CDF of Single Element Signal Strength & Diversity Combiner Output

Strength Relative to Mean (dB)

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Single ElementMRC Diversity

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Strength Relative to Mean (dB)

Pro

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bsci

ssa

) Single ElementMRC Diversity

(a) (b)

Figure 7-90. CDF of received signal strength using maximal ratio combining and using a single antenna for 15 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

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-3

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CDF of Single Element Signal Strength & Diversity Combiner Output

Strength Relative to Mean (dB)

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Single ElementMRC Diversity

-25 -20 -15 -10 -5 0 5 10 1510

-3

10-2

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100CDF of Single Element Signal Strength & Diversity Combiner Output

Strength Relative to Mean (dB)

Pro

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tren

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< A

bsci

ssa

)

Single ElementMRC Diversity

(a) (b)

Figure 7-91. CDF of received signal strength using maximal ratio combining and using a single antenna for 22.5 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

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-3

10-2

10-1

100

CDF of Single Element Signal Strength & Diversity Combiner Output

Strength Relative to Mean (dB)

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ssa

)

Single ElementMRC Diversity

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10-2

10-1

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Strength Relative to Mean (dB)

Pro

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bsci

ssa

)

Single ElementMRC Diversity

(a) (b)

Figure 7-92. CDF of received signal strength using maximal ratio combining and using a single antenna for 30 degree elevation angle for (a) simulated (GAGE) channel impulse responses and (b) measured channels.

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Table 7-25. Approximate diversity gain for simulated and measured air-to-ground channel impulse responses.

Diversity Gain (dB)

10% CDF Level 1% CDF Level Elevation

Angle Simulated Measured Simulated Measured

7.5 0.75 0.75 4 2.5

15 0.5 0.75 1 2

22.5 <0.25 0.25 0.25 1

30 <0.25 <0.25 0.25 0.25

7.3.7 Two-Dimensional Rake Receiver

Two-dimensional rake receiver processing was used to produce the CDFs shown in Figure 7-33

through Figure 7-38. Using four fingers, the receiver processing coherently combined multipath

components in space and delay. The CDFs show relative received signal envelope power with

and without the use of a two-dimensional rake receiver for simulated and measured air-to-ground

channels. Approximate gains at 10% and 1% CDF levels achieved through the use of the two-

dimensional rake are shown in Table 7-26. Simulated and measured gains at the 1% CDF level

were similar and showed decreasing gain with increasing elevation angle. Up to 8 dB of gain at

the 1% CDF level was achieved for simulated channels at and up to 7 dB for measured channels

was achieved. Gains at the 10 % CDF level were small.

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10-2

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CDF of Single Element Signal Strength & 2-D Rake Output

Strength Relative to Mean (dB)

Pro

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Single Element (Channel 1) 2-D Rake (4 fingers per chan)

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10-2

10-1

100CDF of Single Element Signal Strength & 2-D Rake Output

Strength Relative to Mean (dB)

Pro

babi

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< A

bsci

ssa

)

Single Element (Channel 1) 2-D Rake (4 fingers per chan)

(a) (b)

Figure 7-93. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 7.5 degree elevation angle for (a) simulated (GAGE) channel

impulse responses and (b) measured channels.

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10-2

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100

CDF of Single Element Signal Strength & 2-D Rake Output

Strength Relative to Mean (dB)

Pro

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Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-25 -20 -15 -10 -5 0 5 10 15

10-2

10-1

100CDF of Single Element Signal Strength & 2-D Rake Output

Strength Relative to Mean (dB)

Pro

babi

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tren

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< A

bsci

ssa

)

Single Element (Channel 1) 2-D Rake (4 fingers per chan)

(a) (b)

Figure 7-94. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 15 degree elevation angle for (a) simulated (GAGE) channel

impulse responses and (b) measured channels.

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CDF of Single Element Signal Strength & 2-D Rake Output

Strength Relative to Mean (dB)

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Single Element (Channel 1) 2-D Rake (4 fingers per chan)

-25 -20 -15 -10 -5 0 5 10 15

10-2

10-1

100CDF of Single Element Signal Strength & 2-D Rake Output

Strength Relative to Mean (dB)

Pro

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< A

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)

Single Element (Channel 1) 2-D Rake (4 fingers per chan)

(a) (b)

Figure 7-95. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 22.5 degree elevation angle for (a) simulated (GAGE)

channel impulse responses and (b) measured channels.

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10-2

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100

CDF of Single Element Signal Strength & 2-D Rake Output

Strength Relative to Mean (dB)

Pro

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Single Element (Channel 1) 2-D Rake (4 fingers per chan)

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10-2

10-1

100CDF of Single Element Signal Strength & 2-D Rake Output

Strength Relative to Mean (dB)

Pro

babi

lity

( S

tren

gth

< A

bsci

ssa

)

Single Element (Channel 1) 2-D Rake (4 fingers per chan)

(a) (b)

Figure 7-96. CDF of received signal strength relative to mean using a two-dimensional rake receiver (4 fingers) and using a single antenna (no rake) for 30 degree elevation angle for (a) simulated (GAGE) channel

impulse responses and (b) measured channels.

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Table 7-26. Approximate fading levels differences between 2-D rake output and single channel output for air-to-ground channels computed from simulated channel impulse responses and measured channels.

Fading Level Relative to Mean Signal Strength –

2-D Rake Output Minus Single Channel Output

(dB)

10% CDF Level 1% CDF Level

Elevation

Angle

Simulated Measured Simulated Measured

7.5 3.5 0.5 8 7

15 1.5 0.5 2.5 3

22.5 <0.5 0.5 1 2

30 0.5 0.5 0.5 1.5

7.3.8 GAGE Comparison Summary

Comparison of the GAGE model with the air-to-ground measurements resulted in the following

observations:

• In general, the GAGE model performs satisfactorily with respect to comparisons of RMS

delay spread characteristics, fading characteristics, MRC diversity gains, and two-

dimensional rake receiver gains.

• RMS delay spread characteristics of simulated channels accurately follow characteristics

of measured channels when reflection loss is tuned. CDFs of RMS delay spread show

agreement when the model is tuned based on mean RMS delay spread. RMS delay

spread characteristics of measured and simulated channels show the same trend with

changes in elevation angle.

• Differences in excess delay spread results between measured and modeled channels vary

depending on elevation angle and excess delay spread level. For the 10 dB level,

simulated channels based on the GAGE model tend underestimate excess delay spread.

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At larger levels, excess delay spread results tend to match for lower elevation angles but

deviate for higher elevation angles.

• Using the GAGE model, simulated and measured vector channel impulse responses

appear to compare well with respect to MRC antenna diversity characteristics. Although

gains are small, and thereby difficult to judge accurately, differences in diversity gains

were 1.5 dB or less.

• Results using a two-dimensional rake receiver showed a favorable comparison between

measured and modeled channels. Gain differences of only 1 dB or less were noted for

the 1% CDF level; gain differences for the 10% CDF level were 3 dB or less. For the 7.5

degree elevation angle, measurements and simulations both resulted in large gain (7 dB

and 8 dB respectively). Gains at the 1% CDF for other elevation angles were modest, on

the order of 1 dB to 3 dB for measured and simulated channels.

7.4 Summary

Three geometric channel models have been compared to measurements of channels from which

model input parameters were derived. Ideally, the characteristics of measured and modeled

channels would exactly match. However, because model results rely on theoretical statistical

distributions that summarize behavior of the channel, at least slight errors in modeling are

expected.

The ESR and GBSBE models shared the deficiency of not being able to produce strong clusters

of multipath components that were apparent in measured power-delay profiles. Scatter plots of

multipath strength for the GBSBE model indicated that multipath components were sparsely

scattered for early delays compared to measurements. The ESR model performed better in this

regard by providing a means to distribute multipath scatterers more densely in regions that

induce multipath with early delays.

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The ESR model performed better than the GBSBE model for producing simulated channel

impulse responses with RMS delay spreads that matched measured channels. For NLOS

channels, percentage differences between mean RMS delay spreads of ESR-simulated channels

and those of measured channels ranged from approximately 3% to 33%, while percentage

differences for GBSBE-simulated channels ranged from approximately 73% to 86%. The ESR

model also generally performed better with respect to LOS mean RMS delay spread results. For

the GAGE model, provisions for variable reflection losses based on elevation angle resulted in

only single-digit percent differences between measured and simulated mean RMS delay spread

results.

Simulations of multipath fading showed that the ESR model performs better than the GBSBE

model for its ability to produce channels with fading characteristics that match those of measured

channels. Relative signal strength CDFs showed that measured NLOS fading was Rayleigh

distributed, and channels produced by the ESR model were closer to Rayleigh than channels

produced by the GBSBE model. CDFs of envelope fading for LOS channels showed that

measured channels exhibited Rician fading characteristics, as did the channels produced by the

ESR and GBSBE models. However, the CDFs of the ESR model better match the CDFs of the

measurements with regard to the Rician K-factor. For the GAGE model, CDFs of fading for

simulated channels aligned very well with CDFs of fading for measured channels. Measured and

simulated air-to-ground channels exhibited Rician fading with similar K-factors.

The ESR and GBSBE models produced similar results with respect to antenna diversity gain for

NLOS channels. For LOS channels, the ESR model produced gains that were on average

approximately 3 dB higher than measured results at the 1% CDF level, and the GBSBE model

produced gains that were on average approximately 2 dB lower than measured results at the 1%

CDF level. While exact values and differences of diversity gains vary, measured channels with

large diversity gains were generally associated with modeled channels with large diversity gains.

Likewise, simulations of channels with modest measured gains generally produced simulated

responses with modest gains.

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The ESR and GBSBE models both underestimated the gain achievable using a two-dimensional

rake receiver. At the 1% CDF level, the mean difference between gains achieved for measured

responses and gains achieved for simulated responses using the ESR model was 8 dB. For the

GBSBE model, the mean difference was 6 dB. For the GAGE model, simulated two-

dimensional rake results generally matched those based on measurements.

The models generally demonstrated a good ability to produce channel impulse responses with

reasonable values for RMS delay spread, excess delay spread, fading envelopes, diversity gain,

and gain using a two dimensional rake receiver. Although some simulated output values

deviated from measured results, those values were still within ranges that are sensible for the

environments modeled. The key to accurately modeling a target environment is to tune the input

parameters of the model such that the simulated channel impulse responses exhibit the important

characteristics of the target environment. Once tuned, a model can be used to generate an

arbitrarily large amount of channels for testing communication system designs through

simulations. With this in mind, the true value of these geometric models is the ability to use a

relatively small amount of measurement data to generate an enormous amount of channel data.

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315

Chapter 8 Conclusion

This research has addressed areas of radio channel measurement and modeling, smart antennas,

and software radio. A union of these areas helped produce a new measurement system and new

research results applicable to design and analysis of systems using antenna arrays.

8.1 Summary of Research

A survey of published literature on antenna array theory provided direction for this research.

Smart antenna arrays are a proven method for increasing capacity, improving performance, and

enhancing quality of service for wireless communication systems. Designing successful smart

antenna systems requires channel measurements and models for testing and validation of

algorithms.

Development of the wideband measurement receiver successfully demonstrated the benefits and

feasibility of an object-oriented, software radio architecture. Demand for the system over

approximately five years illustrated the value of a flexible software radio receiver architecture.

Over the same period of time, ease of capabilities expansion and maintainability highlighted the

advantages of encapsulation and abstraction inherent in an object-oriented design. Provisions for

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316

future applications built into the system at design time and an interface to standardized

simulation software allowed implementation of sponsored research and classroom applications

that had not been envisioned for the system during its development.

Channel models of various types were researched and a new technique for three-dimensional

geometric channel modeling was developed using ellipsoids. The ellipsoidal geometry was

applied to the problem of modeling air-to-ground channels. Equations appropriate for addressing

air-to-ground channel modeling were derived and used for analysis and simulation of multipath

time-of-arrival and direction-of-arrival characteristics for a ground-based receiver. Experience

gained through this work formed a basis for measurement planning, vector channel simulation,

and channel model evaluation.

Measurements produced results for characterization and input parameters for channel models.

Terrestrial measurements were designed to meet the needs of channel model evaluation. Air-to-

ground measurements characterized a channel not often studied in addition to producing data for

channel model testing. Measured power-delay profiles were processed to characterize time

dispersion in radio channels using RMS delay spread and excess delay spread, and maximum

multipath delays were computed for input to geometric channel models. Quantitative

measurement results on multipath strength trends, multipath counts versus delay, path loss

exponents, and signal envelope fading will assist researchers dealing with the types of channels

studied here.

A channel simulator was developed to implement and evaluate three geometric channel models.

The simulator demonstrated steps beyond what was clearly defined for the models in

publications. These steps were required for accurate simulation of characteristics observed in

actual radio channels, such as strength variations due to stochastic properties of the environment

and fading of multipath components across an antenna array. The simulator can be used for

future research in propagation and communication system simulation, and it can be expanded to

include other channel models or improvements on currently supported models.

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Three geometric channel models (ESR, GBSBE, and GAGE) were evaluated based on their

ability to produce channel impulse responses with characteristics that matched characteristics of

measured power-delay profiles. The models demonstrated a reasonable ability to represent

measured channels with respect to RMS delay spread, excess delay spread, fading envelopes,

diversity gain, and gain using a two dimensional rake receiver. Most deviations away from

measured characteristics were relatively minor in that the resulting characteristics were within

limits for reasonable the types of channels measured, and similar discrepancies could be

expected when comparing the measurements presented here with measurements at other sites in

similar propagation environments. Tuning of model input parameters is a recommended method

of achieving specific characteristics of target environments. The advantage of channel models is

the ability to use summarizing statistics based on relatively few measurements to generate a far

larger number channel impulse responses for simulation.

8.2 Original Contributions

This research has produced the following contributions:

• A fully functional, software-defined radio receiver was designed and constructed; this

system continued to be used by multiple researchers for other research projects.

• An application of object-oriented, multi-threaded software design techniques to software

radio architecture was demonstrated.

• A geometric air-to-ground ellipsoidal channel model was developed and tested; analytical

and simulated results yield insight into the air-to-ground radio channel.

• Evaluations of existing geometric channel models were performed and documented in

detail.

• Measurement techniques were developed to characterize and model multipath strength

variations, correlation of multipath component strengths, and multi-leg propagation for

air-to-ground channels.

• A multi-topic compilation of literature on modern software development techniques,

smart antennas, software radios, channel modeling, and channel measurements.

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This research is directly responsible for new radio channel measurements, experimental results,

and demonstration capabilities:

• Terrestrial channel measurements, air-to-ground channel measurements, and

multiple antenna array experiments were performed to serve multiple research

projects (sponsored by Allen Telecom, Altera, DARPA, Grayson Wireless, LGIC,

Office of Naval Research, Texas Instruments, and NASA/Virginia Space Grant

Consortium).

• Wideband measurements were performed along highways in Blacksburg, Virginia

and Richmond, Virginia to characterize channels and measure multipath isolation

between antennas used for single-frequency repeaters (sponsored by Allen

Telecom, MIKOM).

• Low-to-ground wideband channel measurements were made over line-of-sight

and forested paths at 300 MHz and 1.9 GHz (sponsored by ITT

Aerospace/Communications Division).

• In-building wideband channels were measured for wireless LAN (802.11)

propagation and interference research (sponsored by CNS/Virginia Tech).

• Performance of transmit diversity was measured and demonstrated in indoor

channels (sponsored by Texas Instruments).

• The software-defined receiver was used to test adaptive antenna array algorithms

developed by graduate students for a software radio course (Virginia Tech).

• Power-delay profiles for indoor and outdoor channels were processed for research

and development of hidden Markov models (sponsored by LGIC).

• Measurements in NLOS and LOS environments were processed to support space-

time processing research and hidden Markov modeling for the NAVCIITI

program (sponsored by Office of Naval Research).

• Improvements of MPEG video signal transmissions using antenna diversity were

demonstrated with the software-defined receiver; the receiver communicated with

a MPEG test bed over a TCP/IP network to form a distributed simulation platform

(sponsored by DARPA).

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319

• Measurement receiver and test bed demonstrations were performed for

representatives of Congress and federal government to showcase wireless

research at Virginia Tech.

• Received signal measurements and channel measurements were performed for

development of the VT-STAR MIMO test bed system (sponsored by MPRG

Industrial Affiliates).

• Numerous demonstrations of the measurement receiver and test bed were

performed for visitors to Virginia Tech, including industrial sponsors, academic

colleagues, symposium attendees, government representatives, and private

donors.

8.3 Future Work

This research has revealed opportunities for future work on the following topics:

Measurements and measurement systems

• The techniques and methodologies of the current wideband measurement system should

be used to develop a more portable system with the same or greater capabilities; portions

of software and hardware of the current system could be directly inherited for this

purpose.

• Software for determining direction of arrival of multipath components with high

resolution should be written for the measurement system.

• MIMO channel algorithms should be implemented on the measurement system receiver.

• The FPGA spread-spectrum transmitter developed for this research should be further

developed into a multi-channel transmitter for MIMO channel characterization.

• Measurements in several locations in multiple environments should be performed to

compare channel models to a wider range of measurement results.

• Direction of arrival statistics should be measured in multipath channels and compared

with results of channel models.

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Channel modeling

• Evaluations of statistical- and measurement-based models should be performed and

compared to the capabilities and accuracy of geometric channel models.

• A analysis of the sensitivity of geometric channel model output to change of model input

parameters should be performed.

• The geometric air-to-ground channel model should be compared against high-altitude and

long-range airborne measurements to determine applicability.

Smart Antennas

• New and existing antenna array configurations and algorithms should be tested

simultaneously with channel measurements to establish relationships between array

performance and channel characteristics.

• Performance of various beamforming algorithms applied to measured and simulated

channels should be compared.

• Existing smart antenna simulation code should be slightly modified so that they become

software radio modules and can be evaluated in actual channels using the measurement

receiver.

8.4 Closing

In summary, this research has produced several developments in radio channel measurements

and channel modeling related to smart antennas. The results should serve engineers and

researchers who continue work in propagation and wireless communication system design. As

long as wireless communications continues to develop, radio channels will need to be measured,

characterized, and modeled for applications to come.

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321

Epilogue

The metaphorical lead character of this dissertation, as of this writing, remains alive and well. I

feel a sense of pride in seeing that the measurement system’s usefulness has delayed its

inevitable cannibalization, a fate that seems to befall all hardware creations as a sacrifice to build

better and faster systems constructed from scratch and starved for components. Such

resourcefulness along with perseverance drive our field, a discipline in which an enormous effort

on the part of the individual marks the next blaze along a faint trail for the next explorer. Of

great significance are the accomplishments of pioneers. Of greater significance is the inspiration

of minds who follow.

During one of my excursions from academia, an island whose surrounding waters can isolate and

protect yet periodically madden, I discovered Giovanni de Lutero’s (Dosso Dossi) Learned Man

of Antiquity, an Italian painting circa 1520 that symbolized for me the power of math and

science. The remarkably muscular man in this striking image wore the expression of a scholar,

whose brawn seemed to be built not by lifting the stone tablet he firmly held in his extended arm,

but by pursuit of the unreadable but recognizable mathematical expressions carved into the

tablet. The scholar stared beyond the painting’s border, toward a brightness that was divine in

spite of this scientific threat to a world of religious explanations. This work depicted a secular

transition of thought with the approval of God, and it was a prophetic painting of societal

direction for the next five-hundred years.

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EPILOGUE

322

My life’s theme of science and math delivered me to engineering, and my father ignited my

interest in telecommunications as I recall from my earliest memories of listening to dinner-table

conversations after his workdays at the phone company. Wireless was (and is) the magic show

of telecommunications, drawing into its sideshow tent many kids and adults and adult-kids, and

I’ve spent decades trying to figure out how to perform as many tricks as possible. What I’ve had

to come to accept is that each magician in wireless has his or her own niche, and not one

thoroughly understands all of the illusions.

Wireless will follow a path to destinations we cannot yet conceive. While I’ve heard pundits

speak of approaching saturation in the wireless field, I can say that after climbing to this doctoral

peak, I see plenty of open space and a future that extends beyond any visible horizon. Maybe it

takes a climb to a summit, not necessarily doctoral, and an unobstructed view only possible at the

top, to look toward the fringe of mist and know that beyond what is immediately visible there is

overwhelming potential along the adventurous trails ahead.

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323

Appendix A Measurement Receiver MATLAB Signal Interface

A.1 MATLAB Interface Overview

The measurement receiver includes software to interface with the MATLAB engine. The

interface has been fully tested with MATLAB version 5.3.1. The MATLAB interface allows m-

files written for MATLAB to execute using actual signal data from the measurement receiver.

By connecting an m-file to the measurement receiver through the interface, a MATLAB

simulation defined by the m-file becomes an actual radio processing module as part of the

measurement receiver, operating on signal snapshots from all four channels in real time.

The interface works by inserting variables in the MATLAB workspace and filling these variables

with signal data and other data. Once the variables are populated, the measurement receiver

software instructs MATLAB to call the user’s m-file. The framework allows for results to be

plotted on a single figure (subplots are allowed). The m-file is called once each time a snapshot

of the four channels is available; if the m-file completes in a time period longer than the

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324

between-snapshot period, then the m-file will not be called until MATLAB has completed

processing the m-file. For best results, all m-files that are called by the m-file named in the

interface should be placed in the same folder (disk directory).

MATLABInterfaceSoftware

Data Source

Received Dataor

Logged Data

MATLAB ENGINEMeasurementReceiver

MainApplication

Object

Variables• Execution of m-file• Plotting of data

UserM-File

Called witheach snapshot

MATLABInterfaceSoftware

Data Source

Received Dataor

Logged Data

MATLAB ENGINEMeasurementReceiver

MainApplication

Object

Variables• Execution of m-file• Plotting of data

UserM-File

Called witheach snapshot

Figure A-1. Data flow through measurement receiver to MATLAB workspace.

A.2 Workspace Variables

The measurement receiver software automatically opens the MATLAB engine when the

MATLAB interface is started. When the interface is instructed to execute by the user, the

measurement receiver software passes data to the MATLAB workspace in several variables. The

variables passed into the workspace are described in Table A-1. The table shows the variable

name, the type of variables and numbers expected, and a description of the contents.

The variables Ch1Signal, Ch2Signal, Ch3Signal, Ch4Signal are vectors that contain the sampled

signal data. The length of the vectors is variable and depends upon the configuration of the

measurement receiver; typically 15,000 samples are sufficient for applications such as multipath

profile characterization algorithms. Each element of the vectors represents a sample taken by the

A/D converter. The vectors are synchronized, meaning that the sample represented in the first

element of Ch1Signal was sampled at the same instant as the first elements of Ch2Signal,

Ch3Signal, and Ch4Signal. In other words, Ch1Signal[n] is sampled at the same time as

Ch2Signal[n], Ch3Signal[n], and Ch4Signal[n].

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The samples represented by Ch1Signal, Ch2Signal, Ch3Signal, Ch4Signal are actually sampled

IF. Typically, a center IF frequency of 150 MHz is used, but there is no restriction on using

other bands within the 200 KHz to 400 MHz IF bandwidth. As an example, if a 2050 MHz

sinusoid is received by channel one and a 1900 MHz local oscillator frequency is used, then

Ch1Signal will contain a sinusoid with a frequency of 150 MHz. In addition, consecutive

samples in Ch1Signal will be separated in time by 1/SampleRate, and the magnitude of each

sample is in units of volts referenced to the channel one antenna port.

SweepNum represents the snapshot number assigned to the snapshot by the measurement

receiver. This number gives a counter to use as a reference when processing multiple snapshots

with m-files and the MATLAB interface. The TimeStamp variable is a constant-length string

that indicates the time and date at which snapshot was acquired by the measurement receiver; all

signal vectors for the associated snapshot are acquired simultaneously at the time given in

TimeStamp.

A.3 Real-Time Plotting

The MATLAB interface automatically opens a MATLAB figure for each instance of the

interface. This means that the m-file called by the interface can plot on the single figure opened

by the interface. Because the interface needs to handle figures for multiple instances of the

interface, the figure(.) command in MATLAB generally should not be used in the m-file.

However, subplots are permitted using the subplot(.) command in the m-file.

Plotting is typically performed at the end of the m-file to display the results. If no condition

statements exist around the plot command, the plot will be generated each time the m-file is

called and, therefore, each time the measurement receiver passes signal data to the MATLAB

workspace. To create a plot, use the plot(.) command in the m-file. The associated title(.),

xlabel(.), ylabel(.), and axis(.) commands may be used.

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Table A-1. Description of variables passed into MATLAB workspace by measurement receiver.

Variable Name Type Description Ch1Signal 1xn matrix (vector) of

double-precision values. Signal data from channel one of the measurement receiver. Units are volts referenced to the antenna port (50 ohms real impedance). Length of vector (n) is determined by the snapshot length in samples taken by the measurement receiver.

Ch2Signal 1xn matrix (vector) of double-precision values.

Signal data from channel two of the measurement receiver. Units are volts referenced to the antenna port (50 ohms real impedance). Length of vector (n) is determined by the snapshot length in samples taken by the measurement receiver.

Ch3Signal 1xn matrix (vector) of double-precision values.

Signal data from channel three of the measurement receiver. Units are volts referenced to the antenna port (50 ohms real impedance). Length of vector (n) is determined by the snapshot length in samples taken by the measurement receiver.

Ch4Signal 1xn matrix (vector) of double-precision values.

Signal data from channel four of the measurement receiver. Units are volts referenced to the antenna port (50 ohms real impedance). Length of vector (n) is determined by the snapshot length in samples taken by the measurement receiver.

SampleRate Scalar, double-precision value

Sample rate (samples/sec) used by the measurement receiver to sample signals at each channel.

SweepNum Scalar, integer Snapshot number used as an index to keep track of snapshots. Snapshots from each channel with the same SweepNum value were sampled simultaneously.

TimeStamp String, constant-length Time stamp corresponding to the time a particular snapshot of channels was acquired. Example: Thu Jun 28 15:20:29.592 2001

A.4 Example M-File

An m-file listing that shows how to use the signal data and how to produce real-time plots is

shown in Figure A-2. This m-file uses the Ch2Signal variable that is inserted into the MATLAB

workspace by the measurement receiver software. The fast Fourier transform (FFT) of

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Ch2Signal is computed and stored in the ChSpec variable. The frequency vector FreqMHz

whose elements correspond to the elements of ChSpec is computed using the SampleRate

variable, which is also inserted into the MATLAB workspace by the measurement receiver. A

calibration factor is subtracted from the ChSpec vector; this calibration factor is determined

experimentally using a receiver input signal of known power.

% This file serves as an example of using m-files with VIPER. % An FFT is performed using the signal from channel 2, and the % FFT is plotted. W. Newhall 2001 % Receiver software puts Ch2Signal, SampleRate, etc., in the workspace. % Set local oscillator offset for correct frequency axis LocalOscillator = 1900; % LO freq in MHz % Take the FFT of the Channel 2 Signal ChSpec = abs( fft( Ch2Signal ) ); ChSpecDb = 20*log10( ChSpec ); NumFFTPts = length( ChSpec ); % Calculate frequency vector FreqStep = SampleRate / (NumFFTPts-1); Freq = 0:FreqStep:SampleRate; FreqMHz = Freq/1e6 + LocalOscillator; % Points to plot and calibration offset Pts = 1:(NumFFTPts/2); ChSpecDb = ChSpecDb - 67.5; % Calibration factor for FFT plot % Plot the spectrum plot( FreqMHz(Pts), ChSpecDb(Pts) ); grid on; title( 'FFT of Ch2Signal' ); xlabel( 'Frequency (MHz)' ); ylabel( 'dBm' );

Figure A-2. Sample m-file listing showing how to use the signal data and produce real-time plots.

The m-file is executed in the measurement receiver software by launching the MATLAB

interface from the menu bar. The MATLAB interface application is shown in Figure A-3. The

path to the m-file and the m-file name are entered into the application edit boxes. The m-file can

be executed once or continuously per selection chosen on the application window.

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Figure A-3. MATLAB interface application launched from the measurement receiver software.

Figure A-4 shows the result of one snapshot when running the example m-file listed in Figure

A-2. The received signal was a BPSK-modulated PN sequence centered at 2050 MHz. The RF

filter band limiting can be seen at 2000 MHz and 2100 MHz. The lowbass IF filter cutoff is

evident at 2300 MHz where the noise falls sharply.

Figure A-4. Spectrum plot produced by m-file listed in Figure A-2.

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A.5 Steps for Developing m-files for the Measurement Receiver

The following steps suggest a concise method for developing m-files for the measurement

receiver.

1. Understanding data format: The measurement receiver produces measurements of

voltage-versus-time of an intermediate-frequency (IF) signal. MATLAB can be used to

process this data.

2. Explore measurement receiver data: Obtain sample data in *.mat format. Load data

into MATLAB using load command in MATLAB. Each *.mat file is one snapshot of

data from the measurement receiver . Explore this data to be sure it is understood. This

is exactly the type of data that will be placed in the MATLAB workspace when m-file is

called by the measurement receiver in real time.

3. Design algorithms using sample data: Design algorithms in MATLAB m-files so that

they accept sampled IF signals. At the beginning of the m-file, use the load command to

load a snapshot of sample data (stored in the *.mat file). Later, the load command will be

removed once the m-file has been demonstrated to work successfully on the sample data.

If the m-file doesn’t work using the sample data, it will not work when called in real-time

by the measurement receiver. Successful operation on the sample data is a must.

4. Use phase and amplitude calibration if necessary: Each channel of signal data may

have phase and amplitude offsets relative to the other channels. Using the *.mat file that

contains signals acquired through a signal splitter, determine phase and amplitude

calibration constants. These constants should be applied to signals by algorithms that

need to know the phase and amplitude offsets of the RF front end channels.

5. Playback data: Use the playback feature of the measurement receiver software to test

your m-file on logged data. The *.vdf files contain binary measurement receiver data.

• Run ViperExe off of the CD (or copy all files to your hard drive).

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• Use FILE->START PLAYBACK and then select the file you want to play back.

• Then, APPLICATIONS->VIPER MATLAB, then enter the path and your m-file name

in the edit boxes and select EXECUTE. NOTE: MATLAB does not work with

spaces in folder names, so do not use spaces (if necessary, change the actual

folder path where your m-files are stored). Also do not use ".m" at end of m-file

name when entering the m-file name in the measurement receiver software.

• FILE->STOP PLAYBACK can be used to stop the playback of data.

6. Execute m-file using real-time data: When the m-file works on playback data, then it

can be executed on the receiver in real time. With the measurement receiver set up

correctly, select CONTROL -> CONFIGURE RECEIVER and select the options appropriate for

the experiment. SELECT CONTROL -> START RECEIVER to start the acquisition of

snapshots. Use the APPLICATIONS->VIPER MATLAB feature as described in the previous

step.

7. Changing m-file while running measurement receiver: When changing the m-file

while playing back files with VIPER (e.g., to experiment with different constants or

algorithms within the m-file), stop the VIPER MATLAB application (but not necessarily

playback of the file) with the STOP button, save the m-file, type “clear all <enter>” in the

MATLAB workspace. Then, hit EXECUTE in the VIPER MATLAB application to

restart the execution with the new m-file. This is necessary because MATLAB may

cache values and code when “clear all” is not used.

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Appendix B VT-STAR Development

B.1 Overview

VT-STAR (Virginia Tech Space-Time Advanced Receiver) was developed as a test bed for

space-time processing. VT-STAR consists of a transmitter and receiver, each with two-element

antenna arrays, for implementing two-by-two MIMO (multiple-input, multiple-output) channel

algorithms. The VT-STAR system was built concurrently with research presented in this

dissertation and influenced ideas for array processing. Further descriptions of VT-STAR and its

applications are described in [Goz01]. Results of experiments performed with VT-STAR are

presented in [Goz02b].

B.2 VT-STAR Transmitter

The VT-STAR transmitter uses a TMS320C67 DSP board and four THS 5x61 digital-to-analog

conversion (DAC) boards to generate in-phase (I) and quadrature (Q) baseband signals.

Generation of baseband rather than intermediate frequency (IF) signals was used so that

bandwidth capabilities of the transmitter could be maximized. The RF section of the transmitter

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accepts as input the baseband signals produced by the DAC boards and modulates RF signals

transmitted through the radio channels using two transmitter antennas.

Each branch of the transmitter RF section uses two stages of frequency up-conversion to produce

modulated signals centered at 2050 MHz (see Figure B-1 and Figure B-2). The two RF branches

use local oscillators locked to a common reference. The first up-conversion stage in each branch

accepts in-phase and quadrature inputs from the DAC boards and creates a modulated

intermediate frequency (IF) signal at 68 MHz. A single 68 MHz local oscillator drives the I/Q

modulator in each branch using a signal splitter. The second frequency up-conversion stage

translates the 68 MHz IF signal up to 2050 MHz using a second local oscillator at 1982 MHz,

and the 2050 MHz modulated signal is filtered and amplified. Two vertically-polarized, co-

planar, quarter-wavelength monopole antennas transmit the signal through the radio channel.

THS56x1DAC Board

I/Q ModZFMIQ-70ML

SplitterZESC-2-11

THS56x1DAC Board

THS56x1DAC Board

THS56x1DAC Board

I/Q ModZFMIQ-70ML

68 MHz

10 MHzRef

Signal Gen

X

X

SplitterZESC-2-11

BPFfo = 2050 MHz

BPFfo = 2050 MHz

1982 MHz

1982 MHz

2050 MHz

2050 MHz

ZEM-4300

ZEM-4300

TM

S32

0C67

DS

P

Atten

THS56x1DAC Board

I/Q ModZFMIQ-70ML

SplitterZESC-2-11

THS56x1DAC Board

THS56x1DAC Board

THS56x1DAC Board

I/Q ModZFMIQ-70ML

68 MHz

10 MHzRef

10 MHzRef

Signal Gen

X

X

SplitterZESC-2-11

BPFfo = 2050 MHz

BPFfo = 2050 MHz

1982 MHz

1982 MHz

2050 MHz

2050 MHz

ZEM-4300

ZEM-4300

TM

S32

0C67

DS

P

AttenAtten

Figure B-1. Transmitter section of VT-STAR.

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APPENDIX B – VT-STAR DEVELOPMENT

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Figure B-2. Photograph of VT-STAR transmitter section.

B.3 VT-STAR Receiver

The VT-STAR receiver uses an RF section followed by a THS 1206 four-channel digital-to-

analog converter board and a TMS320C67 DSP board to process received signals. The receiver

RF section has two antennas to receive the signals, and the received spectrum is down-converted

to I and Q baseband signals. Baseband rather than IF signals are sampled to maximize the

bandwidth capabilities of the receiver.

Each branch of the receiver RF section uses two stages of frequency down-conversion to produce

baseband I and Q outputs suitable for sampling by the analog-to-digital converters (see Figure

B-3 and Figure B-4). Two vertically-polarized, co-planar, quarter-wavelength monopole

antennas are used to receive signals. The received signals are filtered and amplified prior to the

first frequency down-conversion stage. A single 1982 MHz local oscillator translates the 2050

MHz received signal to a 68 MHz IF. The IF signal is amplified and filtered prior to being

down-converted to baseband I/Q by the demodulators. A second local oscillator in the receiver

produces a 68 MHz sinusoid that is split to drive the I/Q demodulators.

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BPF2050 MHz

XBPF

68 MHzI/Q DemodZFMIQ-70D

LPF

SplitterZESC-2-11

SplitterZESC-2-11

10 MHzRef

ZEM-4300

ZHL-1724HLN

ZFL-1000GH

ZFL-1000H

AGC

TH

S12

06 A

DC

TM

S32

0C67

DS

P

SLP1.9

BPF2050 MHz

XBPF

68 MHzI/Q DemodZFMIQ-70D

LPF

ZEM-4300

ZHL-1724HLN

ZFL-1000GH

ZFL-1000H

AGC

SLP1.9

68 MHz1982 MHz

1982 MHz

2050 MHz

2050 MHz

LPF

LPF

BPF2050 MHz

XBPF

68 MHzI/Q DemodZFMIQ-70D

LPF

SplitterZESC-2-11

SplitterZESC-2-11

10 MHzRef

10 MHzRef

ZEM-4300

ZHL-1724HLN

ZFL-1000GH

ZFL-1000H

AGC

TH

S12

06 A

DC

TM

S32

0C67

DS

P

SLP1.9

BPF2050 MHz

XBPF

68 MHzI/Q DemodZFMIQ-70D

LPF

ZEM-4300

ZHL-1724HLN

ZFL-1000GH

ZFL-1000H

AGC

SLP1.9

68 MHz1982 MHz

1982 MHz

2050 MHz

2050 MHz

LPF

LPF

Figure B-3. Receiver section of the VT-STAR.

Figure B-4. Photograph of VT-STAR receiver RF section.

The VT-STAR operating frequency of 2050 MHz was chosen because of propagation similarities

compared to the U.S. PCS band, worldwide 3G radio bands, and the U.S. 2.4 GHz unlicensed

band. Performance improvements demonstrated in the 2050 MHz band by VT-STAR would be

realizable by worldwide wireless communication systems operating in nearby bands. Two stages

of frequency conversion were chosen to allow amplification to be divided among the stages,

mitigating receiver instability due to high gain at a single band within each chain. Monopole

antennas were selected because of their simple design, demonstrating that performance gains can

be realized using antennas that are practical for handheld wireless devices. Antenna spacing can

be varied on the VT-STAR to test the performance of the system versus antenna spacing for

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different radio environments. The receiver RF chains were designed to accept automatic gain

control (AGC) signals so that the DSP can control the gain of the RF front end. Imbalances

between the I and Q channels of the chains are characterized and compensated with scaling

factors in DSP.

Table B-1. Specifications for VT-STAR transmitter and receiver.

RF Parameter Value

Center Frequency 2050 MHz

Maximum Signal Bandwidth 750 KHz

Receiver Noise Floor (Antenna Port) -110 dBm

Maximum Receiver Input Power -60 dBm

Transmitter Input Baseband I/Q, 35 mV RMS

Receiver Output Baseband I/Q, 140 mV RMS

Transmit Power (Maximum/Nominal) 28 dBm / 0 dBm

Transmitter/Receiver Input/Output Impedance 50 ohm

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Appendix C Channel Model Simulator Parameters

The parameters for the channel model simulator presented in Chapter 6 are documented in this

appendix. Variables are shown exactly as the are used in MATLAB. The purpose is to aid

future users and developers of the simulator.

C.1 Top Level Structures

When the simulator is run, the simulation channel parameters, vector channel results, and plot

parameters are the only variables seen with the MALAB ‘whos’ function. All simulator input

and output are stored in these structures.

» whos

Name Size Bytes Class

ChanParams 1x1 2384 struct array

PLOT_PARAMS 1x1 660 struct array (global)

VecChan 1x1 5320 struct array

Grand total is 444 elements using 8364 bytes

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»

C.2 Channel Parameters Structure

The channel parameters structure contains the input used by the simulator. Scalars, vectors, and

cell arrays are stored in fields