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Brian L. Evans Lead Graduate Students Aditya Chopra, Kapil Gulati , and Marcel Nassar In collaboration with Eddie Xintian Lin, Alberto Alcocer Ochoa, Srikathyayani Srikanteswara, and Keith R. Tinsley at Intel Labs. - PowerPoint PPT Presentation
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Radio Frequency Interference Sensing and Mitigation in
Wireless Receivers
Talk at Intel Labs at Hillsboro, Oregon
Wireless Networking and Communications Group
12 Apr 2010
Brian L. Evans
Lead Graduate StudentsAditya Chopra, Kapil Gulati, and Marcel Nassar
In collaboration with Eddie Xintian Lin, Alberto Alcocer Ochoa,Srikathyayani Srikanteswara, and Keith R. Tinsley at Intel Labs
Outline
Introduction Problem Definition Statistical Modeling of Radio Frequency Interference Receiver Design to Mitigate Radio Frequency Interference Conclusions Future work
Wireless Networking and Communications Group
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RFI
Introduction
Wireless Networking and Communications Group
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Wireless Communication Sources
• Closely located sources• Coexisting protocols
Non-CommunicationSources
Electromagnetic radiations
Computational Platform• Clocks, busses, processors• Co-located transceivers
antenna
baseband processor
(Wi-Fi)
(WiMAX Basestation)
(WiMAX Mobile)
(Bluetooth)
(Microwave)
(Wi-Fi) (WiMAX)
Radio Frequency Interference (RFI)
Limits wireless communication performance Impact of LCD noise on throughput for an embedded Wi-Fi
(IEEE 802.11g) receiver [Shi, Bettner, Chinn, Slattery & Dong, 2006]
4
Wireless Networking and Communications Group
Problem Definition
Problem: Co-channel and adjacent channel interference, and platform noise degrade communication performance
Approach: Statistical modeling of RFI Solution: Receiver design
Listen to the environment Estimate parameters for RFI statistical models Use parameters to mitigate RFI
Goal: Improve communication performance 10-100x reduction in bit error rate (this talk) 10-100x improvement in network throughput (future work)
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Multiple communication and non-communication sources System Model
Point process to model interferer locations Poisson
(uncoordinated, e.g. ad hoc) Poisson-Poisson cluster
(with user clustering, e.g. femtocell)
Sum interference Goal: Closed form statistics to model tail probability
Statistical Modeling of RFI
Wireless Networking and Communications Group
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PathlossFadingInterferer emissions
Tail probability governs communication performance
Statistical Models (isotropic, zero centered)
Symmetric Alpha Stable [Furutsu & Ishida, 1961] [Sousa, 1992]
Characteristic function
Gaussian Mixture Model [Sorenson & Alspach, 1971]
Amplitude distribution
Middleton Class A (w/o Gaussian component) [Middleton, 1977]
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Poisson Field of Interferers
Wireless Networking and Communications Group
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• Cellular networks• Hotspots (e.g. café)
• Sensor networks• Ad hoc networks
• Dense Wi-Fi networks• Networks with contention
based medium access
Symmetric Alpha Stable Middleton Class A (form of Gaussian Mixture)
Poisson-Poisson Cluster Field of Interferers
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• Cluster of hotspots (e.g. marketplace)
• In-cell and out-of-cell femtocell users in femtocell networks
• Out-of-cell femtocell users in femtocell networks
Symmetric Alpha Stable Gaussian Mixture Model
Fitting Measured Laptop RFI Data
Statistical-physical models fit data better than Gaussian
Wireless Networking and Communications Group
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Smaller KL divergence• Closer match in distribution• Does not imply close match in
tail probabilities
Radiated platform RFI• 25 RFI data sets from Intel• 50,000 samples at 100 MSPS• Laptop activity unknown to us
0 5 10 15 20 250
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Measurement Set
Kul
lbac
k-Le
ible
r di
verg
ence
Symmetric Alpha StableMiddleton Class AGaussian Mixture ModelGaussian
Platform RFI sources• May not be Poisson distributed• May not have identical emissions
Results on Measured RFI Data
For measurement set #23
11
Wireless Networking and Communications Group
Tail probability governs communication performance• Bit error rate• Outage probability
0 1 2 3 4 5 6 7 8 910
-20
10-15
10-10
10-5
100
Threshold Amplitude (a)
Tai
l Pro
babi
litie
s [P
(X >
a)]
EmpiricalMiddleton Class ASymmteric Alpha StableGaussianGaussian Mixture Model
Receiver Design to Mitigate RFI
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RTS
CTS
Example: Wi-Fi networksRTS / CTS: Request / Clear to send Interference statistics similar to Case III
Guard zone
Design receivers using knowledge of RFI statistics
Physical Layer (this talk)• Receiver pre-filtering• Receiver detection• Forward error correction
Medium Access Control Layer• Interference sense and avoid• Optimize guard zone size
(e.g. transmit power control)
RFI Mitigation in SISO systems
Communication performance
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Pulse Shaping Pre-filtering Matched
FilterDetection
Rule
Interference + Thermal noise
Pulse shapeRaised cosine
10 samples per symbol10 symbols per pulse
ChannelA = 0.35 = 5 × 10-3
Memoryless
Method Comp. Complexity
Detection Perform.
Correlation Low Low
Bayesian detection High High
Myriad pre-filtering Medium Medium
Binary Phase Shift Keying
-40 -35 -30 -25 -20 -15 -10 -5
10-3
10-2
10-1
100
Signal to Noise Ratio (SNR) [in dB]
Sym
bol E
rror
Rat
e
Correlation ReceiverBayesian DetectionMyriad Pre-filtering
14
-10 -5 0 5 10 15 20
10-3
10-2
10-1
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
Optimal ML Receiver (for Gaussian noise)Optimal ML Receiver (for Middleton Class A)Sub-Optimal ML Receiver (Four-Piece)Sub-Optimal ML Receiver (Two-Piece)
Wireless Networking and Communications Group
RFI Mitigation in 2 x 2 MIMO systems
A Noise Characteristic
Improve-ment
0.01 Highly Impulsive ~15 dB0.1 Moderately
Impulsive ~8 dB
1 Nearly Gaussian ~0.5 dB
Improvement in communication performance over conventional Gaussian ML receiver at symbol
error rate of 10-2
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
Conventional Gaussian ML Receiver
Proposed Receivers
Wireless Networking and Communications Group
RFI Mitigation in 2 x 2 MIMO systems 15
Complexity AnalysisReceiver
Quadratic Forms
Exponential
Comparisons
Gaussian ML M2 0 0
Optimal ML 2M2 2M2 0
Sub-optimal ML (Four-Piece) 2M2 0 2M2
Sub-optimal ML (Two-Piece) 2M2 0 M2
Complexity Analysis for decoding M-level QAM modulated signal
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
-10 -5 0 5 10 15 20
10-3
10-2
10-1
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
Optimal ML Receiver (for Gaussian noise)Optimal ML Receiver (for Middleton Class A)Sub-Optimal ML Receiver (Four-Piece)Sub-Optimal ML Receiver (Two-Piece)
Conventional Gaussian ML Receiver
Proposed Receivers
RFI Mitigation Using Error Correction
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Decoder 1Parity 1
Systematic Data
Decoder 2
Interleaver
Parity 2 Interleaver
-
-
-
-
Interleaver
Turbo decoder
Decoding depends on the RFI statistics 10 dB improvement at BER 10-5 can be achieved using
accurate RFI statistics [Umehara, 2003]
Summary
Radio frequency interference affects wireless transceivers RFI mitigation can improve communication performance Our contributions
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RFI Modeling
• Co-channel interference in ad hoc, cellular, and femtocell networks[Gulati, Evans, Andrews & Tinsley, submitted 2009][Gulati, Chopra, Evans & Tinsley, Globecom 2009]
• Computational platform noise[Nassar, Gulati, DeYoung, Evans & Tinsley, ICASSP 2008, JSPS 2009]
• Microwave oven interference[Nassar, Lin & Evans, submitted 2010]
Receiver Design
• Single carrier, single antenna systems[Nassar, Gulati, DeYoung, Evans & Tinsley, ICASSP 2008, JSPS 2009]
• Single carrier, 2 x 2 MIMO systems[Gulati, Chopra, Heath, Evans, Tinsley & Lin, Globecom 2008]
Current and Future Work
RFI Modeling Temporal modeling Multi-antenna modeling
Analysis and Bounds on Communication Performance Physical layer (filtering, detection, and error correction) Medium access control layer protocols
RFI Mitigation Extensions to multicarrier (OFDM) systems Extensions to multi-antenna (MIMO) systems Extensions to multipath channels
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Related Publications
Journal Publications• K. Gulati, B. L. Evans, J. G. Andrews, and K. R. Tinsley, “Statistics of Co-Channel
Interference in a Field of Poisson and Poisson-Poisson Clustered Interferers”, IEEE Transactions on Signal Processing, submitted Nov. 29, 2009.
• M. Nassar, K. Gulati, M. R. DeYoung, B. L. Evans and K. R. Tinsley, “Mitigating Near-Field Interference in Laptop Embedded Wireless Transceivers”, Journal of Signal Processing Systems, Mar. 2009, invited paper.
Conference Publications• M. Nassar, X. E. Lin, and B. L. Evans, “Stochastic Modeling of Microwave Oven
Interference in WLANs”, Int. Global Comm. Conf., Dec. 6-10, 2010, submitted.• K. Gulati, B. L. Evans, and K. R. Tinsley, “Statistical Modeling of Co-Channel
Interference in a Field of Poisson Distributed Interferers”, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., Mar. 14-19, 2010.
• K. Gulati, A. Chopra, B. L. Evans, and K. R. Tinsley, “Statistical Modeling of Co-Channel Interference”, Proc. IEEE Int. Global Communications Conf., Nov. 30-Dec. 4, 2009.
Cont…
19
Wireless Networking and Communications Group
Related Publications
Conference Publications (cont…)• A. Chopra, K. Gulati, B. L. Evans, K. R. Tinsley, and C. Sreerama, “Performance Bounds
of MIMO Receivers in the Presence of Radio Frequency Interference”, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., Apr. 19-24, 2009.
• K. Gulati, A. Chopra, R. W. Heath, Jr., B. L. Evans, K. R. Tinsley, and X. E. Lin, “MIMO Receiver Design in the Presence of Radio Frequency Interference”, Proc. IEEE Int. Global Communications Conf., Nov. 30-Dec. 4th, 2008.
• M. Nassar, K. Gulati, A. K. Sujeeth, N. Aghasadeghi, B. L. Evans and K. R. Tinsley, “Mitigating Near-Field Interference in Laptop Embedded Wireless Transceivers”, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., Mar. 30-Apr. 4, 2008.
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Wireless Networking and Communications Group
Software Releases• K. Gulati, M. Nassar, A. Chopra, B. Okafor, M. R. DeYoung, N. Aghasadeghi, A. Sujeeth,
and B. L. Evans, "Radio Frequency Interference Modeling and Mitigation Toolbox in MATLAB", version 1.4.1 beta, Apr. 11, 2010.
UT Austin RFI Modeling & Mitigation Toolbox
Freely distributable toolbox in MATLAB Simulation environment for RFI modeling and mitigation
RFI generation Measured RFI fitting Parameter estimation algorithms Filtering and detection methods Demos for RFI modeling and mitigation
Latest Toolbox ReleaseVersion 1.4.1 beta, Apr. 11, 2010
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http://users.ece.utexas.edu/~bevans/projects/rfi/software/index.html
Snapshot of a demo
Usage Scenario #1
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User System Simulator(e.g. WiMAX simulator)
RFI Generation
•RFI_MakeDataClassA.m•RFI_MakeDataAlphaStable.m….….
Parameter Estimation
•RFI_EstMethodofMoments.m•RFI_EstAlphaS_Alpha.m….….
Receivers•RFI_myriad_opt.m•RFI_BiVarClassAMLRx.m….….
RFI Toolbox
Usage Scenario #223
Measured RFI data
RFI Toolbox Statistical Modeling DEMO
SISO Communication Performance DEMO File Transfer DEMOMIMO Communication
Performance DEMO
Wireless Networking and Communications Group
Thanks !
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Wireless Networking and Communications Group
References
RFI Modeling1. D. Middleton, “Non-Gaussian noise models in signal processing for telecommunications: New
methods and results for Class A and Class B noise models”, IEEE Trans. Info. Theory, vol. 45, no. 4, pp. 1129-1149, May 1999.
2. K. Furutsu and T. Ishida, “On the theory of amplitude distributions of impulsive random noise,” J. Appl. Phys., vol. 32, no. 7, pp. 1206–1221, 1961.
3. J. Ilow and D . Hatzinakos, “Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers”, IEEE transactions on signal processing, vol. 46, no. 6, pp. 1601-1611, 1998.
4. E. S. Sousa, “Performance of a spread spectrum packet radio network link in a Poisson field of interferers,” IEEE Transactions on Information Theory, vol. 38, no. 6, pp. 1743–1754, Nov. 1992.
5. X. Yang and A. Petropulu, “Co-channel interference modeling and analysis in a Poisson field of interferers in wireless communications,” IEEE Transactions on Signal Processing, vol. 51, no. 1, pp. 64–76, Jan. 2003.
6. E. Salbaroli and A. Zanella, “Interference analysis in a Poisson field of nodes of finite area,” IEEE Transactions on Vehicular Technology, vol. 58, no. 4, pp. 1776–1783, May 2009.
7. M. Z. Win, P. C. Pinto, and L. A. Shepp, “A mathematical theory of network interference and its applications,” Proceedings of the IEEE, vol. 97, no. 2, pp. 205–230, Feb. 2009.
25
Wireless Networking and Communications Group
References
Parameter Estimation1. S. M. Zabin and H. V. Poor, “Efficient estimation of Class A noise parameters via the EM
[Expectation-Maximization] algorithms”, IEEE Trans. Info. Theory, vol. 37, no. 1, pp. 60-72, Jan. 1991 .
2. G. A. Tsihrintzis and C. L. Nikias, "Fast estimation of the parameters of alpha-stable impulsive interference", IEEE Trans. Signal Proc., vol. 44, Issue 6, pp. 1492-1503, Jun. 1996.
Communication Performance of Wireless Networks3. R. Ganti and M. Haenggi, “Interference and outage in clustered wireless ad hoc networks,” IEEE
Transactions on Information Theory, vol. 55, no. 9, pp. 4067–4086, Sep. 2009.4. A. Hasan and J. G. Andrews, “The guard zone in wireless ad hoc networks,” IEEE Transactions on
Wireless Communications, vol. 4, no. 3, pp. 897–906, Mar. 2007.5. X. Yang and G. de Veciana, “Inducing multiscale spatial clustering using multistage MAC contention
in spread spectrum ad hoc networks,” IEEE/ACM Transactions on Networking, vol. 15, no. 6, pp. 1387–1400, Dec. 2007.
6. S. Weber, X. Yang, J. G. Andrews, and G. de Veciana, “Transmission capacity of wireless ad hoc networks with outage constraints,” IEEE Transactions on Information Theory, vol. 51, no. 12, pp. 4091-4102, Dec. 2005.
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Wireless Networking and Communications Group
References
Communication Performance of Wireless Networks (cont…)5. S. Weber, J. G. Andrews, and N. Jindal, “Inducing multiscale spatial clustering using multistage MAC
contention in spread spectrum ad hoc networks,” IEEE Transactions on Information Theory, vol. 53, no. 11, pp. 4127-4149, Nov. 2007.
6. J. G. Andrews, S. Weber, M. Kountouris, and M. Haenggi, “Random access transport capacity,” IEEE Transactions On Wireless Communications, Jan. 2010, submitted. [Online]. Available: http://arxiv.org/abs/0909.5119
7. M. Haenggi, “Local delay in static and highly mobile Poisson networks with ALOHA," in Proc. IEEE International Conference on Communications, Cape Town, South Africa, May 2010.
8. F. Baccelli and B. Blaszczyszyn, “A New Phase Transitions for Local Delays in MANETs,” in Proc. of IEEE INFOCOM, San Diego, CA,2010, to appear.
Receiver Design to Mitigate RFI9. A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment-
Part I: Coherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 197710.J.G. Gonzalez and G.R. Arce, “Optimality of the Myriad Filter in Practical Impulsive-Noise
Environments”, IEEE Trans. on Signal Processing, vol 49, no. 2, Feb 2001
27
Wireless Networking and Communications Group
References
Receiver Design to Mitigate RFI (cont…)3. S. Ambike, J. Ilow, and D. Hatzinakos, “Detection for binary transmission in a mixture of Gaussian
noise and impulsive noise modelled as an alpha-stable process,” IEEE Signal Processing Letters, vol. 1, pp. 55–57, Mar. 1994.
4. G. R. Arce, Nonlinear Signal Processing: A Statistical Approach, John Wiley & Sons, 2005.5. Y. Eldar and A. Yeredor, “Finite-memory denoising in impulsive noise using Gaussian mixture
models,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 48, no. 11, pp. 1069-1077, Nov. 2001.
6. J. H. Kotecha and P. M. Djuric, “Gaussian sum particle ltering,” IEEE Transactions on Signal Processing, vol. 51, no. 10, pp. 2602-2612, Oct. 2003.
7. J. Haring and A.J. Han Vick, “Iterative Decoding of Codes Over Complex Numbers for Impulsive Noise Channels”, IEEE Trans. On Info. Theory, vol 49, no. 5, May 2003.
8. Ping Gao and C. Tepedelenlioglu. “Space-time coding over mimo channels with impulsive noise”, IEEE Trans. on Wireless Comm., 6(1):220–229, January 2007.
RFI Measurements and Impact9. J. Shi, A. Bettner, G. Chinn, K. Slattery and X. Dong, "A study of platform EMI from LCD panels –
impact on wireless, root causes and mitigation methods,“ IEEE International Symposium on Electromagnetic Compatibility, vol.3, no., pp. 626-631, 14-18 Aug. 2006
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Wireless Networking and Communications Group
Backup Slides
Introduction Interference avoidance , alignment, and cancellation methods Femtocell networks
Statistical Modeling of RFI Computational platform noise Impact of RFI Assumptions for RFI Modeling Transients in digital FIR filters Poisson field of interferers Poisson-Poisson cluster field of interferers
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Backup
Backup
Backup
Backup
Backup
Backup
Backup
Backup
Backup Slides (cont…)
Gaussian Mixture vs. Alpha Stable Middleton Class A, B, and C models
Middleton Class A model Expectation maximization overview Results: EM for Middleton Class A
Symmetric Alpha Stable Extreme order statistics based estimator for Alpha Stable
Video over impulsive channels Demonstration #1 Demonstration #2
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Backup
Backup
Backup
Backup
Backup
Backup
Backup
Backup
Backup
Backup Slides (cont…)
RFI mitigation in SISO systems Our contributions Results: Class A Detection Results: Alpha Stable Detection
RFI mitigation in MIMO systems Our contributions
Performance bounds for SISO systems Performance bounds for MIMO systems Extensions for multicarrier systems Turbo codes in impulsive channels
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Backup
Backup
Backup
Backup
Backup
Backup
Backup
Backup
Interference Mitigation Techniques
Interference avoidance CSMA / CA
Interference alignment Example:
[Cadambe & Jafar, 2007]
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Return
Interference Mitigation Techniques (cont…)
Interference cancellationRef: J. G. Andrews, ”Interference Cancellation for Cellular Systems: A Contemporary Overview”, IEEE Wireless Communications Magazine, Vol. 12, No. 2, pp. 19-29, April 2005
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Return
Femtocell Networks
Reference:V. Chandrasekhar, J. G. Andrews and A. Gatherer, "Femtocell Networks: a Survey", IEEE Communications Magazine, Vol. 46, No. 9, pp. 59-67, September 2008
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Return
Common Spectral Occupancy
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Standard Carrier (GHz)
Wireless Networking Interfering Clocks and Busses
Bluetooth 2.4 Personal Area Network
Gigabit Ethernet, PCI Express Bus, LCD clock harmonics
IEEE 802. 11 b/g/n 2.4 Wireless LAN
(Wi-Fi)Gigabit Ethernet, PCI Express Bus,
LCD clock harmonics
IEEE 802.16e
2.5–2.69 3.3–3.8
5.725–5.85
Mobile Broadband(Wi-Max)
PCI Express Bus,LCD clock harmonics
IEEE 802.11a 5.2 Wireless LAN
(Wi-Fi)PCI Express Bus,
LCD clock harmonics
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Impact of RFI
Calculated in terms of desensitization (“desense”) Interference raises noise floor Receiver sensitivity will degrade to maintain SNR
Desensitization levels can exceed 10 dB for 802.11a/b/g due to computational platform noise [J. Shi et al., 2006]
Case Sudy: 802.11b, Channel 2, desense of 11dB More than 50% loss in range Throughput loss up to ~3.5 Mbps for very low receive signal strengths
(~ -80 dbm)
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floor noise RX
ceInterferenfloor noise RXlog10 10desense
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Impact of LCD clock on 802.11g
Pixel clock 65 MHz LCD Interferers and 802.11g center frequencies
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LCD Interferers
802.11g Channel
Center Frequency
Difference of Interference from Center Frequencies
Impact
2.410 GHz Channel 1 2.412 GHz ~2 MHz Significant
2.442 GHz Channel 7 2.442 GHz ~0 MHz Severe
2.475 GHz Channel 11 2.462 GHz ~13 MHz Just outside Ch. 11. Impact minor
Return
Assumptions for RFI Modeling
Key assumptions for Middleton and Alpha Stable models[Middleton, 1977][Furutsu & Ishida, 1961] Infinitely many potential interfering sources with same effective
radiation power Power law propagation loss Poisson field of interferers with uniform intensity l
Pr(number of interferers = M |area R) ~ Poisson(M; lR) Uniformly distributed emission times Temporally independent (at each sample time)
Limitations Alpha Stable models do not include thermal noise Temporal dependence may exist
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Return
50 100 150 200
-0.5
0
0.5
Inpu
t
50 100 150 200
-1
-0.5
0
0.5
1
Filt
er O
utpu
t
Transients in Digital FIR Filters
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25-Tap FIR Filter• Low pass• Stopband freq. 0.22 (normalized)
Input Output
Freq = 0.16
Interference duration = 10 * 1/0.22 Interference duration = 100 x 1/0.22
Transients
Transients Significant w.r.t. Steady State
100 200 300 400 500 600
-0.5
0
0.5
Inpu
t
100 200 300 400 500 600-1
-0.5
0
0.5
1
Filt
er O
utpu
t
Transients Ignorable w.r.t. Steady State
Return
Poisson Field of Interferers
Interferers distributed over parametric annular space
Log-characteristic function
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Return
Poisson Field of Interferers
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Return
Poisson Field of Interferers
Simulation Results (tail probability)
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0.1 0.2 0.3 0.4 0.5 0.6 0.710
-3
10-2
10-1
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[ P (
|Y| >
y)
]
Simulated
Symmetric Alpha Stable
0.1 0.2 0.3 0.4 0.5 0.6 0.710
-15
10-10
10-5
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[ P (
|Y| >
y)
]
SimulatedSymmetric Alpha StableGaussianMiddleton Class A
Gaussian and Middleton Class A models are not applicable since mean intensity is infinite
Case I: Entire Plane Case III: Infinite-area with guard zone
Return
Poisson Field of Interferers
Simulation Results (tail probability)
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Case II: Finite area annular region
0 0.1 0.2 0.3 0.4 0.5 0.6 0.710
-15
10-10
10-5
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[P(|
Y| >
y)]
SimulatedSymmetric Alpha StableGaussianMiddleton Class A
Return
Poisson-Poisson Cluster Field of Interferers
Cluster centers distributed as spatial Poisson process over
Interferers distributed as spatial Poisson process
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Return
Poisson-Poisson Cluster Field of Interferers
Log-Characteristic function
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Return
Poisson-Poisson Cluster Field of Interferers
Simulation Results (tail probability)
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0.1 0.2 0.3 0.4 0.5 0.6 0.710
-12
10-10
10-8
10-6
10-4
10-2
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[ P (
|Y| >
y)
]
SimulatedSymmetric Alpha Stable
GaussianGaussian Mixture Model
0.1 0.2 0.3 0.4 0.5 0.6 0.710
-4
10-3
10-2
10-1
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[ P (
|Y| >
y)
]
Simulated
Symmetric Alpha Stable
Gaussian and Gaussian mixture models are not applicable since mean intensity is infinite
Case I: Entire Plane Case III: Infinite-area with guard zone
Return
Poisson-Poisson Cluster Field of Interferers
Simulation Results (tail probability)
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Case II: Finite area annular region
0 0.1 0.2 0.3 0.4 0.5 0.6 0.710
-15
10-10
10-5
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[P(|
Y| >
y)]
SimulatedSymmetric Alpha StableGaussianGaussian Mixture Model
Return
Gaussian Mixture vs. Alpha Stable
Gaussian Mixture vs. Symmetric Alpha Stable
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Gaussian Mixture Symmetric Alpha StableModeling Interferers distributed with Guard
zone around receiver (actual or virtual due to pathloss function)
Interferers distributed over entire plane
Pathloss Function
With GZ: singular / non-singularEntire plane: non-singular
Singular form
Thermal Noise
Easily extended(sum is Gaussian mixture)
Not easily extended (sum is Middleton Class B)
Outliers Easily extended to include outliers Difficult to include outliers
Return
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Middleton Class A, B and C Models
Class A Narrowband interference (“coherent” reception)Uniquely represented by 2 parameters
Class B Broadband interference (“incoherent” reception)Uniquely represented by six parameters
Class C Sum of Class A and Class B (approx. Class B)
[Middleton, 1999]
Return
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Middleton Class A model
Probability Density Function
1
2!)(
2
2
02
2
2
Am
where
em
Aezf
m
z
m m
mA
Zm
-10 -5 0 5 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Noise amplitude
Pro
bability d
ensity f
unction
PDF for A = 0.15, = 0.8
A
Parameter
Description RangeOverlap Index. Product of average number of emissions per second and mean duration of typical emission
A [10-2, 1]
Gaussian Factor. Ratio of second-order moment of Gaussian component to that of non-Gaussian component
Γ [10-6, 1]
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Expectation Maximization Overview
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5151
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Results: EM Estimator for Class A52
PDFs with 11 summation terms50 simulation runs per setting
1000 data samplesConvergence criterion:
1e-006 1e-005 0.0001 0.001 0.01
10
15
20
25
30
K
Num
ber
of I
tera
tions
Number of Iterations taken by the EM Estimator for A
A = 0.01
A = 0.1
A = 1
Iterations for Parameter A to Converge
1e-006 1e-005 0.0001 0.001 0.01
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
x 10-3
K
Fra
ctio
nal M
SE
= |
(A -
Aes
t) /
A |
2
Fractional MSE of Estimator for A
A = 0.01
A = 0.1
A = 1
Normalized Mean-Squared Error in A
2
)(A
AAANMSE est
est
7
1
1 10ˆ
ˆˆ
n
nn
A
AA
K = A G
Return
53
Wireless Networking and Communications Group
Results: EM Estimator for Class A
• For convergence for A [10-2, 1], worst-case number of iterations for A = 1
• Estimation accuracy vs. number of iterations tradeoff
Return
54
Wireless Networking and Communications Group
Symmetric Alpha Stable Model
Characteristic Function
Closed-form PDF expression only forα = 1 (Cauchy), α = 2 (Gaussian),α = 1/2 (Levy), α = 0 (not very useful)
Approximate PDF using inverse transform of power series expansion
Second-order moments do not exist for α < 2 Generally, moments of order > α do not exist
||)( je
PDF for = 1.5, = 0, = 10
-50 0 500
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Noise amplitude
Pro
babili
ty d
ensity f
unction
Parameter Description Range
Characteristic Exponent. Amount of impulsiveness
Localization. Analogous to mean
Dispersion. Analogous to variance
αδ
]2,0[α
),( ),0(
Backup
Backup
Return
55
Wireless Networking and Communications Group
Parameter Estimation: Symmetric Alpha Stable
Based on extreme order statistics [Tsihrintzis & Nikias, 1996]
PDFs of max and min of sequence of i.i.d. data samples PDF of maximum PDF of minimum
Extreme order statistics of Symmetric Alpha Stable PDF approach Frechet’s distribution as N goes to infinity
Parameter Estimators then based on simple order statistics Advantage: Fast/computationally efficient (non-iterative) Disadvantage: Requires large set of data samples (N~10,000)
)( )](1[ )(
)( )( )(1
:
1:
xfxFNxf
xfxFNxf
XN
Nm
XN
NM
Return
Parameter Estimators for Alpha Stable
Wireless Networking and Communications Group
5656
0 < p < α
Return
57
Wireless Networking and Communications Group
Parameter Est.: Symmetric Alpha Stable Results
• Data length (N) of 10,000 samples
• Results averaged over 100 simulation runs
• Estimate α and “mean” g directly from data
• Estimate “variance” g from α and δ estimates
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09MSE in estimates of the Characteristic Exponent ()
Characteristic Exponent:
Mea
n S
quar
ed E
rror
(M
SE
)
Mean squared error in estimate of characteristic exponent α
Return
58
Wireless Networking and Communications Group
Parameter Est.: Symmetric Alpha Stable Results
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
1
2
3
4
5
6
7MSE in estimates of the Dispersion Parameter ()
Characteristic Exponent:
Mea
n S
quar
ed E
rror
(M
SE
)
Mean squared error in estimate of dispersion (“variance”)
Mean squared error in estimate of localization (“mean”)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
1
2
3
4
5
6
7MSE in estimates of the Dispersion Parameter ()
Characteristic Exponent:
Mea
n S
quar
ed E
rror
(M
SE
)
Return
Extreme Order Statistics
Wireless Networking and Communications Group
59
Return
60
Video over Impulsive Channels
Video demonstration for MPEG II video stream 10.2 MB compressed stream from camera (142 MB uncompressed) Compressed file sent over additive impulsive noise channel Binary phase shift keying
Raised cosine pulse10 samples/symbol10 symbols/pulse length
Composite of transmitted and received MPEG II video streamshttp://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB_correlation.wmv Shows degradation of video quality over impulsive channels with
standard receivers (based on Gaussian noise assumption)Wireless Networking and Communications Group
Additive Class A Noise ValueOverlap index (A) 0.35Gaussian factor (G) 0.001SNR 19 dB
Return
Video over Impulsive Channels #2
Video demonstration for MPEG II video stream revisited 5.9 MB compressed stream from camera (124 MB uncompressed) Compressed file sent over additive impulsive noise channel Binary phase shift keying
Raised cosine pulse10 samples/symbol10 symbols/pulse length
Composite of transmitted video stream, video stream from a correlation receiver based on Gaussian noise assumption, and video stream for a Bayesian receiver tuned to impulsive noise
http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB.wmv
Wireless Networking and Communications Group
61
Additive Class A Noise ValueOverlap index (A) 0.35Gaussian factor (G) 0.001SNR 19 dB
Return
62
Video over Impulsive Channels #2
Structural similarity measure [Wang, Bovik, Sheikh & Simoncelli, 2004]
Score is [0,1] where higher means better video quality
Frame number
Bit error rates for ~50 million bits sent:
6 x 10-6 for correlation receiver
0 for RFI mitigating receiver (Bayesian)
Return
63
Wireless Networking and Communications Group
Our Contributions
Computer Platform Noise Modelling
Evaluate fit of measured RFI data to noise models• Middleton Class A model• Symmetric Alpha Stable
Parameter Estimation
Evaluate estimation accuracy vs complexity tradeoffs
Filtering / Detection Evaluate communication performance vs complexity tradeoffs• Middleton Class A: Correlation receiver, Wiener filtering,
and Bayesian detector• Symmetric Alpha Stable: Myriad filtering, hole punching,
and Bayesian detector
Mitigation of computational platform noise in single carrier, single antenna systems [Nassar, Gulati, DeYoung, Evans & Tinsley, ICASSP 2008, JSPS 2009]
Return
64
Wireless Networking and Communications Group
Filtering and Detection
Pulse Shaping Pre-Filtering Matched
FilterDetection
Rule
Impulsive Noise
Middleton Class A noise Symmetric Alpha Stable noise
Filtering Wiener Filtering (Linear)
Detection Correlation Receiver (Linear) Bayesian Detector
[Spaulding & Middleton, 1977] Small Signal Approximation to
Bayesian detector[Spaulding & Middleton, 1977]
Filtering Myriad Filtering
Optimal Myriad [Gonzalez & Arce, 2001]
Selection Myriad Hole Punching
[Ambike et al., 1994]
Detection Correlation Receiver (Linear) MAP approximation
[Kuruoglu, 1998]
AssumptionMultiple samples of the received signal are available• N Path Diversity [Miller, 1972]• Oversampling by N [Middleton, 1977]
Return
65
Wireless Networking and Communications Group
Results: Class A Detection
Pulse shapeRaised cosine
10 samples per symbol10 symbols per pulse
ChannelA = 0.35
= 0.5 × 10-3
Memoryless
Method Comp. Complexity
Detection Perform.
Correl. Low LowWiener Medium LowBayesian S.S. Approx.
Medium High
Bayesian High High-35 -30 -25 -20 -15 -10 -5 0 5 10 15
10-5
10-4
10-3
10-2
10-1
100
SNR
Bit
Err
or R
ate
(BE
R)
Correlation ReceiverWiener FilteringBayesian DetectionSmall Signal Approximation
Communication Performance Binary Phase Shift KeyingReturn
66
Wireless Networking and Communications Group
Results: Alpha Stable Detection
Use dispersion parameter g in place of noise variance to generalize SNR
Method Comp. Complexity
Detection Perform.
Hole Punching
Low Medium
Selection Myriad
Low Medium
MAP Approx.
Medium High
Optimal Myriad
High Medium
-10 -5 0 5 10 15 20
10-2
10-1
100
Generalized SNR (in dB)
Bit
Err
or R
ate
(BE
R)
Matched FilterHole PunchingMAPMyriad
Communication Performance Same transmitter settings as previous slideReturn
67
Wireless Networking and Communications Group
MAP Detection for Class A
Hard decision Bayesian formulation [Spaulding & Middleton, 1977]
Equally probable source
Z+S=X:H
Z+S=X:H
22
11 1
2
1
11
22
H
H
)H|X)p(p(H
)H|X)p(p(H=)XΛ(
1
2
1
1
2
H
H
Z
Z
)SX(p
)SX(p=)XΛ(
Return
Wireless Networking and Communications Group
MAP Detection for Class A: Small Signal Approx.68
Expand noise PDF pZ(z) by Taylor series about Sj = 0 (j=1,2)
Approximate MAP detection rule
Logarithmic non-linearity + correlation receiver Near-optimal for small amplitude signals
ji
N
=i i
Z
ZjΤ
ZZjZ sx
)X(p)X(p=S)X(p)X(p)SX(p
1
Correlation Receiver
1 ln1
ln1
2
1
11i
12i
H
H
N
=iiZ
i
N
=iiZ
i
)(xpdxd
s
)(xpdxd
s
)XΛ(
We use 100 terms of the series expansion for
d/dxi ln pZ(xi) in simulations
Return
69
Wireless Networking and Communications Group
Incoherent Detection
Bayesian formulation [Spaulding & Middleton, 1997, pt. II]
Small signal approximation
Z(t)+θ)(t,S=X(t):H
Z(t)+θ)(t,S=X(t):H
22
11
1
2
1
1
2
1
2
H
H
θ
θ
)X(p
)X(p=
)p(θp(θH|Xp(
)p(θp(θH|Xp(
=)XΛ(
phase :φamplitude:a
φ
a=θ and where
ln
1
sincos
sincos
2
1
2
11
2
11
2
12
2
12
)(xpdx
d=)l(xwhere
tω)l(x+tω)l(x
tω)l(x+tω)l(x
iZi
i
H
H
N
=iii
N
=iii
N
=iii
N
=iii
Correlation receiver
Return
70
Wireless Networking and Communications Group
Filtering for Alpha Stable Noise
Myriad filtering Sliding window algorithm outputs myriad of a sample window Myriad of order k for samples x1,x2,…,xN [Gonzalez & Arce, 2001]
As k decreases, less impulsive noise passes through the myriad filter As k→0, filter tends to mode filter (output value with highest frequency)
Empirical Choice of k [Gonzalez & Arce, 2001]
Developed for images corrupted by symmetric alpha stable impulsive noise
22
11 minargˆ,,
i
N
ikNM xkxxg
1
2),(
k
Return
Wireless Networking and Communications Group
Filtering for Alpha Stable Noise (Cont..)71
Myriad filter implementation Given a window of samples, x1,…,xN, find β [xmin, xmax] Optimal Myriad algorithm
1. Differentiate objective function polynomial p(β) with respect to β
2. Find roots and retain real roots3. Evaluate p(β) at real roots and extreme points4. Output β that gives smallest value of p(β)
Selection Myriad (reduced complexity)1. Use x1, …, xN as the possible values of β
2. Pick value that minimizes objective function p(β)
22
1)(
i
N
ixkp
Return
72
Wireless Networking and Communications Group
Filtering for Alpha Stable Noise (Cont..)
Hole punching (blanking) filters Set sample to 0 when sample exceeds threshold [Ambike, 1994]
Large values are impulses and true values can be recovered Replacing large values with zero will not bias (correlation) receiver for
two-level constellation If additive noise were purely Gaussian, then the larger the threshold,
the lower the detrimental effect on bit error rate Communication performance degrades as constellation size
(i.e., number of bits per symbol) increases beyond two
hp
hp
T>nx
Tnxnx
][0
][][hhp
Return
73
Wireless Networking and Communications Group
MAP Detection for Alpha Stable: PDF Approx.
SαS random variable Z with parameters a , , d g can be written Z = X Y½ [Kuruoglu, 1998] X is zero-mean Gaussian with variance 2 g Y is positive stable random variable with parameters depending on a
PDF of Z can be written as a mixture model of N Gaussians[Kuruoglu, 1998]
Mean d can be added back in Obtain fY(.) by taking inverse FFT of characteristic function & normalizing
Number of mixtures (N) and values of sampling points (vi) are tunable parameters
N
iiY
iY
N
i
v
z
vf
vfezp
i
1
2
2
1
2
,0,
2
2
2
Return
74
Wireless Networking and Communications Group
Results: Alpha Stable Detection
Return
75
Wireless Networking and Communications Group
Complexity Analysis for Alpha Stable Detection
Method Complexity per symbol
Analysis
Hole Puncher + Correlation Receiver
O(N+S) A decision needs to be made about each sample.
Optimal Myriad + Correlation Receiver
O(NW3+S) Due to polynomial rooting which is equivalent to Eigen-value decomposition.
Selection Myriad + Correlation Receiver
O(NW2+S) Evaluation of the myriad function and comparing it.
MAP Approximation O(MNS) Evaluating approximate pdf(M is number of Gaussians in mixture)
Return
76
Wireless Networking and Communications Group
Extensions to MIMO systems
Radio Frequency Interference Modeling and Receiver Design for MIMO systemsRFI Model Spatial
Corr.Physical Model
Comments
Middleton Class A No Yes • Uni-variate model• Assume independent or uncorrelated
noise for multiple antennasReceiver design:[Gao & Tepedelenlioglu, 2007] Space-Time Coding[Li, Wang & Zhou, 2004] Performance degradation in receivers
Weighted Mixture of Gaussian Densities
Yes No • Not derived based on physical principles
Receiver design:[Blum et al., 1997] Adaptive Receiver Design
Bivariate Middleton Class A[McDonald & Blum, 1997]
Yes Yes • Extensions of Class A model to two-antenna systems
Return
77
Wireless Networking and Communications Group
Our Contributions
RFI Modeling • Evaluated fit of measured RFI data to the bivariate Middleton Class A model [McDonald & Blum, 1997]
• Includes noise correlation between two antennas Parameter Estimation
• Derived parameter estimation algorithm based on the method of moments (sixth order moments)
Performance Analysis
• Demonstrated communication performance degradation of conventional receivers in presence of RFI
• Bounds on communication performance[Chopra , Gulati, Evans, Tinsley, and Sreerama, ICASSP 2009]
Receiver Design • Derived Maximum Likelihood (ML) receiver• Derived two sub-optimal ML receivers with reduced
complexity
2 x 2 MIMO receiver design in the presence of RFI[Gulati, Chopra, Heath, Evans, Tinsley & Lin, Globecom 2008]
Return
78
Wireless Networking and Communications Group
Bivariate Middleton Class A Model
Joint spatial distribution
Parameter Description Typical Range
Overlap Index. Product of average number of emissions per second and mean duration of typical emission
Ratio of Gaussian to non-Gaussian component intensity at each of the two antennas
Correlation coefficient between antenna observations
Return
79
Wireless Networking and Communications Group
Results on Measured RFI Data
50,000 baseband noise samples represent broadband interference
Estimated Parameters
Bivariate Middleton Class A
Overlap Index (A) 0.313
2D-KL Divergence
1.004
Gaussian Factor (G1) 0.105
Gaussian Factor (G2) 0.101
Correlation (k) -0.085
Bivariate Gaussian
Mean (µ) 0
2D-KL Divergence
1.6682
Variance (s1) 1
Variance (s2) 1
Correlation (k) -0.085
-4 -3 -2 -1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
1.2
1.4
Noise amplitude
Pro
ba
bili
ty D
en
sity
Fu
nct
ion
Measured PDFEstimated MiddletonClass A PDFEqui-powerGaussian PDF
Marginal PDFs of measured data compared with estimated model densities
Return
80
2 x 2 MIMO System
Maximum Likelihood (ML) receiver
Log-likelihood function
Wireless Networking and Communications Group
System Model
Sub-optimal ML Receiversapproximate
Return
Wireless Networking and Communications Group
Sub-Optimal ML Receivers81
Two-piece linear approximation
Four-piece linear approximation
-5 -4 -3 -2 -1 0 1 2 3 4 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
z
Ap
pro
xma
tion
of
(z)
(z)
1(z)
2(z)
chosen to minimizeApproximation of
Return
82
Wireless Networking and Communications Group
Results: Performance Degradation
Performance degradation in receivers designed assuming additive Gaussian noise in the presence of RFI
-10 -5 0 5 10 15 2010
-5
10-4
10-3
10-2
10-1
100
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
SM with ML (Gaussian noise)SM with ZF (Gaussian noise)Alamouti coding (Gaussian noise)SM with ML (Middleton noise)SM with ZF (Middleton noise)Alamouti coding (Middleton noise)
Simulation Parameters• 4-QAM for Spatial Multiplexing (SM)
transmission mode• 16-QAM for Alamouti transmission
strategy• Noise Parameters:
A = 0.1, 1= 0.01, 2= 0.1, k = 0.4
Severe degradation in communication performance in
high-SNR regimes
Return
83
-10 -5 0 5 10 15 20
10-3
10-2
10-1
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
Optimal ML Receiver (for Gaussian noise)Optimal ML Receiver (for Middleton Class A)Sub-Optimal ML Receiver (Four-Piece)Sub-Optimal ML Receiver (Two-Piece)
Wireless Networking and Communications Group
Results: RFI Mitigation in 2 x 2 MIMO
A Noise Characteristic
Improve-ment
0.01 Highly Impulsive ~15 dB0.1 Moderately
Impulsive ~8 dB
1 Nearly Gaussian ~0.5 dB
Improvement in communication performance over conventional Gaussian ML receiver at symbol
error rate of 10-2
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
Return
Wireless Networking and Communications Group
Results: RFI Mitigation in 2 x 2 MIMO 84
Complexity AnalysisReceiver
Quadratic Forms
Exponential
Comparisons
Gaussian ML M2 0 0
Optimal ML 2M2 2M2 0
Sub-optimal ML (Four-Piece) 2M2 0 2M2
Sub-optimal ML (Two-Piece) 2M2 0 M2
Complexity Analysis for decoding M-level QAM modulated signal
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
-10 -5 0 5 10 15 20
10-3
10-2
10-1
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
Optimal ML Receiver (for Gaussian noise)Optimal ML Receiver (for Middleton Class A)Sub-Optimal ML Receiver (Four-Piece)Sub-Optimal ML Receiver (Two-Piece)
Return
85
Wireless Networking and Communications Group
Performance Bounds (Single Antenna)
Channel capacity
Case I Shannon Capacity in presence of additive white Gaussian noise
Case II (Upper Bound) Capacity in the presence of Class A noiseAssumes that there exists an input distribution which makes output distribution Gaussian (good approximation in high SNR regimes)
Case III (Practical Case) Capacity in presence of Class A noiseAssumes input has Gaussian distribution (e.g. bit interleaved coded modulation (BICM) or OFDM modulation [Haring, 2003])
NXY System Model
)()(
)|()(
);(max}}{),({ 2
NhYh
XYhYh
YXICsX EXExf
Return
86
Wireless Networking and Communications Group
Performance Bounds (Single Antenna)
Channel capacity in presence of RFI
NXY
-40 -30 -20 -10 0 10 200
5
10
15
SNR [in dB]
Cap
acity
(bi
ts/s
ec/H
z)
Channel Capacity
X: Gaussian, N: Gaussian
Y:Gaussian, N:ClassA (A = 0.1, = 10-3)
X:Gaussian, N:ClassA (A = 0.1, = 10-3)
System Model
ParametersA = 0.1, Γ = 10-3
Capacity
)()(
)|()(
);(max}}{),({ 2
NhYh
XYhYh
YXICsX EXExf
Return
87
Wireless Networking and Communications Group
Performance Bounds (Single Antenna)
Probability of error for uncoded transmissions
)(!
2
0m
AWGNe
m
mA
e Pm
AeP
-40 -30 -20 -10 0 10 2010
-7
10-6
10-5
10-4
10-3
10-2
10-1
100
dmin
/ [in dB]
Pro
babi
lity
of e
rror
Probability of error (Uncoded Transmission)
AWGN
Class A: A = 0.1, = 10-3
12 A
m
m
BPSK uncoded transmission
One sample per symbol
A = 0.1, Γ = 10-3
[Haring & Vinck, 2002]
Return
88
Wireless Networking and Communications Group
Performance Bounds (Single Antenna)
Chernoff factors for coded transmissions
N
kkk ccC
PPEP
1
'
'
),,(min
)(
cc
-20 -15 -10 -5 0 5 10 1510
-3
10-2
10-1
100
dmin
/ [in dB]
Che
rnof
f F
acto
r
Chernoff factors for real channel with various parameters of A and MAP decoding
Gaussian
Class A: A = 0.1, = 10-3
Class A: A = 0.3, = 10-3
Class A: A = 10, = 10-3
PEP: Pairwise error probability
N: Size of the codeword
Chernoff factor:
Equally likely transmission for symbols
),,(min ' kk ccC
Return
89
Performance Bounds (2x2 MIMO)
Wireless Networking and Communications Group
Return
90
Wireless Networking and Communications Group
Performance Bounds (2x2 MIMO)
Channel capacity
Case I Shannon Capacity in presence of additive white Gaussian noise
Case II (Upper Bound) Capacity in presence of bivariate Middleton Class A noise. Assumes that there exists an input distribution which makes output distribution Gaussian for all SNRs.
Case III (Practical Case) Capacity in presence of bivariate Middleton Class A noiseAssumes input has Gaussian distribution
System Model
Return
91
Wireless Networking and Communications Group
Performance Bounds (2x2 MIMO)
Channel capacity in presence of RFI for 2x2 MIMO
System Model
Capacity
-40 -30 -20 -10 0 10 200
5
10
15
20
25
SNR [in dB]
Mut
ual I
nfor
mat
ion
(bits
/sec
/Hz)
Channel Capacity with Gaussian noiseUpper Bound on Mutual Information with Middleton noiseGaussian transmit codebook with Middleton noise
Parameters:A = 0.1, G1 = 0.01, G2 = 0.1, k = 0.4
Return
92
Wireless Networking and Communications Group
Performance Bounds (2x2 MIMO)
Probability of symbol error for uncoded transmissions
Parameters:A = 0.1, G1 = 0.01, G2 = 0.1, k = 0.4
Pe: Probability of symbol error
S: Transmitted code vector
D(S): Decision regions for MAP detector
Equally likely transmission for symbols
Return
93
Wireless Networking and Communications Group
Performance Bounds (2x2 MIMO)
Chernoff factors for coded transmissions
N
ttt ssC
ssPPEP
1
'
'
),,(min
)(
PEP: Pairwise error probabilityN: Size of the codewordChernoff factor:Equally likely transmission for symbols
),,(min ' kk ccC
-30 -20 -10 0 10 20 30 4010
-8
10-6
10-4
10-2
100
dt2 / N
0 [in dB]
Che
rnof
f Fac
tor
Middleton noise (A = 0.5)Middleton noise (A = 0.1)Middleton noise (A = 0.01)Gaussian noise
Parameters:G1 = 0.01, G2 = 0.1, k = 0.4
Return
94
Performance Bounds (2x2 MIMO)
Cutoff rates for coded transmissions Similar measure as channel capacity Relates transmission rate (R) to Pe for a length T codes
Wireless Networking and Communications Group
Return
95
Performance Bounds (2x2 MIMO)
Wireless Networking and Communications Group
Cutoff rate
-30 -20 -10 0 10 20 30 400
0.5
1
1.5
2
2.5
3
3.5
4
SNR [in dB]
Cut
off R
ate
[bits
/tran
smis
sion
]
BPSK, Middleton noiseBPSK, Gaussian noiseQPSK, Middleton noiseQPSK, Gaussian noise16QAM, Middleton noise16QAM, Gaussian noise
Return
96
Wireless Networking and Communications Group
Extensions to Multicarrier Systems
Impulse noise with impulse event followed by “flat” region Coding may improve communication performance In multicarrier modulation, impulsive event in time domain
spreads over all subcarriers, reducing effect of impulse Complex number (CN) codes [Lang, 1963]
Unitary transformations Gaussian noise is unaffected (no change in 2-norm Distance) Orthogonal frequency division multiplexing (OFDM) is a
special case: Inverse Fourier Transform As number of subcarriers increase, impulsive noise case
approaches the Gaussian noise case [Haring 2003]
Return
Turbo Codes in Presence of RFI
Wireless Networking and Communications Group
97
Decoder 1Parity 1Systematic Data
Decoder 2
Parity 2
1
-
-
-
-
A-priori Information
Depends on channel statistics
Independent of channel statistics
Gaussian channel:
Middleton Class A channel:
Independent of channel statistics
Extrinsic Information
Leads to a 10dB improvement at BER of 10-5 [Umehara03]
Return
Recommended