Design of Interference-Aware Wireless Communication Systems Wireless Networking and Communications...
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Design of Interference-Aware Wireless Communication Systems Wireless Networking and Communications Group 2 Dec 2010 Brian L. Evans Lead Graduate Students
Design of Interference-Aware Wireless Communication Systems
Wireless Networking and Communications Group 2 Dec 2010 Brian L.
Evans Lead Graduate Students Aditya Chopra, Kapil Gulati, and
Marcel Nassar Collaborators from Intel Labs Current: Nageen
Himayat, Kirk Skeba, and Srikathyayani Srikanteswara Past:
Chaitanya Sreerama, Eddie X. Lin, Alberto A. Ochoa, and Keith R.
Tinsley
Slide 2
Outline Introduction Problem definition Summary of last talk
(in Apr. 2010) at Intel Labs Recent results RFI Modeling: Spatial
and Temporal dependence RFI Mitigation: Multi-carrier systems
Conclusions Future work Wireless Networking and Communications
Group 2 Radio Frequency Interference (RFI)
Slide 3
Introduction Wireless Networking and Communications Group 3
Wireless Communication Sources Closely located sources Coexisting
protocols Non-Communication Sources Electromagnetic radiations
Computational Platform Clocks, busses, processors Co-located
transceivers antenna baseband processor (Wi-Fi) (WiMAX Basestation)
(WiMAX Mobile) (Bluetooth) (Microwave) (Wi-Fi)(WiMAX)
Slide 4
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 10-100x improvement
in network throughput Wireless Networking and Communications Group
4
Slide 5
Designing Interference-Aware Receivers Wireless Networking and
Communications Group 5 RTS CTS RTS / CTS: Request / Clear to send
Guard zone Example: Dense WiFi Networks
Slide 6
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] Wireless Networking and Communications Group
6
Slide 7
Summary of Last Talk: RFI Modeling Wireless Networking and
Communications Group 7 Sensor networks Ad hoc networks Dense Wi-Fi
networks Cluster of hotspots (e.g. marketplace) In-cell and
out-of-cell femtocell users Out-of-cell femtocell users Cellular
networks Hotspots (e.g. caf) Symmetric Alpha Stable Ad hoc and
Cellular networks Single Antenna Instantaneous statistics Femtocell
networks Single Antenna Instantaneous statistics Gaussian Mixture
Model
Slide 8
Summary of Last Talk: RFI Modeling Validated for Laptop
radiated RFI Slides available at:
http://users.ece.utexas.edu/~bevans/projects/rfi/talks/April2010RFIMitigationTalk.html
Wireless Networking and Communications Group 8 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
Slide 9
Summary of Last Talk: RFI Mitigation Communication Performance
Wireless Networking and Communications Group 9 Pulse Shaping
Pre-filtering Matched Filter Detection Rule Interference + Thermal
noise Single carrier, single antenna (SISO)Single carrier, two
antenna (2x2 MIMO) ~ 20 dB ~ 8 dB 10 100x reduction in Bit Error
Rate
Slide 10
Extended to include spatial and temporal dependence
Multivariate extensions of Symmetric Alpha Stable Gaussian mixture
model RFI Modeling: Extensions Wireless Networking and
Communications Group 10 Multi-antenna receivers Symbol errors Burst
errors Coded transmissions Delays in network
Slide 11
RFI Modeling: Spatial Dependence System Model Common and
exclusive interferers Characterizes receiver separation and
directional shielding Joint RFI statistics helpful in choosing
spatial transmit and receive techniques Wireless Networking and
Communications Group 11 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 1
Slide 12
RFI Modeling: Spatial Dependence An impulsive event at one
antenna increases probability of impulse event at other antennae
Translated environmental parameters to spatial dependence Wireless
Networking and Communications Group 12 |RFI at antenna 2| |RFI at
antenna 1| |RFI at antenna 2| SPATIALLY INDEPENDENT SPATIALLY
ISOTROPIC
Slide 13
RFI Modeling: Temporal Dependence System Model Interference is
dependent across time slots Wireless Networking and Communications
Group 13
Slide 14
RFI Modeling: Joint Interference Statistics Throughput
performance of ad hoc networks Wireless Networking and
Communications Group 14 Ad hoc networks Multivariate Symmetric
Alpha Stable Cellular networks Multivariate Gaussian Mixture Model
Network throughput improved by optimizing distribution of ON Time
of users (MAC parameter) ~1.6x
Slide 15
RFI Mitigation: Multi-carrier systems Single Carrier vs.
Multi-Carrier: Intuition Wireless Networking and Communications
Group 15 Symbols Impulsive Noise Symbols Impulsive Noise High
Amplitude Impulse Impulse energy concentrated in one symbol Symbol
Lost Impulse energy spread across symbols Noise dependent across
subcarriers Optimal decoding: exponential complexity! Single
CarrierMulti Carrier (OFDM)
Slide 16
RFI Mitigation: Multi-carrier systems Proposed Receiver
Iterative Expectation Maximization (EM) based on noise model
Communication Performance Wireless Networking and Communications
Group 16 Simulation Parameters BPSK Modulation Interference Model
2-term Gaussian Mixture Model ~ 5 dB
Slide 17
Summary Wireless Networking and Communications Group 17
Physical (PHY) Layer Single Antenna (past work) Multi-Antenna
Receivers Temporal Modeling Statistical Modeling of RFI: (a)Uni- or
Multi-variate Gaussian Mixture (b)Uni- or Multi-variate Symmetric
Alpha Stable Medium Access Control (MAC) Layer (a)Detection and
Pre-filtering methods (b)Single- and Two-antenna receivers
(c)Single- and Multi-carrier systems RFI Mitigation: (a)Microwave
Oven Interference (b)Performance of Ad hoc Networks RFI Avoidance
and Mitigation: Impact: 10-100x improvement in communication
performance
Slide 18
Current and Future Work Wireless Networking and Communications
Group 18 Physical (PHY) Layer Medium Access Control (MAC) Layer RFI
Avoidance and Mitigation: Statistical Modeling of RFI:
(a)Multi-carrier Multi-antenna systems (b)Non-stationary RFI
Communication Performance Analysis MIMO transmit and receive
strategies Improving Communication Performance Detection and
Pre-filtering methods Error correction coding Interference
Avoidance Spectrum Sensing Impact: Improved communication
performance RFI Avoidance and Mitigation: Network Performance
Analysis Different MAC strategies Improving Network Performance
Optimizing MAC parameters MAC algorithms to reduce interference
Interference Avoidance Resource Allocation (time, frequency)
Impact: Improved network-wide performance Cognitive Radios
Slide 19
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 Release
Version 1.5, Aug. 16, 2010 Wireless Networking and Communications
Group 19
http://users.ece.utexas.edu/~bevans/projects/rfi/software/index.html
Snapshot of a demo
Slide 20
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, to be
published, Dec., 2010. 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. Conf. on Comm., Jan.
5-9, 2011, Kyoto, Japan, 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 20 Wireless Networking and
Communications Group
Slide 21
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. 21 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 1.5, Aug. 16, 2010.
Slide 22
Thanks ! 22 Wireless Networking and Communications Group
Slide 23
References RFI Modeling 1.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. 12061221, 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. 17431754, 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. 6476, 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. 17761783, 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. 205230, Feb. 2009. 23 Wireless Networking and
Communications Group
Slide 24
References Parameter Estimation 1.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
Networks 1.R. Ganti and M. Haenggi, Interference and outage in
clustered wireless ad hoc networks, IEEE Transactions on
Information Theory, vol. 55, no. 9, pp. 40674086, Sep. 2009. 2.A.
Hasan and J. G. Andrews, The guard zone in wireless ad hoc
networks, IEEE Transactions on Wireless Communications, vol. 4, no.
3, pp. 897906, Mar. 2007. 3.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. 13871400, Dec. 2007. 4.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.
24 Wireless Networking and Communications Group
Slide 25 do not exist PDF for = 1.5, = 0, = 10
ParameterDescriptionRange Characteristic Exponent. Amount of
impulsiveness Localization. Analogous to mean Dispersion. Analogous
to variance Backup Return">
57 Wireless Networking and Communications Group Symmetric Alpha
Stable Model Characteristic Function Closed-form PDF expression
only for = 1 (Cauchy), = 2 (Gaussian), = 1/2 (Levy), = 0 (not very
useful) Approximate PDF using inverse transform of power series
expansion Second-order moments do not exist for < 2 Generally,
moments of order > do not exist PDF for = 1.5, = 0, = 10
ParameterDescriptionRange Characteristic Exponent. Amount of
impulsiveness Localization. Analogous to mean Dispersion. Analogous
to variance Backup Return
Slide 58
58 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
Frechets 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)
Return
Slide 59
Parameter Estimators for Alpha Stable Wireless Networking and
Communications Group 59 0 < p < Return
Slide 60
60 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 and mean
directly from data Estimate variance from and estimates Mean
squared error in estimate of characteristic exponent Return
Slide 61
61 Wireless Networking and Communications Group Parameter Est.:
Symmetric Alpha Stable Results Mean squared error in estimate of
dispersion (variance) Mean squared error in estimate of
localization (mean) Return
Slide 62
Extreme Order Statistics Wireless Networking and Communications
Group 62 Return
Slide 63
63 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 pulse 10
samples/symbol 10 symbols/pulse length Composite of transmitted and
received MPEG II video streams
http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo1
9dB_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 NoiseValue Overlap index (A)0.35 Gaussian factor ( ) 0.001
SNR19 dB Return
Slide 64
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 pulse 10
samples/symbol 10 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_demo1
9dB.wmv Wireless Networking and Communications Group 64 Additive
Class A NoiseValue Overlap index (A)0.35 Gaussian factor ( ) 0.001
SNR19 dB Return
Slide 65
65 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
Slide 66
66 Wireless Networking and Communications Group Our
Contributions Mitigation of computational platform noise in single
carrier, single antenna systems [Nassar, Gulati, DeYoung, Evans
& Tinsley, ICASSP 2008, JSPS 2009] Return
Slide 67
67 Wireless Networking and Communications Group Filtering and
Detection Pulse Shaping Pre-Filtering Matched Filter Detection 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] Assumption Multiple samples of the
received signal are available N Path Diversity [Miller, 1972]
Oversampling by N [Middleton, 1977] Assumption Multiple samples of
the received signal are available N Path Diversity [Miller, 1972]
Oversampling by N [Middleton, 1977] Return
Slide 68
RFI Mitigation in SISO systems Communication performance
Wireless Networking and Communications Group 68 Pulse Shaping
Pre-filtering Matched Filter Detection Rule Interference + Thermal
noise Pulse shape Raised cosine 10 samples per symbol 10 symbols
per pulse Channel A = 0.35 = 5 10 -3 Memoryless Binary Phase Shift
Keying Return
Slide 69
69 Wireless Networking and Communications Group Results: Class
A Detection Pulse shape Raised cosine 10 samples per symbol 10
symbols per pulse Channel A = 0.35 = 0.5 10 -3 Memoryless
Communication Performance Binary Phase Shift Keying Return
Slide 70
70 Wireless Networking and Communications Group Results: Alpha
Stable Detection Use dispersion parameter in place of noise
variance to generalize SNR Communication Performance Same
transmitter settings as previous slide Return
Slide 71
71 Wireless Networking and Communications Group MAP Detection
for Class A Hard decision Bayesian formulation [Spaulding &
Middleton, 1977] Equally probable source Return
Slide 72
Wireless Networking and Communications Group MAP Detection for
Class A: Small Signal Approx. 72 Expand noise PDF p Z (z) by Taylor
series about S j = 0 (j=1,2) Approximate MAP detection rule
Logarithmic non-linearity + correlation receiver Near-optimal for
small amplitude signals Correlation Receiver We use 100 terms of
the series expansion for d/dx i ln p Z (x i ) in simulations
Return
Slide 73
73 Wireless Networking and Communications Group Incoherent
Detection Bayesian formulation [Spaulding & Middleton, 1997,
pt. II] Small signal approximation Correlation receiver Return
Slide 74
74 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 x
1,x 2,,x N [Gonzalez & Arce, 2001] As k decreases, less
impulsive noise passes through the myriad filter As k0, 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
Return
Slide 75
Wireless Networking and Communications Group Filtering for
Alpha Stable Noise (Cont..) 75 Myriad filter implementation Given a
window of samples, x 1,,x N, find [x min, x max ] Optimal Myriad
algorithm 1. Differentiate objective function polynomial p( ) with
respect to 2. Find roots and retain real roots 3. Evaluate p( ) at
real roots and extreme points 4. Output that gives smallest value
of p( ) Selection Myriad (reduced complexity) 1. Use x 1, , x N as
the possible values of 2. Pick value that minimizes objective
function p( ) Return
Slide 76
76 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
Return
Slide 77
77 Wireless Networking and Communications Group MAP Detection
for Alpha Stable: PDF Approx. SS random variable Z with parameters
, can be written Z = X Y [Kuruoglu, 1998] X is zero-mean Gaussian
with variance 2 Y is positive stable random variable with
parameters depending on PDF of Z can be written as a mixture model
of N Gaussians [Kuruoglu, 1998] Mean can be added back in Obtain f
Y (.) by taking inverse FFT of characteristic function &
normalizing Number of mixtures (N) and values of sampling points (v
i ) are tunable parameters Return
Slide 78
78 Wireless Networking and Communications Group Results: Alpha
Stable Detection Return
Slide 79
79 Wireless Networking and Communications Group Complexity
Analysis for Alpha Stable Detection Return
Slide 80
80 Wireless Networking and Communications Group Extensions to
MIMO systems Return
Slide 81
81 Wireless Networking and Communications Group Our
Contributions 2 x 2 MIMO receiver design in the presence of RFI
[Gulati, Chopra, Heath, Evans, Tinsley & Lin, Globecom 2008]
Return
Slide 82
82 Wireless Networking and Communications Group Bivariate
Middleton Class A Model Joint spatial distribution Return
Slide 83
83 Wireless Networking and Communications Group Results on
Measured RFI Data 50,000 baseband noise samples represent broadband
interference Marginal PDFs of measured data compared with estimated
model densities Return
Slide 84
84 2 x 2 MIMO System Maximum Likelihood (ML) receiver
Log-likelihood function Wireless Networking and Communications
Group System Model Sub-optimal ML Receivers approximate Return
Slide 85
Wireless Networking and Communications Group Sub-Optimal ML
Receivers 85 Two-piece linear approximation Four-piece linear
approximation chosen to minimize Approximation of Return
Slide 86
86 Wireless Networking and Communications Group Results:
Performance Degradation Performance degradation in receivers
designed assuming additive Gaussian noise in the presence of RFI
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, = 0.4 Severe degradation in
communication performance in high-SNR regimes Return
Slide 87
87 Wireless Networking and Communications Group Results: RFI
Mitigation in 2 x 2 MIMO 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, = 0.4)
Return
Slide 88
Wireless Networking and Communications Group Results: RFI
Mitigation in 2 x 2 MIMO 88 Complexity Analysis Complexity Analysis
for decoding M-level QAM modulated signal Communication Performance
(A = 0.1, 1 = 0.01, 2 = 0.1, = 0.4) Return
Slide 89
89 Wireless Networking and Communications Group Performance
Bounds (Single Antenna) Channel capacity Case IShannon Capacity in
presence of additive white Gaussian noise Case II(Upper Bound)
Capacity in the presence of Class A noise Assumes 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 noise Assumes input has Gaussian
distribution (e.g. bit interleaved coded modulation (BICM) or OFDM
modulation [Haring, 2003] ) System Model Return
Slide 90
90 Wireless Networking and Communications Group Performance
Bounds (Single Antenna) Channel capacity in presence of RFI System
Model Parameters A = 0.1, = 10 -3 Capacity Return
Slide 91
91 Wireless Networking and Communications Group Performance
Bounds (Single Antenna) Probability of error for uncoded
transmissions BPSK uncoded transmission One sample per symbol A =
0.1, = 10 -3 [Haring & Vinck, 2002] Return
Slide 92
92 Wireless Networking and Communications Group Performance
Bounds (Single Antenna) Chernoff factors for coded transmissions
PEP: Pairwise error probability N: Size of the codeword Chernoff
factor: Equally likely transmission for symbols Return
Slide 93
93 Performance Bounds (2x2 MIMO) Wireless Networking and
Communications Group Return
Slide 94
94 Wireless Networking and Communications Group Performance
Bounds (2x2 MIMO) Channel capacity Case IShannon 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 noise Assumes
input has Gaussian distribution System Model Return
Slide 95
95 Wireless Networking and Communications Group Performance
Bounds (2x2 MIMO) Channel capacity in presence of RFI for 2x2 MIMO
System Model Capacity Parameters : A = 0.1, 1 = 0.01, 2 = 0.1, =
0.4 Return
Slide 96
96 Wireless Networking and Communications Group Performance
Bounds (2x2 MIMO) Probability of symbol error for uncoded
transmissions Parameters : A = 0.1, 1 = 0.01 2 = 0.1, = 0.4 Pe:
Probability of symbol error S: Transmitted code vector D(S):
Decision regions for MAP detector Equally likely transmission for
symbols Return
Slide 97
97 Wireless Networking and Communications Group Performance
Bounds (2x2 MIMO) Chernoff factors for coded transmissions PEP:
Pairwise error probability N: Size of the codeword Chernoff factor:
Equally likely transmission for symbols Parameters : 1 = 0.01 2 =
0.1, = 0.4 Return
Slide 98
98 Performance Bounds (2x2 MIMO) Cutoff rates for coded
transmissions Similar measure as channel capacity Relates
transmission rate (R) to P e for a length T codes Wireless
Networking and Communications Group Return
Slide 99
99 Performance Bounds (2x2 MIMO) Wireless Networking and
Communications Group Cutoff rate Return
Slide 100
100 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
Slide 101
Turbo Codes in Presence of RFI Wireless Networking and
Communications Group 101 Decoder 1 Parity 1 Systematic Data Decoder
2 Parity 2 - - - - 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
Slide 102
RFI Mitigation Using Error Correction Wireless Networking and
Communications Group 102 Decoder 1 Parity 1 Systematic Data Decoder
2 Interleaver Parity 2 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] Return
Slide 103
Usage Scenario #1 Wireless Networking and Communications Group
103 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
Return
Slide 104
Usage Scenario #2 104 Measured RFI data RFI Toolbox Statistical
Modeling DEMO SISO Communication Performance DEMO File Transfer
DEMO MIMO Communication Performance DEMO Wireless Networking and
Communications Group Return