Design of Interference-Aware Wireless Communication Systems Wireless Networking and Communications...

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

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)

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)

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

Designing Interference-Aware Receivers Wireless Networking and Communications Group 5 RTS CTS RTS / CTS: Request / Clear to send Guard zone Example: Dense WiFi Networks

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

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

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

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

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

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

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

RFI Modeling: Temporal Dependence System Model Interference is dependent across time slots Wireless Networking and Communications Group 13

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

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)

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

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

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

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

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

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.

Thanks ! 22 Wireless Networking and Communications Group

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

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

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

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

Parameter Estimators for Alpha Stable Wireless Networking and Communications Group 59 0 < p < Return

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

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

Extreme Order Statistics Wireless Networking and Communications Group 62 Return

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

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

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

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

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

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

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

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

71 Wireless Networking and Communications Group MAP Detection for Class A Hard decision Bayesian formulation [Spaulding & Middleton, 1977] Equally probable source Return

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

73 Wireless Networking and Communications Group Incoherent Detection Bayesian formulation [Spaulding & Middleton, 1997, pt. II] Small signal approximation Correlation receiver Return

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

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

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

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

78 Wireless Networking and Communications Group Results: Alpha Stable Detection Return

79 Wireless Networking and Communications Group Complexity Analysis for Alpha Stable Detection Return

80 Wireless Networking and Communications Group Extensions to MIMO systems Return

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

82 Wireless Networking and Communications Group Bivariate Middleton Class A Model Joint spatial distribution Return

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

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

Wireless Networking and Communications Group Sub-Optimal ML Receivers 85 Two-piece linear approximation Four-piece linear approximation chosen to minimize Approximation of Return

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

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

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

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

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

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

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

93 Performance Bounds (2x2 MIMO) Wireless Networking and Communications Group Return

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

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

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

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

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

99 Performance Bounds (2x2 MIMO) Wireless Networking and Communications Group Cutoff rate Return

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

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

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

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

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

Design of Interference-Aware Wireless Communication Systems Wireless Networking and Communications...

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