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 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

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 2 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)

Radio Frequency Interference (RFI)  Limits wireless communication performance  Impact of LCD noise on throughput for an embedded Wi-Fi (IEEE g) 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  x reduction in bit error rate (this talk)  x improvement in network throughput (future work) Wireless Networking and Communications Group 5

 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 6 Pathloss Fading Interferer 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] Wireless Networking and Communications Group 7

Poisson Field of Interferers Wireless Networking and Communications Group 8 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 Wireless Networking and Communications Group 9 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 10 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 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

Receiver Design to Mitigate RFI Wireless Networking and Communications Group 12 RTS CTS Example: Wi-Fi networks RTS / CTS: Request / Clear to send Interference statistics similar to Case III Guard zone  Design receivers using knowledge of RFI statistics

RFI Mitigation in SISO systems  Communication performance Wireless Networking and Communications Group 13 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 × Memoryless Binary Phase Shift Keying

14 Wireless Networking and Communications Group RFI Mitigation in 2 x 2 MIMO systems Improvement in communication performance over conventional Gaussian ML receiver at symbol error rate of Communication Performance (A = 0.1,  1 = 0.01,  2 = 0.1,  = 0.4) Conventional Gaussian ML Receiver Proposed Receivers

Wireless Networking and Communications Group RFI Mitigation in 2 x 2 MIMO systems 15 Complexity Analysis Complexity Analysis for decoding M-level QAM modulated signal Communication Performance (A = 0.1,  1 = 0.01,  2 = 0.1,  = 0.4) Conventional Gaussian ML Receiver Proposed Receivers

RFI Mitigation Using Error Correction Wireless Networking and Communications Group 16 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 can be achieved using accurate RFI statistics [Umehara, 2003]

Summary  Radio frequency interference affects wireless transceivers  RFI mitigation can improve communication performance  Our contributions Wireless Networking and Communications Group 17

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 Wireless Networking and Communications Group 18

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, 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 , 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, 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 , 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, 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, 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 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 Release Version beta, Apr. 11, 2010 Wireless Networking and Communications Group 21 Snapshot of a demo

Usage Scenario #1 Wireless Networking and Communications Group 22 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 #2 23 Measured RFI data RFI Toolbox Statistical Modeling DEMO SISO Communication Performance DEMO File Transfer DEMO MIMO Communication Performance DEMO Wireless Networking and Communications Group

Thanks ! 24 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 , May 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, 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 , 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 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 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 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 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 , Jan 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 , Jun 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. 4067–4086, Sep 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 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 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 , Dec 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 , Nov J. G. Andrews, S. Weber, M. Kountouris, and M. Haenggi, “Random access transport capacity,” IEEE Transactions On Wireless Communications, Jan. 2010, submitted. [Online]. Available: 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 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 RFI 1.A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment- Part I: Coherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep 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 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 G. R. Arce, Nonlinear Signal Processing: A Statistical Approach, John Wiley & Sons, 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 , Nov J. H. Kotecha and P. M. Djuric, “Gaussian sum particle ltering,” IEEE Transactions on Signal Processing, vol. 51, no. 10, pp , Oct 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 Ping Gao and C. Tepedelenlioglu. “Space-time coding over mimo channels with impulsive noise”, IEEE Trans. on Wireless Comm., 6(1):220–229, January RFI Measurements and Impact 1.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 , Aug 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 Wireless Networking and Communications Group 29 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 Wireless Networking and Communications Group 30 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 Wireless Networking and Communications Group 31 Backup

Interference Mitigation Techniques  Interference avoidance  CSMA / CA  Interference alignment  Example: [Cadambe & Jafar, 2007] Wireless Networking and Communications Group 32 Return

Interference Mitigation Techniques (cont…)  Interference cancellation Ref: J. G. Andrews, ”Interference Cancellation for Cellular Systems: A Contemporary Overview”, IEEE Wireless Communications Magazine, Vol. 12, No. 2, pp , April 2005 Wireless Networking and Communications Group 33 Return

Femtocell Networks Reference: V. Chandrasekhar, J. G. Andrews and A. Gatherer, "Femtocell Networks: a Survey", IEEE Communications Magazine, Vol. 46, No. 9, pp , September 2008 Wireless Networking and Communications Group 34 Return

Common Spectral Occupancy Wireless Networking and Communications Group 35 Return

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 a/b/g due to computational platform noise [J. Shi et al., 2006] Case Sudy: b, 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) Wireless Networking and Communications Group 36 Return

Impact of LCD clock on g  Pixel clock 65 MHz  LCD Interferers and g center frequencies Wireless Networking and Communications Group 37 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 Pr(number of interferers = M |area R) ~ Poisson(M; R)  Uniformly distributed emission times  Temporally independent (at each sample time)  Limitations  Alpha Stable models do not include thermal noise  Temporal dependence may exist Wireless Networking and Communications Group 38 Return

Transients in Digital FIR Filters Wireless Networking and Communications Group Tap FIR Filter Low pass Stopband freq (normalized) InputOutput Freq = 0.16 Interference duration = 10 * 1/0.22 Interference duration = 100 x 1/0.22 Transients Transients Significant w.r.t. Steady StateTransients Ignorable w.r.t. Steady State Return

Poisson Field of Interferers  Interferers distributed over parametric annular space  Log-characteristic function Wireless Networking and Communications Group 40 Return

Poisson Field of Interferers Wireless Networking and Communications Group 41 Return

Poisson Field of Interferers  Simulation Results (tail probability) Wireless Networking and Communications Group 42 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) Wireless Networking and Communications Group 43 Case II: Finite area annular region Return

Poisson-Poisson Cluster Field of Interferers  Cluster centers distributed as spatial Poisson process over  Interferers distributed as spatial Poisson process Wireless Networking and Communications Group 44 Return

Poisson-Poisson Cluster Field of Interferers  Log-Characteristic function Wireless Networking and Communications Group 45 Return

Poisson-Poisson Cluster Field of Interferers  Simulation Results (tail probability) Wireless Networking and Communications Group 46 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) Wireless Networking and Communications Group 47 Case II: Finite area annular region Return

Gaussian Mixture vs. Alpha Stable  Gaussian Mixture vs. Symmetric Alpha Stable Wireless Networking and Communications Group 48 Gaussian MixtureSymmetric Alpha Stable ModelingInterferers distributed with Guard zone around receiver (actual or virtual due to pathloss function) Interferers distributed over entire plane Pathloss Function With GZ: singular / non-singular Entire plane: non-singular Singular form Thermal Noise Easily extended (sum is Gaussian mixture) Not easily extended (sum is Middleton Class B) OutliersEasily extended to include outliersDifficult to include outliers Return

49 Wireless Networking and Communications Group 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 CSum of Class A and Class B (approx. Class B) [Middleton, 1999] Return

50 Wireless Networking and Communications Group Middleton Class A model  Probability Density Function PDF for A = 0.15,  = 0.8 ParameterDescriptionRange Overlap 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] Return

Expectation Maximization Overview Wireless Networking and Communications Group 51 Return

Wireless Networking and Communications Group Results: EM Estimator for Class A 52 PDFs with 11 summation terms 50 simulation runs per setting 1000 data samples Convergence criterion: Iterations for Parameter A to ConvergeNormalized Mean-Squared Error in A K = A  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 for α = 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 PDF for  = 1.5,  = 0,  = 10 ParameterDescriptionRange Characteristic Exponent. Amount of impulsiveness Localization. Analogous to mean Dispersion. Analogous to variance 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) Return

Parameter Estimators for Alpha Stable Wireless Networking and Communications Group 56 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”  directly from data Estimate “variance”  from α and δ estimates Mean squared error in estimate of characteristic exponent α Return

58 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 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 pulse 10 samples/symbol 10 symbols/pulse length  Composite of transmitted and received MPEG II video streams 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 (  ) 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 9dB.wmv Wireless Networking and Communications Group 61 Additive Class A NoiseValue Overlap index (A)0.35 Gaussian factor (  ) SNR19 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 for correlation receiver 0 for RFI mitigating receiver (Bayesian) Return

63 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

64 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

65 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 × Memoryless Communication Performance Binary Phase Shift Keying Return

66 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

67 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. 68  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

69 Wireless Networking and Communications Group Incoherent Detection  Bayesian formulation [Spaulding & Middleton, 1997, pt. II]  Small signal approximation 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 x 1,x 2,…,x N [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 Return

Wireless Networking and Communications Group Filtering for Alpha Stable Noise (Cont..) 71  Myriad filter implementation  Given a window of samples, x 1,…,x N, find β  [x min, x max ]  Optimal Myriad algorithm 1. Differentiate objective function polynomial p( β ) with respect to β 2. Find roots and retain real roots 3. Evaluate p( β ) at real roots and extreme points 4. Output β that gives smallest value of p( β )  Selection Myriad (reduced complexity) 1. Use x 1, …, x N as the possible values of β 2. Pick value that minimizes objective function p( β ) 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 Return

73 Wireless Networking and Communications Group MAP Detection for Alpha Stable: PDF Approx.  SαS random variable Z with parameters ,  can be written Z = X Y ½ [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

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

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

76 Wireless Networking and Communications Group Extensions to MIMO systems Return

77 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

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

79 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

80  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 81  Two-piece linear approximation  Four-piece linear approximation chosen to minimize Approximation 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 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

83 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 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 84 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

85 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

86 Wireless Networking and Communications Group Performance Bounds (Single Antenna)  Channel capacity in presence of RFI System Model Parameters A = 0.1, Γ = Capacity Return

87 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, Γ = [Haring & Vinck, 2002] Return

88 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

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

90 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

91 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

92 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

93 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

94 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

95 Performance Bounds (2x2 MIMO) Wireless Networking and Communications Group  Cutoff rate 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 1 Parity 1 Systematic Data Decoder 2 Parity 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 [Umehara03] Return