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Statistical Signal Processing for Sensing and Mitigating Impulsive Noise in Communication Receivers

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## Statistical Signal Processing for Sensing and Mitigating Impulsive Noise in Communication Receivers

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**Wireless Networking and Communications Group**Prof. Brian L. Evans Lead Graduate Students Aditya Chopra, Kapil Gulati and Marcel Nassar In collaboration with Eddie Xintian Lin, Alberto Alcocer Ochoa,Chaitanya Sreerama and Keith R. Tinsley at Intel Labs Statistical Signal Processing for Sensing and Mitigating Impulsive Noise in Communication Receivers Talk at Texas Instruments in Dallas, Texas**Outline**2 • Introduction • Single carrier single antenna systems • Radio frequency interference modeling • Estimation of interference model parameters • Filtering/detection • Multi-input multi-output (MIMO) single carrier systems • Co-channel interference modeling • Conclusions • Future work Wireless Networking and Communications Group**Impulsive Noise**Almost instantaneous (impulse-like) phenomenon Unwanted “clicks” and “pops” in an audio recording Non-Gaussian statistics Models electromagnetic interference through conduction as well as induction (via radiation) Example sources Stopping and starting of electrical devices Clocks and harmonics Communication transmission Talk focuses on modeling asynchronous non-periodic noise**Radio Frequency Interference**Electromagnetic interference from radiation Limits wireless communication performance Applications of RFI modeling Sense and mitigate strategies for coexistenceof wireless networks and services Sense and avoid strategies for cognitive radio We focus on sense and mitigate strategies for wireless receivers embedded in notebooks Platform noise from user’s computer subsystems Co-channel interference from other in-band wireless networks and services**Computational Platform Noise**5 • Objectives • Develop offline methods to improve communication performance in presence of computer platform RFI • Develop adaptive online algorithms for these methods • Approach • Statistical modeling of RFI • Filtering/detection based on estimated model parameters Backup Within computing platforms, wireless transceivers experience radio frequency interference from clocks and busses We will use noise and interference interchangeably Wireless Networking and Communications Group**Impact of RFI**6 • Impact of LCD noise on throughput for an IEEE 802.11g embedded wireless receiver[Shi, Bettner, Chinn, Slattery & Dong, 2006] Backup Backup Wireless Networking and Communications Group**Statistical Modeling of RFI**7 • Radio frequency interference • Sum of independent radiation events • Predominantly non-Gaussian impulsive statistics • Key statistical-physical models • Middleton Class A, B, C models • Independent of physical conditions (canonical) • Sum of independent Gaussian and Poisson interference • Symmetric Alpha Stable models • Approximation of Middleton Class B model Backup Backup Wireless Networking and Communications Group**Assumptions for RFI Modeling**8 • 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 Wireless Networking and Communications Group**Our Contributions**9 Mitigation of computational platform noise in single carrier, single antenna systems [Nassar, Gulati, DeYoung, Evans & Tinsley, ICASSP 2008, JSPS 2009] Wireless Networking and Communications Group**Parameter**Description Range 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] Middleton Class A model 10 • Probability Density Function PDF for A = 0.15,= 0.8 Wireless Networking and Communications Group**Symmetric Alpha Stable Model**11 • 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 Backup PDF for = 1.5, = 0, = 10 Backup Wireless Networking and Communications Group**Example Power Spectral Densities**• Middleton Class A • Symmetric Alpha Stable Characteristic Exponent (a) = 1.5 Localization (d) = 0 Dispersion (g) = 10 Overlap Index (A) = 0.15 Gaussian Factor (G) = 0.1 Simulated Densities**Estimation of Noise Model Parameters**13 • Middleton Class A model • Based on Expectation Maximization [Zabin & Poor, 1991] • Find roots of second and fourth order polynomials at each iteration • Advantage: Small sample size is required (~1000 samples) • Disadvantage: Iterative algorithm, computationally intensive • Symmetric Alpha Stable Model • Based on Extreme Order Statistics [Tsihrintzis & Nikias, 1996] • Parameter estimators require computations similar to mean and standard deviation computations • Advantage: Fast / computationally efficient (non-iterative) • Disadvantage: Requires large set of data samples (~10000 samples) Backup Backup Wireless Networking and Communications Group**Results on Measured RFI Data**14 14 • 25 radiated computer platform RFI data sets from Intel • 50,000 samples taken at 100 MSPS KL Divergence: Kullback-Leibler divergence Wireless Networking and Communications Group**Results on Measured RFI Data**Best fit for 25 data sets under different platform RFI conditions KL divergence plotted for three candidate distributions vs. data set number Smaller KL value means closer fit 15 Gaussian Class A Alpha Stable**Video over Impulsive Channels**16 • 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 keyingRaised cosine pulse10 samples/symbol10 symbols/pulse length • Composite of transmitted and received MPEG II video streams http://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**Filtering and Detection**• Assumption • Multiple samples of the received signal are available • N Path Diversity [Miller, 1972] • Oversampling by N[Middleton, 1977] 17 Impulsive Noise Pulse Shaping Pre-Filtering Matched Filter Detection Rule 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] Backup Backup Backup Backup Backup Backup Wireless Networking and Communications Group**Results: Class A Detection**18 Communication Performance Binary Phase Shift Keying Backup Backup Backup Wireless Networking and Communications Group**Results: Alpha Stable Detection**19 Backup Communication Performance Same transmitter settings as previous slide Backup Backup Backupc Backup Backup Use dispersion parameter g in place of noise variance to generalize SNR Wireless Networking and Communications Group**Video over Impulsive Channels #2**20 • 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 keyingRaised 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**Video over Impulsive Channels #2**Structural similarity measure [Wang, Bovik, Sheikh & Simoncelli, 2004] Score is [0,1] where higher means better video quality Bit error rates for ~50 million bits sent: 6 x 10-6 for correlation receiver 0 for RFI mitigating receiver (Bayesian) Frame number**Extensions to MIMO systems**22 Backup Wireless Networking and Communications Group**Our Contributions**23 2 x 2 MIMO receiver design in the presence of RFI[Gulati, Chopra, Heath, Evans, Tinsley & Lin, Globecom 2008] Backup Backup Backup Wireless Networking and Communications Group**Results: RFI Mitigation in 2 x 2 MIMO**24 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) Wireless Networking and Communications Group**Results: RFI Mitigation in 2 x 2 MIMO**25 Complexity Analysis for decoding M-level QAM modulated signal Complexity Analysis Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4) Wireless Networking and Communications Group**Co-Channel Interference Modeling**26 26 • Region of interferer locations determines interference model [Gulati, Chopra, Evans & Tinsley, Globecom 2009] Symmetric Alpha Stable Middleton Class A Wireless Networking and Communications Group**Co-Channel Interference Modeling**27 27 • Propose unified framework to derive narrowband interference models for ad-hoc and cellular network environments • Key result: tail probabilities (one minus cumulative distribution function) Case 3-a: Cellular network (mobile user) Case 1: Ad-hocnetwork Wireless Networking and Communications Group**Conclusions**28 • Radio Frequency Interference from computing platform • Affects wireless data communication transceivers • Models include Middleton and alpha stable distributions • RFI mitigation can improve communication performance • Single carrier, single antenna systems • Linear and non-linear filtering/detection methods explored • Single carrier, multiple antenna systems • Optimal and sub-optimal receivers designed • Bounds on communication performance in presence of RFI • Results extend to co-channel interference modeling Wireless Networking and Communications Group**RFI Mitigation Toolbox in MATLAB**29 • Provides a simulation environment for • RFI generation • Parameter estimation algorithms • Filtering and detection methods • Demos for communication performance analysis Latest Toolbox Release Version 1.4 beta, Dec. 14th 2009 Snapshot of a demo http://users.ece.utexas.edu/~bevans/projects/rfi/software/index.html Wireless Networking and Communications Group**Publications and Presentations**30 • Journal and conference papers M. Nassar, K. Gulati, M. R. DeYoung, B. L. Evans and K. R. Tinsley, “Mitigating Near-Field Interference in Laptop Embedded Wireless Transceivers”, J. of Signal Proc. Systems, Mar 2009, invited paper. 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, Las Vegas, NV USA. 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, New Orleans, LA USA. 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, Taipei, Taiwan, accepted. 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, Honolulu, HI USA, accepted. K. Gulati, A. Chopra, B. L. Evans and K. R. Tinsley, “Statistical Modeling of Co-Channel Interference in a Field of Poisson and Poisson Distributed Interferers”, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., Mar. 15-19, 2010, Dallas, TX USA. • Project Web site http://users.ece.utexas.edu/~bevans/projects/rfi/index.html Wireless Networking and Communications Group**Future Work**31 • Extend RFI modeling for • Adjacent channel interference • Multi-antenna systems • Temporally correlated interference • Multi-input multi-output (MIMO) single carrier systems • RFI modeling and receiver design • Multicarrier communication systems • Coding schemes resilient to RFI • System level techniques to reduce computational platform generated RFI Backup Wireless Networking and Communications Group**32**Thank You. Questions ? Wireless Networking and Communications Group**References**33 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.F. McDonald and R.S. Blum. “A physically-based impulsive noise model for array observations”, Proc. IEEE Asilomar Conference on Signals, Systems& Computers, vol 1, 2-5 Nov. 1997. [3] 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. [4] 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. Parameter Estimation [5] 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 [6] 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 RFI Measurements and Impact [7] 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 onElectromagnetic Compatibility, vol.3, no., pp. 626-631, 14-18 Aug. 2006 Wireless Networking and Communications Group**References (cont…)**34 Filtering and Detection [8] A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment-Part I: Coherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 1977 [9] A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment Part II: Incoherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 1977 [10] 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 [11] 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. [12] J. G. Gonzalez and G. R. Arce, “Optimality of the myriad filter in practical impulsive-noise environments,” IEEE Trans. on Signal Proc, vol. 49, no. 2, pp. 438–441, Feb 2001. [13] E. Kuruoglu, “Signal Processing In Alpha Stable Environments: A Least Lp Approach,” Ph.D. dissertation, University of Cambridge, 1998. [14] 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 [15] 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. Wireless Networking and Communications Group**Backup Slides**35 • Most backup slides are linked to the main slides • Miscellaneous topics not covered in main slides • Performance bounds for single carrier single antenna system in presence of RFI Backup Wireless Networking and Communications Group**Common Spectral Occupancy**36 Return Wireless Networking and Communications Group**Impact of RFI**37 • 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) Return Wireless Networking and Communications Group**Impact of LCD clock on 802.11g**38 • Pixel clock 65 MHz • LCD Interferers and 802.11g center frequencies Return Wireless Networking and Communications Group**[Middleton, 1999]**Middleton Class A, B and C Models 39 • 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) Return Backup Wireless Networking and Communications Group**Middleton Class B Model**40 • Envelope statistics • Envelope exceedence probability density (APD), which is 1 – cumulative distribution function (CDF) Return Wireless Networking and Communications Group**Middleton Class B Model (cont…)**41 • Middleton Class B envelope statistics Return Wireless Networking and Communications Group**Parameters**Description Typical Range Impulsive Index AB [10-2, 1] Ratio of Gaussian to non-Gaussian intensity ΓB [10-6, 1] Scaling Factor NI [10-1, 102] Spatial density parameter α [0, 4] Effective impulsive index dependent on α A α [10-2, 1] Inflection point (empirically determined) εB > 0 Middleton Class B Model (cont…) 42 • Parameters for Middleton Class B model Return Wireless Networking and Communications Group**Accuracy of Middleton Noise Models**43 Return Magnetic Field Strength, H (dB relative to microamp per meter rms) ε0 (dB > εrms) Percentage of Time Ordinate is Exceeded P(ε > ε0) Soviet high power over-the-horizon radar interference [Middleton, 1999] Fluorescent lights in mine shop office interference [Middleton, 1999] Wireless Networking and Communications Group**Symmetric Alpha Stable PDF**44 • Closed form expression does not exist in general • Power series expansions can be derived in some cases • Standard symmetric alpha stable model for localization parameter = 0 Return Wireless Networking and Communications Group**Symmetric Alpha Stable Model**45 • Heavy tailed distribution Return Density functions for symmetric alpha stable distributions for different values of characteristic exponent alpha: a) overall density and b) the tails of densities Wireless Networking and Communications Group**Parameter Estimation: Middleton Class A**46 • Expectation Maximization (EM) • E Step: Calculate log-likelihood function \w current parameter values • M Step: Find parameter set that maximizes log-likelihood function • EM Estimator for Class A parameters [Zabin & Poor, 1991] • Express envelope statistics as sum of weighted PDFs • Maximization step is iterative • Given A, maximize K (= AG). Root 2nd order polynomial. • Given K, maximize A. Root 4th order polynomial Return Backup Results Backup Wireless Networking and Communications Group**Expectation Maximization Overview**47 Return Wireless Networking and Communications Group**Results: EM Estimator for Class A**48 Return Normalized Mean-Squared Error in A Iterations for Parameter A to Converge K = AG PDFs with 11 summation terms 50 simulation runs per setting 1000 data samples Convergence criterion: Wireless Networking and Communications Group**Results: EM Estimator for Class A**49 Return • For convergence for A [10-2, 1], worst-case number of iterations for A = 1 • Estimation accuracy vs. number of iterations tradeoff Wireless Networking and Communications Group**Parameter Estimation: Symmetric Alpha Stable**50 • 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 Results Backup Wireless Networking and Communications Group