MIMO Receiver Design in the Presence of Radio Frequency Interference Wireless Networking and Communications Group MIMO Receiver Design in the Presence of Radio Frequency Interference Kapil Gulati†, Aditya Chopra†, Robert W. Heath Jr. †, Brian L. Evans†, Keith R. Tinsley ‡ and Xintian E. Lin‡ †The University of Texas at Austin ‡ Intel Corporation 2 December 2008 IEEE Globecom 2008

We will use the terms noise and interference interchangeably Problem Definition Within computing platforms, wireless transceivers experience radio frequency interference (RFI) from clocks and busses. Major sources of interference: LCD clock harmonics PCI Express busses We will use the terms noise and interference interchangeably Our approach Statistical modeling of RFI Detection based on estimated model parameters We consider a 2 x 2 MIMO system in presence of RFI Wireless Networking and Communications Group

Radio Frequency Interference Modeling and Receiver Design Prior Work Radio Frequency Interference Modeling and Receiver Design RFI Model Spatial Corr. Physical Model Comments Middleton Class A No Yes Uni-variate model Assume independent or uncorrelated noise for multiple antennas Receiver design: [Gao & Tepedelenlioglu, 2007] Space-Time Coding [Li, Wang & Zhou, 2004] Performance degradation in receivers Weighted Mixture of Gaussian Densities Not derived based on physical principles Receiver design: [Blum et al., 1997] Adaptive Receiver Design Bivariate Middleton Class A [McDonald & Blum, 1997] Extensions of Class A model to two-antenna systems Wireless Networking and Communications Group

Proposed Contributions RFI Modeling Evaluated fit of measured RFI data to the bivariate Middleton Class A model [McDonald & Blum, 1997] Includes noise correlation between two antennas Parameter Estimation Derived parameter estimation algorithm based on the method of moments Performance Analysis Demonstrated communication performance degradation of conventional receivers in presence of RFI Receiver Design Derived Maximum Likelihood (ML) receiver Derived two sub-optimal ML receivers with reduced complexity Wireless Networking and Communications Group

Bivariate Middleton Class A Model Joint Spatial Distribution Parameter Description Typical Range Overlap Index. Product of average number of emissions per second and mean duration of typical emission Ratio of Gaussian to non-Gaussian component intensity at each of the two antennas Correlation coefficient between antenna observations Wireless Networking and Communications Group

Results on Measured RFI Data 50,000 baseband noise samples represent broadband interference Backup Estimated Parameters Bivariate Middleton Class A Overlap Index (A) 0.313 2D- KL Divergence 1.004 Gaussian Factor (G1) 0.105 Gaussian Factor (G2) 0.101 Correlation (k) -0.085 Bivariate Gaussian Mean (µ) 2D- KL Divergence 1.6682 Variance (s1) 1 Variance (s2) Marginal PDFs of measured data compared with estimated model densities Wireless Networking and Communications Group

Sub-optimal ML Receivers System Model 2 x 2 MIMO System Maximum Likelihood (ML) Receiver Log-Likelihood Function Sub-optimal ML Receivers approximate Wireless Networking and Communications Group

Sub-Optimal ML Receivers Two-Piece Linear Approximation Four-Piece Linear Approximation Approximation of chosen to minimize 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, k = 0.4 Severe degradation in communication performance in high-SNR regimes 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 A Noise Characteristic Improve-ment 0.01 Highly Impulsive ~15 dB 0.1 Moderately Impulsive ~8 dB 1 Nearly Gaussian ~0.5 dB 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 Complexity Analysis for decoding M-QAM modulated signal Receiver Quadratic Forms Exponential Comparisons Gaussian ML M2 Optimal ML 2M2 Sub-optimal ML (Four-Piece) 3M2 Sub-optimal ML (Two-Piece) Complexity Analysis Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4) Wireless Networking and Communications Group

Conclusions RFI Modeling Used bivariate Middleton Class A model Fits measured RFI data better than Gaussian model Parameter Estimation Derived parameter estimation algorithm based on the method of moments Performance Analysis Severe degradation in communication performance in the presence of RFI Receiver Design Optimal and two sub-optimal ML receivers proposed Improvement over Gaussian ML (at SER of 10-2) ~15 dB [Highly Impulsive] ~ 8 dB [Moderately Impulsive] Same as Gaussian ML in presence of Gaussian noise Backup Wireless Networking and Communications Group

Thank You, Questions ? Wireless Networking and Communications Group

References RFI Modeling Parameter Estimation [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 on Electromagnetic Compatibility, vol.3, no., pp. 626-631, 14-18 Aug. 2006 Wireless Networking and Communications Group

References (cont…) 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

Parameter Estimation Return Parameter Estimator for Bivariate Middleton Class A model Moment Generating Function Wireless Networking and Communications Group

Parameter Estimation (cont…) Return Wireless Networking and Communications Group

Parameter Estimators Wireless Networking and Communications Group Return Wireless Networking and Communications Group

Measured Fitting Notes on measured RFI data Radio used to listen to the platform noise only (when no data communication ongoing) Noise assumed to be broadband Do not expect bivariate Middleton Class A to fit perfectly Expect bivariate Class A to model much better than Gaussian Kullback-Leibler (KL) divergence Return Wireless Networking and Communications Group

Impact of RFI Impact of LCD noise on throughput performance for a 802.11g embedded wireless receiver [Shi et al., 2006] Backup Wireless Networking and Communications Group

Impact of RFI Calculated in terms of desensitization (“desense”) Interference raises noise floor Receiver sensitivity will degrade to maintain SNR Desensitization levels can exceed 10 dB for 802.11a/b/g due to computational platform noise [J. Shi et al., 2006] Case Sudy: 802.11b, Channel 2, desense of 11dB More than 50% loss in range Throughput loss up to ~3.5 Mbps for very low receive signal strengths (~ -80 dbm) Return Wireless Networking and Communications Group

Assumptions for RFI Modeling Key Assumptions [Middleton, 1977][Furutsu & Ishida, 1961] Infinitely many potential interfering sources with same effective radiation power Power law propagation loss Poisson field of interferers Pr(number of interferers = M |area R) ~ Poisson Poisson distributed emission times Temporally independent (at each sample time) Limitations [Alpha Stable]: Does not include thermal noise Temporal dependence may exist Wireless Networking and Communications Group

Middleton Class A, B and C Models Return 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) Backup Wireless Networking and Communications Group

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

Middleton Class B Model 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…) Middleton Class B Envelope Statistics Return Wireless Networking and Communications Group

Middleton Class B Model (cont…) Parameters for Middleton Class B Model Return 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 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 Backup PDF for  = 1.5,  = 0 and  = 10 Backup Parameter Description Range Characteristic Exponent. Amount of impulsiveness Localization. Analogous to mean Dispersion. Analogous to variance Wireless Networking and Communications Group

Fitting Measured RFI Data Broadband RFI data 80,000 samples collected using 20GSPS scope Backup Estimated Parameters Symmetric Alpha Stable Model Localization (δ) 0.0043 Distance 0.0514 Characteristic exp. (α) 1.2105 Dispersion (γ) 0.2413 Middleton Class A Model Overlap Index (A) 0.1036 0.0825 Gaussian Factor (Γ) 0.7763 Gaussian Model Mean (µ) 0.2217 Variance (σ2) 1 Distance: Kullback-Leibler divergence Wireless Networking and Communications Group

Fitting Measured RFI Data Best fit for 25 data sets under different conditions Wireless Networking and Communications Group

Filtering and Detection Methods Middleton Class A noise Symmetric Alpha Stable noise Filtering Wiener Filtering (Linear) Detection Correlation Receiver (Linear) MAP (Maximum a posteriori probability) detector [Spaulding & Middleton, 1977] Small Signal Approximation to MAP detector [Spaulding & Middleton, 1977] Filtering Myriad Filtering [Gonzalez & Arce, 2001] Hole Punching Detection Correlation Receiver (Linear) MAP approximation Backup Backup Backup Backup Backup 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 Method Comp. Complexity Detection Perform. Correl. Low Wiener Medium MAP Approx. High MAP Wireless Networking and Communications Group

Results: Alpha Stable Detection Backup Method Comp. Complexity Detection Perform. Hole Punching Low Medium Selection Myriad MAP Approx. High Optimal Myriad Backup Use dispersion parameter g in place of noise variance to generalize SNR Wireless Networking and Communications Group

Performance Bounds (2x2 MIMO) Channel Capacity [Chopra et al., submitted to ICASSP 2009] Return System Model Case I Shannon Capacity in presence of additive white Gaussian noise Case II (Upper Bound) Capacity in presence of bivariate Middleton Class A noise. Assumes that there exists an input distribution which makes output distribution Gaussian for all SNRs. Case III (Practical Case) Capacity in presence of bivariate Middleton Class A noise Assumes input has Gaussian distribution Wireless Networking and Communications Group

Performance Bounds (2x2 MIMO) Channel Capacity in presence of RFI for 2x2 MIMO [Chopra et al., submitted to ICASSP 2009] Return System Model Capacity Parameters: A = 0.1, G1 = 0.01, G2 = 0.1, k = 0.4 Wireless Networking and Communications Group

Performance Bounds (2x2 MIMO) Probability of symbol error for uncoded transmissions [Chopra et al., submitted to ICASSP 2009] Return Pe: Probability of symbol error S: Transmitted code vector D(S): Decision regions for MAP detector Equally likely transmission for symbols Parameters: A = 0.1, G1 = 0.01, G2 = 0.1, k = 0.4 Wireless Networking and Communications Group

Performance Bounds (2x2 MIMO) Chernoff factors for coded transmissions [Chopra et al., submitted to ICASSP 2009] Return PEP: Pairwise error probability N: Size of the codeword Chernoff factor: Equally likely transmission for symbols Parameters: G1 = 0.01, G2 = 0.1, k = 0.4 Wireless Networking and Communications Group