Mitigating Near-field Interference in Laptop Embedded Wireless Transceivers Marcel Nassar(1), Kapil Gulati(1) , Arvind K. Sujeeth(1), Navid Aghasadeghi(1), Brian L. Evans(1), Keith R. Tinsley(2)‏ (1) The University of Texas at Austin, Austin, Texas, USA (2) System Technology Lab, Intel, Hillsborough, Oregon, USA 2008 IEEE International Conference on Acoustics, Speech, and Signal Processing 3rd April, 2008 1

We’ll be using noise and interference interchangeably Problem Definition Within computing platforms, wireless transceivers experience radio frequency interference (RFI) from clocks/busses PCI Express busses LCD clock harmonics Approach Statistical modelling of RFI Filtering/detection based on estimation of model parameters Past Research Potential reduction in bit error rates by factor of 10 or more [Spaulding & Middleton, 1977] Backup We’ll be using noise and interference interchangeably 2 2

Computer Platform Noise Modelling RFI is combination of independent radiation events Has predominantly non-Gaussian statistics Statistical-Physical Models (Middleton Class A, B, C)‏ Independent of physical conditions (universal)‏ Sum of independent Gaussian and Poisson interference Models electromagnetic interference Alpha-Stable Processes Models statistical properties of “impulsive” noise Approximation for Middleton Class B (broadband) noise Backup 3 3

Proposed Contributions Computer Platform Noise Modelling Evaluate fit of measured RFI data to noise models Narrowband Interference: Middleton Class A model Broadband Interference: Symmetric Alpha Stable Parameter Estimation Evaluate estimation accuracy vs complexity tradeoffs Filtering / Detection Evaluate communication performance vs. complexity tradeoffs Middleton Class A: Correlation receiver, Wiener filtering and Bayesian detector Symmetric Alpha Stable: Correlation receiver Wiener filtering and Myriad filtering 4

Middleton Class A Model Backup Probability Density Function for A = 0.15, = 0.8 Power Spectral Density 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] 5 5

Symmetric Alpha Stable Model Backup Probability Density Function for  = 1.5,  = 0 and  = 10 Power Spectral Density for = 1.5,  = 0 and  = 10 Parameter Description Range Characteristic Exponent. Amount of impulsiveness Localization. Analogous to mean Dispersion. Analogous to variance 6 6

Estimation of Noise Model Parameters For Middleton Class A Model Expectation maximization (EM) [Zabin & Poor, 1991] Finds roots of second and fourth order polynomials at each iteration Advantage Small sample size required (~1000 samples)‏ Disadvantage Iterative algorithm, computationally intensive For Symmetric Alpha Stable Model Based on extreme order statistics [Tsihrintzis & Nikias, 1996] Parameter estimators require computations similar to mean and standard deviation. Advantage Fast / computationally efficient (non-iterative)‏ Disadvantage Requires large set of data samples (~ 10,000 samples)‏ Backup Backup 7 7

Symmetric Alpha Stable Model Middleton Class A Model Results of Measured RFI Data for Broadband Noise Backup Data set of 80,000 samples collected using 20 GSPS scope Estimated Parameters Symmetric Alpha Stable Model Localization (δ) 0.0043 Characteristic exp. (α) 1.2105 Dispersion (γ) 0.2413 Middleton Class A Model Overlap Index (A) 0.1036 Gaussian Factor (Γ) 0.7763 Gaussian Model Mean (µ) Variance (σ2) 1 8 8

Alternate Adaptive Model Filtering and Detection – System Model Alternate Adaptive Model Signal Model Multiple samples/copies of the received signal are available: N path diversity [Miller, 1972] Oversampling by N [Middleton, 1977] Using multiple samples increases gains vs. Gaussian case because impulses are isolated events over symbol period Impulsive Noise Backup s[n] gtx[n] v[n] grx[n] Λ(.)‏ Pulse Shape Pre-Filtering Matched Filter Decision Rule N samples per symbol 9

We assume perfect estimation of noise model parameters Filtering and Detection We assume perfect estimation of noise model parameters Class A Noise Correlation Receiver (linear)‏ Wiener Filtering (linear)‏ Coherent Detection using MAP (Maximum A posteriori Probability) detector [Spaulding & Middleton, 1977] Small Signal Approximation to MAP Detector [Spaulding & Middleton, 1977] Alpha Stable Noise Myriad Filtering [Gonzalez & Arce, 2001] MAP Approximation Hole Puncher Backup Backup Backup Backup Backup Backup 10 10

Class A Detection - Results Pulse shape Raised cosine 10 samples per symbol 10 symbols per pulse Channel A = 0.35  = 0.5 × 10-3 Memoryless Method Comp. Detection Perform. Correl. Low Wiener Medium Approx. High MAP 11

Alpha Stable Results Method Comp. Detection Perform. Hole Punching Low Medium Selection Myriad MAP Approx. High Optimal Myriad 12

Conclusion Class A Noise MAP High Performance High Complexity MAP approximation Medium Complexity Correlation Receiver Low Performance Low Complexity Wiener Filtering Alpha Stable Noise MAP Approximation Optimal Myriad Medium Performance Selection Myriad Hole Puncher T 13

Thank you, Questions?

References [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] 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 [3] 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 [4] 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 [5] 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 [6] B. Widrow et al., “Principles and Applications”, Proc. of the IEEE, vol. 63, no.12, Sep. 1975. [7] 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 15 15

References (cont…)‏ [8] S. Ambike, J. Ilow, and D. Hatzinakos, “Detection for binary transmission in a mixture of gaussian noise and impulsive noise modeled as an alpha-stable process,” IEEE Signal Processing Letters, vol. 1, pp. 55–57, Mar. 1994. [9] J. G. Gonzalez and G. R. Arce, “Optimality of the myriad filter in practical impulsive- noise enviroments,” IEEE Trans. on Signal Proc, vol. 49, no. 2, pp. 438–441, Feb 2001. [10] E. Kuruoglu, “Signal Processing In Alpha Stable Environments: A Least Lp Approach,” Ph.D. dissertation, University of Cambridge, 1998. [11] J. Haring and A.J. Han Vick, “Iterative Decoding of Codes Over Complex Numbers for Impuslive Noise Channels”, IEEE Trans. On Info. Theory, vol 49, no. 5, May 2003 [12] G. Beenker, T. Claasen, and P. van Gerwen, “Design of smearing filters for data transmission systems,” IEEE Trans. on Comm., vol. 33, Sept. 1985. [13] G. R. Lang, “Rotational transformation of signals,” IEEE Trans. Inform. Theory, vol. IT–9, pp. 191–198, July 1963. [14] 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. [15] 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. 16

BACKUP SLIDES 17

Interfering Clocks and Busses Common Spectral Occupancy Standard Carrier (GHz)‏ Wireless Networking Interfering Clocks and Busses Bluetooth 2.4 Personal Area Network Gigabit Ethernet, PCI Express Bus, LCD clock harmonics IEEE 802. 11 b/g/n Wireless LAN (Wi-Fi)‏ IEEE 802.16e 2.5–2.69 3.3–3.8 5.725–5.85 Mobile Broadband (Wi-Max)‏ PCI Express Bus, LCD clock harmonics IEEE 802.11a 5.2 18 18

Extend results to multiple RF sources on single chip Potential Impact Improve communication performance for wireless data communication subsystems embedded in PCs and laptops Achieve higher bit rates for the same bit error rate and range, and lower bit error rates for the same bit rate and range Extend range from wireless data communication subsystems to wireless access point Extend results to multiple RF sources on single chip 19 19

Accuracy of Middleton Noise Models 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] 20 20

Middleton Class A, B, C Models Class A Narrowband interference (“coherent” reception) Uniquely represented by two parameters Class B Broadband interference (“incoherent” reception) Uniquely represented by six parameters Class C Sum of class A and class B (approx. as class B)‏ 21 21

Probability Density Function for A = 0.15, G = 0.1 Middleton Class A Model Probability density function (pdf) Probability Density Function for A = 0.15, G = 0.1 Parameters 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]

Symmetric Alpha Stable Model Characteristic function: Parameters Characteristic exponent indicative of thickness of tail of impulsiveness Localization (analogous to mean) Dispersion (analogous to variance) No closed-form expression for pdf except for α = 1 (Cauchy), α = 2 (Gaussian), α = 1/2 (Levy) and α = 0 (not very useful) Could approximate pdf using inverse transform of power series expansion of characteristic function

Symmetric Alpha Stable Model Middleton Class A Model Results of Measured RFI Data for Broadband Noise Data set of 80,000 samples collected using 20 GSPS scope Estimated Parameters Symmetric Alpha Stable Model Localization (δ) 0.0043 KL Divergence 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 24 24

Coherent Detection – Small Signal Approximation Expand noise pdf pZ(z) by Taylor series about Sj = 0 (j=1,2)‏ Optimal decision rule & threshold detector for approximation Optimal detector for approximation is logarithmic nonlinearity followed by correlation receiver We use 100 terms of the series expansion for d/dxi ln pZ(xi) in simulations Backup 25 25

Hole Punching (Blanking) Filter Sets sample to 0 when sample exceeds threshold [Ambike, 1994] Intuition: Large values are impulses and true value cannot be recovered Replace large values with zero will not bias (correlation) receiver If additive noise were purely Gaussian, then the larger the threshold, the lower the detrimental effect on bit error rate 26

Filtering and Detection – Alpha Stable Model MAP detection: remove nonlinear filter Decision rule is given by (p(.) is the SαS distribution)‏ Approximations for SαS distribution: Method Shortcomings Reference Series Expansion Poor approximation when series length shortened [Samorodnitsky, 1988] Polynomial Approx. Poor approximation for small x [Tsihrintzis, 1993] Inverse FFT Ripples in tails when α < 1 Simulation Results 27

MAP Detector – PDF Approximation SαS random variable Z with parameters  ,  can be written Z = X Y½ [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 fY(.) by taking inverse FFT of characteristic function & normalizing Number of mixtures (N) and values of sampling points (vi) are tunable parameters 28

Bit Error Rate (BER) Performance in Alpha Stable Noise 29

Symmetric Alpha Stable Process PDF 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 30

Estimation of Middleton Class A Model Parameters Expectation maximization E: Calculate log-likelihood function w/ current parameter values M: Find parameter set that maximizes log-likelihood function EM estimator for Class A parameters [Zabin & Poor, 1991] Expresses envelope statistics as sum of weighted pdfs Maximization step is iterative Given A, maximize K (with K = A Γ). Root 2nd-order polynomial. Given K, maximize A. Root 4th-order poly. (after approximation). Backup Backup 31 31

Estimation of Symmetric Alpha Stable Parameters Based on extreme order statistics [Tsihrintzis & Nikias, 1996] PDFs of max and min of sequence of independently and identically distributed (IID) data samples follow 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)‏ Backup Backup Backup 32 32

Class A Parameter Estimation Based on APD (Exceedance Probability Density) Plot 33 33

Odd-order moments are zero [Middleton, 1999] Class A Parameter Estimation Based on Moments Moments (as derived from the characteristic equation)‏ Parameter estimates e2 = e4 = e6 = Odd-order moments are zero [Middleton, 1999] 2 34 34

Middleton Class B Model Envelope Statistics Envelope exceedance probability density (APD) which is 1 – cumulative distribution function 35 35

Class B Envelope Statistics 36

Parameters for Middleton Class B Noise 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 37 37

Class B Exceedance Probability Density Plot 38 38

Expectation Maximization Overview 39 39

Maximum Likelihood for Sum of Densities 40 40

EM Estimator for Class A Parameters Using 1000 Samples Normalized Mean-Squared Error in A ×10-3 PDFs with 11 summation terms 50 simulation runs per setting Convergence criterion: Example learning curve Iterations for Parameter A to Converge 41

Results of EM Estimator for Class A Parameters 42

Extreme Order Statistics 43 43

Estimator for Alpha-Stable 44 44

Results for Symmetric Alpha Stable Parameter Estimator Data length (N) was 10,000 samples Results averaged over 100 simulation runs Estimate α and “mean” δ directly from data Estimate “variance” γ from α and δ estimates Continued next slide Mean squared error in estimate of characteristic exponent α 45

Results for Symmetric Alpha Stable Parameter Estimator Mean squared error in estimate of localization (“mean”)   = 10 Mean squared error in estimate of dispersion (“variance”)   = 5 46

Wiener Filtering – Linear Filter Optimal in mean squared error sense when noise is Gaussian Model Design d(n): desired signal d(n): filtered signal e(n): error w(n): Wiener filter x(n): corrupted signal z(n): noise d(n): ^ d(n)‏ z(n)‏ ^ w(n)‏ x(n)‏ w(n)‏ x(n)‏ d(n)‏ ^ e(n)‏ Minimize Mean-Squared Error E { |e(n)|2 } 47 47

Wiener Filtering – Finite Impulse Response (FIR) Case Wiener-Hopf equations for FIR Wiener filter of order p-1 General solution in frequency domain desired signal: d(n) power spectrum: (e j ) correlation of d and x: rdx(n) autocorrelation of x: rx(n) Wiener FIR Filter: w(n) corrupted signal: x(n) noise: z(n)‏ 48 48

Raised Cosine Pulse Shape Wiener Filtering – 100-tap FIR Filter Pulse shape 10 samples per symbol 10 symbols per pulse Raised Cosine Pulse Shape Transmitted waveform corrupted by Class A interference Received waveform filtered by Wiener filter n Channel A = 0.35  = 0.5 × 10-3 SNR = -10 dB Memoryless 49 49

Bayes formulation [Spaulding & Middleton, 1997, pt. II] Incoherent Detection Bayes formulation [Spaulding & Middleton, 1997, pt. II] Small signal approximation 50 50

Incoherent Detection Optimal Structure: Incoherent Correlation Detector The optimal detector for the small signal approximation is basically the correlation receiver preceded by the logarithmic nonlinearity. 51 51

Coherent Detection – Class A Noise Comparison of performance of correlation receiver (Gaussian optimal receiver) and nonlinear detector [Spaulding & Middleton, 1997, pt. II] 52 52

Coherent Detection – Small Signal Approximation Near-optimal for small amplitude signals Suboptimal for higher amplitude signals Correlation Receiver Antipodal A = 0.35  = 0.5×10-3 Communication performance of approximation vs. upper bound [Spaulding & Middleton, 1977, pt. I] 53 53

Non-linear (in the signal) polynomial filter Volterra Filters Non-linear (in the signal) polynomial filter By Stone-Weierstrass Theorem, Volterra signal expansion can model many non-linear systems, to an arbitrary degree of accuracy. (Similar to Taylor expansion with memory). Has symmetry structure that simplifies computational complexity Np = (N+p-1) C p instead of Np. Thus for N=8 and p=8; Np=16777216 and (N+p-1) C p = 6435. 54 54

Adaptive Noise Cancellation Computational platform contains multiple antennas that can provide additional information regarding the noise Adaptive noise canceling methods use an additional reference signal that is correlated with corrupting noise [Widrow et al., 1975] s : signal s+n0 :corrupted signal n0 : noise n1 : reference input z : system output 55 55

Haring’s Receiver Simulation Results 56

Coherent Detection in Class A Noise with Γ = 10-4 Correlation Receiver Performance SNR (dB)‏ SNR (dB)‏ 57 57

Myriad Filtering Myriad Filters exhibit high statistical efficiency in bell-shaped impulsive distributions like the SαS distributions. Have been used as both edge enhancers and smoothers in image processing applications. In the communication domain, they have been used to estimate a sent number over a channel using a known pulse corrupted by additive noise. (Gonzalez 1996)‏ In this work, we used a sliding window version of the myriad filter to mitigate the impulsiveness of the additive noise. (Nassar et. al 2007)‏ 58

Bayesian formulation [Spaulding and Middleton, 1977] MAP Detection corrupted signal Decision Rule Λ(X)‏ Hard decision Bayesian formulation [Spaulding and Middleton, 1977] H1 or H2 Equally probable source 59 59

Results 60

MAP Detector – PDF Approximation SαS random variable Z with parameters a , d, g can be written Z = X Y½ [Kuruoglu, 1998] X is zero-mean Gaussian with variance 2 g Y is positive stable random variable with parameters depending on a Pdf of Z can be written as a mixture model of N Gaussians [Kuruoglu, 1998] Mean d can be added back in Obtain fY(.) by taking inverse FFT of characteristic function & normalizing Number of mixtures (N) and values of sampling points (vi) are tunable parameters

Sliding window algorithm Outputs myriad of sample window Myriad Filtering Sliding window algorithm Outputs myriad of sample window Myriad of order k for samples x1, x2, … , xN [Gonzalez & Arce, 2001] As k decreases, less impulsive noise gets through myriad filter As k→0, filter tends to mode filter (output value with highest freq.) Empirical choice of k: [Gonzalez & Arce, 2001]

Myriad Filtering – Implementation Given a window of samples x1,…,xN, find β  [xmin, xmax] Optimal myriad algorithm Differentiate objective function polynomial p(β) with respect to β Find roots and retain real roots Evaluate p(β) at real roots and extremum Output β that gives smallest value of p(β) Selection myriad (reduced complexity) Use x1,…,xN as the possible values of β Pick value that minimizes objective function p(β) Backup

Hole Punching (Blanking) Filter Sets sample to 0 when sample exceeds threshold [Ambike, 1994] Intuition: Large values are impulses and true value cannot be recovered Replace large values with zero will not bias (correlation) receiver If additive noise were purely Gaussian, then the larger the threshold, the lower the detrimental effect on bit error rate

N is oversampling factor S is constellation size W is window size Complexity Analysis Method Complexity per symbol Analysis Hole Puncher + Correlation Receiver O(N+S) A decision needs to be made about each sample. Optimal Myriad + Correlation Receiver O(NW3+S) Due to polynomial rooting which is equivalent to Eigen-value decomposition. Selection Myriad + Correlation Receiver O(NW2+S) Evaluation of the myriad function and comparing it. MAP Approximation O(MNS) Evaluating approximate pdf (M is number of Gaussians in mixture) N is oversampling factor S is constellation size W is window size