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Improving Wireless Data Transmission Speed and Reliability to Mobile Computing Platforms

Improving Wireless Data Transmission Speed and Reliability to Mobile Computing Platforms. Prof. Brian L. Evans 1. Preliminary Results. Improving Wireless Data Transmission Speed and Reliability to Mobile Computing Platforms.

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Improving Wireless Data Transmission Speed and Reliability to Mobile Computing Platforms

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  1. Improving Wireless Data Transmission Speed and Reliability to Mobile Computing Platforms Prof. Brian L. Evans1 Preliminary Results Improving Wireless Data Transmission Speed and Reliability to Mobile Computing Platforms in collaboration with Marcel Nassar1, Kapil Gulati1,Arvind K. Sujeeth1, Navid Aghasadeghi1 and Keith R. Tinsley2 1 The University of Texas at Austin, Austin, Texas USA 2 System Technology Lab, Intel, Hillsborough, Oregon USA American University of Beirut 15th July 2008

  2. Outline Problem definition Noise modelling Estimation of noise model parameters Filtering and detection Conclusion and future work 2

  3. Problem Definition • Within computing platforms, wirelesstransceivers experience radio frequencyinterference (RFI) from clocks/busses • PCI Express busses • LCD clock harmonics Approach • Statistical modelling of RFI • Filtering/detection based on estimation of model parameters • Previous Research • Potential reduction in bit error rates by factor of 10 or more[Spaulding & Middleton, 1977] We’ll be using noise and interference interchangeably 3

  4. 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 2.4 Wireless LAN (Wi-Fi)‏ Gigabit Ethernet, PCI Express Bus, LCD clock harmonics IEEE 802.16e-2005 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 Wireless LAN (Wi-Fi)‏ PCI Express Bus,LCD clock harmonics Common Spectral Occupancy 4

  5. 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 Backup 5

  6. 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: Myriad filtering, hole punching, and Bayesian detector Proposed Contributions 6

  7. Outline Problem definition Noise modelling Estimation of noise model parameters Filtering and detection Conclusion and future work 7

  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] Middleton Class A Model Power Spectral Density for A = 0.15, = 0.8 Probability Density Function for A = 0.15, = 0.8 8

  9. 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 Probability density function (pdf) PDF for A = 0.15, = 0.8 9

  10. Symmetric Alpha Stable Model Power Spectral Density for = 1.5,  = 0 and  = 10 Probability Density Function for  = 1.5,  = 0 and  = 10 10

  11. Symmetric Alpha Stable Model 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 • Does not have second-order moment Backup PDF for  = 1.5,  = 0 and  = 10 11

  12. Outline Problem definition Noise modelling Estimation of noise model parameters Filtering and detection Conclusion and future work 12

  13. 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 (~1,000 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. • AdvantageFast / computationally efficient (non-iterative)‏ • Disadvantage Requires large set of data samples (~10,000 samples)‏ Backup Backup 13

  14. Results of Measured RFI Data for Broadband Noise Backup Data set of 80,000 samples collected using 20 GSPS scope Distance: Kullback-Leibler divergence 14

  15. Expectation-Maximization Estimator for Class A Noise Normalized Mean-Squared Error in A Iterations for Parameter A to Converge PDFs with 11 summation terms 50 simulation runs per setting 1000 data samples Convergence criterion: ×10-3 K = AG 15

  16. Expectation-Maximization Estimator for Class A Noise • For convergence for A [10-2, 1], worst-case number of iterations for A = 1 • Estimation accuracy vs. number of iterations tradeoff

  17. Symmetric Alpha Stable Parameter Estimator Data length (N) of 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 Mean squared error in estimate of characteristic exponent α 17

  18.  = 10  = 5 Mean squared error in estimate of localization (“mean”)  Mean squared error in estimate of dispersion (“variance”)  Symmetric Alpha Stable Parameter Estimator 18

  19. Outline Problem definition Noise modelling Estimation of noise model parameters Filtering and detection Conclusion and future work 19

  20. Matched Filter v[n] Pulse Shape Pre-Filtering s[n] gtx[n] grx[n] Λ(.)‏ Filtering and Detection – System Model Alternate Adaptive Model Impulsive Noise • 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 Backup Decision Rule N samples per symbol 20

  21. Filtering and Detection – Methods 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] • Symmetric Alpha Stable Noise • Correlation receiver (linear)‏ • Myriad filtering[Gonzalez & Arce, 2001] • MAP approximation • Hole punching Backup Backup Backup Backup Backup Backup 21

  22. Class A Detection – Results Pulse shapeRaised cosine10 samples per symbol10 symbols per pulse ChannelA = 0.35 = 0.5 × 10-3Memoryless 22

  23. Hole Punching (Blanking) for Pre-Filtering • Sets sample to 0 when sample exceeds threshold [Ambike, 1994] • Large values are impulses and true value cannot be recovered • Replacing large values with zero will not bias (correlation) receiver for two-level constellations • 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 23

  24. Myriad Filtering for Pre-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 passes through myriad filter • As k→0, filter tends to mode filter (output value with highest freq.) Empirical choice of k: [Gonzalez & Arce, 2001] Developed for images corrupted by additive symmetric alpha stable impulsive noise

  25. Myriad Filter Implementation Given a window of samples x1,…,xN, find β [xmin, xmax] Optimal myriad algorithm • Differentiate objective functionpolynomial 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

  26. Symmetric Alpha Stable Detection – Results Use dispersion parameter g in place of noise variance to generalize SNR 26

  27. 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: Myriad filtering, hole punching, and Bayesian detector Conclusion – Proposed Contributions 27

  28. Conclusion – Filtering and Detection T 28

  29. Conclusion – Contributions Publications 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. Software Releases RFI Mitigation Toolbox Version 1.1 Beta (Released November 21st, 2007) Version 1.0 (Released September 22nd, 2007) http://users.ece.utexas.edu/~bevans/projects/rfi/software.html Project Web Site http://users.ece.utexas.edu/~bevans/projects/rfi/index.html 29

  30. Conclusion – Future Work on Impulsive Noise • Communication performance bounds on single-carrier single-antenna detection • Multi-input multi-output (MIMO) single-carrier receivers • Performance analysis of standard MIMO receivers using multivariate noise models • Optimal and sub-optimal maximum likelihood (ML) 2 2 receiver • To be presented at 2008 Globecom Conference in December • Multicarrier receivers • Modelling co-channel interference Backup Backup Backup 30

  31. Thank you, Questions?

  32. 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 32

  33. 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. 33

  34. BACKUP SLIDES

  35. 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 multipleRF sources on single chip 35

  36. 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] 36

  37. [Middleton, 1999] Middleton Class A, B, C Models Class ANarrowband interference (“coherent” reception) Uniquely represented by two parameters Class BBroadband interference (“incoherent” reception) Uniquely represented by six parameters Class CSum of class A and class B (approx. as class B)‏ 37

  38. 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 38

  39. 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 ford/dxi ln pZ(xi) in simulations Backup 39

  40. 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 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: 40

  41. 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 amixture 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 41

  42. Bit Error Rate (BER) Performance in Alpha Stable Noise 42

  43. Class A Parameter Estimation Based on APD (Exceedance Probability Density) Plot 43

  44. e2 = e4 = e6 = Class A Parameter Estimation Based on Moments Moments (as derived from the characteristic equation)‏ Parameter estimates Odd-order momentsare zero[Middleton, 1999] 2 44

  45. Middleton Class B Model Envelope Statistics Envelope exceedance probability density (APD) which is 1 – cumulative distribution function 45

  46. Class B Envelope Statistics 46

  47. 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 Parameters for Middleton Class B Noise 47

  48. Class B Exceedance Probability Density Plot 48

  49. 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. Root4th-order poly. (after approximation). Backup Backup 49

  50. Expectation Maximization Overview 50

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