1. Design of Interference-Aware Wireless Communication Systems Wireless Networking and Communications Group 2 Dec 2010 Brian L. Evans Lead Graduate Students Aditya Chopra, Kapil Gulati, and Marcel Nassar Collaborators from Intel Labs Current: Nageen Himayat, Kirk Skeba, and Srikathyayani Srikanteswara Past: Chaitanya Sreerama, Eddie X. Lin, Alberto A. Ochoa, and Keith R. Tinsley

2. Outline  Introduction  Problem definition  Summary of last talk (in Apr. 2010) at Intel Labs  Recent results  RFI Modeling: Spatial and Temporal dependence  RFI Mitigation: Multi-carrier systems  Conclusions  Future work Wireless Networking and Communications Group 2 Radio Frequency Interference (RFI)

3. 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)

4. 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  10-100x reduction in bit error rate  10-100x improvement in network throughput Wireless Networking and Communications Group 4

5. Designing Interference-Aware Receivers Wireless Networking and Communications Group 5 RTS CTS RTS / CTS: Request / Clear to send Guard zone Example: Dense WiFi Networks

6. 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 6

7. Summary of Last Talk: RFI Modeling Wireless Networking and Communications Group 7 Sensor networks Ad hoc networks Dense Wi-Fi networks Cluster of hotspots (e.g. marketplace) In-cell and out-of-cell femtocell users Out-of-cell femtocell users Cellular networks Hotspots (e.g. café) Symmetric Alpha Stable Ad hoc and Cellular networks Single Antenna Instantaneous statistics Femtocell networks Single Antenna Instantaneous statistics Gaussian Mixture Model

8. Summary of Last Talk: RFI Modeling  Validated for Laptop radiated RFI  Slides available at: http://users.ece.utexas.edu/~bevans/projects/rfi/talks/April2010RFIMitigationTalk.html Wireless Networking and Communications Group 8 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

9. Summary of Last Talk: RFI Mitigation  Communication Performance Wireless Networking and Communications Group 9 Pulse Shaping Pre-filtering Matched Filter Detection Rule Interference + Thermal noise Single carrier, single antenna (SISO)Single carrier, two antenna (2x2 MIMO) ~ 20 dB ~ 8 dB 10 – 100x reduction in Bit Error Rate

10.  Extended to include spatial and temporal dependence  Multivariate extensions of  Symmetric Alpha Stable  Gaussian mixture model RFI Modeling: Extensions Wireless Networking and Communications Group 10 Multi-antenna receivers Symbol errors Burst errors Coded transmissions Delays in network

11. RFI Modeling: Spatial Dependence  System Model  Common and exclusive interferers  Characterizes receiver separation and directional shielding  Joint RFI statistics helpful in choosing spatial transmit and receive techniques Wireless Networking and Communications Group 11 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 1

12. RFI Modeling: Spatial Dependence  An impulsive event at one antenna increases probability of impulse event at other antennae  Translated environmental parameters to spatial dependence Wireless Networking and Communications Group 12 |RFI at antenna 2| |RFI at antenna 1| |RFI at antenna 2| SPATIALLY INDEPENDENT SPATIALLY ISOTROPIC

13. RFI Modeling: Temporal Dependence  System Model  Interference is dependent across time slots Wireless Networking and Communications Group 13

14. RFI Modeling: Joint Interference Statistics  Throughput performance of ad hoc networks Wireless Networking and Communications Group 14 Ad hoc networks Multivariate Symmetric Alpha Stable Cellular networks Multivariate Gaussian Mixture Model Network throughput improved by optimizing distribution of ON Time of users (MAC parameter) ~1.6x

15. RFI Mitigation: Multi-carrier systems  Single Carrier vs. Multi-Carrier: Intuition Wireless Networking and Communications Group 15 Symbols Impulsive Noise Symbols Impulsive Noise High Amplitude Impulse Impulse energy concentrated in one symbol Symbol Lost Impulse energy spread across symbols Noise dependent across subcarriers Optimal decoding: exponential complexity! Single CarrierMulti Carrier (OFDM)

16. RFI Mitigation: Multi-carrier systems  Proposed Receiver  Iterative Expectation Maximization (EM) based on noise model  Communication Performance Wireless Networking and Communications Group 16 Simulation Parameters BPSK Modulation Interference Model 2-term Gaussian Mixture Model ~ 5 dB

17. Summary Wireless Networking and Communications Group 17 Physical (PHY) Layer Single Antenna (past work) Multi-Antenna Receivers Temporal Modeling Statistical Modeling of RFI: (a)Uni- or Multi-variate Gaussian Mixture (b)Uni- or Multi-variate Symmetric Alpha Stable Medium Access Control (MAC) Layer (a)Detection and Pre-filtering methods (b)Single- and Two-antenna receivers (c)Single- and Multi-carrier systems RFI Mitigation: (a)Microwave Oven Interference (b)Performance of Ad hoc Networks RFI Avoidance and Mitigation: Impact: 10-100x improvement in communication performance

18. Current and Future Work Wireless Networking and Communications Group 18 Physical (PHY) Layer Medium Access Control (MAC) Layer RFI Avoidance and Mitigation: Statistical Modeling of RFI: (a)Multi-carrier Multi-antenna systems (b)Non-stationary RFI Communication Performance Analysis MIMO transmit and receive strategies Improving Communication Performance Detection and Pre-filtering methods Error correction coding Interference Avoidance Spectrum Sensing Impact: Improved communication performance RFI Avoidance and Mitigation: Network Performance Analysis Different MAC strategies Improving Network Performance Optimizing MAC parameters MAC algorithms to reduce interference Interference Avoidance Resource Allocation (time, frequency) Impact: Improved network-wide performance Cognitive Radios

19. 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 1.5, Aug. 16, 2010 Wireless Networking and Communications Group 19 http://users.ece.utexas.edu/~bevans/projects/rfi/software/index.html Snapshot of a demo

20. 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, to be published, Dec., 2010. 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. Conf. on Comm., Jan. 5-9, 2011, Kyoto, Japan, 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. 14-19, 2010. 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. Cont… 20 Wireless Networking and Communications Group

21. 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. 19-24, 2009. 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. 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. 21 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 1.5, Aug. 16, 2010.

22. Thanks ! 22 Wireless Networking and Communications Group

23. 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. 1129-1149, May 1999. 2.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. 3.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. 4.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. 1992. 5.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. 2003. 6.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 2009. 7.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. 2009. 23 Wireless Networking and Communications Group

24. 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. 60-72, Jan. 1991. 2.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. 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. 2009. 2.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. 2007. 3.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. 2007. 4.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. 4091-4102, Dec. 2005. 24 Wireless Networking and Communications Group

25. 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. 4127-4149, Nov. 2007. 6.J. G. Andrews, S. Weber, M. Kountouris, and M. Haenggi, “Random access transport capacity,” IEEE Transactions On Wireless Communications, Jan. 2010, submitted. [Online]. Available: http://arxiv.org/abs/0909.5119 http://arxiv.org/abs/0909.5119 7.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 2010. 8.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. 1977 2.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 25 Wireless Networking and Communications Group

26. 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. 1994. 4.G. R. Arce, Nonlinear Signal Processing: A Statistical Approach, John Wiley & Sons, 2005. 5.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. 1069-1077, Nov. 2001. 6.J. H. Kotecha and P. M. Djuric, “Gaussian sum particle ltering,” IEEE Transactions on Signal Processing, vol. 51, no. 10, pp. 2602-2612, Oct. 2003. 7.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. 8.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. 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. 626-631, 14-18 Aug. 2006 26 Wireless Networking and Communications Group

27. 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  Measured RFI Fitting Wireless Networking and Communications Group 27 Backup

28. 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 28 Backup

29. 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 29 Backup

30. Backup Slides (cont…)  RFI Toolbox Wireless Networking and Communications Group 30 Backup

31. Interference Mitigation Techniques  Interference avoidance  CSMA / CA  Interference alignment  Example: [Cadambe & Jafar, 2007] Wireless Networking and Communications Group 31 Return

32. 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. 19-29, April 2005 Wireless Networking and Communications Group 32 Return

33. Femtocell Networks Reference: V. Chandrasekhar, J. G. Andrews and A. Gatherer, "Femtocell Networks: a Survey", IEEE Communications Magazine, Vol. 46, No. 9, pp. 59-67, September 2008 Wireless Networking and Communications Group 33 Return

34. Common Spectral Occupancy Wireless Networking and Communications Group 34 Return

35. 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) Wireless Networking and Communications Group 35 Return

36. Impact of LCD clock on 802.11g  Pixel clock 65 MHz  LCD Interferers and 802.11g center frequencies Wireless Networking and Communications Group 36 Return

37. 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 37 Return

38. Transients in Digital FIR Filters Wireless Networking and Communications Group 38 25-Tap FIR Filter Low pass Stopband freq. 0.22 (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

39. Poisson Field of Interferers  Interferers distributed over parametric annular space  Log-characteristic function Wireless Networking and Communications Group 39 Return

40. Poisson Field of Interferers Wireless Networking and Communications Group 40 Return

41. Poisson Field of Interferers Wireless Networking and Communications Group 41 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) Return

42. 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

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

44. 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

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

46. Poisson-Poisson Cluster Field of Interferers Wireless Networking and Communications Group 46 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 Return

47. Poisson-Poisson Cluster Field of Interferers  Simulation Results (tail probability) Wireless Networking and Communications Group 47 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

48. Poisson-Poisson Cluster Field of Interferers  Simulation Results (tail probability) Wireless Networking and Communications Group 48 Case II: Finite area annular region Return

49. Fitting Measured Laptop RFI Data  Statistical-physical models fit data better than Gaussian Wireless Networking and Communications Group 49 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 Return

50. Results on Measured RFI Data  For measurement set #23 50 Wireless Networking and Communications Group Tail probability governs communication performance Bit error rate Outage probability Return

51. Gaussian Mixture vs. Alpha Stable  Gaussian Mixture vs. Symmetric Alpha Stable Wireless Networking and Communications Group 51 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

52. 52 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

53. 53 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

54. Expectation Maximization Overview Wireless Networking and Communications Group 54 Return

55. Wireless Networking and Communications Group Results: EM Estimator for Class A 55 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

56. 56 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

57. 57 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

58. 58 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

59. Parameter Estimators for Alpha Stable Wireless Networking and Communications Group 59 0 < p < α Return

60. 60 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

61. 61 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

62. Extreme Order Statistics Wireless Networking and Communications Group 62 Return

63. 63 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 http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo1 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 (  ) 0.001 SNR19 dB Return

64. 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 http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo1 9dB.wmv Wireless Networking and Communications Group 64 Additive Class A NoiseValue Overlap index (A)0.35 Gaussian factor (  ) 0.001 SNR19 dB Return

65. 65 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 10 -6 for correlation receiver 0 for RFI mitigating receiver (Bayesian) Return

66. 66 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

67. 67 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

68. RFI Mitigation in SISO systems  Communication performance Wireless Networking and Communications Group 68 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 × 10 -3 Memoryless Binary Phase Shift Keying Return

69. 69 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 Communication Performance Binary Phase Shift Keying Return

70. 70 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

71. 71 Wireless Networking and Communications Group MAP Detection for Class A  Hard decision  Bayesian formulation [Spaulding & Middleton, 1977]  Equally probable source Return

72. Wireless Networking and Communications Group MAP Detection for Class A: Small Signal Approx. 72  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

73. 73 Wireless Networking and Communications Group Incoherent Detection  Bayesian formulation [Spaulding & Middleton, 1997, pt. II]  Small signal approximation Correlation receiver Return

74. 74 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

75. Wireless Networking and Communications Group Filtering for Alpha Stable Noise (Cont..) 75  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

76. 76 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

77. 77 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

78. 78 Wireless Networking and Communications Group Results: Alpha Stable Detection Return

79. 79 Wireless Networking and Communications Group Complexity Analysis for Alpha Stable Detection Return

80. 80 Wireless Networking and Communications Group Extensions to MIMO systems Return

81. 81 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

82. 82 Wireless Networking and Communications Group Bivariate Middleton Class A Model  Joint spatial distribution Return

83. 83 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

84. 84  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

85. Wireless Networking and Communications Group Sub-Optimal ML Receivers 85  Two-piece linear approximation  Four-piece linear approximation chosen to minimize Approximation of Return

86. 86 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

87. 87 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 Communication Performance (A = 0.1,  1 = 0.01,  2 = 0.1,  = 0.4) Return

88. Wireless Networking and Communications Group Results: RFI Mitigation in 2 x 2 MIMO 88 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

89. 89 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

90. 90 Wireless Networking and Communications Group Performance Bounds (Single Antenna)  Channel capacity in presence of RFI System Model Parameters A = 0.1, Γ = 10 -3 Capacity Return

91. 91 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 = 10 -3 [Haring & Vinck, 2002] Return

92. 92 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

93. 93 Performance Bounds (2x2 MIMO) Wireless Networking and Communications Group Return

94. 94 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

95. 95 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

96. 96 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

97. 97 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

98. 98 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

99. 99 Performance Bounds (2x2 MIMO) Wireless Networking and Communications Group  Cutoff rate Return

100. 100 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

101. Turbo Codes in Presence of RFI Wireless Networking and Communications Group 101 Decoder 1 Parity 1 Systematic Data Decoder 2 Parity 2 - - - - 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 10 -5 [Umehara03] Return

102. RFI Mitigation Using Error Correction Wireless Networking and Communications Group 102 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 10 -5 can be achieved using accurate RFI statistics [Umehara, 2003] Return

103. Usage Scenario #1 Wireless Networking and Communications Group 103 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 Return

104. Usage Scenario #2 104 Measured RFI data RFI Toolbox Statistical Modeling DEMO SISO Communication Performance DEMO File Transfer DEMO MIMO Communication Performance DEMO Wireless Networking and Communications Group Return