Non-Parametric Methods for Mitigating Interference in OFDM Receivers

1. Wireless Networking and Communications Group Prof. Brian L. Evans Department of Electrical and Computer Engineering The University of Texas at Austin In collaboration with PhD studentsMs. Jing Lin and Mr. Marcel Nassar Non-Parametric Methods forMitigating Interference in OFDM Receivers American University of Beirut

2. Outline • Motivation • System model • Prior work • Sparse Bayesian learning • Proposed algorithms and results • Conclusion Wireless Networking and Communications Group

3. Mobile Internet Data: The Big Picture • Observations • 2x increase/year in data traffic: 1000x increase next 10 years • Demand is increasing exponentially but revenues are not • Revenue and traffic suddenly decoupled vs. voice service • Business models remain fuzzy especially for video • Consequences to industry • Restrict data usage (unpopular) OR • Decrease cost per bit exponentially (how?) OR • Lose money and/or watch network collapse (current status) Source: J. G. Andrews, "Wireless 1000x?", University of Notre Dame Seminar, May 5, 2011. Wireless Networking and Communications Group

4. Heterogeneity: Make Cells Smaller/Smarter • Demand handled by different networks • Macrocells guarantee basic coverage and require fast dedicated backhaul • Picocells target traffic “hotspots” • Femtocellsmust interoperate w/ cellularnetworks with minimal coordination Basestations pico Tower-mounted macrocell femto Source: J. G. Andrews, "Wireless 1000x?", University of Notre Dame Seminar, May 5, 2011. Wireless Networking and Communications Group

5. Wireless Interference Interference Co-channel Adjacent channel Out-of-platform In-platform Channel 11 (a) (a) Channel 11 Duration (c) (b) (d) Guard zone Channel 9 Example: Dense Wi-Fi Networks Wireless Networking and Communications Group

6. In-Platform Interference • May severely degrade communication performance • Impact of LCD noise on throughput for IEEE 802.11g embedded wireless receiver[Shi, Bettner, Chinn, Slattery & Dong, 2006] Wireless Networking and Communications Group

7. Low-Voltage Power Line Noise Measurement on 20 Mar 2011 on low-voltage US apartment power outlet at 5:00 am Powerline comm. standards use either 40-90 kHz or 10-500 kHz Impulsive noise is 45-50 dB above the noise floor Wireless Networking and Communications Group [Nassar, Gulati, Mortazavi & Evans, 2011]

8. Heterogeneity: Receiver’s Perspective • Antennas • Non-Communication • Sources • Electromagnetic radiations • Wireless Communication • Sources • Uncoordinated Transmissions • Baseband Processor • Computational Platform • Clocks, busses, processors • Other embedded transceivers • Network heterogeneity leads to the increase of uncoordinated interference at the receiver Wireless Networking and Communications Group

9. Statistical Modeling of Interference Middleton Class A (form of Gaussian Mixture) Symmetric Alpha Stable • Dense Wi-Fi networks • Networks with contention based medium access • Cellular networks • Hotspots (e.g. café) • Sensor networks • Ad hoc networks Wireless Networking and Communications Group [Gulati, Evans, Andrews & Tinsley, 2010]

10. Statistical Modeling of Interference Gaussian Mixture Model Symmetric Alpha Stable • In-cell and out-of-cell femtocell users in femtocell networks • Out-of-cell femtocell users in femtocell networks • Cluster of hotspots (e.g. marketplace) Wireless Networking and Communications Group [Gulati, Evans, Andrews & Tinsley, 2010]

11. Statistical Modeling of Interference • Low-voltage power lines • Multiple noisesources • 1% of impulses exceed1 ms in duration • Amplitude statistics • By derivation, model is Gaussian mixture • Gaussian mixture best fit for tail probabilities Data captured on power outlet in apartment in Austin, Texas USA, 20 Mar 2011 Fit blocks of 14 ms of data sampled at 1 MSample/s (blocks of 14000 samples) Wireless Networking and Communications Group [Nassar, Gulati, Mortazavi & Evans, 2011]

12. Statistical Models of Impulsive Noise 12 • 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

13. Orthogonal Frequency Division Multiplexing • Divides transmission band into narrow subchannels • Null tones at band edges for reducing spectral leakage • Null tones in low signal-to-noise ratio (SNR) subchannels • Pilot tones for synchronization and channel estimation • Power loading per subcarrier to increase data rates • Subchannel processing combats multipath effects • Better resilience to impulsive noise vs. single carrier • Used in modern data communications standards • Wireless: IEEE802.11a/g/n, cellular LTE • Powerline: PRIME, G3, IEEE1901.2 Wireless Networking and Communications Group

14. System Model Need • Proposed impulsive noise mitigation in OFDM receiver • No assumption of a specific impulsive noise model • Exploit sparse nature of impulsive noise Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

15. OFDM Receivers in Impulsive Noise • DFT spreads out impulsive energy across all tones • SNR of each tone is decreased • Receiver performance degrades • Noise in each tone is asymptotically Gaussian (as ) Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

16. Parametric Methods • Use parameterized functional forms of noise statistics • Need to estimate and track noise parameters • Suffer degradation in performance • Due to model mismatch or parameter mismatch • When noise statistics are changing rapidly • Not dependent on null tones • Higher throughput when noise statistics are slowly varying • Complexity in parameter estimation and tracking • OFDM decoders: high complexity for optimality and low-complexity approximations may work well enough Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

17. Prior Work Semi-nonParametric Methods (Threshold Selection) Parametric Methods nonParametric Method Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

18. Sparse Bayesian Learning • Underdetermined linear regression : observation vector : sparse weight vector : i.i.d. Gaussian noise w/ variance : overcomplete basis • SBL algorithm Parameterized Gaussian prior o: Estimate by computing maximum likelihood (ML) using expectation maximization Estimate w from posterior mean: • Guaranteed to converge to sparse solution • Fewer local minima vs. other compressed sampling algorithms Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

19. Estimation Using Null Tones • Noise observed on null tones is DFT matrix, = , and sparse weight vector and • Estimate e by sparse Bayesian learning • Parameterized Gaussian prior imposed on e • ML estimation of two hyper-parameters • Minimum mean-square estimate of e • Receiver block diagram M: # of known tones N: total # of tones Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

20. Estimation Using All Tones • Joint estimation of data and noise • is DFT matrix and = • Treat as a third hyper-parameter to be estimated • is relaxed to be continuous variables to guarantee convergence of expectation maximization algorithm • Estimate of sent to channel equalizer and MAP detector with hard decisions after impulsive noise mitigation • Receiverblockdiagram M: # of known tones N: total # of tones Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

21. Communication Performance Simulations • In different impulsive noise scenarios ~10dB ~6dB ~6dB ~8dB ~4dB Parametric (no null tones =>higher throughput) Gaussian mixture model Middleton Class A model Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

22. Communication Performance Simulations • In different impulsive noise scenarios (continued) ~7dB ~4dB Symmetric alpha stable model Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

23. Communication Performance Simulations • Performance of first algorithm as number of known tones decreases • SNR is 0 dB • 256 tones • Middleton Class A noise • In both algorithms, theEM algorithm converges after a few iterations Wireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

24. Comparison Parametric Methods Non-Parametric Methods • Based on formula for impulsive noise distribution • Needs parameter estimation • Good for slowly varying noise statistics • Suffer from model mismatch in fast varying environments • High complexity for optimal decoders • No assumption of noise statistics • Uses null tones in each OFDM symbol • Robust in fast varying noise environments • Potential reduction in throughput due to null tones (if not already in standard) Wireless Networking and Communications Group

25. Conclusions and Future Work • Proposed impulsive noise reduction algorithms • Assume real-valued OFDM symbols (G3, PRIME, ADSL) • Use null + pilot tones to give 4-6 dB SNR gain in simulation • Use all tones to give 8-10 dB SNR gain in simulation • Future work • Extend to complex-valued OFDM symbols (802.11a/b/n, LTE) • Track impulsive noise OFDM symbol to OFDM symbol • Incorporate knowledge of noise statistics • Add channel estimation • Analyze performance with coding and with correlated noise Wireless Networking and Communications Group

26. References • G. Caire, T. Al-Naffouri, and A. Narayanan, “Impulse noise cancellation in OFDM: an application of compressed sensing,” Proc. IEEE Int. Sym. on Info. Theory, 2008, pp. 1293–1297. • 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. • K. Gulati, B. Evans, J. Andrews, and K. Tinsley, “Statistics of cochannel interference in a field of Poisson and Poisson-Poisson clustered interferers,” IEEE Trans. on Signal Proc., vol. 58, no. 12, pp. 6207–6222, 2010. • J. Haring and A. Vinck, “Iterative decoding of codes over complex numbers for impulsive noise channels,” IEEE Trans. Info. Theory, vol. 49, no. 5, pp. 1251–1260, 2003. • J. Lin, M. Nassar, and B. L. Evans, “Non-Parametric Impulsive Noise Mitigation in OFDM Systems Using Sparse Bayesian Learning,” Proc.IEEE Int. Global Communications Conf., Dec. 5-9, 2011. • D. Middleton, “Statistical-Physical Models of Electromagnetic Interference”, IEEE Trans. On Electromagnetic Compatibility, vol. 19, no. 3, Aug. 1977, pp. 106-127. • D. Middleton, “Non-Gaussian noise models in signal processing for telecommunications: new methods an results for Class a and Class b noise models,” IEEE Trans. on Info. Theory, vol. 45, no. 4, pp. 1129–1149, 1999. Wireless Networking and Communications Group

27. References • M. Nassar, K. Gulati, M. DeYoung, B. Evans, and K. Tinsley, “Mitigating near-field interference in laptop embedded wireless transceivers,” Journal of Signal Proc. Sys., pp. 1–12, 2009. • M. Nassar, K. Gulati, Y. Mortazavi, and B. L. Evans, “Statistical Modeling of Asynchronous Impulsive Noise in Powerline Communication Networks”, Proc.IEEE Int. Global Communications Conf., Dec. 5-9, 2011. • M. Nassar and B. L. Evans, "Low Complexity EM-based Decoding for OFDM Systems with Impulsive Noise", Proc. Asilomar Conf. on Signals, Systems and Computers, Nov. 6-9, 2011. • H. W. Sorenson and D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums”, Automatica, vol. 7, no. 4, July 1971, pp. 465-479. • E. S. Sousa, “Performance of a spread spectrum packet radio network link in a Poisson field of interferers,” IEEE Trans. on Info. Theory, vol. 38, no. 6, pp. 1743–1754, Nov. 1992. • D. Wipf and B. Rao, “Sparse Bayesian learning for basis selection,” IEEE Trans. Signal Proc., vol. 52, no. 8, pp. 2153–2164, 2004. Wireless Networking and Communications Group

28. BACK UP SLIDES Wireless Networking and Communications Group

29. 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 Return Wireless Networking and Communications Group

30. 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 Return Wireless Networking and Communications Group

31. Problem Statement • Designing wireless transceivers to mitigate residual RFI Thermal noise RFI Channel 11 Transmit signal Pre-Filter Conventional Receiver Channel 11 Duration Distribution of Duration Guard zone Channel 9 Example: Dense Wi-Fi Networks Wireless Networking and Communications Group

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

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

34. Poisson-Poisson Cluster Field of Interferers • Cluster centers distributed as spatial Poisson process over • Interferers distributed as spatial Poisson process Return Wireless Networking and Communications Group

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

36. Gaussian Mixture vs. Alpha Stable • Gaussian Mixture vs. Symmetric Alpha Stable Return Wireless Networking and Communications Group

37. 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 Return PDF for A = 0.15,= 0.8 Wireless Networking and Communications Group

38. Home Power Line Noise Measurement Wireless Networking and Communications Group

39. Home Power Line Noise Measurement Spectrally-ShapedBackground Noise Wireless Networking and Communications Group

40. Home Power Line Noise Measurement Narrowband Noise Spectrally-ShapedBackground Noise Wireless Networking and Communications Group

41. Home Power Line Noise Measurement Periodic and Asynchronous Noise Narrowband Noise Spectrally-ShapedBackground Noise Wireless Networking and Communications Group

42. Analytical Models for Powerline Noise Wireless Networking and Communications Group

43. Expectation Maximization Overview 43 Return Wireless Networking and Communications Group

44. 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 keyingRaised cosine pulse10 samples/symbol10 symbols/pulse length • Composite of transmitted and received MPEG II video streams http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB_correlation.wmv • Shows degradation of video quality over impulsive channels with standard receivers (based on Gaussian noise assumption) Return Wireless Networking and Communications Group

45. Video over Impulsive Channels #2 45 • Video demonstration for MPEG II video stream revisited • 5.9 MB compressed stream from camera (124 MB uncompressed) • Compressed file sent over additive impulsive noise channel • Binary phase shift keyingRaised cosine pulse10 samples/symbol10 symbols/pulse length • Composite of transmitted video stream, video stream from a correlation receiver based on Gaussian noise assumption, and video stream for a Bayesian receiver tuned to impulsive noise http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB.wmv Return Wireless Networking and Communications Group

46. Video over Impulsive Channels #2 Structural similarity measure [Wang, Bovik, Sheikh & Simoncelli, 2004] Score is [0,1] where higher means better video quality Return Bit error rates for ~50 million bits sent: 6 x 10-6 for correlation receiver 0 for RFI mitigating receiver (Bayesian) Frame number