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Low Complexity EM-based Decoding for OFDM Systems with Impulsive Noise

Low Complexity EM-based Decoding for OFDM Systems with Impulsive Noise. Marcel Nassar and Brian L. Evans Wireless Networking and Communications Group The University of Texas at Austin. Asilomar Conference on Signals, Systems, and Computers 2011. Wireless Transceivers. antennas.

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Low Complexity EM-based Decoding for OFDM Systems with Impulsive Noise

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  1. Low Complexity EM-based Decoding for OFDM Systems with Impulsive Noise Marcel Nassar and Brian L. Evans Wireless Networking and Communications Group The University of Texas at Austin Asilomar Conference on Signals, Systems, and Computers 2011

  2. Wireless Transceivers • antennas • Computational Platform • Clocks, busses, processors • Other embedded transceivers • Non-Communication Sources • Electromagnetic radiations • baseband processor • Wireless Communication • Sources • Uncoordinated Transmissions Wireless Networking and Communications Group

  3. Powerline Communications • Microwave Ovens • Ingress Broadcast Stations • Receiver • Home Devices • Light Dimmers • Fluorescent Bulbs Wireless Networking and Communications Group

  4. Noise Modeling • Modeling the first order statistics of noise • Gaussian Mixture Model • Middleton Class A • Symmetric Alpha Stable • Some Fitted Parameters for GM Platform Noise Powerline Noise Wireless Networking and Communications Group

  5. System Model • Consider an OFDM communication system • Noise Model: a K-term Gaussian Mixture • Assumptions: • Channel is fixed during an OFDM symbol • Channel state information (CSI) at the receiver • Noise is stationary • Noise parameters at the receiver impulsive noise OFDM symbol normalized SNR received symbol DFT matrix circulant channel can be estimated during quiet time Wireless Networking and Communications Group

  6. Problem Statement • OFDM detection problem • Transformed detection problem (DFT operation) Exponential in N (N in hundreds) • no efficient code representation for • not symbol decodable Has a product formSymbol Decodable • for Gaussian noise, statistics are preserved • for impulsive noise, dependency is introduced No Product FormExponential in N Wireless Networking and Communications Group

  7. Single Carrier (SC) vs. OFDM Gaussian Mixture with • Low SNR: SC better • High SNR: OFDM better • OFDM provides time diversity through the FFT operation • Lot of other reasons to choose OFDM SC outperforms OFDM OFDM outperforms SC Wireless Networking and Communications Group

  8. SC vs. OFDM: Intuition Single Carrier OFDM N modulated symbols Time-domain OFDM Symbol High Amplitude Impulse High Amplitude Impulse Impulsive Noise Impulsive Noise After FFT • Impulse energy concentrated in one symbol • Symbol lost • Impulse energy spread across symbols • Loss depends on impulse amplitude and SNR Wireless Networking and Communications Group

  9. Prior Work • Parametric Methods (statistical noise model) • Haring 2001: Time-domain MMSE estimate • With noise state information and without it • Non-Parametric Methods (no statistical noise model) • Haring 2000: iterative thresholding • Low complexity • Threshold not flexible • Caire 2008: compressed sensing approach • Uses null tones • Corrects only few impulses on practical systems • Lin 2011: sparse Bayesian approach • Uses null tones Wireless Networking and Communications Group

  10. Gaussian Mixture (GM) Noise • A K-term Gaussian Mixture can be viewed as a Gaussian distribution governed by a latent variable S • The distribution of W is given by: • The latent variable S can be viewed as noise state information (NSI) S W Wireless Networking and Communications Group

  11. GM Noise in OFDM Systems • Given perfect noise state information (NSI) • Estimation of time domain OFDM symbols [Haring 2002] • Approach: • MMSE With NSI: • MMSE Without NSI: Exponential in N (Central Limit Theorem) n is not identically distributed, taking FFT is suboptimal Wireless Networking and Communications Group

  12. Expectation-Maximization Algorithm • Iterative algorithm • Finds feature given the observation such that • Uses unobserved data that simplifies the evaluation • Iteration step i : • E-step: Average over given and • M-step: Choose to maximize this average • Given the right initialization converges to the solution Might be difficult to compute directly Easier to evaluate Wireless Networking and Communications Group

  13. EM-Based Iterative Decoding • S is treated as a latent variable, X is the parameter • The E-step can be written as: • The M-step can be written as: • The E-step can be interpreted as the detection problem with perfect NSI given by • As a result, we approximate the M-step by the MMSE estimate with perfect NSI Exponential in N Wireless Networking and Communications Group

  14. Simulation Results Gaussian Mixture with • Initialize to MMSE without CSI • Approaches MMSE with CSI • Works well for impulses of around 20dB above background noise Wireless Networking and Communications Group

  15. Thank you Questions! Wireless Networking and Communications Group

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