November 9th, 2010 Low Complexity EM-based Decoding for OFDM Systems with Impulsive Noise Asilomar Conference on Signals, Systems, and Computers Marcel Nassar and Brian L. Evans Wireless Networking and Communications Group The University of Texas at Austin

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

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

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

can be estimated during quiet time  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 System Model Wireless Networking and Communications Group 5 impulsive noise normalized SNR DFT matrix OFDM symbol received symbol circulant channel

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

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

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

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 9

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) Wireless Networking and Communications Group 10 SW

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

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 Wireless Networking and Communications Group 12 Might be difficult to compute directly Easier to evaluate

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 Wireless Networking and Communications Group 13 Exponential in N

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

Questions! Thank you 15 Wireless Networking and Communications Group