Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures

Many approaches have been studied for the array processing problem when the additive noise is modeled with a Gaussian distribution, but these schemes typically perform poorly when the noise is non-Gaussian and/or impulsive. T his paper is concerned with maximum likelihood array processing in non-Gaus sian noise. We present the Cramer-Rao bound on the variance of angle-of-arr ival estimates for'arbitrary additive, independent, identically distributed (iid), symmetric, non-Gaussian noise. Then, we focus on non-Gaussian noise modeling with a finite Gaussian mixture distribution, which is capable of representing a broad class of non-Gaussian distributions that include heavy tailed, impulsive cases arising in wireless communications and other appli cations. Based on the Gaussian mixture model, we develop an expectation-max imization (EM) algorithm for estimating the source locations, the signal wa veforms, and the noise distribution parameters. The important problems of d etecting the number of sources and obtaining initial parameter estimates fo r the iterative EM algorithm are discussed in detail. The initialization pr ocedure by itself is an effective algorithm for array processing in impulsi ve noise. Novel features of the EM algorithm and the associated maximum lik elihood formulation include a nonlinear beamformer that separates multiple source signals in non-Gaussian noise and a robust covariance matrix estimat e that suppresses impulsive noise while also performing a model-based inter polation to restore the low-rank signal subspace. The EM approach yields im provement over initial robust estimates and is valid for a nide SNR range. The results are also robust to pdf model mismatch and work well with infini te variance cases such as the symmetric stable distributions. Simulations c onfirm the optimality of the EM estimation procedure in a variety of cases, including a multiuser communications scenario. We also compare with existi ng array processing algorithms for non-Gaussian noise.