Conditional Expected Likelihood Technique for Compound Gaussian and Gaussian Distributed Noise Mixtures

Abstract

Expected likelihood (EL) technique for quality assessment of parameter estimates of signals embedded in Gaussian noise is extended in this paper over the case where useful signals are immersed in a mixture of compound Gaussian and Gaussian-distributed noises. The main problem here is that analytical expressions for distributions of such mixtures do not exist in most cases. Moreover, in some cases like $K$ -distributed noise only, where closed-form expressions for the data distribution are available, the traditional Cramer–Rao bound does not exist. This makes the EL technique even more important for parameter estimation performance assessment. In this paper, for the so-called conditional model, we introduce test statistics whose distribution for the true (actual) parameters does not depend on these parameters and specifics of texture distribution, which makes them applicable for EL applications. We illustrate the utility of this EL technique by studying and predicting the performance breakdown of some direction of arrival estimators in a mixture of $K$ -distributed and Gaussian noise.