Array processing for signals with non-zero means in colored noise fields

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Array processing in spatially correlated noise fields is a difficult problem which cannot be solved without constraining either the noise or the signals in various ways. In this paper we assume that the signals impinging on the array have non-zero means. We show that the problem of array processing in completely general spatially colored noise fields is solvable under the previous assumption. In fact we argue that the non-zero mean signal assumption probably is one of the simplest conditions which makes array processing in colored noise possible. We also present a maximum-likelihood (ML) methodology for signal detection and parameter estimation. The derivation of the ML processor under the aforementioned assumption is conceptually straightforward and its implementation is standard. We provide a statistical analysis of the ML signal parameter estimator along with an expression for the associated Cramer–Rao bound (CRB) matrix. Finally, we include some numerical examples to show the type of performance that can be achieved by the estimation and detection approach proposed in this paper.