MAXIMUM-LIKELIHOOD-ESTIMATION OF SIGNAL POWER IN SENSOR ARRAY IN THE PRESENCE OF UNKNOWN NOISE FIELD

A simple approximate maximum likelihood (AML) estimator is derived for estimating a power of a single signal with a rank-one spatial covaria nce matrix known a priori except for a scaling. The noise field is ass umed to be spatially uncorrelated and to have different unknown powers in each array sensor. The derivation of the AML estimator is carried out under the assumptions of a large number of samples and a weak sign al. The variance of the introduced AML estimator is compared with the exact Cramer-Rao bound (CRB) of this estimation problem. It is shown a nalytically that the variance of the estimation errors and the corresp onding CRB coincide asymptotically in the majority of practically impo rtant cases. The analogy between the presented AML estimator and the w ell-known ML estimator, which is derived under equal noise variance as sumption (this estimator is based on the matched processing and is usu ally termed as conventional beamformer), is considered. This analogy e nables straightforward extension of the AML estimator to the case of w ell-separated weak multiple sources with unknown locations and conside ration of it as a variant of conventional beamformer for unknown noise field scenarios. The analytical results are verified by computer simu lations.