ML estimation of signal power in the presence of unknown noise field-simple approximate estimator and explicit Cramer-Rao bound

A simple approximate maximum likelihood (AML) estimator is derived for estimating a power of a single signal with rank-one spatial covariance matrix known a priori except for scaling. The noise are assumed to have different and unknown powers in each array sensor. The variance of the introduced AML estimator is compared with the exact Cramer-Rao bound (CRB) of this estimation problem analytically and by computer simulations. It is shown analytically that the AML estimator achieves the CRB in the majority of practically important cases. Computer simulations have been performed showing that the estimation errors of the AML estimator are very close to the CRB for a wide SNR range