On maximum-likelihood localization of coherent signals

We consider the problem of localizing multiple signal sources in the special case where all the signals are known a priori to be coherent. A maximum-likelihood estimator (MLE) is constructed for this special case and its asymptotical performance is analyzed via the Cramer-Rao bound (CRB). It is proved that the CRB for this case is identical to the CRB for the case that no prior knowledge on coherency is exploited thus establishing a quite surprising result that asymptotically the localization errors are not reduced by exploiting this prior knowledge. Also we prove that in the coherent case the deterministic signals model and the stochastic signals model yield MLE's that are asymptotically identical. Simulation results confirming these theoretical results are included.