Direction-of-arrival estimation of an amplitude-distorted wavefront

In a number of array signal processing applications, such as underwater source localization, the propagation medium is not homogeneous, which causes a distortion of the wavefront received by the array. There has been some interest in the direction-of-arrival (DOA) estimation of such distorted wavefronts. Most works on this problem considered the so-called multiplicative noise scenario based on the rather strong assumption that the distortion is random and can be parameterized by a small number of parameters. To gain robustness against mismodeling, we assume a scenario in which the wavefront amplitude is distorted in a completely arbitrary way. Our main contribution consists of showing how to eliminate all nuisance (distortion) parameters from the likelihood function corresponding to such a scenario and obtain a robust maximum likelihood DOA estimate by means of a simple one-dimensional (1-D) search. Despite its simplicity, it is shown that the estimator has a performance close to the Cramer-Rao Bound (CRB), for which we derive a closed-form expression. Moreover, its accuracy is comparable with that of estimators that require knowledge of the form of amplitude distortions.