Correspondence Theoretical Performance Analysis of the W-ABORT Detector

Abstract—In a recent paper we introduced a modification of the adaptive beamformer orthogonal rejection test (ABORT) for adaptive detection of signals in unknown noise, by supposing under the null hypothesis the pres-ence of signals orthogonal to the nominal steering vector in the whitened observation space. We will refer to this new receiver as the whitened adap-tive beamformer orthogonal rejection test (W-ABORT). Through Monte Carlo simulations this new detector was shown to provide better rejection capabilities of mismatched (e.g., sidelobe) signals than existing ones, like ABORT or the adaptive coherence estimator (ACE), but at the price of a certain loss in terms of detection of matched (i.e., mainlobe) signals. The aim of this paper is to provide a theoretical validation of this fact. We con-sider both the case of distributed targets and point-like targets. We provide a statistical characterization of the W-ABORT test statistic, under the null hypothesis, and for matched and mismatched signals under the alterna-tive hypothesis. For distributed targets, the probability of false alarm an