A computationally efficient two-step implementation of the GLRT

In this paper, the performance of a new two-step adaptive detection algorithm is analyzed. The two-step GLRT consists of an initial adaptive matched filter (AMF) test followed by a generalized likelihood ratio test (GLRT). Analytical expressions are provided for the probability of false alarm (P_FA) and the probability of detection (P_D) in unknown complex Gaussian interference. The analysis shows that the two-step GLRT significantly reduces the computational load over the GLRT while maintaining detection and sidelobe rejection performance commensurate with the GLRT. The two-step GLRT detection algorithm is also compared with another two-step detection algorithm: the adaptive sidelobe blanker (ASB). Both the two-step GLRT and the ASB are characterized in terms of the mainbeam detection performance and the rejection of sidelobe targets. We demonstrate that for a given P_FA, the two-step GLRT has a broad range of threshold pairs (one threshold for the AMF test and one for the GLRT) that provide performance identical to the GLRT. This is in contrast with the ASB, where the threshold pairs that maximize the P_D are a function of the target´s signal-to-interference-plus-noise ratio (SINR). Hence, for a fixed pair of thresholds, the two-step GLRT can provide slightly better mainbeam detection performance than the ASB in the transition region from low to high detection probabilities