|A Computationally Efficient Two-Step Implementation of the GLRT
Nicholas Pulsone and Michael Zatman
MIT Lincoln Laboratory
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Abstract 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 (PFA) and the probability of detection (PD) in unknown interference modeled as a multivariate complex Gaussian process. 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 to another two-step detection
algorithm, the Adaptive Sidelobe Blanker (ASB). Both the two-step GLRT and the ASB are
characterized in terms of mainbeam detection performance and the rejection of sidelobe
targets. In particular, for a given PFA the two-step GLRT has a broad range of threshold
pairs (one threshold for the AMF Test and one for the GLRT) that provide GLRT-like
mainbeam detection performance. This is in contrast to the ASB, where the threshold pairs
that maximize PD are a function of the target's signal-to-interference-plus-noise ratio.
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 PDs.
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