Beamforming algorithms are typically designed to maximize their output signal-to-interference-and-noise power ratio (SINR), under the assumption that doing so will optimize the probability of detection (P_d), given a design probability of false alarm (P_f ), in the ensuing detection algorithm. An alternative performance metric, the J-divergence detection currency (JDC), is employed here to represent performance before and after beamforming. Building on early use of the J-divergence in modeling array processing performance, the basic analysis is extended to account for correlated multipath signals and shaded conventional beamforming. The reduction in performance observed in practical adaptive beamforming algorithms that must estimate the array covariance matrix (ACM) or its eigen-structure is then assessed for processors having a beta-distributed SINR loss factor, representing a number of popular processors. Simple approximations to the JDC in this scenario that are accurate at low SINR, as well as more involved ones for higher SINR, are presented along with the tools required to evaluate them. The analysis presented in this report allows assessing the potential gain in performance from combining multipath signals and the losses incurred by ACM estimation in a metric that is easily combined across multiple measurements, is more closely related to the (P_d, P_f ) detection metrics than SINR, and can be evaluated throughout the signal and information processing chain.

Acknowledgments

This report was sponsored by the Office of Naval Research, Code 32, Undersea Signal Processing, through Naval Sea Systems Command contract N00024-21-D-6400 under task order N00024-22-F-8714.