Distributed MIMO Passive Radar Target Detection: Holy Trinity, Durbin, and Gradient Tests

This article addresses the problem of target detection in a two-channel distributed multiple-input-multiple-output (MIMO) passive radar. In this scenario, multiple distributed transmitters emit signals that are received by the two-channel distributed receivers, one channel for surveillance and the other for reference. Both receiver channels are utilized to formulate the target detection problem as a binary composite hypothesis testing problem. To tackle this, we develop five detectors based on the generalized likelihood ratio test, Rao, Wald, Gradient, and Durbin criteria. This framework for two-channel distributed MIMO PR target detection takes into account noisy reference channels (RCs). The invariance principle is employed here to show that all uncertainties affecting threshold setting can be consolidated into the direct-path signal power-to-noise ratio (DNR) in the RCs. We also introduce the concept of "level of test," which allows us to effectively adjust the detection thresholds irrespective of the DNR values of the RCs. Among the proposed detectors, the Rao-based test exhibits superior and robust performance. Furthermore, the results demonstrate that the proposed detectors outperform the existing alternatives.