Persymmetric Adaptive Detectors in Homogeneous and Partially Homogeneous Environments

This paper addresses the problem of detecting a signal in partially homogeneous and homogeneous environments. In partially homogeneous environments, i.e., both the test data and training data share the same noise covariance matrix structure up to an unknown scaling factor, a persymmetric adaptive coherence estimator (Per-ACE) detector is proposed. By exploiting the persymmetric structure of the covariance matrix, the Per-ACE can reduce training data requirements. Furthermore, the expressions for the probabilities of false alarm and detection are derived along with the distribution of the loss factor β. In homogeneous environments, a persymmetric adaptive matched filter (Per-AMF) detector has been presented. However, its probability of detection has not been obtained yet. Thus, we derive the expression for the probability of detection. For both the Per-ACE and Per-AMF, numerical results of these proposed expressions are confirmed with those of Monte Carlo trials. In addition, simulation results show that the proposed Per-ACE outperforms the conventional ACE in training-limited scenarios.