ROC Performance Prediction for Cooperative Radar-Communications via Wilks' Theorem

The theoretical analysis of a generalized likelihood ratio test (GLRT) detector is a difficult problem in general due to nonlinear searches involved in estimating unknown target parameters. Wilks' theorem provides a useful framework for asymptotic analysis of the GLRT when the likelihood function for the data model is a differentiable function of the unknown parameters. In a shared spectrum environment, the signal received by the radar consists of the target return as well as unknown signals transmitted from in-band communications (comms.) users. If the data model assumes that the interfering comms. symbols belong to a discrete constellation, the differentiability condition is not satisfied. In this paper, we apply Wilks' theorem to predict the asymptotic detection performance of the GLRT for a cooperative radar-comms. receiver by considering a model that operates under the assumption that the comms. symbols can assume any complex value. Furthermore, for the case of phase-shift keying (PSK)-modulated symbols, we apply Wilks' theorem based on a constant-modulus (CM) model that assumes without loss of generality that the symbols are restricted to lie on the unit circle. We derive closed-form expressions for the quantities determining the Wilks' distribution parameter for the case when the binary PSK (BPSK) constellation is used. We derive the GLRT detectors for both models and propose an alternating-minimization implementation for the PSK-based model. We present numerical results showing very good agreement between the empirical receiver operating characteristic (ROC) performance of the GLRT detector and the theoretical performance predicted by Wilks' theorem.