MAP Ratio Test Detector for Radar System

Abstract

In some radar applications, neither the channel parameters nor the transmitted signal are known a-priori at the radar receiver. As such, both the transmitted signal as well as the channel parameters are random variables. Given the knowledge of distributions of the unknown parameters, we propose a maximum a-posteriori (MAP) ratio test (MAPRT) detector that incorporates this knowledge into its decision making process. This MAP approach is a generalization of past approaches such as the generalized likelihood ratio test (GLRT) detectors, where the estimates of the unknown parameters are obtained using maximum likelihood (ML) estimation. Assuming no knowledge of transmit waveforms, we derive the test statistics for bi-static and multi-static radar systems, when the noise power is both known and unknown. For the case of known noise variance in the bi-static radar system, we derive an exact closed-form expression for the probability of false alarm (PFA) and an approximate expression for the probability of detection (PD). For the multi-static case with known noise power, we derive upper bounds on PFA and PD. Numerical simulations verify the accuracy of the derived expressions and demonstrate that the proposed MAPRT detector performs significantly better than the GLRT-based detectors, especially when the signal-to-noise ratio (SNR) associated with the surveillance channel or sample size assumes small values.