The PAMF Detector is a Parametric Rao Test

The Rao test for an adaptive signal detection prob- lem in space-time adaptive processing (STAP) applications is derived by modeling the disturbance signal as a multichannel autoregressive (AR) process. Interestingly, the Rao test takes a form identical to that of the recently introduced parametric adaptive matched filter (PAMF) detector. The equivalence corrob- orates that the Rao/PAMF detector is an asymptotic generalized likelihood ratio test (GLRT). The asymptotic distribution of the test statistic is obtained in closed-form, which is a central Chi- squared distribution with two degrees of freedom under H0 and, respectively, a noncentral Chi-squared distribution with two degrees of freedom and a noncentrality parameter determined by the output signal-to-noise-and-interference (SINR) ratio of a temporal whitening filter. Therefore, the Rao/PAMF achieves asymptotic constant false alarm rate (CFAR). Numerical results show that these results are accurate in predicting the performance of the Rao/PAMF detector even with moderate data support. I. INTRODUCTION