Multichannel Parametric Rao Detector

The parametric Rao test for a multichannel adaptive signal detection problem is derived by modeling the disturbance signal as a multichannel autoregressive (AR) process. Interestingly, the parametric Rao test takes a form identical to that of the recently introduced parametric adaptive matched filter (PAMF) detector. The equivalence offers new insights into the performance and implementation of the PAMF detector. Specifically, the Rao/PAMF detector is asymptotically (for large samples) a parametric generalized likelihood ratio test (GLRT), due to an asymptotic equivalence between the Rao test and the GLRT. The asymptotic distribution of the Rao test statistic is obtained in closed-form, which follows an exponential distribution under H₀ and, respectively, a non-central Chi-squared distribution with two degrees of freedom under H₁. The non-centrality parameter of the non-central Chi-squared distribution is determined by the output signal-to-interference-plus-noise ratio (SINR) of a temporal whitening filter. Since the asymptotic distribution under H₀ is independent of the unknown parameters, the Rao/PAMF asymptotically achieves constant false alarm rate (CFAR). Numerical results show that these results are accurate in predicting the performance of the parametric Rao/PAMF detector even with moderate data support