Parametric Rao Test for Multichannel Adaptive Generalized Detector

The parametric Rao test for multichannel signal detection by the adaptive generalized detector (GD) constructed based on the generalized approach to signal processing in noise is derived by modeling the disturbance signal as a multichannel autoregressive process. The parametric Rao test takes a form identical to that of parametric GD for space-time adaptive processing in airborne surveillance radar systems and other similar applications. The equivalence offers new in-sights into the performance and implementation of the GD. Specifically, the Rao/GD is an asymptotically (in the case of large samples) parametric generalized likelihood ratio test generalized detector (GLRT GD) due to an asymptotic equivalence between the Rao test and the GLRT/ GD. The asymptotic distribution of the Rao/GD test statistic is obtained in the closed form, which follows an exponential distribution under the null hypothesis (the target return signal is absent) and, respectively, a non-central Chi-squared distribution with two degrees of freedom under the alternative hypothesis (the target return signal is present). The noncentrality parameter of noncentral Chi-squared distribution is determined by the output signal-to-interference-plus-noise ratio of a temporal whitening filter. Since the asymptotic distribution at the null hypothesis is independent of the unknown parameters, the Rao/GD asymptotically achieves constant false alarm rate (CFAR) GD. Numerical results show that these results are superior in predicting the performance of the parametric adaptive matched filter even with moderate data support. Key-Words: Generalized detector, space-time adaptive processing, multichannel generalized detector, adaptive matched filter, adaptive coherence estimator detector, clutter, jamming.