Parametric GLRT for multichannel adaptive signal detection

We consider herein the problem of detecting a multichannel signal in the presence of spatially and temporally colored disturbance. A parametric generalized likelihood ratio test (GLRT) is developed by modeling the disturbance as a multichannel autoregressive (AR) process. The parametric GLRT differs from Kelly's widely known GLRT which does not utilize any parametric model for the disturbance signal. Maximum likelihood (ML) parameter estimation underlying the parametric GLRT is examined. It is shown that the ML estimator for the alternative hypothesis is non-linear and there exists no closed-form expression. An alternative asymptotic ML (AML) estimator is presented, which yields asymptotically optimum parameter estimates at a reduced complexity. The performance of the parametric GLRT is studied by considering challenging cases with limited or no training signals for parameter estimation. Such cases (especially when training is unavailable) are of great interest in detecting signals in heterogeneous, fast changing, or dense-target environments. Compared with the recently introduced parametric adaptive matched filter (PAMF) and parametric Rao detectors, the parametric GLRT achieves higher data efficiency, offering improved detection performance in general.