A GLRT for multichannel radar detection in the presence of both compound Gaussian clutter and additive white Gaussian noise

Motivated by multichannel radar detection applications in the presence of both white Gaussian noise and Gaussian clutter with unknown power, we develop maximum likelihood parameter estimates for the disturbance process. Both cases with known and unknown white noise variance are treated. As the estimators do not admit closed-form solutions, numerical iterative procedures are developed that are guaranteed to at least converge to the local maximum. The developed estimates allow us to construct a generalized likelihood ratio test (GLRT) for the detection of a signal with constant but unknown amplitude. This GLRT has important applications in multichannel radar detection involving both white Gaussian noise and spherically invariant random process clutter and is shown to have better detection performance and CFAR property compared with existing statistics.