Adaptive detector statistics using moment-based approximations

Adaptive filtering techniques are used for many detection applications such as communications and radar, yet the complicated statistics of adaptive detectors frustrate a closed form analysis of their performance. This paper offers a partial solution to this problem by providing closed form moments of the adaptive matched filter (AMF) and generalized likelihood ratio test (GLRT) that can be used in a Laguerre series expansion to efficiently complete the probabilities of detection and false alarm of these adaptive detectors. The radar case is considered in particular. Furthermore, exact closed form statistics of the AMF are given which are convenient for probability of false alarm computations and describing the asymptotic behavior of this test.