On the maximal invariant statistic for adaptive radar detection in partially homogeneous disturbance with persymmetric covariance

This letter deals with the problem of adaptive signal detection in partially homogeneous and persymmetric Gaussian disturbance within the framework of invariance theory. First, a suitable group of transformations leaving the problem invariant is introduced and the maximal invariant statistic (MIS) is derived. Then, it is shown that the (two-step) generalized-likelihood ratio test, Rao, and Wald tests can be all expressed in terms of the MIS, thus proving that they all ensure a constant false-alarm rate.