  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 (CFAR).
