Uniformly most powerful invariant detection in spherically invariant random vector distributed clutter

This study deals with the problem of detecting a radar target with unknown complex amplitude in the presence of clutter modelled as a spherically invariant random vector (SIRV). It is proved that, under a quite mild technical condition, the normalised matched filter (NMF) is the uniformly most powerful invariant (UMPI) detector in SIRV disturbance. The developed proof is based on the theory of total positive functions of order two.