UMP invariance of the multirank adaptive coherence estimator

The adaptive coherence estimator, or ACE, is a uniformly most powerful (UMP)-invariant detection statistic is presented in this paper. The proof that ACE is a one-dimensional maximal invariant was based on a relatively simple extension of an earlier work done by the authors on maximal invariant statistics for detection of rank-1 signals. In this paper we consider the multirank version of ACE, needed for scenarios when the signal waveform is uncertain. It also can be shown to be a maximal invariant, and by extension UMP-invariant, but the proof requires a more detailed analysis of the transformation group properties.