A canonical representation for distributions of adaptive matched subspace detectors

We present a unified derivation of the distributions for adaptive versions of matched subspace detectors (MSDs) derived by Scharf (see Statistical Signal Processing, Addison-Wesley, and IEEE Trans. Signal Processing, 1996). These include: (1) the matched filter detector, (2) the gain invariant (CFAR) matched filter detector (3) the phase invariant matched subspace detector, and (4) the gain invariant (CFAR) and phase invariant matched subspace detector. We show that all these detectors can be decomposed into representations that are simple functions of the same five statistically independent, chi-squared or normal, scalar random variables. This canonical representation has at least three advantages: (1) the behavior of these detectors can easily be related to that of the non-adaptive detectors from which they are derived (2) moments can be simply obtained from the distributions of the scalar random variables, and (3) Monte Carlo simulations of the distributions can be implemented more efficiently.