Performance evaluation of adaptive subspace detectors, based on stochastic representations

In this paper we present a technique for evaluating the moments of "adaptive" detectors, where the noise co-variance is estimated from training data, rather than assumed to be known a priori. It is based on the method of "stochastic representations" recently presented in [1]. These representations express adaptive detectors as simple functions of the same set of five statistically independent scalar random variables. They may be applied to a whole class of detectors, which includes the adaptive versions of the matched subspace detectors shown to be UMP-invariant and GLRT in [2] and [3], and to the adaptive GLRT detector of Kelly [4]. Using a stochastic representation, the moments of any member of this class may be evaluated without the need to derive its density or characteristic function. The first two moments give a convenient measure for how the SNR loss improves as the number of training vectors, M, increases. In this paper, the analysis is presented using the example of the adaptive version of the matched filter, illustrated in Figure 1.