A Unified Theory of Adaptive Subspace Detection Part II: Numerical Examples

Abstract

This paper is devoted to the performance analysis of the detectors proposed in the companion paper (Orlando et al., 2022) where a comprehensive design framework is presented for the adaptive detection of subspace signals. The framework addresses four variations on subspace detection: the subspace may be known or known only by its dimension; consecutive visits to the subspace may be unconstrained or they may be constrained by a prior probability distribution. In this paper, Monte Carlo simulations are used to compare the detectors derived in (Orlando et al., 2022) with estimate-and-plug (EP) approximations of the generalized likelihood ratio (GLR) detectors. Remarkably, some of the EP approximations appear here for the first time (at least to the best of the authors' knowledge). The numerical examples indicate that GLR detectors are effective for the detection of partially-known signals affected by inherent uncertainties due to the system or the operating environment. In particular, if the signal subspace is known, GLR detectors tend to ouperform EP detectors. If, instead, the signal subspace is known only by its dimension, the performance of GLR and EP detectors is very similar. Actually, there does not exist a general rule for recommending the first-order approach with respect to the second-order one and vice versa. Nevertheless, the analysis contains a specific case where the second-order detectors can outperform the first-order detectors.