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

TL;DR

This paper evaluates the performance of adaptive subspace detectors, comparing generalized likelihood ratio and estimate-and-plug methods through Monte Carlo simulations, highlighting their effectiveness under various knowledge conditions.

Contribution

It introduces and compares the first known estimate-and-plug approximations of GLR detectors for adaptive subspace detection, providing new insights into their relative performance.

Findings

GLR detectors outperform EP when the subspace is fully known.

EP approximations perform similarly to GLR when only the subspace dimension is known.

Monte Carlo simulations validate the effectiveness of GLR detectors in uncertain environments.

Abstract

This paper is devoted to the performance analysis of the detectors proposed in the companion paper 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 generalized likelihood ratio (GLR) detectors derived in [1] with estimate-and-plug (EP) approximations of the GLR detectors. Remarkably, 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 outperform EP detectors. If, instead, the signal subspace is known only by its dimension, the performance of GLR and EP detectors is very similar.