A KL-Domain Estimator-Correlator Framework for Gaussian Signal Detection in WGN and Unknown Channels

Abstract

This paper addresses the problem of Gaussian random signal detection in white Gaussian noise under unknown frequency-selective multipath channels. While the classical Estimator-Correlator (EC) receiver achieves theoretical optimality, its reliance on perfect a-priori knowledge of the signal covariance matrix leads to severe performance degradation when the channel is unknown. To resolve this limitation, we propose a robust adaptive Karhunen-Loeve (KL) domain EC framework that exploits a short training block to perform an online Eigenvalue Decomposition (EVD), dynamically estimating the effective received signal subspace without requiring explicit channel inversion. An asymptotic performance analysis is conducted using large deviations theory, characterizing the error exponent decay rates as a function of spectral distortion between the true and estimated covariance structures. Monte Carlo simulations validate the proposed framework under a severe frequency-selective multipath channel, demonstrating improved ROC performance, convergence behavior, and robustness compared to the classical mismatched EC baseline.