SNR Estimation in Linear Systems with Gaussian Matrices

TL;DR

This paper introduces a novel, highly accurate algorithm for estimating the SNR in linear systems with Gaussian matrices, using random matrix theory and ridge regression, requiring no prior statistical knowledge.

Contribution

The paper presents a new closed-form SNR estimation method for linear systems with Gaussian matrices and correlated signals, leveraging random matrix theory without prior distribution assumptions.

Findings

The proposed algorithm achieves high accuracy in SNR estimation.

Simulation results confirm the method's robustness and precision.

No prior statistical knowledge of signal or noise is needed.

Abstract

This paper proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results are provided, and show that the proposed method is very accurate.