Maximum Likelihood SNR Estimation of Linearly-Modulated Signals over Time-Varying Flat-Fading SIMO Channels

TL;DR

This paper introduces novel maximum likelihood estimators for instantaneous SNR over fast time-varying SIMO channels, applicable to linearly-modulated signals, with closed-form bias correction and an EM-based NDA approach validated by extensive simulations.

Contribution

It develops the first ML SNR estimators for fast-varying channels, including bias correction for DA and an EM-based NDA method applicable to any linearly-modulated signals.

Findings

Estimators closely match the CRLB across practical SNRs.

NDA estimator provides accurate soft symbol estimates.

Proposed methods outperform classical slow-varying channel techniques.

Abstract

In this paper, we tackle for the first time the problem of maximum likelihood (ML) estimation of the signal-to-noise ratio (SNR) parameter over time-varying single-input multiple-output (SIMO) channels. Both the data-aided (DA) and the non-data-aided (NDA) schemes are investigated. Unlike classical techniques where the channel is assumed to be slowly time-varying and, therefore, considered as constant over the entire observation period, we address the more challenging problem of instantaneous (i.e., short-term or local) SNR estimation over fast time-varying channels. The channel variations are tracked locally using a polynomial-in-time expansion. First, we derive in closed-form expressions the DA ML estimator and its bias. The latter is subsequently subtracted in order to obtain a new unbiased DA estimator whose variance and the corresponding Cram\'er-Rao lower bound (CRLB) are also derived in closed form. Due to the extreme nonlinearity of the log-likelihood function (LLF) in the NDA case, we resort to the expectation-maximization (EM) technique to iteratively obtain the exact NDA ML SNR estimates within very few iterations. Most remarkably, the new EM-based NDA estimator is applicable to any linearly-modulated signal and provides sufficiently accurate soft estimates (i.e., soft detection) for each of the unknown transmitted symbols. Therefore, hard detection can be easily embedded in the iteration loop in order to improve its performance at low to moderate SNR levels. We show by extensive computer simulations that the new estimators are able to accurately estimate the instantaneous per-antenna SNRs as they coincide with the DA CRLB over a wide range of practical SNRs.