A Hybrid Envelope-IQ Moment-Based Non-Data-Aided SNR Estimator for QPSK

In this work, we investigate non-data-aided (NDA) signal-to-noise ratio (SNR) estimation for quadrature phase-shift keying (QPSK) communications over the additive white Gaussian noise (AWGN) channel. We propose a moment-based estimator that exploits the 2nd and 4th-order moments of simultaneously the envelope and the complex values of the received signal. We show that the suggested estimator outperforms existing 2nd and 4th-order moment-based estimators and that it achieves asymptotically the non-data-aided normalized Cramér–Rao lower bound (NDA-NCRLB). Besides, we analytically justify the performance of the suggested estimator with respect to classical estimators, including in the presence of residual phase noise.

I. Introduction

Signal-to-noise ratio (SNR) estimation is a crucial step for digital receivers due to its usage in synchronization, symbol/sequence detection, error correction decoding, etc. SNR estimators can be classified into two main families, i) data-aided (DA) estimators which assume the prior knowledge of certain symbols (a.k.a. pilots), and ii) non-data-aided (NDA) estimators which do not assume any deterministic knowledge of the data. In this work, we will mostly be interested in NDA estimators since they exploit the whole received packet and are better suited for spectrally efficient communications. The rich literature of NDA SNR estimation highlights several strategies: maximum likelihood (ML)-based and Bayesian methods [1], [2], moment-based [3], [4], [5], [6], [7], cyclostationarity-based [8], expectation-maximization (EM)-based [9], [10], and entropy-based [11], to cite only these few.