Design of Data-Aided SNR Estimator Robust to Frequency Offset for MPSK Signals

Data-aided (DA) signal-to-noise ratio (SNR) estimation is required especially at low SNR. The conventional maximum likelihood (ML) DA SNR estimator requires perfect carrier phase estimation and frequency recovery. In this paper, we propose a novel carrier frequency robust DA SNR estimator with its improved variant using autocorrelation of received MPSK symbols. Computer simulations are used to examine their performance in terms of mean estimation value (MEV) and normalized mean square error (NMSE). For the example system in simulations, the MEV of proposed estimator is accurate enough with normalized frequency error on the order of symbol rate. However, its NMSE can not reach DA normalized Cramer-Rao bound (NCRB) even with large observatory length, whereas its NMSE may perform a little worse at high SNR for short pilot symbols. On the other hand, fortunately the its improved variant can reach NCRB with enough pilot symbols. What's more, the proposed DA SNR estimators can operate under large frequency errors or before the frequency recovery unit with baud rate. The implementation complexity is also analyzed.