Shrinkage-based biased signal-to-noise ratio estimator using pilot and data symbols for linearly modulated signals

In diverse engineering problems including wireless communications, the estimate of the signal-to-noise ratio (SNR) is required. In this study, the authors develop a shrinkage-based SNR estimator in the data-aided and non-data-aided schemes for higher M-ary phase-shift-keying (M ≥ 8) and quadrature amplitude modulations. The observed Cramér-Rao lower bound is used as the variance of the expectation maximisation estimator to determine the optimal shrinkage factor. Simulation results show that the normalised mean-squared error of the proposed method is lower than that of the expectation maximisation method for low and moderate SNR conditions.