Biased SNR estimation using pilot and data symbols in BPSK and QPSK systems

In wireless communications, knowledge of the signal-to-noise ratio is required in diverse communication applications. In this paper, we derive the variance of the maximum likelihood estimator in the data-aided and non-data-aided schemes for determining the optimal shrinkage factor. The shrinkage factor is usually the constant that is multiplied by the unbiased estimate and it increases the bias slightly while considerably decreasing the variance so that the overall mean squared error decreases. The closed-form biased estimators for binary-phase-shift-keying and quadrature-phase-shift-keying systems are then obtained. Simulation results show that the mean squared error of the proposed method is lower than that of the maximum likelihood method for low and moderate signal-to-noise ratio conditions.