Asymptotic Performances of a Signal-To-Noise Ratio Moment-Based Estimator for Real Sinusoids in Additive Noise

We considered the problem of the estimation of signal-to-noise ratio (SNR) with a real deterministic sinusoid with unknown frequency, phase and amplitude in additive Gaussian noise of unknown variance. A blind SNR estimator that does not require the knowledge of the instantaneous frequency of the sinusoid, through separate estimation of signal and noise power, was derived using the method of moments, a general method to derive estimators based on high-order moments. Statistical performances of the proposed estimators were studied theoretically through derivation of Cramer-Rao lower bounds (CRLBs) and asymptotic variances. Furthermore, results from Monte-Carlo simulations that confirm the validity of the theoretical analysis are presented along with some comments on the use of proposed estimators in practical applications.