Blind Signal-to-Noise Ratio Estimation of Real Sinusoid in Additive Noise

Abstract

We consider the problem of 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. The method of moments, a general method to derive estimators based on high-order moments, is used to derive 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. Cramer-Rao lower bounds (CRLBs) are also derived for estimators of signal and noise power and then, for SNR estimators. We show through numerical simulations the statistical performances of the estimators, that we compare to the corresponding CRLBs, and discuss their use in practical applications.