Abstract
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.
Highlights
We consider the problem of estimation of the signal-to-noise ratio (SNR) when a deterministic real sinusoid with unknown parameters is corrupted by additive white Gaussian noise
In this paper we propose a moment-based SNR estimator for a deterministic real sinusoid in additive noise that is formed by the ratio of the estimators of the signal power and noise power
It is possible to obtain with the method of moments, blind estimators for signal power, noise power and signal-to-noise ratio when a deterministic real sinusoid is corrupted by additive white
Summary
We consider the problem of estimation of the signal-to-noise ratio (SNR) when a deterministic real sinusoid with unknown parameters is corrupted by additive white Gaussian noise. The case of complex rather than real deterministic sinusoids in additive noise has been addressed in [6], wherein an SNR estimator derived with the method of moments [7] that makes use of second and fourth order moments was proposed (M2 M4 -estimator). We derived a new general formula for even-order moments of the observed signal that is useful to provide the second and fourth moments required by the method of moments, and for the study of statistical performances of the proposed estimators. This paper extends some of the results presented in [12] by providing new general formulas for any even-order moments and covariance matrices of the vectors of sample moments, and by studying statistical performances of the proposed estimators with theoretical asymptotic analyses that confirm the numerical results obtained with Monte-Carlo simulations. The paper is organized as follows: in Section 2 we derive the estimators starting from a general result on the even-order moment for the given signal model; in Section 3 we derive the Cramer–Rao lower bounds for all proposed estimators; in Section 4 the asymptotic performances of the proposed estimators are derived; in Section 5 results from Monte-Carlo simulations are presented along with comparisons with the CRLBs and the asymptotic performances; in Section 6 we draw the conclusions
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