## 1 Introduction  
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. This problem is encountered in different fields of engineering; for example, in telecommunications [1], in radar systems [2] and in smart-grid applications. Indeed, this study started from the need for accurate measurement of the SNR in a test-bed used for synchrophasor measurement before estimation of the parameters of the sinusoidal voltage [3, 4]. The same problem has been studied in [5], wherein [PERSON] et al. proposed an algorithm for SNR estimation based on autocorrelation and modified covariance methods for autoregressive spectral estimation and required the reliable estimate of the frequency of the sinusoid. 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 (\(M_{2}M_{4}\)-estimator). It does not require the complex sinusoid frequency estimate, and for this reason, it belongs to the class of blind SNR estimators and may find applications in all those cases where the frequency estimate may not be available or frequency may be varying over the observation interval. In recent years, moment-based SNR estimators have attracted the interest of researchers in the telecommunications field where second and fourth order moments based estimators have been employed for estimation of the SNR of modulated signals in additive white Gaussian noise and flat-fading channels. In [1, 8], for example, the SNR \(M_{2}M_{4}\)-estimator was proposed for phase-shift keying (PSK) modulated signals as a blind estimator that does not require the knowledge of transmitted data. In [9] more general moments-based SNR estimators were derived for multi-level constellations,such as generic quadrature amplitude modulation (QAM) constellations, and the SNR \(M_{2}M_{4}\)-estimator was derived as a special case of moment-based estimators that make use of higher-order moments. In [10] an estimator that uses also the sixth-order moment of the received data for non-constant modulus constellations was proposed in order to improve performances. Further extensions of the method for multilevel constellations were proposed in [11]. In [9; 10; 11] performances of the proposed estimators were theoretically studied and results based on asymptotic analyses were reported. 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. The proposed estimators belong to the class of the second-and-fourth-order moments estimators that can be obtained by application of the method of moments [7] and do not require the reliable frequency estimate, as in [5]. We derived a new general formula for even-order moments of the observed signal that is useful not only to provide the second and fourth moments required by the method of moments, but also for the study of statistical performances of the proposed estimators. Since asymptotic analyses carried out in [9; 10; 11] assume random signals in random noise and cannot immediately be extended to deterministic signals, we also derived a new general expression for covariance matrices useful for asymptotic analysis of performances of moment-based estimators when the signal corrupted by the noise is deterministic. Results from asymptotic analyses and Monte-Carlo simulations are presented along with the corresponding Cramer-Rao lower bounds (CRLB), and we reveal that the proposed estimators have good performances in a wide range of operating conditions. In same cases performances are very close to the optimum.