Abstract
The moment-based signal-to-noise (SNR) estimator was proposed for a complex sinusoidal signal with a deterministic but unknown phase corrupted by additive Gaussian noise by Sekhar and Sreenivas. The authors studied its performances only through numerical examples and concluded that the proposed estimator is asymptotically efficient and exhibits finite sample super-efficiency for some combinations of signal and noise power. In this paper, we derive the analytical asymptotic performances of the proposed SNR estimator, and we show that, contrary to what it has been concluded by Sekhar and Sreenivas, the proposed estimator is neither (asymptotically) efficient nor super-efficient. We also show that when dealing with deterministic signals, the covariance matrix needed to derive asymptotic performances must be explicitly derived as its known general form for random signals cannot be extended to deterministic signals. Numerical examples are provided whose results confirm the analytical findings.
Highlights
In [1], the authors address the problem of estimating the signal-to-noise ratio (SNR) in the case of a complex sinusoidal signal with a deterministic but unknown phase corrupted by additive Gaussian noise
Care is needed when analytical asymptotic performances are derived in the deterministic case, since, in general, it is not possible to extend the results obtained for the random signals to deterministic signals, and in this paper, we extend to the complex case what has been already shown in the case of real deterministic a sinusoid in [10]
The paper is organized as follows: in Section 2, it is shown the derivation of evenorder moments and estimators for signal and noise power as well as the SNR; in Section 3, asymptotic variances for all the estimators under investigation are derived; details of derivations are presented in Appendices A and B; we provide some numerical examples in Section 4; in Section 5, we draw the conclusions
Summary
The authors consider a signal model very similar to the M-PSK vector model for the AWGN channel, with the only difference being the deterministic nature of the unknown phase Under this assumption, the derivation in [1] is quite cumbersome. In [6,7,8], the performances of the proposed momentbased estimators are studied in terms of asymptotic variance and CRLBs. care is needed when analytical asymptotic performances are derived in the deterministic case, since, in general, it is not possible to extend the results obtained for the random signals to deterministic signals, and in this paper, we extend to the complex case what has been already shown in the case of real deterministic a sinusoid in [10]. The paper is organized as follows: in Section 2, it is shown the derivation of evenorder moments and estimators for signal and noise power as well as the SNR; in Section 3, asymptotic variances for all the estimators under investigation are derived; details of derivations are presented in Appendices A and B; we provide some numerical examples in Section 4; in Section 5, we draw the conclusions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
