Signal-to-noise ratio estimation using higher-order moments

• Published in: Signal processing 2006-04, Vol.86 (4), p.716-732
• Main Authors: Sekhar, S. Chandra, Sreenivas, T.V.
• Format: Article
• Language: English
• Subjects: Applied sciences; Cramer–Rao bound; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Information, signal and communications theory; Instantaneous frequency; Mean square error; Moments; Phase signal; Signal and communications theory; Signal, noise; Signal-to-noise ratio; Telecommunications and information theory
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2005.06.003

We consider the problem of estimation of the signal-to-noise ratio (SNR) of an unknown deterministic complex phase signal in additive complex white Gaussian noise. The phase of the signal is arbitrary and is not assumed to be known a priori unlike many SNR estimation methods that assume phase synchronization. We show that the moments of the complex sequences exhibit useful mean-ergodicity properties enabling a “method-of-moments” (MoM)-SNR estimator. The Cramer–Rao bounds (CRBs) on the signal power, noise variance and logarithmic-SNR are derived. We conduct experiments to study the efficiency of the SNR estimator. We show that the estimator exhibits finite sample super-efficiency/inefficiency and asymptotic efficiency, depending on the choice of the parameters. At 0 dB SNR, the mean square error in log-SNR estimation is approximately 2 dB 2 . The main feature of the MoM estimator is that it does not require the instantaneous phase/frequency of the signal, a priori. Infact, the SNR estimator can be used to track the instantaneous frequency (IF) of the phase signal. Using the adaptive pseudo-Wigner–Ville distribution technique, the IF estimation accuracy is the same as that obtained with perfect SNR knowledge and 8–10 dB better compared to the median-based SNR estimator.