On Threshold SNR in Estimating the Frequency and Phase of a Noisy Single Sinusoid

The paper investigates the signal-to-noise ratio (SNR) threshold effect in estimating the frequency and phase of a single sinusoid over the additive white Gaussian noise. This is done by making use of the results on the time-domain, phase-based estimator and the additive observation phase noise (AOPN) models developed in the work of Fu and Kam (2013). Specifically, the relationship between the threshold SNR and the similarity/dissimilarity of the Tikhonov distribution model of the AOPN to the corresponding Gaussian approximation is studied from three different but relevant aspects, namely, the series convergence, the Kullback-Leibler (KL) divergence and the AOPN variance. The interconnection that exists among these three aspects is revealed. In comparison to the mean-square-error-based approach, the AOPN-based approach proposed here has an advantage that it can lead to an analytical result on the performance of threshold SNR.