Digital-PLL Assisted Frequency Estimation with Improved Error Variance

In this paper we present a novel frequency estimation technique, assisted by an imperfect second order arctan based Digital Phase-Locked Loop (D-PLL), for complex single sinusoidal signals in additive white Gaussian noise. The imperfect loop contains the frequency information in its phase error process, at steady state, which is then used to estimate the frequency after the signal has been acquired by the D-PLL. For N samples, this particular estimator has a lower bound on the frequency error variance proportional to 1/N which is different to the well known Maximum Likelihood (ML) estimator that has a lower bound proportional to 1/N³ known as the Cramer-Rao bound (CRB). However, for given combinations of the loop parameters of the D-PLL, the error variance of the proposed estimator gives an improvement over the CRB for small values of N. We also present some detailed noise analysis on the proposed frequency estimator and derive a lower bound for the frequency error variance.