Non-iterative Frequency Estimator Based on Approximation of the Wiener-Khinchin Theorem

Abstract

A closed form frequency estimator is derived for estimating the frequency of a complex exponential signal, embedded in white Gaussian noise. The new estimator consists of the fast Fourier transform (FFT) as the coarse estimation and the phase of autocorrelation lags as the fine-frequency estimator. In the fine-frequency estimation, autocorrelations are calculated from the power-spectral density of the signal, based on the Wiener-Khinchin theorem. For simplicity and suppressing the effect of noise, only the spectrum lines around the actual tone are used. Simulation results show that, the performance of the proposed estimator is approaching the Cramer-Rao Bound (CRB), and has a lower SNR threshold compared with other existing estimators.