Single-Tone Frequency Estimation by Weighted Least-Squares Interpolation of Fourier Coefficients

Frequency estimation of a single complex exponential signal embedded in additive white Gaussian noise is a major topic of research in many engineering areas. This work presents further investigations on this problem with regards to the fine estimation task, which is accomplished through a suitable interpolation of the discrete Fourier transform (DFT) coefficients of the observation data. The focus is on fast real-time applications, where iterative estimation methods can hardly be applied due to their latency and complexity. After deriving the analytical expression of the Cramér-Rao bound (CRB) for general values of the system parameters, we present a new DFT interpolation scheme based on the weighted least-squares (WLS) rule, where the optimum weights are precomputed through a numerical search and stored in the receiver. In contrast to many existing alternatives, the proposed method can employ an arbitrary number of DFT samples so as to achieve a good trade-off between system performance and complexity. Simulation results and theoretical analysis indicate that, at sufficiently high signal-to-noise ratios, the estimation accuracy is close to the relevant CRB at any value of the frequency error. This provides some advantage with respect to non-iterative competing schemes, without incurring any penalty in processing requirement.