An Improved Frequency Estimator Using Auxiliary DFT Samples: CRB Performance Across All Signal Lengths

Abstract

Accurate frequency estimation is a pivotal problem in signal processing with numerous applications including communications, radar, and power systems. Although substantial research efforts have been directed toward better frequency estimators, the main challenges remain intact. The performance of an ideal estimator should be exactly on the Cr & aacute;mer-Rao bound (CRB) for large signal lengths and very close to the CRB for small signal lengths, while its computational cost should be minimal. In this article, we propose an accurate and computationally efficient discrete Fourier transform (DFT)-based frequency estimation algorithm that meets all these challenges. The proposed algorithm leverages the ratio of two auxiliary DFT coefficients, requiring only three iterations to converge for typical practical signal lengths. We optimize the parameters to ensure that our algorithm achieves the best performance for both large and small signal lengths. We also present a slightly different version of our algorithm that increases its breakdown threshold performance. Our results demonstrate that this method outperforms existing estimators, particularly in low signal-to-noise ratio conditions and with shorter signal lengths, while maintaining a low computational load. Extensive simulations validate theoretical claims, indicating that the proposed algorithm represents a significant advance in frequency estimation for diverse applications.