Low-Complexity High-Resolution Frequency Estimation of Multi-Sinusoidal Signals

High-resolution frequency estimation is crucial for some applications. Accordingly, the present study proposes three high-performance computationally-efficient methods for high-resolution frequency estimators, which are designed based on a modified likelihood function. Traditional maximum likelihood based approaches for high-resolution frequency estimation are inefficient since the associated optimization problem is non-convex. Accordingly, in the first estimator proposed in this study, the amplitudes and frequencies of the multi-sinusoidal signals are estimated iteratively based on a simple linear Taylor approximation and a low-dimensional closed-form solution in every iteration. In the second estimator, the frequencies are determined directly using a primal decomposition approach and a gradient descent search method. Finally, a novel low-complexity parallel interference cancellation (PIC)-based frequency estimation approach is developed. The simulation results show that the proposed designs not only meet the Cramér-Rao lower bound (CRLB) in most cases of the conducted examples, but also possess lower computational complexity than existing state-of-the-art approaches.