Efficient off-grid frequency estimation via ADMM with residual shrinkage and learning enhancement

To address the challenges in off-grid frequency estimation, such as computational complexity and sparse frequency recovery, in this paper, we propose a novel data-driven approach for off-grid frequency estimation. Specifically, in terms of computational complexity, the off-grid frequency estimation problem is first formulated by transforming the iterative process of the model-based alternating direction method of multipliers (ADMM) into a shallow neural network architecture for improving efficiency and convergence. Moreover, within the framework, the dictionary used for frequency domain transform is adaptively learned with a unitary matrix constraint. Thus the ability of deep learning to understand the physical mechanisms behind signals is explored and analyzed. Besides, in terms of sparse frequency recovery, the instance-specific sparsity for frequency representation is ensured by a residual shrinkage module. Unlike existing black-box network frameworks, our ADMM-based framework offers interpretability. Finally, through extensive simulations and comparisons, the proposed method demonstrates superior estimation accuracy and computational efficiency compared with traditional iteration-based methods.