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.

中文翻译：

---

通过 ADMM 进行高效的离网频率估计，具有残差收缩和学习增强


为了解决离网频率估计中的挑战，例如计算复杂性和稀疏频率恢复，在本文中，我们提出了一种新的数据驱动离网频率估计方法。具体来说，在计算复杂度方面，首先通过将基于模型的交替方向乘子法 （ADMM） 的迭代过程转化为浅层神经网络架构来制定离网频率估计问题，以提高效率和收敛性。此外，在该框架内，用于频域变换的字典是通过酉矩阵约束自适应学习的。因此，探索和分析了深度学习理解信号背后的物理机制的能力。此外，在稀疏频率恢复方面，残差收缩模块确保了频率表示的实例特定稀疏性。与现有的黑盒网络框架不同，我们基于 ADMM 的框架提供了可解释性。最后，通过大量的仿真和比较，与传统的基于迭代的方法相比，所提方法表现出优异的估计精度和计算效率。