Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.7.2023.4.02

Volume 7, Issue 4, 1 August 2023, Pages 467-485

 

Abstract. Beamforming is one of the most important techniques to enhance the quality of signal in array sensor signal processing, and the performance of a beamformer is usually related to the design of array configuration and beamformer weight. Recently, it was realized that the sparsity of the filter coefficients can reduce the cost of signal acquisition and communication, and as a consequence, the sparse broadband beamformer design attracts more and more attentions. In this paper, we first propose a proximal sparse beamformer design model which obtains the sparse and robust filter coefficients through solving a composite optimization problem. The objective function of the model is the sum of a least squares term, a proximal term, and an -regularization term. The least squares term reflects the data fidelity; the proximal term, whose center is predetermined via a simple least squares, enhances the robustness; while the term ensures the sparsity of the solution. This model not only maintains the authenticity of the least squares solution, but also ensures the sparsity of the filter coefficients. A significant feature of the model is that we use `partial’ data to obtain the least squares solution and use another `partial’ data to construct the data fidelity term, which can evidently decrease the computational cost. For solving the composite optimization problem, we tailor several popular algorithms, such as the alternating direction method of multipliers, the forward-backward splitting method, and the Douglas-Rachford splitting method. Numerical results observably exhibit the improvements of the proposed approach over existing works in both effectiveness and efficiencies.

 

How to Cite this Article:
Y. Chen, Z. Li, X. Cai, D. Han, Sparse broadband beamformer design via proximal optimization techniques, J. Nonlinear Var. Anal. 7 (2023), 467-485.