On the 2D Beampattern Optimization of Sparse Group-Constrained Robust Capon Beamforming with Conformal Arrays

Abstract

To overcome the problems of the high sidelobe levels and low computational efficiency of traditional Capon-based beamformers in optimizing the two-dimensional (elevation–azimuth) beampatterns of conformal arrays, in this paper, we propose a robust Capon beamforming method with sparse group constraints that is solved using the alternating-direction method of multipliers (ADMM). A robustness constraint based on worst-case performance optimization (WCPO) is imposed on the standard Capon beamformer (SCB) and then the sparse group constraints are applied to reduce the sidelobe level. The constraints are two sparsity constraints: the group one and the individual one. The former was developed to exploit the sparsity between groups based on the fact that the sidelobe can be divided into several different groups according to spatial regions in two-dimensional beampatterns, rather than different individual points in one-dimensional (azimuth-only) beampatterns. The latter is considered to emphasize the sparsity within groups. To solve the optimization problem, we introduce the ADMM to obtain the closed-form solution iteratively, which requires less computational complexity than the existing methods, such as second-order cone programming (SOCP). Numerical examples show that the proposed method can achieve flexible sidelobe-level control, and it is still effective in the case of steering vector mismatch.