A Low-complexity Beampattern Shaping Method for Large-scale Rectangular Phased Arrays

To address the high computational complexity of beamforming in large-scale rectangular phased arrays, this paper proposes a low-complexity beampattern shaping method based on dimension decoupling, which markedly enhances design efficiency and beampattern adjustment flexibility. By fully exploiting the configuration characteristics of rectangular arrays, an analytical beamforming expression is derived that decouples the azimuth and elevation steering vectors. This transformation converts the traditional high-dimensional weight vector design problem into a joint optimization of two low-dimensional weight vectors, thereby substantially reducing computational complexity. On this basis, an optimization model is formulated that minimizes the peak sidelobe level under constraints on beam levels and noise output power. To solve the resultant optimization problem, an iterative algorithm based on the proximal alternating direction method of multipliers is developed, and sufficient conditions for algorithmic convergence are rigorously derived to ensure solution stability and reliability. Simulation results demonstrate that the proposed method substantially improves computational efficiency and enables flexible adjustment of mainlobe width and null depth according to prior information. Furthermore, it achieves a precise trade-off between peak sidelobe suppression and signal-to-noise ratio loss, exhibiting excellent potential for engineering applications.