Low-Complexity Design of Polynomial Beamformers for Uniform Linear Arrays

Polynomial beamformers with uniform linear arrays (ULAs) have shown effective dynamic beam-steering capability over a wide azimuthal range via real-time parameter tuning. Nevertheless, this is at the cost of substantial design and implementation complexities in beamformer system architectures. To mitigate the computational limitations inherent to the existing design method, this paper proposes a low-complexity optimization method. The proposed method initiates a theoretical exploration of the intrinsic symmetry properties in standardized array configurations, a critical but frequently underutilized characteristic embedded within the existing design method. Through rigorous analysis, we reveal symmetric interdependencies among beamformer coefficients. Based on this finding, we develop a symmetry-driven design method that exploits these relationships to reduce computational load. By reducing approximately 50% of redundant coefficients from the optimization parameter space, the proposed method achieves significant complexity reduction while maintaining beamforming operational integrity. Simulation results demonstrate that the proposed method is superior to the existing counterpart with comparable computational complexity.