Low-Complexity Gradient-Based Algorithm for Phase-Only Pattern Synthesis

This study developed a gradient-based algorithm to synthesize arbitrary power patterns with only element phases. This algorithm does not rely on any general-purpose nonlinear solver and requires only a matrix computation toolbox; thus, the algorithm is compatible with different platforms. The algorithm locally finds the analytical gradient, and therefore reduces the time for computing the gradient. The pattern synthesis performance of the proposed algorithm was evaluated for linear arrays with continuous phase control, linear arrays with quantized phase control, and planar arrays with continuous phase control. The performance of the proposed algorithm was also compared with that of general-purpose optimization algorithms. For both linear and planar arrays, the proposed algorithm obtained solutions with comparable lower SLLs in small arrays, with improvement in SLL in large arrays and time-increasing rate with the array size. Therefore, the results of this study suggest that the proposed algorithm is highly suitable for generating radiation power patterns for large arrays.