Fast Array Response Adjustment With Phase-Only Constraint: A Geometric Approach

This paper presents a geometric approach to fast array response adjustment with phase-only constraint. The devised algorithm can precisely and rapidly adjust the array response of a given point by only tuning the excitation phases of a preassigned weight vector. We geometrically reformulate the phase-only array response adjustment as a polygon construction problem, which can be solved by edge rotation in the complex plane. On this basis, we carry out a detailed analysis of the solution of polygon construction and specify the range of the feasible phase. To avoid the undesirable pattern distortion and obtain less pattern variations in the uncontrolled region, an effective and analytical phase determination approach is presented. The proposed algorithm provides an analytical solution and guarantees a precise phase-only adjustment without pattern distortion. In addition, our algorithm does not impose any restriction on the given weight vector and has a low computational complexity. Representative examples are presented to demonstrate the effectiveness of the proposed algorithm under various situations.