The Influence of Gain and Phase Mismatches on Beam Patterns in Phased Arrays

Practical implementations of phased arrays suffer from per-antenna gain, phase, and delay mismatches, which can significantly worsen the maximum sidelobe level (SLL) of beampatterns. The existing literature either analyzes specific structured mismatch patterns or derives per-angle marginal statistics under random mismatches, which fail to characterize global beampattern metrics such as the maximum SLL. To address this limitation, we propose a frequency-domain framework in which the beampattern is described by a tapering-window-dependent base function evaluated along a deformation determined by the array architecture and signal bandwidth. This formulation enables a spectral analysis of mismatches, revealing that element-wise errors generate weighted replicas of the ideal beampattern whose amplitudes are given by the discrete Fourier transform of the mismatch sequence. Building on this insight, we derive an approximation of the maximum SLL distribution under random gain and phase mismatches. The resulting expressions enable yield-oriented design and rapid design-space exploration without relying on computationally intensive Monte-Carlo simulations.