Statistical Analysis of Antenna Array Systems with Perturbations in Phase, Gain and Element Positions

In this paper, we statistically analyze the effect of hardware impairments on power pattern of antenna array systems. We consider a linear array and formulate the stochastic beam pattern as a function of variations in phase, gain and element positions. By deriving a closed-form expression for the variance of the power pattern, we express how the performance of antenna array can be degraded in each angle, allowing for investigation of the role of each parameter in the final power pattern variations. The proposed closed-form expression serves as a tractable tool for analyzing the effect of perturbations in different settings.