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.