Improved statistical model on the effect of random errors in the phase and amplitude of element excitations on the array radiation pattern

Due to errors in the phase and amplitude of element excitations in an antenna array, the array radiation pattern gets distorted. In order to derive statistical results on this distortion, specifically on determining the probability of exceeding a certain sidelobe level (SLL), it is often assumed that the magnitude of the array amplitude pattern follows a Rician distribution. It is shown that the Rician distribution implies two assumptions, and therefore, a more general Beckmann distribution is proposed to describe the distribution of the magnitude of the array amplitude pattern. Using Monte Carlo simulations, it is shown that the use of a Beckmann distribution outperforms the Rician distribution. Also, the seemingly counterintuitive result that the maximum probability of exceeding a certain SLL, in general, does not have to be at the angle where the highest sidelobe in the error-free case is located, is obtained. Due to this result, the importance of using an angular probability plot is emphasized. Furthermore, a physical explanation for the observed seemingly counterintuitive behavior is given.