Statistical Model for Approximating Gains of Arrays With Unequal Normally Distributed Errors

Abstract

This study presents a statistical model for approximating the gains of arrays with normally distributed errors. Based on Taylor expansion, the array gains were approximated using the generalized chi-square variables, after which the estimations were verified using Monte Carlo simulations. The proposed model can also be applied to more complex problems such as radiated phases, cascaded circuits, arrays with pointing errors, and line-of-sight (LOS) channels between arrays. The mean and variance of the array gains were evaluated using analytical expressions and simplified generalized chi-square variables, and the variables were found to produce high accuracy in cases of small errors. Unlike traditional models, the proposed statistical model can both approximate the gains of arrays with unequal element errors and estimate other errors using second-order Taylor polynomials, thus showing great flexibility in managing complex problems.