Stochastic Method of Moments (SMoM) Analysis of Wire Antenna Arrays With Random Elements Locations

In this article, we propose a full-wave numerical approach called stochastic method of moments (SMoM), for analyzing the effects of uncertainties in the locations of elements in a random antenna array on its performance characteristics. Using SMoM with subdomain basis functions converts the governing mixed potential integral equation to a matrix equation consisting of closed-form functions in terms of the random parameters. We then apply MacLaurin’s series expansions on the derived matrix equation to find the stochastic current distributions on the array elements with controllable accuracy using different orders of MacLaurin’s series. In this way, the mean values and standard deviations of the current distributions of array elements, and their other performance characteristics can be determined easily. The proposed method enjoys fast computation as well as controllable accuracy, and its results are compared with those obtained by the Monte Carlo method for verification.

I. Introduction

Uncertainty in the geometrical parameters of microwave circuits and elements of antenna arrays can significantly affect their electromagnetic responses and outputs [1], [2]. For this reason, analyzing the stochastic performance of these structures has been of great interest to many researchers. One of the very first investigations in analyzing random antenna arrays with randomly spaced elements has been carried out by Lo [3] in his remarkable contribution. Although mutual coupling between elements plays a significant role in the response of a random antenna array, it has been neglected in that contribution and also in many other articles (see [4]–[6] for instance). One of the first studies on the effects of mutual couplings in a random array using a circuit model was given [7].