The Extended Manifold for Antenna Arrays

The paper investigates a general parametric model for the manifold of polarization sensitive arrays based on representing each antenna by a collection of short dipoles. The manifold has a simple form consisting of an extended isotropic manifold, vertical and horizontal direction vectors and a constant non-square coupling matrix. The resulting manifold captures the effects of coupling, polarization and antenna characteristics. It provides an accurate representation of the analytic manifold which is based on electromagnetic theory. Three methods for computing the Coupling Matrix are described based on: (i) the current distributions in the antennas, (ii) its approximation by a sum of Kronecker products, and (iii) least-squares fit of the analytic and extended manifolds. The accuracy of these manifolds is illustrated by numerical examples.

I. Introduction

High-resolution signal processing techniques for antenna arrays have been a subject of extensive research for the past several decades. These techniques rely on knowledge of the “array manifold,” the vector of complex voltages measured at the output of an antenna array when an electromagnetic wave originating from a given direction (azimuth and elevation) impinges on the array [1], [2]. The array manifold depends on the antennas used in the array and their positions. The characteristics and locations of the antennas affect the electromagnetic coupling between antennas in the array, the sensitivity of the array to signal polarization, and the radiation pattern. Proper modeling of these effects is necessary in order to obtain a very accurate array manifold which is essential for high-resolution array processing [3], [4].