Finite Beam Depth Analysis for Large Arrays

TL;DR

This paper analyzes how the shape and size of large antenna arrays influence the near-field beam depth, deriving analytical expressions and revealing dependencies on array geometry and orientation for improved spatial multiplexing.

Contribution

It provides the first analytical characterization of 3 dB beam depth in large arrays, linking array shape and size to near-field beam behaviors and approximating non-broadside patterns.

Findings

BD increases towards end-fire directions.

Array shape affects beam depth order: ULA, circular, square.

Approximation of non-broadside beams by smaller broadside arrays.

Abstract

Most wireless communication systems operate in the far-field region of antennas and antenna arrays, where waves are planar and beams have infinite depth. When antenna arrays become electrically large, it is possible that the receiver is in the radiative near-field of the transmitter, and vice versa. Recent works have shown that near-field beamforming exhibits a finite depth, which enables a new depth-based spatial multiplexing paradigm. In this paper, we explore how the shape and size of an array determine the near-field beam behaviors. In particular, we investigate the $3$ dB beam depth (BD), defined as the range of distances where the gain is greater than half of the peak gain. We derive analytical gain and BD expressions and prove how they depend on the aperture area and length. For non-broadside transmissions, we find that the BD increases as the transmitter approaches the end-fire direction of the array. Furthermore, it is sufficient to characterize the BD for a broadside transmitter, as the beam pattern with a non-broadside transmitter can be approximated by that of a smaller/projected array with a broadside transmitter. Our analysis demonstrates that the BD can be ordered from smallest to largest as ULA, circular, and square arrays.