Beamforming Gain with Nonideal Phase Shifters

TL;DR

This paper develops a universal framework to quantify the beamforming gain loss caused by nonideal phase shifters, revealing that the shortfall depends on the convex hull perimeter of feasible coefficients and becomes maximal with many antennas.

Contribution

It introduces a fundamental geometric characterization of beamforming gain shortfall due to nonideal phase shifters applicable across various configurations.

Findings

Shortfall is determined by the convex hull perimeter of feasible coefficients.

The shortfall approaches the maximum as the number of antennas increases.

The framework applies to transmitter, receiver, and reconfigurable surfaces.

Abstract

This research sets forth a universal framework to characterize the beamforming gain achievable with arbitrarily nonideal phase shifters. Precisely, the maximum possible shortfall relative to the gain attainable with ideal phase shifters is established. Such shortfall is shown to be fundamentally determined by the perimeter of the convex hull of the set of feasible beamforming coefficients on the complex plane. This result holds regardless of whether the beamforming is at the transmitter, at the receiver, or at a reconfigurable intelligent surface. In i.i.d. fading channels, the shortfall hardens to the maximum possible shortfall as the number of antennas grows.