# Beamforming Codebook Compensation for Beam Squint with Channel Capacity Constraint

## TL;DR

This paper addresses the challenge of beam squint in wideband millimeter wave beamforming, proposing a codebook design that compensates for beam squint to enhance channel capacity in phased array systems.

## Contribution

The paper introduces a novel codebook design algorithm that compensates for beam squint effects, improving channel capacity under bandwidth constraints.

## Key findings

- Beam squint reduces channel capacity in uniform linear arrays.
- The proposed codebook improves capacity by up to 17.8%.
- Denser codebooks are needed as bandwidth increases.

## Abstract

Analog beamforming with phased arrays is a promising technique for 5G wireless communication in millimeter wave bands. A beam focuses on a small range of angles of arrival or departure and corresponds to a set of fixed phase shifts across frequency due to practical hardware constraints. In switched beamforming, a discrete codebook consisting of multiple beams is used to cover a larger angle range. However, for sufficiently large bandwidth, the gain provided by the phased array is frequency dependent even if the radiation pattern of the antenna elements is frequency independent, an effect called beam squint. This paper shows that the beam squint reduces channel capacity of a uniform linear array (ULA). The beamforming codebook is designed to compensate for the beam squint by imposing a channel capacity constraint. For example, our codebook design algorithm can improve the channel capacity by 17.8% for a ULA with 64 antennas operating at bandwidth of 2.5 GHz and carrier frequency of 73 GHz. Analysis and numerical examples suggest that a denser codebook is required to compensate for the beam squint compared to the case without beam squint. Furthermore, the effect of beam squint is shown to increase as bandwidth increases, and the beam squint limits the bandwidth given the number of antennas in the array.