Theoretical and Experimental Assessment of Large Beam Codebook at mmWave Devices: How Much is Enough?

TL;DR

This paper analyzes how large mmWave beam codebooks can be effectively reduced to a few steering vectors without significant performance loss, balancing beam gain and search time.

Contribution

It provides a closed-form expression for angular coverage and demonstrates experimentally that small codebooks can approximate large ones effectively.

Findings

Large codebooks can be significantly reduced in size.

Few steering vectors suffice for near-maximum gain.

Theoretical and experimental validation supports codebook size reduction.

Abstract

Modern millimeter wave (mmWave) transceivers come with a large number of antennas, each of which can support thousands of phase shifter configurations. This capability enables beam sweeping with fine angular resolution, but results in large codebook sizes that can span more than six orders of magnitude. On the other hand, the mobility of user terminals and their randomly changing orientations require constantly adjusting the beam direction. A key focus of recent research has been on the design of beam sweeping codebooks that balance a trade-off between the achievable gain and the beam search time, governed by the codebook size. In this paper, we investigate the extent to which a large codebook can be reduced to fewer steering vectors while covering the entire angular space and maintaining performance close to the maximum array gain. We derive a closed-form expression for the angular coverage range of a steering vector, subject to maintaining a gain loss within \(\gamma\) dB (e.g., 2\, dB) with respect to the maximum gain achieved by an infinitely large codebook. We demonstrate, both theoretically and experimentally, that a large beam-steering codebooks (such as the \(1024^{16}\) set considered in our experiment) can be reduced to just a few steering vectors. This framework serves as a proof that only a few steering vectors are sufficient to achieve near-maximum gain, challenging the common belief that a large codebook with fine angular resolution is essential to fully reap the benefits of an antenna array.