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

Bora Bozkurt, Hasan Atalay Gunel, Mohaned Chraiti, Ibrahim Hokelek, Ali Gorcin, Ali Ghrayeb

TL;DR

The paper tackles the challenge of beam sweeping in mmWave systems with large antenna arrays by deriving a closed-form angular-coverage bound for steering vectors under a gain-loss constraint γ and by formulating a set-cover-based offline codebook refinement. It proves that large codebooks can be pruned to a handful of steering vectors while preserving near-maximum array gain for both ULA and URA, with α* determining the coverage bounds. The authors support theory with experiments using a 4×4 URA at 25.1 GHz, showing that the codebook size can drop from $(2^M)^N$ to as few as 14 steering vectors while maintaining the gain gap within γ dB in most cases. This work demonstrates a practical, side-information-free approach to balance search efficiency and array performance, enabling faster beam alignment in mobile mmWave scenarios.

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 \(γ\) 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.

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

TL;DR

The paper tackles the challenge of beam sweeping in mmWave systems with large antenna arrays by deriving a closed-form angular-coverage bound for steering vectors under a gain-loss constraint γ and by formulating a set-cover-based offline codebook refinement. It proves that large codebooks can be pruned to a handful of steering vectors while preserving near-maximum array gain for both ULA and URA, with α* determining the coverage bounds. The authors support theory with experiments using a 4×4 URA at 25.1 GHz, showing that the codebook size can drop from to as few as 14 steering vectors while maintaining the gain gap within γ dB in most cases. This work demonstrates a practical, side-information-free approach to balance search efficiency and array performance, enabling faster beam alignment in mobile mmWave scenarios.

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 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 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.
Paper Structure (18 sections, 2 theorems, 63 equations, 6 figures, 3 tables, 2 algorithms)

This paper contains 18 sections, 2 theorems, 63 equations, 6 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivations
  3. Related Work
  4. CSI-based beam-steering
  5. Codebook based beam-steering
  6. Problem Statement
  7. Contributions
  8. System Model
  9. Angular coverage of a steering vector
  10. The case of ULA
  11. The case of an URA
  12. Codebook refinement as a set cover problem
  13. The ULA Case
  14. The URA Case
  15. Experimental Results
  16. ...and 3 more sections

Key Result

Lemma 1

Considering moderately large number of antennas $N$ (e.g., higher than six), there exists a constant $\alpha^{*}$ such that the following inequality holds for $\alpha^{*}$ is the smallest strictly positive root of

Figures (6)

  • Figure 1: Illustration of the effect of the beam sweeping step on the array gain.
  • Figure 2: Achievable-to-maximum array gain as a function of the angle deviation $\Delta$ for different values of $\theta$.
  • Figure 3: Azimuthal-elevation vs Cartesian coordinates systems
  • Figure 4: Experiment environments
  • Figure 5: Achievable vs. Maximum Array Gain: The achievable gain is obtained using the refined codebook $\zeta_R$, while the maximum gain is determined by scanning the entire initial codebook $\zeta$.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Lemma 1
  • proof
  • Remark 1
  • Remark 2
  • Lemma 2
  • proof