Hierarchical Codebook Design and Analytical Beamforming Solution for IRS-Assisted Communication

• Published in: IEEE transactions on wireless communications Vol. 23; no. 8; pp. 8924 - 8938
• Main Authors: Liu, Xiyuan, Wu, Qingqing, Hu, Die, Wang, Rui, Wu, Jun
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Array signal processing; Arrays; Beamforming; Channel estimation; Complexity; Continuity (mathematics); continuous array factor; hierarchical codebook; Intelligent reflecting surface; MIMO communication; Misalignment; Phased arrays; Reconfigurable intelligent surfaces; Search algorithms; Sidelobes; Time complexity; Training; Wireless communication
• ISSN: 1536-1276; 1558-2248
• DOI: 10.1109/TWC.2024.3357112

In intelligent reflecting surface (IRS) assisted communication, beam search is usually time-consuming as the multiple-input multiple-output (MIMO) of IRS is usually very large. The hierarchical codebook is a widely accepted method for reducing the complexity of searching time. The performance of this method strongly depends on the design scheme of beamforming of different beamwidths. In this paper, a non-constant phase difference (NCPD) beamforming algorithm is proposed. To implement the NCPD algorithm, we first model the phase shift of IRS as a continuous function and then determine the parameters of the continuous function through the analysis of its array factor. Then, we propose a hierarchical codebook and two beam training schemes, namely the joint searching (JS) scheme and direction-wise searching (DWS) scheme by using the NCPD algorithm which can flexibly change the width, direction, and shape of the beam formed by the IRS array. Numerical results show that the NCPD algorithm is more accurate with smaller side lobes, and also more stable on IRS of different sizes compared to other wide beam algorithms. The misalignment rate of the beam formed by the NCPD method is significantly reduced. The time complexity of the NCPD algorithm is constant, thus making it more suitable for solving the beamforming design problem with practically large IRS.