Hierarchical Codebook Design for Beam Alignment in Terahertz Ultra-Massive MIMO Systems

Terahertz (THz) communication systems are promising solutions for meeting the rapidly growing data traffic demand driven by an increasing number of Internet of Things (IoT) devices. Despite the potential of THz communication systems, they have the disadvantage of extremely high beam training overhead. Hierarchical beam training has been proposed as a technique to reduce this overhead. To perform beam alignment successfully while reducing overhead, it is important to design a wide beam, i.e., a low-resolution beam identical to the ideal beam, which has the shape of a rectangular function. While several conventional wide beams, obtained by solving optimization problems, closely approximate the ideal beam, it remains unclear whether designing the beam to closely resemble the ideal beam, without achieving an identical match, is truly effective in reducing beam misalignment. Motivated by this, we explore the feasibility of designing a beam identical to the ideal beam pattern and evaluate whether closely resembling the ideal beam pattern is effective in mitigating beam misalignment. Furthermore, we propose a novel codebook design scheme based on second-order cone programming (SOCP) for THz ultra-massive multiple input multiple output (UM-MIMO) systems to reduce beam misalignment in hierarchical beam training. This scheme introduces two additional criteria to the conventional codebook design problem, specifically addressing the considerations of worst-case detection gain and coverage-edge gain, which are directly aimed at mitigating beam misalignment. Additionally, we present a low-complexity codebook design approach for real-time implementation. Numerical results demonstrate that the proposed codebook reduces beam misalignment effectively.