Near-Field Codebook Design for IRS-Assisted mmWave Communication Systems

Large intelligent reflecting surfaces (IRSs) possess a large near-field (NF) range, which makes their configuration challenging. To reduce the potentially significant overhead associated with configuring these large IRSs, phase shift codebooks are a promising approach. However, most existing IRS codebooks focus on maximizing the beamforming gain of the IRS, rather than optimizing the signal-to-noise ratio (SNR) at the receiver, which is more critical to the quality of service (QoS). In this paper, we introduce an IRS codebook design that maximizes the minimum SNR within a target receiver volume by optimizing the IRS phase shifts. We observe that, in the considered NF range, maximizing the IRS reflection gain for the farthest surface of the target receiving volume is equivalent to maximizing the SNR within the entire volume. Based on this observation, we derive an analytical phase shift design, where each unit cell (UC) of the IRS focuses on a specific point. Next, we formulate a nonconvex optimization problem, for a second, improved codebook design, and find a local optimum for the minimum SNR based on sucessive convex approximation (SCA). The optimized design reveals a trade-off between the minimum SNR and the codebook size, while achieving excellent performance across the entire considered NF. Numerical evaluations show that both proposed designs outperform several baseline schemes from the literature.