Hierarchical Codebook-Based Analog Beamforming Design for SIM-Assisted Communication Systems

Abstract

Stacked intelligent metasurface (SIM) can perform signal processing in the wave domain by intelligently optimizing the phase shifts of transmissive meta-elements on each layer. However, it typically requires high overhead to acquire channel state information. In this letter, we propose a hierarchical codebook design for SIM-assisted multiuser multiple-input single-output (MISO) systems. Specifically, we first introduce a beam alignment problem where we design the hierarchical codewords for uniform planar arrays using the alternating optimization algorithm. Each layer of the codewords searches the entire angular domain to avoid the decrease in beam alignment accuracy caused by beam aliasing. Secondly, based on these predesigned codewords, we propose a channel training-based protocol that identifies the optimal beam direction through cumulative selection counts. Finally, numerical simulations are provided to evaluate the performance of the proposed scheme.