Optimization-based Phase-shift Codebook Design for Large IRSs

In this letter, we focus on large intelligent reflecting surfaces (IRSs) and propose a new codebook construction method to obtain a set of pre-designed phase-shift configurations for the IRS unit cells. Since the complexity of online optimization and the overhead for channel estimation scale with the size of the phase-shift codebook, the design of small codebooks is of high importance. We consider both continuous and discrete phase-shift designs and formulate the codebook construction as optimization problems. To solve the optimization problems, we propose an optimal algorithm for the discrete phase-shift design and a locally optimal solution for the continuous design. Simulation results show that the proposed algorithms facilitate the construction of codebooks of different sizes and with different beamwidths. Moreover, the performance of the discrete phase-shift design with 2-bit quantization is shown to approach that of the continuous phase-shift design. Finally, our simulation results show that the proposed designs enable large transmit power savings compared to the existing linear and quadratic codebook designs.