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In this study, we analyze the codebook design used for analog beamforming.Analog beamforming and combining suffer from a subspace sampling limitation,that is, the receiver cannot directly observe the channel coefficients;instead, the receiver observes a noisy version of their weighted combination.To resolve this, the transmitter and the receiver usually collaborate todetermine the best beamformer combiner pair during the beam-sweeping process.This is done by evaluating a limited number of codewords chosen from apre-defined codebook. In this study, we propose a new framework inspired by thegeneralized Lloyd algorithm to design analog beamforming codebooks thatoptimize various performance metrics including the average beamforming gain,the outage, and the average data rate. The flexibility of our framework enablesus to design beamforming codebooks for any array shapes including uniformlinear and planar arrays. The other practical complexity in analog beamformingis the low resolution of the phase shifters. Therefore, we have extended ouralgorithm to create quantized codebooks that outperform the existing codebooksin literature. We have also provided extensive simulations to verify thesuperiority of our proposed codebook as compared with the existing codebooks.

A New Codebook Design for Analog Beamforming in Millimeter-wave Communication