Analog Beamforming with Low Resolution Phase Shifters

In this letter, we consider analog beamforming using low resolution phase shifters for millimeter waves communications. We propose a hierarchical codebook design, where the beamforming vectors in the codebook are grouped into multiple levels and the preferred beamforming vector at each level is constructed to approximate an amplitude beamforming gain mask by using a low complexity local search algorithm. We show, by simulations, that the proposed codebook using low resolution phase shifters outperforms the existing schemes using high resolution phase shifters.