Transmit Equal Gain Beamforming Using Lattice Quantizers

We investigate the use of lattices in phase quantizers and equal gain beamformers. We propose proper scaling methods so that the Voronoi regions of all lattice points are regular in the phase quantizers. As a result, existing fast algorithm for various lattices can be applied directly. In addition, we derive the number B of quantization bits with the proposed scaling. We found that the proposed scaling leads to efficient quantization bits. Some of the proposed scaling can even achieve integer B. Moreover, we analyze the mean square error for the proposed phase quantizers. Simulation results corroborate the theoretical results.