Efficient Hybrid A/D Beamforming for Millimeter-Wave Systems Using Butler Matrices

Hybrid analog/digital (A/D) beamforming architectures are low complexity alternatives to fully digital designs in large antenna setups. Recent research efforts have been set out to find low-complexity algorithms, which have low implementation complexity in the analog domain. In this paper, we propose a two-stage hybrid precoding design assuming hardware constraints that avoid the use of adaptive phase-shifters (PSs) by introducing a novel combination of Butler matrices (BMs) to feed a uniform planar array (UPA). With several fixed beams, we propose an algorithm to design the analog precoding matrix in the first stage, while in the second stage, hybrid-beamforming (HBF)-weighted minimum mean square error (WMMSE) is proposed for baseband precoding by taking into account the analog precoding matrix designed in the first stage. The proposed algorithm shows fast convergence, thanks to the analog precoder design, which helps the HBF-WMMSE algorithm to converge within a few iterations. Compared with the classical matched filter (MF) and minimum mean square error (MMSE) solutions, HBF-WMMSE outperforms the latter in terms of sum-rate, especially in the low signal-to-noise-ratio (SNR) regime. Simulation results further show that the partially connected Butler matrices (PCBMS) approach implemented with fixed-PSs exhibit superior energy-efficiency while maintaining higher spectral-efficiency as compared to the partially connected analog phase shifting (PCAPS) network implemented with variable-PSs.