Hybrid Analog-Digital Beamforming: How Many RF Chains and Phase Shifters Do We Need?

Abstract

This paper considers hybrid beamforming (HB) for downlink multiuser massive MIMO systems with frequency selective channels. For this system, first we quantify the required number of radio frequency (RF) chains and phase shifters (PSs) such that the proposed HB achieves the same performance as that of the digital beamforming (DB) which utilizes N (number of transmitter antennas) RF chains. We show that the performance of the DB can be achieved with our HB just by utilizing rt RF chains and 2rt(N − rt + 1) PSs, where rt ≤ N is the rank of the combined digital precoder matrices of all sub-carriers. Second, we provide a simple and novel approach to reduce the number of PSs with only a negligible performance degradation. Numerical results reveal that only 20 − 40 PSs per RF chain are sufficient for practically relevant parameter settings. Finally, for the scenario where the deployed number of RF chains (Na) is less than rt, we propose a simple user scheduling algorithm to select the best set of users in each sub-carrier. Simulation results validate theoretical expressions, and demonstrate the superiority of the proposed HB design over the existing HB designs in both flat fading and frequency selective channels.