An Efficient Low-Complexity Method to Calculate Hybrid Beamforming Matrices for mmWave Massive MIMO Systems

In the context of a massive MIMO system, the number of RF chains increases prohibitively. To solve the problem, hybrid beamforming (BF) has been proposed. Nevertheless, the amplitude constraint of the analog part in hybrid BF limits achieving the optimal performance given by the optimal digital BF. Some studies have been conducted recently to relax the amplitude constraint by deploying multiple phase shifters and switches (that select phase shifters) in the hybrid beamforming structures. The tremendous number of switches in the structure makes the problem of switch state selection very complex. In this paper, we propose an efficient low-complexity algorithm to obtain the optimal switch states. In the proposed algorithm, we decompose the main problem into sub-ones to reduce the complexity and solve the problem using a finite search space. The results of our study suggest that the optimal solution will be attainable by searching through less than 1% of the search space, if the number of phase levels exceeds 14. Moreover, the proposed algorithm has the potential to perfectly implement linear beamformers, designed for fully digital architectures, in a hybrid structure, while applying the minimum number of RF chains. Finally, the simulation results prove the efficiency of the algorithm and confirm the sufficiency of the analog part of the BF to achieve the optimal digital BF performance just by applying a few number of fixed phase shifters.