Hybrid beamforming design with finite-resolution phase-shifters for frequency selective massive MIMO channels

Massive multiple-input multiple-output (MIMO) theoretical performance results have attracted the attention of the community due to the possibility of increasing the spectral efficiency in wireless communications. The performance potential is mainly conditioned to the use of digital beamforming techniques which demand one radio-frequency (RF) chain per antenna element. For large arrays, this implementation may result in high complexity, power consumption, and cost. To reduce the number of RF chains, we use a hybrid beamforming (HB) architecture of an analog beamformer implemented by using phase-shifters and a low-dimensional digital beamformer. The performance of the HB depends on the resolution of the phase-shifters. However, very few works in the literature take into account finite phase-shifters. In this paper, we address the problem of designing HB in frequency selective channels using finite-resolution phase-shifters. The strategy is to exploit the second-order statistics of the channel and a least-square formulation to obtain the discrete phase of each phase-shifter. The digital part is derived based on analog solution to maximize the single-user MIMO system sum-rate. This solution requires a number of RF chains compared to the rank of the spatial covariance matrix which is far lower than ones demanded to implement the full digital beamforming. The simulation results show that the proposed technique can achieve a sum-rate performance very close to that of the digital beamforming assuming low-rank channels.