On the Number of RF Chains and Phase Shifters, and Scheduling Design with Hybrid Analog-Digital Beamforming

This paper considers hybrid beamforming (HB) for downlink multiuser massive multiple input multiple output (MIMO) systems with frequency selective channels. For this system, first we determine 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 $r_t$ RF chains and $2r_t(N-r_t + 1)$ PSs, where $r_t \leq N$ 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 $(N_a)$ is less than $r_t$, 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.Comment: IEEE Transactions on Wireless Communications (Minor Revision

Low-Complexity Hybrid Beamforming for Massive MIMO Systems in Frequency-Selective Channels

Hybrid beamforming for frequency-selective channels is a challenging problem as the phase shifters provide the same phase shift to all of the subcarriers. The existing approaches solely rely on the channel's frequency response and the hybrid beamformers maximize the average spectral efficiency over the whole frequency band. Compared to state-of-the-art, we show that substantial sum-rate gains can be achieved, both for rich and sparse scattering channels, by jointly exploiting the frequency and time domain characteristics of the massive multiple-input multiple-output (MIMO) channels. In our proposed approach, the radio frequency (RF) beamformer coherently combines the received symbols in the time domain and, thus, it concentrates signal's power on a specific time sample. As a result, the RF beamformer flattens the frequency response of the "effective" transmission channel and reduces its root mean square delay spread. Then, a baseband combiner mitigates the residual interference in the frequency domain. We present the closed-form expressions of the proposed beamformer and its performance by leveraging the favorable propagation condition of massive MIMO channels and we prove that our proposed scheme can achieve the performance of fully-digital zero-forcing when number of employed phase shifter networks is twice the resolvable multipath components in the time domain.Comment: Accepted to IEEE Acces