In this paper, we consider hybrid beamforming designs for multiuser massive multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) systems. Aiming at maximizing the weighted spectral efficiency, we propose one alterna
ting maximization framework where the analog precoding is optimized by Riemannian manifold optimization. If the digital precoding is optimized by a locally optimal algorithm, we obtain a locally optimal alternating maximization algorithm. In contrast, if we use a weighted minimum mean square error (MMSE)-based iterative algorithm for digital precoding, we obtain a suboptimal alternating maximization algorithm with reduced complexity in each iteration. By characterizing the upper bound of the weighted arithmetic and geometric means of mean square errors (MSEs), it is shown that the two alternating maximization algorithms have similar performance when the user specific weights do not have big differences. Verified by numerical results, the performance gap between the two alternating maximization algorithms becomes large when the ratio of the maximal and minimal weights among users is very large. Moreover, we also propose a low-complexity closed-form method without iterations. It employs matrix decomposition for the analog beamforming and weighted MMSE for the digital beamforming. Although it is not supposed to maximize the weighted spectral efficiency, it exhibits small performance deterioration compared to the two iterative alternating maximization algorithms and it qualifies as a good initialization for iterative algorithms, saving thereby iterations.
In this correspondence, we analytically characterize the benefit of digital processing in uplink massive multiple-input multiple-output (MIMO) with sub-connected hybrid architecture. By assuming that the number of radio frequency (RF) chains is equal
to that of users, we characterize achievable rates of both pure analog detection and hybrid detection under the i.i.d. Rayleigh fading channel model. From the derived expressions, we discover that the analog processing can outperform the hybrid processing using the maximal ratio combining (MRC) or zero-forcing (ZF) criterion in cases under some engineering assumptions. Performance comparison of the schemes are presented under tests with various numbers of users and numbers of antennas at the base station.
