Hybrid Analog and Digital Beamforming for RIS-Assisted mmWave Communications

Reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) communications has been envisioned as a prominent technology for future wireless networks, since it is capable of simultaneously providing abundant spectrum resources and favorable propagation environments. The small wavelength at mmWave bands also enables the widespread use of large antenna arrays, of which the hybrid beamforming structure has emerged as a cost-effective solution. In this paper, we aim to minimize the sum-mean-square-error (sum-MSE) in the RIS-assisted mmWave multiuser multiple input multiple output (MU-MIMO) system by jointly optimizing the hybrid analog-digital precoders and the RIS reflection matrix. We demonstrate that the role of RIS in assisting mmWave communications can be completely replaced by a large-scale Kronecker-structured hybrid array. Moreover, an accelerated Riemannian gradient algorithm using majorization minimization technique is proposed to tackle the unit-modulus constrained analog precoder/RIS design. Under the assumption of perfect channel state information (CSI), we firstly consider the single-user MIMO (SU-MIMO) setup and propose an effective alternating minimization (AM) procedure to characterize the system performance limit. Moreover, a two-stage scheme is developed for low-complexity implementation. This AM procedure is then extended to the general MU-MIMO scenario. In addition, we develop a novel enhanced regularized zero-forcing (ERZF) scheme for simultaneously combating strong noise in the low-SNR regime and mitigating multi-user interference (MUI) in the high-SNR regime. The optimality of our proposed algorithms is validated for some simplified practical scenarios. Numerical results illustrate that the proposed algorithms outperform existing benchmark schemes in terms of the actual complexity and performance.