Low-Complexity Beamforming Algorithms for IRS-Aided Single-User Massive MIMO mmWave Systems

This paper considers intelligent reflecting surface (IRS)-aided single-user (SU) massive multiple-input multiple-output (mMIMO) millimeter wave (mmWave) downlink communication system. We aim to maximize the achievable spectral efficiency by separately designing the passive beamforming and active precoding (combining) through a decoupling strategy to reduce computational complexity. We propose two algorithms for passive beamforming design, which are followed by singular value decomposition (SVD) of the effective channel matrix to generate the active precoding and combining matrices at the bases station (BS) and user equipment (UE), respectively. The first algorithm employs the SVD of the BS-IRS and the IRS-UE channel matrices to generate the unitary matrices. These matrices are used to develop the optimization problem, which is solved via a Riemannian conjugate gradient (RCG)-based algorithm, yielding a passive beamforming vector. In the second algorithm, we propose a greedy-search (GS)-based method to select the array response vectors and their corresponding path gains of the mmWave channels between the BS (IRS) and IRS (UE) required to formulate the optimization problem, which is also solved via the RCG-based algorithm, resulting in a passive beamforming vector. The simulation results show that the proposed schemes achieve an improved trade-off between the spectral efficiency and computational complexity.