Reconfigurable intelligent surfaces (RISs) have huge potential to improve spectral and energy efficiency in future wireless systems at a minimal cost. However, early prototype results indicate that deploying hundreds or thousands of reflective elements is necessary for significant performance gains. Motivated by this, our study focuses onlarge-scaleRIS-assisted multi-user (MU) multiple-input multiple-output (MIMO) systems. In this context, we propose an efficient algorithm to jointly design the precoders at the base station (BS) and the phase shifts at the RIS to maximize the weighted sum rate (WSR). In particular, leveraging an equivalent lower-dimensional reformulation of the WSR maximization problem, we derive a closed-form solution to optimize the precoders using the successive convex approximation (SCA) framework. While the equivalent reformulation proves to be efficient for the precoder optimization, we offer numerical insights into why the original formulation of the WSR optimization problem is better suited for the phase shift optimization. Subsequently, we develop a scaled projected gradient method (SPGM) and a novel line search procedure to optimize RIS phase shifts. Notably, we show that the complexity of the proposed methodscales linearly with the number of BS antennas and RIS reflective elements. Extensive numerical experiments demonstrate that the proposed algorithm significantly reduces both time and computational complexity while achieving higher WSR compared to baseline algorithms.

We present a low-complexity algorithm for jointly designing active and passive beamforming to maximize the weighted sum-rate (WSR) in downlink RIS-assisted communication systems. We exploit an equivalent, lower-dimensional reformulation of the WSR maximization problem to derive a closed-form solution for active beamforming optimization using the successive convex approximation (SCA) framework. For passive beamforming, we propose a scaled projected gradient method (SPGM) algorithm and a novel line search technique to improve performance. Notably, we demonstrate that the complexity of the proposed method scales linearly with the number of BS antennas and RIS reflective elements. Extensive numerical experiments demonstrate that our proposed algorithm significantly reduces both run time and computational complexity, while enhancing WSR performance over known benchmarks.

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.

The hybrid precoding and combining algorithms for mmWave massive multiple-input multiple-output (MIMO) systems must consider the trade-off between the complexity and performance of the system. Unfortunately, because of the unit-norm constraint imposed by the use of phase shifters, the optimization of the radio frequency (RF) precoder and combiner becomes a non-convex problem. As a consequence, the algorithm for hybrid precoding and combining design often incurs high complexity. This paper proposes a low-complexity algorithm for hybrid precoding and combining design based on array response vectors. The proposed algorithm considers a decoupled optimization scheme between the RF and baseband domains for the spectral efficiency-maximization problem. In the RF domain, we propose an incremental successive selection method to find a subset of array response vectors from a dictionary, which forms the RF precoding/combining matrices. For the digital domain, we employ singular-value decomposition (SVD) of the low-dimensional effective channel matrix to generate the digital baseband precoder and combiner. Through numerical simulation, we show that the proposed algorithm achieves nearoptimal performance with 89.9 % - 99.4% complexity reduction compared to the conventional state-of-the-art hybrid precoding and combining algorithm.