Scaling Achievable Rates in SIM-aided MIMO Systems with Metasurface Layers: A Hybrid Optimization Framework

We investigate the achievable rate (AR) of a stacked intelligent metasurface (SIM)-aided holographic multiple-input multiple-output (HMIMO) system by jointly optimizing the SIM phase shifts and power allocation. Contrary to earlier studies suggesting that the AR decreases when the number of metasurface layers increases past a certain point for \emph{a fixed SIM thickness}, our findings demonstrate consistent increase. To achieve this, we introduce two problem formulations: one based on directly maximizing the AR (RMax) and the other focused on minimizing inter-stream interference (IMin). To solve the RMax problem, we apply Riemannian manifold optimization (RMO) and weighted minimum mean square error (WMMSE) methods to optimize the SIM phase shifts and power allocation alternately. For the IMin problem, we derive an efficient algorithm that iteratively updates each meta-atom's phase shift using a closed-form expression while keeping others fixed. Our key contribution is integrating these two approaches, where the IMin solution initializes the SIM phase shifts in the first algorithm. This hybrid strategy enhances AR performance across varying numbers of metasurface layers. Simulation results demonstrate that the proposed algorithms outperform existing benchmarks. Most importantly, we show that increasing the number of metasurface layers while keeping the SIM thickness fixed leads to significant AR improvements.

On the Joint Beamforming Design for Large-scale Downlink RIS-assisted Multiuser MIMO Systems

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 on \emph{large-scale } RIS-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 method \emph{scales 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.