Sum-Rate Maximization in Holographic MIMO Communications with Stacked Intelligent Metasurfaces

In this paper, we investigate holographic multiple-input multiple-output communications in a multi-user network assisted by stacked intelligent metasurface (SIM) elements. We use discrete phase shifters as the SIM elements and explore the sum-rate maximization problem in a downlink scenario. Unlike past studies, we assume that the transmit powers at the base station follow a discrete set of power levels, addressing circuit design limitations in generating continuous-valued powers. We propose an alternative optimization technique to iteratively optimize the transmit powers and SIM elements. Specifically, we introduce the filled function (FF) optimization method to optimize the SIM elements and apply a modified version of the FF method to obtain the optimal transmit powers. We assess our optimization methods against state-of-the-art benchmarks, including successive refinement (SR) and mapped projected gradient ascent (MPGA) for SIM elements, as well as water-filling for optimal transmit powers. Simulation results show that our proposed method outperforms SR and MPGS in terms of sum-rate, even though it uses discrete transmit powers.