Stacked Intelligent Metasurfaces for Multiuser Downlink Beamforming in the Wave Domain

Intelligent metasurface has recently emerged as a promising technology that enables the customization of wireless environments by harnessing large numbers of low-cost reconfigurable scattering elements. However, prior studies have predominantly focused on single-layer metasurfaces, which have limitations in terms of wave-domain processing capabilities due to practical hardware limitations. In contrast, this paper introduces a novel stacked intelligent metasurface (SIM) design. Specifically, we investigate the integration of SIM into the downlink of a multiuser multiple-input single-output (MISO) communication system, where an SIM, consisting of a multilayer metasurface structure, is deployed at the base station (BS) to facilitate transmit beamforming in the electromagnetic wave domain. This eliminates the need for conventional digital beamforming and high-resolution digital-to-analog converters at the BS. To this end, an optimization problem is formulated to maximize the sum rate of all user equipments by jointly optimizing the transmit power allocation at the BS and the wave-based beamforming at the SIM, subject to constraints on the transmit power budget and discrete phase shifts. Furthermore, we propose a computationally efficient algorithm for solving the formulated joint optimization problem and elaborate on the potential benefits of employing SIM in wireless networks. Numerical results are illustrated to corroborate the effectiveness of the proposed SIM-enabled wave-based beamforming design and to evaluate the performance improvement achieved by the proposed algorithm compared to various benchmark schemes. It is demonstrated that considering the same number of transmit antennas, the proposed SIM-based system achieves about 200\% improvement in terms of sum rate compared to conventional MISO systems. The code for this paper is available at \url{https://github.com/JianchengAn}.