Stacked Intelligent Metasurfaces for Multiuser Downlink Beamforming in the Wave Domain

TL;DR

This work introduces stacked intelligent metasurfaces (SIM) to perform transmit beamforming directly in the electromagnetic wave domain for downlink multiuser MISO systems, eliminating Digital Beamforming and high-resolution DACs at the BS. It formulates a non-convex joint optimization of transmit powers and SIM phase shifts under a total power budget and discrete phase constraints, and proposes an alternating-optimization algorithm that combines a damped iterative water-filling for power allocation with phase-shift solvers based on successive refinement and projected gradient ascent. The results show that increasing the SIM depth and aperture yields large sum-rate gains (up to ~200% over conventional MISO with the same number of antennas), with discrete-phase implementations approaching continuous performance as the phase resolution increases (e.g., b≥4). The work highlights the potential of wave-domain processing via SIMs for energy-efficient wireless networks and provides a practical framework with convergence and complexity analyses and publicly available code.

Abstract

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}.

Figures (13)

• Figure 1: Comparison of (a) conventional and (b) SIM-based multiuser MISO wireless systems, where binary phase shift keying modulation is adopted.
• Figure 2: Simulation setup for the considered SIM-assisted multiuser downlink MISO system.
• Figure 3: Sum rate $R$ versus the number of metasurface layers $L$ ($N=49$, $b=2$, $M=K=4$, $P_{\text{T}}=10$ dBm).
• Figure 4: Sum rate $R$ versus the number of meta-atoms $N$ on each metasurface layer ($b=2$, $L=7$, $M=K=4$, $P_{\text{T}}=10$ dBm).
• Figure 5: Sum rate $R$ versus the number of quantization bits $b$ ($N=49$, $L=7$, $M=K=4$, $P_{\text{T}}=10$ dBm).

Theorems & Definitions (7)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Remark 6
• Remark 7