Energy-Efficient SIM-assisted Communications: How Many Layers Do We Need?

The stacked intelligent metasurface (SIM), comprising multiple layers of reconfigurable transmissive metasurfaces, is becoming an increasingly viable solution for future wireless communication systems. In this paper, we explore the integration of SIM in a multi-antenna base station for application to downlink multi-user communications, and a realistic power consumption model for SIM-assisted systems is presented. Specifically, we focus on maximizing the energy efficiency (EE) for hybrid precoding design, i.e., the base station digital precoding and SIM wave-based beamforming. Due to the non-convexity and high complexity of the formulated problem, we employ the quadratic transformation method to reformulate the optimization problem and propose an alternating optimization (AO)-based joint precoding framework. Specifically, a successive convex approximation (SCA) algorithm is adopted for the base station precoding design. For the SIM wave-based beamforming, two algorithms are employed: the high-performance semidefinite programming (SDP) method and the low-complexity projected gradient ascent (PGA) algorithm. In particular, the results indicate that while the optimal number of SIM layers for maximizing the EE and spectral efficiency differs, a design of 2 to 5 layers can achieve satisfactory performance for both. Finally, numerical results are illustrated to evaluate the effectiveness of the proposed hybrid precoding framework and to showcase the performance enhancement achieved by the proposed algorithm in comparison to benchmark schemes.