Stacked intelligent metasurface (SIM), which consists of multiple layers of intelligent metasurfaces, is emerging as a promising solution for future wireless communication systems. In this timely context, we focus on broadcast multiple-input multiple-output (MIMO) systems and aim to characterize their energy efficiency (EE) performance. To explore the potential of SIM, we consider both dirty paper coding (DPC) and linear precoding (LP) and formulate the corresponding EE maximization problems. For DPC, we employ the broadcast channel (BC)-multiple-access channel (MAC) duality to obtain an equivalent problem, and optimize users' covariance matrices using the successive convex approximation (SCA) and Dinkelbach's methods. Since the phase shift optimization problem of the SIM meta-elements is one of extremely large size, we adopt a conventional projected gradient-based method for its simplicity. A similar approach is followed for the case of LP. Simulation results show that the proposed optimization methods for the considered SIM-based systems can significantly improve the EE, compared to conventional counterparts. Also, we demonstrate that the number of SIM meta-elements and their distribution across the SIM layers have a significant impact on both the achievable sum-rate and EE performance.

翻译：堆叠智能超表面（SIM）由多层智能超表面构成，正成为未来无线通信系统的一种前景广阔的解决方案。在此背景下，本文聚焦于广播多输入多输出（MIMO）系统，旨在刻画其能效（EE）性能。为探索SIM的潜力，我们同时考虑了脏纸编码（DPC）和线性预编码（LP），并构建了相应的EE最大化问题。对于DPC，我们利用广播信道（BC）-多址信道（MAC）对偶性获得等价问题，并采用逐次凸逼近（SCA）和Dinkelbach方法优化用户的协方差矩阵。由于SIM超表面单元的相移优化问题规模极大，我们采用传统的基于投影梯度的方法以简化计算。对于LP情况也遵循了类似的处理方法。仿真结果表明，与传统方案相比，所提出的基于SIM系统的优化方法能显著提升EE。同时，我们证明了SIM超表面单元的数量及其在SIM各层中的分布对可达和速率与EE性能均有显著影响。