This article presents a study on achievable rate optimization for large stacked intelligent metasurfaces (SIMs) using statistical channel state information (CSI). The research focuses on a multiuser architecture operating in the wave domain, where the goal is to maximize the downlink achievable rate. Unlike previous works that relied on instantaneous CSI, this study uses statistical CSI to reduce overhead and improve efficiency. The authors propose an alternating optimization (AO) algorithm to optimize the phase shifts of the SIM and the allocated transmit power. The system model includes a base station (BS) with multiple antennas communicating with single-antenna user equipments (UEs) through a SIM that performs wave-based processing. The paper also provides a detailed analysis of the achievable rate and the optimization problem, including the derivation of the gradient for the optimization process. Simulation results demonstrate the effectiveness of the proposed approach, showing improvements in the sum spectral efficiency (SE) with larger SIMs and the benefits of using statistical CSI over instantaneous CSI in terms of reduced overhead. The study concludes that the proposed method achieves lower computational complexity and processing latency, making it suitable for future 6G networks.This article presents a study on achievable rate optimization for large stacked intelligent metasurfaces (SIMs) using statistical channel state information (CSI). The research focuses on a multiuser architecture operating in the wave domain, where the goal is to maximize the downlink achievable rate. Unlike previous works that relied on instantaneous CSI, this study uses statistical CSI to reduce overhead and improve efficiency. The authors propose an alternating optimization (AO) algorithm to optimize the phase shifts of the SIM and the allocated transmit power. The system model includes a base station (BS) with multiple antennas communicating with single-antenna user equipments (UEs) through a SIM that performs wave-based processing. The paper also provides a detailed analysis of the achievable rate and the optimization problem, including the derivation of the gradient for the optimization process. Simulation results demonstrate the effectiveness of the proposed approach, showing improvements in the sum spectral efficiency (SE) with larger SIMs and the benefits of using statistical CSI over instantaneous CSI in terms of reduced overhead. The study concludes that the proposed method achieves lower computational complexity and processing latency, making it suitable for future 6G networks.