  Stacked intelligent metasurface (SIM) is an emerging design that consists of
multiple layers of metasurfaces. A SIM enables holographic multiple-input
multiple-output (HMIMO) precoding in the wave domain, which results in the
reduction of energy consumption and hardware cost. On the ground of multiuser
beamforming, this letter focuses on the downlink achievable rate and its
maximization. Contrary to previous works on multiuser SIM, we consider
statistical channel state information (CSI) as opposed to instantaneous CSI to
overcome challenges such as large overhead. Also, we examine the performance of
large surfaces. We apply an alternating optimization (AO) algorithm regarding
the phases of the SIM and the allocated transmit power. Simulations illustrate
the performance of the considered large SIM-assisted design as well as the
comparison between different CSI considerations.
