Efficient Beamforming for Discrete SIM-Aided Multiuser Systems Under Statistical CSI

Abstract: Stacked Intelligent Metasurfaces (SIM) have emerged as a revolutionary architecture for next-generation wireless communications, offering wave-domain signal processing capabilities with significantly reduced hardware complexity compared to conventional systems. However, most existing SIM research assumes continuous phase shifts and perfect instantaneous channel state information (CSI), which are impractical due to hardware discrete phase shift constraints and prohibitive pilot overhead. This paper presents a joint power allocation and discrete phase shift optimization framework for SIM-aided multiuser multiple-input single-output(MISO) downlink systems under statistical CSI. We formulate the achievable sum rate maximization problem considering practical discrete phase constraints and derive a closed-form expression for the average achievable rate under statistical CSI. To tackle the resulting non-convex optimization problem, we decouple the problem by using the weighted minimum mean square error (WMMSE) algorithm and alternating optimization (AO). Subsequently, we utilize the Lagrangian multiplier method and alternating direction method of multipliers (ADMM) to obtain closed-form iterative solutions. Our simulations demonstrate that the proposed algorithm reduces computational complexity by a factor of 50 compared to semi-definite relaxation (SDR) methods, , while maintaining over 85% of the continuous phase shift performance with only 1-bit quantization, highlighting its feasibility for low-cost hardware systems.