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

2026-01-21

AI Summary

This work addresses the challenge of efficient beamforming in stacked intelligent metasurface (SIM)-assisted multiuser MISO downlink systems under statistical channel state information (CSI) and discrete phase-shift constraints. To tackle this, a novel joint optimization method for transmit power allocation and discrete phase shifts is proposed. By leveraging the weighted minimum mean square error (WMMSE) framework and alternating optimization to decouple the problem, closed-form iterative updates are derived using Lagrange multipliers and the alternating direction method of multipliers (ADMM). This approach achieves, for the first time, statistically CSI-based efficient SIM beamforming under practical hardware limitations. The proposed scheme reduces computational complexity by 50× compared to semidefinite relaxation methods and attains over 85% of the performance achievable with continuous phase shifts using only 1-bit phase quantization, thereby significantly alleviating reliance on instantaneous CSI and high-precision phase control.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Web Mining and Content Analysis: Web data generation and simulation

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.

Problem

• Beamforming
• Discrete Phase Shifts
• Statistical CSI
• SIM
• Multiuser MISO

Innovation

• Stacked Intelligent Metasurfaces
• Discrete Phase Shift
• Statistical CSI
• WMMSE-ADMM Optimization
• Low-Complexity Beamforming