Loss-Aware Wave-Domain Beamforming With Stacked Intelligent Metasurfaces for URLLC Systems

Abstract

This paper investigates a stacked intelligent metasurface (SIM)-assisted multiuser multiple-input single-output (MISO) downlink ultra-reliable and low-latency communication (URLLC) system under the finite blocklength (FBL) regime. By leveraging multiple programmable metasurface layers, SIM enables direct wave-domain beamforming with enhanced electromagnetic wave control, which makes it particularly attractive for reliable and delay-sensitive communications. We propose a joint optimization framework for transmit power allocation, user blocklength, and phase shifts across the stacked metasurface layers, with the objective of maximizing the sum rate under the transmit power constraint while accounting for SIM insertion loss. The resulting problem is non-convex due to the coupled optimization variables and the FBL rate expression. To tackle this problem, an alternating optimization (AO) algorithm is developed, where successive convex approximation is adopted for transmit power and blocklength optimization, while projected gradient ascent is employed for SIM phase shift design. Numerical results show that the proposed design achieves up to an 140% higher sum FBL rate than conventional transmission without SIM. In addition, the optimized blocklength allocation provides approximately an 8% gain over equal blocklength allocation, while the impact of practical insertion loss becomes more pronounced in deeper SIMs, with the degradation reaching about 17% for the six-layer configuration. Moreover, the proposed algorithm exhibits fast convergence, making it suitable for low-latency wireless applications and highlighting the potential of SIM-enabled wave-domain beamforming for next-generation mission-critical wireless networks.