Power Minimization under Quality of Service Constraints for MIMO Systems with a RIS-based Transmitter

2026-08-04

AI Summary

This work addresses the problem of minimizing transmit power in reconfigurable intelligent surface (RIS)-assisted virtual multi-user MIMO systems under discrete phase shifts and PSK modulation, subject to quality-of-service constraints formulated as symbol error probability (SEP) or its union bound. To tackle this challenging discrete optimization problem, two efficient strategies are proposed: first, a partial branch-and-bound algorithm that significantly reduces computational complexity while preserving performance; second, for high-resolution RISs, a continuous relaxation approach that transforms the discrete problem into a constrained optimization over a complex oblique manifold, efficiently solved via bisection search. Numerical experiments demonstrate that the proposed methods substantially reduce transmit power across various SEP requirements, achieving an effective trade-off between power efficiency and computational complexity.

Abstract

This study investigates a virtual multiuser multiple-input multiple-output (MU-MIMO) system with PSK modulation, realized with a reconfigurable intelligent surface (RIS)-based transmitter. The study focuses on minimizing transmit power under quality-of-service (QoS) constraints while addressing the associated computational complexity. A discrete phase-shift RIS model is considered, and the power minimization problem is formulated in two scenarios. First, for QPSK user data, the symbol-error probability (SEP) is adopted as the QoS criterion. Second, for general $M$-PSK modulation, the union-bound SEP (UBSEP) is used to define the QoS constraints. Based on the considered formulations, a partial branch-and-bound (PBB) approach is developed, which improves on full branch-and-bound (FBB) methods in the sense of allowing for favorable complexity performance trade-offs. For the special case of high-resolution RIS, the discrete phase-shift set is approximated by its continuous counterpart, enabling the reformulation of the original problems as constrained optimizations on an oblique manifold, which are solved with reduced computational complexity with the proposed bisection method. Numerical results demonstrate the effectiveness of the proposed approaches in minimizing the transmit power for different SEP requirements and showcase the balance between power efficiency and computational complexity

Problem

• Power Minimization
• Quality of Service
• Reconfigurable Intelligent Surface
• MIMO Systems
• Symbol Error Probability

Innovation

• Reconfigurable Intelligent Surface (RIS)
• Power Minimization
• Symbol Error Probability (SEP)
• Partial Branch-and-Bound
• Oblique Manifold Optimization