Globally Optimal Resource Allocation Design for Discrete Phase Shift IRS-Assisted Multiuser Networks with Perfect and Imperfect CSI

TL;DR

This work tackles globally optimal resource allocation for IRS-assisted multiuser MISO systems with discrete phase shifts under both perfect and imperfect CSI. It develops a generalized Benders decomposition (GBD) framework to achieve globally optimal joint BS beamforming and discrete IRS phase design, and complements it with low-complexity successive convex approximation (SCA) algorithms that converge to local optima. For robust operation, it extends the framework to norm-bounded CSI errors using a robust SINR formulation with S-Procedure, providing both GBD-based and penalty-based SCA solutions. The results show that the GBD methods achieve global optima and establish performance upper bounds, while the SCA methods offer fast convergence with substantial gains over state-of-the-art alternating optimization, especially as the number of IRS elements grows. Overall, the proposed approaches enable reliable, power-efficient IRS-aided communications with practical discrete phase shifters and demonstrate robustness to CSI uncertainty.

Abstract

Intelligent reflecting surfaces (IRSs) are a promising low-cost solution for achieving high spectral and energy efficiency in future communication systems by enabling the customization of wireless propagation environments. Despite the plethora of research on resource allocation design for IRS-assisted multiuser wireless communication systems, the optimal design and the corresponding performance upper bound are still not fully understood. To bridge this gap in knowledge, in this paper, we investigate the optimal resource allocation design for IRS-assisted multiuser multiple-input single-output systems employing practical discrete IRS phase shifters. In particular, we jointly optimize the beamforming vector at the base station and the discrete IRS phase shifts to minimize the total transmit power for the cases of perfect and imperfect channel state information (CSI) knowledge. To this end, two novel algorithms based on the generalized Benders decomposition (GBD) method are developed to obtain the globally optimal solution for perfect and imperfect CSI, respectively. Moreover, to facilitate practical implementation, we propose two corresponding low-complexity suboptimal algorithms with guaranteed convergence by capitalizing on successive convex approximation (SCA). In particular, for imperfect CSI, we adopt a bounded error model to characterize the CSI uncertainty and propose a new transformation to convexify the robust quality-of-service constraints. Our numerical results confirm the optimality of the proposed GBD-based algorithms for the considered system for both perfect and imperfect CSI. Furthermore, we unveil that both proposed SCA-based algorithms can attain a locally optimal solution within a few iterations. Moreover, compared with the state-of-the-art solution based on alternating optimization, the proposed low-complexity SCA-based schemes achieve a significant performance gain.

Figures (11)

• Figure 1: An IRS-assisted multiuser MISO system comprising $K=2$ users.
• Figure 2: Flowchart of the algorithms proposed for the case of perfect CSI.
• Figure 3: Flowchart of the algorithms proposed for the case of imperfect CSI.
• Figure 4: IRS-assisted wireless network topology adopted for simulations.
• Figure 5: Convergence behavior of proposed algorithms for different values of $N$ and perfect CSI. The system parameters are set as $\gamma=5$ dB, $B=1$, and $L=2$.

Theorems & Definitions (18)

• Lemma 1
• proof
• Lemma 2
• proof
• Remark 1
• Remark 2
• Lemma 3
• proof
• Proposition 1
• proof