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

TL;DR

This paper develops globally optimal and low-complexity algorithms for resource allocation in IRS-assisted multiuser networks, optimizing beamforming and discrete phase shifts under perfect and imperfect CSI to minimize transmit power.

Contribution

It introduces novel GBD-based algorithms for global optimality and SCA-based methods for practical suboptimal solutions in IRS-assisted systems with discrete phase shifters.

Findings

GBD algorithms achieve global optimality for perfect and imperfect CSI

SCA algorithms converge quickly to locally optimal solutions

Proposed schemes outperform existing methods in performance

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.