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 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 systems employing practical discrete IRS phase shifters. In particular, we jointly optimize the beamforming vector at the base station (BS) 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 (QoS) 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 achieve a close-to-optimal performance within a few iterations. Moreover, compared with the state-of-the-art solution based on the alternating optimization (AO) method, the proposed SCA-based scheme achieves a significant performance gain with low complexity.

翻译：智能反射面（IRS）通过实现无线传播环境的定制化，是未来通信系统中实现高频谱和能量效率的低成本解决方案。尽管针对IRS辅助多用户通信系统的资源分配设计已有大量研究，但其最优设计及相应的性能上界仍未完全明晰。为填补这一理论空白，本文研究了采用实际离散IRS移相器的IRS辅助多用户系统的最优资源分配设计。具体而言，我们联合优化基站（BS）处的波束赋形向量与离散IRS相位偏移，以在完美与不完美信道状态信息（CSI）条件下最小化总发射功率。为此，分别基于广义Benders分解（GBD）方法开发了两种新型算法，分别针对完美与不完美CSI场景获得全局最优解。此外，为促进实际部署，我们利用逐次凸近似（SCA）技术提出了两种具有收敛保障的低复杂度次优算法。特别地，针对不完美CSI，我们采用有界误差模型表征CSI不确定性，并提出一种新型变换将鲁棒服务质量（QoS）约束凸化。数值结果验证了所提GBD算法在完美与不完美CSI下均能实现系统最优性。同时揭示，两种SCA算法均可在数次迭代内达到接近最优的性能。此外，与基于交替优化（AO）的现有方案相比，所提SCA方案在低复杂度下实现了显著的性能增益。