In this paper, we investigate resource allocation for IRS-assisted green multiuser multiple-input single-output (MISO) systems. To minimize the total transmit power, both the beamforming vectors at the access point (AP) and the phase shifts at multiple IRSs are jointly optimized, while taking into account the minimum required quality-of-service (QoS) of multiple users. First, two novel algorithms, namely a penalty-based alternating minimization (AltMin) algorithm and an inner approximation (IA) algorithm, are developed to tackle the non-convexity of the formulated optimization problem when perfect channel state information (CSI) is available. Existing designs employ semidefinite relaxation in AltMin-based algorithms, which, however, cannot ensure convergence. In contrast, the proposed penalty-based AltMin and IA algorithms are guaranteed to converge to a stationary point and a Karush-Kuhn-Tucker (KKT) solution of the design problem, respectively. Second, the impact of imperfect knowledge of the CSI of the channels between the AP and the users is investigated. To this end, a non-convex robust optimization problem is formulated and the penalty-based AltMin algorithm is extended to obtain a stationary solution. Simulation results reveal a key trade-off between the speed of convergence and the achievable total transmit power for the two proposed algorithms. In addition, we show that the proposed algorithms can significantly reduce the total transmit power at the AP compared to various baseline schemes and that the optimal numbers of transmit antennas and IRS reflecting elements, which maximize the system energy efficiency of the considered system, are finite.

中文翻译：

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IRS 协助的绿色通信系统：可证明的收敛性和稳健的优化


在本文中，我们研究了国税局协助的绿色多用户多输入单输出（MISO）系统的资源分配。为了最大限度地降低总发射功率，接入点 (AP) 处的波束成形向量和多个 IRS 处的相移均进行联合优化，同时考虑多个用户的最低服务质量 (QoS) 要求。首先，开发了两种新颖的算法，即基于惩罚的交替最小化（AltMin）算法和内近似（IA）算法，以解决当完美信道状态信息（CSI）可用时公式化优化问题的非凸性。现有设计在基于 AltMin 的算法中采用半定松弛，但这无法确保收敛。相比之下，所提出的基于惩罚的 AltMin 和 IA 算法保证分别收敛到设计问题的驻点和 Karush-Kuhn-Tucker (KKT) 解。其次，研究了 AP 和用户之间信道的 CSI 知识不完善的影响。为此，制定了非凸鲁棒优化问题，并扩展了基于惩罚的 AltMin 算法以获得平稳解。仿真结果揭示了两种算法的收敛速度和可实现的总发射功率之间的关键权衡。此外，我们还表明，与各种基线方案相比，所提出的算法可以显着降低 AP 的总发射功率，并且最大化所考虑系统的系统能效的发射天线和 IRS 反射元件的最佳数量是有限的。