Smart and reconfigurable wireless communication environments can be established by exploiting well-designed intelligent reflecting surfaces (IRSs) to shape the communication channels. In this paper, we investigate how multiple IRSs affect the performance of multi-user full-duplex communication systems under hardware impairment at each node, wherein the base station (BS) and the uplink users are subject to maximum transmission power constraints. Firstly, the uplink-downlink system weighted sum-rate (SWSR) is derived as a system performance metric. Then, we formulate the resource allocation design to maximize the SWSR as an optimization problem which jointly optimizes the beamforming and the combining vectors at the BS, the transmit powers of the uplink users, and the phase shifts of multiple IRSs. Since the SWSR optimization problem is non-convex, an efficient iterative alternating approach is proposed to obtain a suboptimal solution for the design problem. In particular, we first reformulate the main problem into an equivalent weighted minimum mean-square-error form and then transform it into several convex sub-problems which can be analytically solved for given phase shifts. Then, the IRSs phases are optimized via a gradient ascent-based algorithm. Finally, numerical results are presented to clarify how multiple IRSs enhance the performance metric under hardware impairment.

中文翻译：

---

具有硬件损坏的多 IRS 辅助全双工系统的加权和速率最大化

通过利用精心设计的智能反射面 (IRS) 来塑造通信通道，可以建立智能和可重构的无线通信环境。在本文中，我们研究了在每个节点的硬件损坏情况下，多个 IRS 如何影响多用户全双工通信系统的性能，其中基站 (BS) 和上行链路用户受到最大传输功率限制。首先，导出上行-下行系统加权总和速率（SWSR）作为系统性能度量。然后，我们制定了资源分配设计以最大化 SWSR 作为优化问题，该优化问题联合优化了 BS 的波束成形和组合向量、上行链路用户的发射功率以及多个 IRS 的相移。由于 SWSR 优化问题是非凸的，提出了一种有效的迭代交替方法，以获得设计问题的次优解决方案。特别是，我们首先将主要问题重新表述为等效的加权最小均方误差形式，然后将其转换为几个凸子问题，这些子问题可以针对给定的相移进行解析求解。然后，通过基于梯度上升的算法优化 IRS 相位。最后，给出了数值结果，以阐明多个 IRS 如何增强硬件损伤下的性能指标。我们首先将主要问题重新表述为等效的加权最小均方误差形式，然后将其转换为几个凸子问题，这些子问题可以针对给定的相移进行解析求解。然后，通过基于梯度上升的算法优化 IRS 相位。最后，给出了数值结果，以阐明多个 IRS 如何增强硬件损伤下的性能指标。我们首先将主要问题重新表述为等效的加权最小均方误差形式，然后将其转换为几个凸子问题，这些子问题可以针对给定的相移进行解析求解。然后，通过基于梯度上升的算法优化 IRS 相位。最后，给出了数值结果，以阐明多个 IRS 如何增强硬件损伤下的性能指标。