Intelligent reflecting surfaces (IRSs) have emerged as a promising wireless technology for the dynamic configuration and control of electromagnetic waves, thus creating a smart (programmable) radio environment. In this context, we study a multi-IRS assisted two-way communication system consisting of two users that employ full-duplex (FD) technology. More specifically, we deal with the joint IRS location and size (i.e., the number of reflecting elements) optimization in order to minimize an upper bound of system outage probability under various constraints: minimum and maximum number of reflecting elements per IRS, maximum number of installed IRSs, maximum total number of reflecting elements (implicit bound on the signaling overhead) as well as maximum total IRS installation cost. First, the problem is formulated as a discrete optimization problem and, then, a theoretical proof of its NP-hardness is given. Moreover, we provide a lower bound on the optimum value by solving a linear-programming relaxation (LPR) problem. Subsequently, we design two polynomial-time algorithms, a deterministic greedy algorithm and a randomized approximation algorithm, based on the LPR solution. The former is a heuristic method that always computes a feasible solution for which (a posteriori) performance guarantee can be provided. The latter achieves an approximate solution, using randomized rounding, with provable (a priori) probabilistic guarantees on the performance. Furthermore, extensive numerical simulations demonstrate the superiority of the proposed algorithms compared to the baseline schemes. Finally, useful conclusions regarding the comparison between FD and conventional half-duplex (HD) systems are also drawn.

翻译：智能反射面（IRS）作为一种新兴无线技术，能够动态配置和控制电磁波，从而构建智能（可编程）无线电环境。在此背景下，我们研究了一种由两个采用全双工（FD）技术的用户组成的多IRS辅助双向通信系统。具体而言，我们处理IRS位置与尺寸（即反射单元数量）的联合优化问题，以在多种约束条件下最小化系统中断概率的上界：每个IRS的最小和最大反射单元数量、最大可部署IRS数量、最大反射单元总数（隐含的信令开销约束）以及最大总IRS安装成本。首先，该问题被表述为离散优化问题，并给出其NP难解性的理论证明。此外，通过求解线性规划松弛（LPR）问题，我们提供了最优值的下界。随后，基于LPR解，我们设计了两种多项式时间算法：确定性贪心算法和随机化近似算法。前者是一种启发式方法，总能求得可行解，并可提供（后验）性能保证；后者通过随机舍入实现近似解，具有可证明的（先验）概率性能保证。进一步地，大量数值仿真验证了所提算法相较于基准方案的优越性。最后，本文还得出关于FD与传统半双工（HD）系统对比的有用结论。