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：智能反射表面(IRS)已成为一种有希望的动态配置和控制电磁波动态配置和控制的无线技术,因此产生了智能(可编程)无线电环境;在这方面,我们研究一个多IRS协助的双向通信系统,由使用全复(FD)技术的两个用户组成。更具体地说,我们处理IRS的联合位置和大小(即反映元素的数量)优化,以便在各种制约下最大限度地减少系统超值的可能性:每个IRS的反映要素的最小和最大数量、安装的IRS的最大数量、反映要素的最大总数(对信号顶端)以及IRS安装费用的最大总数。首先,问题被表述成一个离散的优化问题,然后提供其NP-硬度的理论证明。此外,我们通过解决线性调整(可编程简化(LPR)问题,我们设计两个多式时间算算算法,一个确定性贪婪的50%结论结论,以及一个最终算法,这个方法以LA为基础,提供一种最终性平比方法。