Intelligent reflecting surface (IRS) can be densely deployed in complex environment to create cascaded line-of-sight (LoS) paths between multiple base stations (BSs) and users via tunable IRS reflections, thereby significantly enhancing the coverage performance of wireless networks. To achieve this goal, it is vital to optimize the deployed locations of BSs and IRSs in the wireless network, which is investigated in this paper. Specifically, we divide the coverage area of the network into multiple non-overlapping cells and decide whether to deploy a BS/IRS in each cell given a total number of BSs/IRSs available. We show that to ensure the network coverage/communication performance, i.e., each cell has a direct/cascaded LoS path with at least one BS, as well as such LoS paths have the average number of IRS reflections less than a given threshold, there is a fundamental trade-off with the deployment cost or the number of BSs/IRSs needed. To optimally characterize this trade-off, we formulate a joint BS and IRS deployment problem based on graph theory, which, however, is difficult to be optimally solved due to the combinatorial optimization involved. To circumvent this difficulty, we first consider a simplified problem with given BS deployment and propose the optimal as well as an efficient suboptimal IRS deployment solution to it, by applying the branch-and-bound method and iteratively removing IRSs from the candidate locations, respectively. Next, an efficient sequential update algorithm is proposed for solving the joint BS and IRS deployment problem. Numerical results are provided to show the efficacy of the proposed design approach and optimization algorithms for the joint BS and IRS deployment. The trade-off between the network coverage performance and the number of deployed BSs/IRSs with different cost ratios is also unveiled.

翻译：智能反射面（IRS）可密集部署于复杂环境中，通过可调IRS反射在多个基站（BS）与用户之间创建级联视距（LoS）路径，从而显著提升无线网络的覆盖性能。为实现这一目标，优化无线网络中BS与IRS的部署位置至关重要，这正是本文的研究内容。具体而言，我们将网络覆盖区域划分为多个互不重叠的小区，并在给定可用BS/IRS总数的情况下，决定每个小区是否部署BS/IRS。研究表明，为确保网络覆盖/通信性能（即每个小区至少与一个BS存在直接/级联LoS路径，且这些LoS路径的IRS平均反射次数低于给定阈值），部署成本或所需BS/IRS数量之间存在基本权衡关系。为最优刻画这一权衡，我们基于图论构建了联合BS与IRS部署问题，但该问题因涉及组合优化而难以求得最优解。为克服这一困难，我们首先考虑给定BS部署的简化问题，分别应用分支定界法与从候选位置迭代移除IRS的方法，提出最优及高效次优的IRS部署解决方案。进而提出高效顺序更新算法求解联合BS与IRS部署问题。数值结果验证了所提设计方案与优化算法在联合BS与IRS部署中的有效性，并揭示了网络覆盖性能与不同成本比例下部署BS/IRS数量之间的权衡关系。