In a wireless network, the spatial location of the transmitters has a large impact on the achievable rate at each user location. The optimal placement of -- for example -- cellular base stations is a difficult non-convex problem, and is usually addressed with simplified propagation models and simplified heuristics that may account for specifics such as the site topology, building locations, and user density. We propose a mathematically rigorous framework for optimal transmitter placement that explicitly integrates detailed site-specific maps, spatial material properties, and realistic signal attenuation. We introduce a novel aggregated network quality functional which captures the essential trade-off between maximizing network coverage and minimizing cost, and establish the problem's sub-modularity under certain practical conditions. To solve the resulting resource-constrained optimization problem for sparse, discrete transmitter configurations, we propose the Interference-Aware Submodular Placement Algorithm (IA-SPA) and prove theoretical performance guarantees on its gap from optimality. IA-SPA is general and can incorporate existing BS locations and prohibited areas (e.g. a lake), making it useful for either clean-slate or incremental deployments. We show the utility of our approach using a ray tracing-based simulation framework applied to 3D maps of San Francisco and Florence, where we compare to known base station deployments by AT&T, T-Mobile and Iliad. We demonstrate that our proposed placement strategy achieves significant increases in mean data rate (about 2x) and edge rate ($2-8$x) compared to existing tower deployments, using the same number of transmitters.

翻译：在无线网络中，发射机的空间位置对每个用户位置的可达速率具有显著影响。以蜂窝基站为例，其最优部署属于困难的非凸优化问题，通常需要借助简化传播模型和启发式算法解决，这些方法可能考虑站点拓扑、建筑布局和用户密度等具体因素。本文提出了一种数学上严格的最优发射机部署框架，该框架显式集成了详尽的场地地图、空间材料特性及实际信号衰减特征。我们引入了一种新颖的聚合网络质量函数，该函数能够捕捉最大化网络覆盖与最小化成本之间的核心权衡，并在特定实际条件下证明了问题的子模性。为解决稀疏离散发射机配置下的资源约束优化问题，我们提出了干扰感知子模部署算法(IA-SPA)，并证明了其与最优解之间差距的理论性能保证。IA-SPA具有通用性，可整合现有基站位置和禁入区域（如湖泊），适用于全新部署或渐进式部署场景。我们通过基于射线追踪的仿真框架验证了该方法的实用性，该框架应用于旧金山和佛罗伦萨的三维地图，并与AT&T、T-Mobile及Iliad的实际基站部署进行了对比。实验表明，在同等发射机数量条件下，我们提出的部署策略相比现有塔站部署使平均数据速率提升约2倍，边缘速率提升2-8倍。