Environment-Aware Network-Level Design of Generalized Pinching-Antenna Systems--Part II: Geometry-Aware Case

This two-part paper aims to develop an environment-aware network-level design framework for generalized pinching-antenna systems to overcome the limitations of conventional link-level optimization, which is tightly coupled to instantaneous user geometry and thus sensitive to user mobility and localization errors. Part I investigates the traffic-aware case, where user presence is characterized statistically by a spatial traffic map and deployments are optimized using traffic-aware network-level metrics. Part II complements Part I by developing geometry-aware, blockage-aware network optimization for pinching-antenna systems in obstacle-rich environments. We introduce a grid-level average signal-to-noise (SNR) model with a deterministic LoS visibility indicator and a discrete activation architecture, where the geometry-dependent terms are computed offline in advance. Building on this model, we formulate two network-level activation problems: (i) average-SNR-threshold coverage maximization and (ii) fairness-oriented worst-grid average-SNR maximization. On the algorithmic side, we prove the coverage problem is NP-hard and derive an equivalent mix-integer linear programming reformulation through binary coverage variables and linear SNR linking constraints. To achieve scalability, we further develop a structure-exploiting coordinate-ascent method that updates one waveguide at a time using precomputed per-candidate SNR contributions. For the worst-grid objective, we adopt an epigraph reformulation and leverage the resulting monotone feasibility in the target SNR, enabling an efficient bisection-based solver with low-complexity feasibility checks over the discrete candidate set. Simulations results validate the proposed designs and quantify their gains under different environments and system parameters.