Power-Conserving Propagation Graph Modeling for Diffuse Scattering Analysis via Rigorous Power Integration

Propagation graph (PG) models offer an efficient framework for simulating multi-link wireless channels through closed-form matrix operations. However, conventional Lambertian scattering-based PG models typically assume uniform power distribution over scattering area, which can violate the power conservation law in scenarios with large tile sizes or strong scattering, leading to spectral radii exceeding unity and invalid matrix inversion. To overcome this limitation, this study developed a physically consistent PG framework that guarantees power conservation regardless of tile size or scattering coefficient. By deriving a closed-form integration expression based on the Lambertian scattering pattern through a coordinate transformation fixed to the receiving tile, the proposed model performs rigorous power integration on each tile. This formulation enables accurate evaluation of power exchange between arbitrarily oriented tiles while introducing only approximately 0.2% additional computational overhead. Simulation results confirm that the proposed model consistently maintains spectral radii below one under various conditions, ensuring both mathematical convergence and physical power conservation, whereas the conventional model violates the power conservation law in most large-scale scenarios. This improvement enhances the reliability and scalability of PG-based multi-link wireless channel modeling in large-scale environments, without sacrificing computational efficiency.