Path Loss Models Based on Stochastic Rays

Two-dimensional percolation lattices are applied to describe wireless propagation environment, and stochastic rays are employed to model the trajectories of radio waves. First, the authors derive the probability that a stochastic ray undergoes certain number of collisions at a specific spatial location. Three classes of stochastic rays with different constraint conditions are considered: stochastic rays of random walks and generic stochastic rays with two different anomalous levels. Subsequently, the authors obtain the closed-form formulation of mean received power of radio waves under non-line-of-sight conditions for each class of stochastic ray. Specifically, the determination of model parameters and the effects of lattice structures on the path loss are investigated. The theoretical results are validated by comparison with the experimental data.