Analytic stochastic propagation model for urban streets

Stochastic ray propagation is a method to retain analytic description in topologies where application of Maxwell´s equations would be ineffective or impossible. In this paper, a probabilistic model describing ray propagation along an urban street is analysed and discussed. The proposed model bears the simplicity of an analytic approach, and even though not fully descriptive of all propagation mechanisms, it provides informative results of wireless propagation in the event of a first-stage analysis. Based on the presented probabilistic formulation, explicit expressions of the power across and at the end of the street are obtained and used to evaluate the behaviour of the considered structure. We confirm our analysis through simulation, by computing the distribution of ray paths along the street. We identify the probabilistic propagation mechanism as the dominant factor for the received power at the end of the street for a travelling wave antenna. By considering multiple distributed point sources across the beginning of the street, the coincidence between the numerical average of the received power and the expected value of the corresponding random variable is exhibited. The proposed formulation can be further used as a basis for analysing similar problems, yielding useful and indicative results.