Probability distribution of stochastic rays and its applications

The probability distribution of radio wave that undergoes certain number of collisions at a specific spatial location should be solved. This probability is used to model radio propagation channels with the method of stochastic rays. The maximum entropy principle in information theory is utilized to calculate the corresponding probability in the current research. Under Manhattan metric, the 2-dimensional and 3-dimensional continuous probability density functions (pdfs) and discrete probability mass functions are calculated. Under Euclidean metric, 2-dimensional and 3-dimensional continuous pdfs and discrete probability mass functions are also calculated, and the pdf of stochastic rays undergoing random walks is derived. The results of theoretical model based on stochastic rays are validated by experimental dada measured in dense urban propagation scenario. The results of the paper are important to the modeling of wireless stochastic propagation channels.