随机射线的概率分布及其应用

在使用随机射线方法建模无线传播信道时，需要求解以反射次数为指标的无线电波经过若干次反射以后达到特定位置的概率分布。该文使用信息论中的最大熵原理，首先计算在Manhattan距离度量下二维和三维空间连续情形和离散情形下随机射线的概率密度函数。然后计算在Euclid距离度量下二维和三维空间连续情形下随机射线的概率密度函数，以及作随机游动的随机射线在二维空间的概率密度函数。使用城市密集传播地区的测量数据验证随机射线理论模型结果的可靠性。所得结果对于无线随机传播信道建模具有理论指导意义。

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.