A Discrete Ray Tracing Method Based on Dijkstra Algorithm for 3D Propagation Environments

In this paper is proposed a discrete ray tracing method by using Dijkstra Algorithm (DA) for electromagnetic field computation in complicated 3D propagation environments such as urban areas and random rough surfaces. The geometry of the problem is constructed by introducing several rectangular obstacles existing in 3D free space. The computational space including obstacle regions is divided into regularly arrayed rectangular solids with nodal points corresponding to their apexes. The connectivity between two nodes, necessary for the DA, is allowed only for the 26 proximate nodes. The apexes of adjacent 8 rectangular solids and the link cost of the connected two nodes are given by the travelling time of optical ray. Thus, the conventional DA provides the total cost matrix and proximity matrix from which the shortest paths from a source node to other nodes can be obtained. Some modifications are made for the original results based on the conventional DA, thus the costs among source, apex and wedge can be replaced by the costs of straight rays among them. The proximity matrix is modified and all rays can be expressed in terms of straight lines between source and wedge (or apex), wedge (or apex) and wedge (or apex). The computed rays are modified to discriminate the shadow and illuminated boundaries correctly. The numerical examples are shown in 2D and 3D ways to demonstrate the effectiveness of the proposed method.