Application of diffraction theory to wireless propagation problems

Summary form only given. Diffraction of UHF radio waves by buildings is an important mechanism by which cellular telephone signals travel around intervening buildings to arrive at street level mobiles. Because of the dimensions of an urban environment are so much larger than the wavelength, numerical solvers of Maxwell´s equations cannot be employed for realistic outdoor links. Since Sommerfeld first solved the problem of plane wave diffraction by a conducting half-plane over 100 years ago, the methodology of geometric optics has been generalized to incorporate the description of diffraction phenomena. Ray methods make use of the localized and sequential nature of wave propagation to give physical insight into the propagation process. In the case of the urban environment, it is necessary to account for many sequential interactions of the rays with the buildings in order to make accurate predictions. However, buildings are usually composed of a series of flat surfaces (walls and roofs) that meet in sharp edges. Specular reflection at the flat surfaces and diffraction at the edges are therefore the dominant wave processes for outdoor links. Special ray tracing codes have been written in order to find ray paths when many interactions with simple elements must be accounted for. We review the basis for, and the special features of these codes. In some geometries, for example when subsequent edges lie in the shadow boundary of previous edges, simple canonical solutions for isolated elements are no longer useful in computing the fields. In these cases, numerical integration of the complementary representation in terms of physical optics may be used to evaluate the effect of the diffraction process. Several such cases are discussed.