Path loss predictions in the presence of buildings on flat terrain: a 3-D vector parabolic equation approach

Starting from a parabolic approximation to the Helmholtz equation, a three-dimensional (3-D) vector parabolic equation technique for calculating path loss in an urban environment is presented. The buildings are assumed to be polygonal in cross section with vertical sides and flat rooftops and the terrain is assumed to be flat. Both buildings and ground are allowed to be lossy and present impedance-type boundary condition to the electromagnetic field. Vector fields are represented in terms of the two components of Hertzian potentials and depolarization of the fields is automatically included in the formulation. A splitstep algorithm is presented for marching the aperture fields along the range. Boundary conditions on the building surfaces are treated by using a local Fourier representation of the aperture fields. Several test cases are considered to check the boundary treatment used in the technique as well as to validate the overall approach. Comparison is shown with uniform theory of diffraction (UTD), exact solutions, as well as with measurements.