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The recent availability of fast numerical methods has rendered the integral-equation approach suitable for practical application to radio planning and site optimization for UHF mobile radio systems. In this paper, we describe a conceptually simple scheme for the efficient computation of UHF radial propagation loss over irregular terrain, which is based on the fast far-field approximation. The method is substantially faster than conventional integral-equation (IE) solution techniques. The technique is improved by incorporating the Green's function perturbation method and we outline a way in which the formulation can be made more exact. Computational issues such as terrain profile truncation and the effect of small-scale roughness are addressed. The method has been applied to gently undulating terrain and compared to published experimental results in the 900-MHz band. It has also been successfully applied to more hilly terrain and to surfaces with buildings added.

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The increase in mobile communications traffic has led to heightened interest in the use of deterministic propagation methods together with digital building and terrain databases for propagation prediction in urban areas. Ray methods have been particularly popular, and there are many papers in the literature describing the performance of various approaches to ray tracing. This paper will describe a powerful, recently developed, threedimensional (3-D) software suite for urban propagation modeling which, although based on 3-D ray tracing (using images), draws upon an ensemble of propagation tools including physical optics using the fast far-field approximation, the parabolic equation approximation for propagation over multiple buildings, and uniform theory of diffraction (UTD). Many ray-tracing methods determine ray paths between the transmitter and a single arbitrary receiver. This paper adopts an approach of a transmitter to a multiple receiver technique, resulting in greatly reduced computational times. The associated method can handle both indoor and outdoor propagation on both flat and undulating terrain. Terrain is represented as a set of triangular two-dimensional (2-D) patches, while buildings and clutter are represented using layers of polygons.

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