This paper presents, a three-dimensional (3D), wideband, ray- tracing propagation prediction model (3D MRT-1) for the characterisation of out-door dispersive microcellular radio channels. The model is based on GO and its variant UTD. The functionality of the model utilises ray-tracing algorithms based on a combination of image theory and a visibility matrix. The visibility algorithm is independent of transmitter and receiver locations. The model takes into account line-of- sight (LoS) paths, ground reflected paths, paths due to reflection from terrain cover (primarily buildings) and paths due to diffraction around and over buildings. In order to characterise the channel the amplitude, phase, polarisation, angle-of-departure (AoD), angle-of-arrival (AoA) and optical path length of each ray is tracked. The software constructs channel impulse responses (CIRs), power delay profiles (PDPs), and calculates relevant channel parameters including signal strength, transmission loss, received power, mean delay spread and RMS delay spread. As part of a validation process, the model was implemented for a residential suburban area of Malvern, UK, at 2.38 GHz. Comparisons between the simulated and measured results confirm the utility of the model.