The increasing demand for greater capacity of mobile communications has led to the petition of more radio spectrum at 1900 MHz for the new personal communication service (PCS) systems. The PCS spectrum is proposed to coexist with current fixed microwave spectrum. This presents cochannel interference control problems which can be avoided with extensive propagation studies in both measurements and predictions. Currently, there is no readily available tool to predict propagation channels for the small coverage area that PCS operates at 1900 MHz. This thesis presents new methods for propagation prediction without relying on measurements but rather local environment geometries and their electrical properties. The propagation prediction tool developed is based on the principle of geometrical optics and Fresnel-Kirchoff diffraction. Geometrical optics enables computer software to automatically trace the propagation of radio wave energy from the transmitter to the receiver. The ray tracing techniques presented are optimized for speed with a little trade-off in accuracy. Also, efficient techniques were developed to find true diffracting building edges in dense urban environments. The propagation prediction software also rely on other commercial software packages such as AutoCAD and GRASS to maintain and manipulate the environmental database as well as displaying prediction results. The software yielded reasonable accuracy when compared against VT campus propagation measurements at 900 MHz and 1900 MHz. / Master of Science