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We use the 3D vectorial Gaussian beam tracing method to model millimeter wave propagation. We simulate the propagation of Gaussian beams in a large scale environment at 62.4 GHz. First, a known far field pattern of the transmitter antenna is expanded into a set of Gaussian beams. We chose Gabor expansion based method to expanding radiating field into Gaussian beams. Then, a Gaussian beam tracing model considering reflections and transmission is used to represent urban microcell propagation. We use a phase matching method to find reflected Gaussian beam The results of the Gaussian beam tracing simulations including line-of-sight (LOS) and non-line-of-sight (NLOS) propagation are compared with the results of the ray tracing method. The results are in good agreement with results of ray tracing technique on the same geometry. Overall coverage map shows the dominant effect of shadowing in the millimeter wave band. The tracing technique is faster and more promising compared to exhausted ray tracing methods.

Point matching technique is applied to a pyramidal horn antenna to expand its aperture field in a wide angular range in terms of Gaussian beams using the Jacobi iterative method. The obtained far field pattern is compared with the results of Gabor's Gaussian beam expansion. Convergence, speed, the impact of initial condition and the selection of sample points is discussed. The implemented point matching scheme is almost as fast and accurate as the Gabor's expansion. It can even be faster and more accurate in some cases especially when the Gaussian beams are neither wide-waisted nor narrow-waisted.