Prolate Spheroidal Coordinates for Modeling Mobile-to-Mobile Channels

Kurzfassung

Often the choice of an appropriate coordinate system permits a simpler solution to a problem. In this work it is shown that in certain cases a prolate spheroidal coordinate system can be advantageous when calculating the delay-dependent Doppler probability density functions for mobile-to-mobile wireless channels. Recently, it was demonstrated how a geometry-based approach can be utilized to compute delay-dependent Doppler pdfs for vehicleto- vehicle channels that violate the WSSUS assumption. However, the corresponding pdfs required quite extensive numerical evaluations. When considering the same modeling problem in prolate spheroidal coordinates, it becomes possible to obtain analytical representations in some special, yet practically relevant cases, and thus simplify the computations of the resulting density functions significantly. Furthermore, it becomes possible to calculate the characteristic function for such a scenario. Thus, we are able to determine the mean Doppler and Doppler spread.