Differential Geometric Description of Future Mobile-to-Mobile Channels

In this paper we present differential geometric concepts for future mobile-to-mobile channel models. Those concepts enable the reader to generalize the channel description and apply it to different mobile-to-mobile scenarios. The geometric description allows for a non-stationary model, which thus incorporates high mobility scenarios, which are very important in future systems. Hereby, the mathematical concepts are similar to the theory of general relativity. Differential forms and coordinate system transforms are part of a tensor description of the channel. Our channel model for mobile-to-mobile channels is based on two important mathematical concepts: prolate spheroidal coordinates and differential forms. Furthermore, both the coordinate transform and the differential forms can be uniformly described by the tensor theory. Thus, we use co- and contravariant tensors to express both the gradient of the Doppler frequency in prolate spheroidal coordinates and differential forms, which are used to calculate the scattering area, in a uniform way.