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Geometric Analysis Of The Doppler Frequency For General Non-Stationary 3d Mobile-To-Mobile Channels Based On Prolate Spheroidal Coordinates, Michael Walter, Dmitriy Shutin, Martin Schmidhammer, David W. Matolak, Alenka Zajic

Faculty Publications

—Mobile-to-mobile channels often exhibit time-variant Doppler frequency shifts due to the movement of transmitter and receiver. An accurate description of the Doppler frequency turns out to be very difficult in Cartesian coordinates and any subsequent algebraic analysis of the Doppler frequency is intractable. In contrast to other approaches, we base our investigation on a geometric description of the Doppler frequency with the following three mathematical pillars: prolate spheroidal coordinate system, algebraic curve theory, and differential forms. The prolate spheroidal coordinate system is more appropriate to algebraically investigate the problem. After the transformation into the new coordinate system, the theory of …