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Algebraic Analysis of the Poles in the Doppler Spectrum for Vehicle-to-Vehicle Channels

In vehicle-to-vehicle (V2V) wireless communications the time-variability of the propagation conditions is a challenge for channel estimation. The width of the Doppler spectrum depends on the propagation delay and the velocity vectors of the vehicles. So far, the time-variant width of the Doppler spectrum has been derived for single-bounce scattering close to the line-of-sight delay and for infinitely large delays. In this contribution, we generalize the time-variant, delay-dependent limiting frequencies for V2V channels for arbitrary delays and velocity vector configurations. The limiting frequencies are obtained by considering the geometric-stochastic channel representation in a prolate spheroidal coordinate system and determining the poles of the resulting Doppler spectrum. The poles in the spectrum are caused by the extrema of the Doppler frequency. Since the global maximum and minimum of the Doppler frequency define the limits of the spectrum, the time-variant delay-dependent width can be calculated in closed form.