Delay-Dependent Doppler Probability Density Functions for Vehicle-to-Vehicle Scatter Channels

Abstract

Novel joint delay Doppler probability density functions for vehicle-to-vehicle communications channels are introduced. Prior measurements of vehicle-to-vehicle channels have unveiled their nonstationarity; thus, the wide-sense stationary and also the uncorrelated scattering assumption for such channels is often violated, which makes their modeling challenging. In this work it is proposed to exploit geometry-based stochastic modeling to cope with the nonstationarity of vehicle-to-vehicle channels. To this end, delay-dependent Doppler pdfs are derived for arbitrary times. It is assumed that scatterers are randomly distributed on an ellipse with two moving vehicles being in its foci. The proposed approach allows reducing the dimensionality of the resulting problem. This in turn leads to a significantly simplified derivation of the delay-dependent Doppler pdfs for general vehicle-to-vehicle propagation environments; moreover, the resulting computations can be performed almost fully analytically. By combining the calculated Doppler pdf with a delay pdf, the joint pdf of delay and Doppler is obtained. The joint pdf then can be put into relation with the generalized local scattering function. The presented modeling approach is simple yet very scalable and accurate, which allows its application in different vehicular scenarios. The obtained modeling results correspond very well with measurement data reported in prior works.Index Terms-Geometric-stochastic channel modeling, nonstationary modeling, scatter channel, vehicle-to-vehicle channel, wideband channel model.

Modeling of Non-WSSUS Double-Rayleigh Fading Channels for Vehicular Communications

“…This equation also shows that the channel's largescale variations are not taken into account by the model in (18), as the instantaneous average power of ( ; ) is a TFinvariant quantity for ∈ [0, 0 ]. We have intentionally neglected such variations to focus the spotlight of our work on the nonstationarities of V2V channels arising from the time-varying nature of the propagation delays.…”

“…Notable contributions to the analytical characterization of non-WSSUS V2V channels have recently been made in [17][18][19] on the basis of the geometry-based statistical modeling approach. The geometrical channel models proposed in these papers assume the propagation of spherical waves to account for the nonstationarities of V2V channels stemming from small-scale propagation.…”

Generic stochastic modeling of vehicle-to-vehicle wireless channels

“…A more generalized model can be viewed in [13] with an additional elliptical ring of single bouncing scatterers surrounding the Tx and Rx. In [14], an algorithmic procedure was presented for determining the delay dependent power spectral density (PSD) with single bouncing scatterers uniformly distributed on an elliptical ring. The models in [11]- [14] considered two dimensional (2-D) multipath propagation.…”

“…In [14], an algorithmic procedure was presented for determining the delay dependent power spectral density (PSD) with single bouncing scatterers uniformly distributed on an elliptical ring. The models in [11]- [14] considered two dimensional (2-D) multipath propagation. Three dimensional (3-D) multipath scattering was considered in [15] with similar double bouncing as in [11].…”

“…A modern modeling approach considers that the channel statistics remain constant within certain time-frequency intervals [14]. In such intervals, which are also regarded as WSS intervals with respect to both time-and frequency-domains, the channel is characterized as doubly underspread and is modelled locally through the so called local scattering function (LSF) [23], [24].…”