Joint Delay Doppler Probability Density Functions for Air-to-Air ChannelsReport as inadecuate

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International Journal of Antennas and Propagation - Volume 2014 2014, Article ID 814218, 11 pages -

Research ArticleInstitute of Communications and Navigation, German Aerospace Center DLR, Oberpfaffenhofen, 82234 Wessling, Germany

Received 15 November 2013; Accepted 2 January 2014; Published 3 April 2014

Academic Editor: Fernando P. Fontan

Copyright © 2014 Michael Walter et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Recent channel measurements indicate that the wide sense stationary uncorrelated scattering assumption is not valid for air-to-air channels. Therefore, purely stochastic channel models cannot be used. In order to cope with the nonstationarity a geometric component is included. In this paper we extend a previously presented two-dimensional geometric stochastic model originally developed for vehicle-to-vehicle communication to a three-dimensional air-to-air channel model. Novel joint time-variant delay Doppler probability density functions are presented. The probability density functions are derived by using vector calculus and parametric equations of the delay ellipses. This allows us to obtain closed form mathematical expressions for the probability density functions, which can then be calculated for any delay and Doppler frequency at arbitrary times numerically.

Author: Michael Walter, Dmitriy Shutin, and Uwe-Carsten Fiebig



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