Scattering function in delay and Doppler induced by motion in a dense multipath environment

The delay spread profile for a dense multipath environment, modeled as a wide sense stationary uncorrelated scatterers (WSSUS) channel, has recently been derived for stationary transmitter-receiver pairs. The result shows the dependence of the profile on transmitter-receiver distance. In this paper we extend the analysis to the case that this distance is changing at constant velocity, inducing different Doppler shifts depending on the relative location of the scatterers. The scattering function is the power spectral density of the received signal, as a function of the delay and Doppler coordinates. It is of interest for the analysis of mobile transmission of systems in which the bandwidth is comparable to, or larger than, the reciprocal delay spread of the communication channel. For evaluation of narrow-band systems the delay-independent power spectral density, known as the Jakes model, is appropriate. When the delay variable is integrated out in the scattering function, the Jakes model is obtained. When the Doppler variable is integrated out, allowing for slight differences in the topological layouts of the two models, the scattering function reduces to the delay spread profile mentioned above.