Empirical relationship between local scattering function and joint probability density function

The fading process describing the propagation effects caused by scattering between two mobile transceivers shows strong non-stationary properties. For its characterization the local scattering function (LSF) and the instantaneous delay Doppler probability density function (pdf) have been introduced. In this paper, a relation between LSF and the joint pdf is investigated. In previous works, it was conjectured that a proportionality relationship between LSF and pdf might exist, similar to the relationship between the scattering function and the delay Doppler pdf in the wide-sense stationary uncorrelated scattering case. The goal here is to demonstrate this proportionality empirically based on the analysis of channel measurements. Both the LSF and the delay Doppler pdf can be combined in order to create a model for mobile-to-mobile (M2M) channels. The LSF is hereby used to process the measurement data and extract information like the stationarity time. With this information the joint delay Doppler pdf can be used to create a realistic simulation environment of the wireless channel for M2M communication systems.