WSSUS model

The WSSUS model ( w ide s ense s tationary u ncorrelated s cattering) provides a statistical description of the transmission behavior of mobile radio channels for the transmission of band-pass signals in the equivalent baseband. In the observation period, the stationarity in the broadest sense and at the same time the uncorrelatedness of the scattering components is guaranteed.

The WSSUS model belongs to the class of WSS models as well as to the class of US models .

Criterion for stationarity in the broadest sense (determined from empirical studies): The mobile station covers a distance that corresponds to a maximum of a few ten times the wavelength of the carrier frequency .

Characterization of WSSUS models

Delay cross power density spectrum ${\displaystyle S_{hh}(\tau _{1}^{'},\tau )}$

Character of non-stationary white noise in terms of delay . ${\displaystyle \tau ^{'}}$

Stationarity in the broadest sense with respect to time (dependence only on the time difference ). ${\displaystyle t}$ ${\displaystyle \tau }$

Doppler cross power density spectrum ${\displaystyle S_{TT}(\nu ^{'},f_{1})}$

Character of non-stationary white noise with respect to the Doppler frequency . ${\displaystyle f}$

Stationarity in the broadest sense in terms of frequency . ${\displaystyle f^{'}}$

Spreading function ${\displaystyle S_{TT}(\tau _{1}^{'},f_{1})}$

Character of non-stationary white noise with respect to the Doppler frequency . ${\displaystyle f}$

Character of non-stationary white noise in terms of delay time . ${\displaystyle \tau ^{'}}$

Time-frequency correlation function ${\displaystyle r_{HH}(\nu ^{'}{,}\tau )}$

Stationarity in the broadest sense in terms of frequency . ${\displaystyle f^{'}}$

Stationarity in the broadest sense with respect to time . ${\displaystyle t}$

Relationship between spectra and functions in WSSUS models

Knowledge of one of the four quantities is sufficient to be able to calculate the other three.