System function and characteristic quantitie's of spatial deterministic Gaussian uncorrelated scattering processes

Spatial deterministic uncorrelated scattering (SDGUS) processes have been introduced recently to model and to simulate space-selective wide-band mobile radio channels. This paper studies the system functions and characteristic quantities of SDGUS processes. Starting from the space-time-variant impulse response, a closed-from expression will be derived for the delay-direction-Doppler power spectral density (PSD) by using time averages. From this function, several other three-dimensional (3-D) and two-dimensional (2-D) system functions can be obtained in closed form by using the Fourier transform. The Fourier transform relationships between all system functions are illustrated. In addition, closed-form solutions are presented, e.g., for the delay PSD, the direction PSD, and the Doppler PSD, only to name a few. Moreover, simple expressions in terms of the model parameters will be provided for various correlation functions (CFs) and the main characteristic quantities of SDGUS models, such as the delay spread, the direction spread, as well as the Doppler spread. The obtained results provide a clear insight into the statistical behaviour of SDGUS models.