On the statistical properties of deterministic simulation models for mobile fading channels

Rice's sum of sinusoids can be used for an efficient approximation of colored Gaussian noise processes and is therefore of great importance to the software and hardware realization of mobile fading channel models. Although several methods can be found in the literature for the computation of the parameters characterizing a proper set of sinusoids, only less is reported about the statistical properties of the resulting (deterministic) simulation model. This is the topic of the present paper, whereby not only the simulation model's amplitude and phase probability density function (pdf) will be investigated, but also higher order statistics [e.g., level-crossing rate (lcr) and average duration of fades (adf's)]. It will be shown that due to the deterministic nature of the simulation model, analytical expressions for the pdf of amplitude and phase, autocorrelation function (acf), cross-correlation function (ccf), lcr, and adf's can be derived, We also propose a new procedure for the determination of an optimal set of sinusoids, i.e., the method results for a given number of sinusoids in an optimal approximation of Gaussian, Rayleigh, and Rice processes with given Doppler power spectral density (psd) properties, It will be shown that the new method can easily be applied to the approximation of various other kinds of distribution functions, such as the Nakagami and Weibull distributions. Moreover, a quasi-optimal parameter computation method is presented.