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

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Abstract
Rice's (9144, 1945) 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, less is reported about the statistical properties of the resulting (deterministic) simulation model. In this paper, not only is the simulation model's amplitude and phase probability density function (PDF) investigated, but also higher order statistics [e.g., level-crossing rate (LCR) and average duration of fades (ADFs)]. It is shown that due to the deterministic nature of the simulation model, analytical expressions for the PDF of the amplitude and phase, autocorrelation function (ACF), crosscorrelation function (CCF), LCR, and ADFs 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 is shown that the new method can easily be applied to the approximation of various other kinds of distribution functions, such as the Nakagami (1960) and Weibull distributions. Moreover, a quasi-optimal parameter computation method is presented.

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