On the Generalized and Modified Suzuki Model (GMSM): Approximations and Level Crossing Statistics

Abstract

The Suzuki model (Susuki, 1977) is traditionally applied to characterize the fast fading-slow fading (Rayleigh-Lognormal) phenomena. Extensions to this model are available in the literature, namely the extended Patzold et al. (1998) and the generalized Tjhung and Chai (1999) and Ramos et al. (2000) Suzuki model. In wireless channels the level crossing statistics, level crossing rate (LCR), average fade duration (AFD) and fade duration distribution (FDD), are important to evaluate the system's performance. The FDD, however, is rather complex to evaluate analytically and the literature deals mainly with the LCR and AFD. Previous works on the level crossing statistics of the Suzuki model and extensions of it, are devoted to LCR and AFD only. Here we proposed the so called GMSM (Nakagami-Gamma) and analyze its LCR and AFD. Using computer simulations we found that the FDD of the GMSM are approximately Gamma distributed. To evaluate the FDD analytically we use our previous results on the level crossing theory (Ramos et al., 2003). To achieve this we propose an approximation of the GMSM by means of carefully selected Gamma distributions. This means that Gamma fading process has an FDD which is approximately Gamma distributed also. The theory and the approximations are opportunely compared with measurements and simulations.