Statistical Model for the Mobile Channel Composite Envelope

Currently, among the main three affectors of transmission quality (represented by the mean probability of a bit error) for a particular digital modulation format, such as eg. GMSK, fast fading seems to be by far mostly dealt with, in particular, analytically, while such an analysis for the other two aspects, namely, slow fading and quasideterministic attenuation of the signal is usually too complex, often resulting with analytic solutions of mainly academic relevance, rather than practical, while numerical and/or simulation methods are very time-consuming and not explicitly conclusive. Therefore, in this paper, we focus simultaneous fast Nakagamian and slow (shadowing) fading, providing the explicit analytical expression for the probability density function of a mobile channel signal composite envelope, and consequently the according assessment of the transmission performance, that is finally supported by extensive computer experiments for characteristic parameter values of fast and slow fading.