On SIR fade statistics in Rayleigh-lognormal channels

An analytical approach to derive the level crossing rate (LCR) and the average fade duration (AFD) for the signal-to-interference ratio (SIR) in a mobile radio system is proposed. The channel model is characterized by a log-normal shadowing component and a Rayleigh fast fading component on the useful link and on interfering links. Shadowing components are assumed to be cross-correlated. The approach can be divided in two steps. The first one mainly consists in extending Wilkinson´s approximation method for the sum of log-normal random variables to the matching of second order statistics of randomly weighted log-normal processes. In particular, the latter approach is used in order to obtain a log-normal approximation for the ratio between total interference and the log-normal component of the useful signal strength. In the second step the SIR is expressed as the product of a Rayleigh process and a log-normal process, and the LCR and AFD are then obtained through the Rice´s (1944) approach. Numerical results are presented in terms of LCR and AFD for various values of cross correlation parameters among shadowing components.