Level crossing rate and average fade duration of EGC systems with cochannel interference in rayleigh fading

Both the first-order signal statistics (e.g., the outage probability) and the second-order signal statistics [e.g., the average level crossing rate (LCR) and the average fade duration (AFD)] are important design criteria and performance measures for wireless communication systems, including the equal gain combining (EGC) systems in the presence of the cochannel interference (CCI). Although the analytical expressions for the outage probability of the coherent EGC systems are exposed to CCI and various fading channels are already known, the respective expressions for the average LCR and the AFD are not available in the literature. This paper presents such analytical expressions for the Rayleigh fading channel, which are obtained by utilizing a novel analytical approach that does not require the explicit expression for the joint probability density function (pdf) of the instantaneous output signal-to-interference ratio and its time derivative. Applying the characteristic function method and the Beaulieu series, we determined the average LCR and the AFD at the output of an interference-limited EGC system with an arbitrary diversity order and an arbitrary number of cochannel interferers in the form of an infinite integral and infinite series. For the dual diversity case, the respective expressions are derived in closed forms in terms of the gamma and beta functions.