Level Crossing Rate and Average Fade Duration of EGC Systems with Cochannel Interference in Rayleigh Fading

TL;DR

This paper derives analytical expressions for the average level crossing rate and fade duration of equal gain combining systems with cochannel interference in Rayleigh fading, using a novel approach that avoids joint PDF calculations.

Contribution

It introduces new analytical formulas for LCR and AFD in EGC systems with interference, applicable to arbitrary diversity orders and interferer counts, including closed-form solutions for dual diversity.

Findings

Derived expressions for LCR and AFD using characteristic function and Beaulieu series.

Closed-form formulas for dual diversity case in terms of gamma and beta functions.

Applicable to interference-limited EGC systems with arbitrary parameters.

Abstract

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 the wireless communication systems, including the equal gain combining (EGC) systems in presence of the cochannel interference (CCI). Although the analytical expressions for the outage probability of the coherent EGC systems exposed to CCI and various fading channels are already known, the respective ones 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 PDF of the instantaneous output signal-to-interference ratio (SIR) 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 forms of an infinite integral and an infinite series. For the dual diversity case, the respective expressions are derived in closed forms in terms of the gamma and the beta functions.