Right Tail Approximation for the Distribution of Lognormal Sum and Its Applications
Bingcheng Zhu, Zaichen Zhang, Lei Wang, Jian Dang, Liang Wu, Julian Cheng, Geoffrey Ye Li · 2020
Lognormal sum is an important stochastic model in many communication related problems. In particular, the right tail of its cumulative distribution function (cdf) determines the error rate and outage probability of many communication systems in high signal-to-noise ratio (SNR) region, for example, amplify-and-forward (AF) relaying systems. However, the current popular approximation approaches, such as Wilkinson and Fenton approximations, fail to characterize the cdf right tail, causing notable asymptotic performance approximation error. In this work, we find a closed-form expression for the cdf right tail of lognormal sums and prove its tightness. Compared with five other popular approximation techniques, the proposed technique is the tightest approximation at the right tail. The new expression enables us to analyze performance of many communication systems and to reveal new insights, as demonstrated by using the dual-hop AF relaying communication system as an example.