In a remarkable display of academic excellence, On Oct. 11, 2023, Eya Ben Amar successfully defended her Masters proposal entitled
“Stochastic differential equations for performance analysis of wireless communication systems”
Committee Chairperson:
Prof. Raúl Tempone, AMCS, KAUST
Committee Members:
Prof. Ajay Jasra, AMCS, KAUST
Prof. Mohamed-Slim Alouini, AMCS, KAUST
Abstract:
This thesis addresses the challenge of characterizing the time-varying nature of fading channels. The current time invariant models often fall short in capturing and tracking these dynamic characteristics. To overcome this limitation, we explore the use of stochastic differential equations (SDEs) to model signal envelope variations, considering scenarios involving Rayleigh, Rice, and Hoyt distributions. Furthermore, it is of practical interest to study the performance of channels modeled by SDEs. The outage probability (OP) has been the most commonly used performance measure. However, it does not provide enough information in specific communication system applications. Second-order statistics, such as level crossing rate (LCR) and average fade duration (AFD), were used for a deeper understanding of the behavior of the channel. In this work, we investigate a more general metric, the fade duration, representing the time during which the signal remains below a specified threshold within the interval [0 T]. Employing various stochastic approaches, including Monte Carlo (MC) and Kolmogorov Backward Equation (KBE), we estimate the complementary cumulative distribution function (CCDF) of the fade duration in the Rayleigh case, and analyze the impact of system parameters on its behavior. Finally, we leverage importance sampling (IS), a known variance reduction technique, to efficiently estimate the tail of the CCDF.
Keywords Fading channels, stochastic differential equations, fade duration, Monte Carlo, Kolmogorov Backward Equation, Importance sampling.
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