Stochastic Differential Equations for Performance Analysis of Wireless Communication Systems

This paper focuses on the performance analysis of time-varying fading channels, introducing a new general metric called fade duration. Fade duration measures the time during which a signal remains below a specified threshold within a fixed time interval. To model the signal, we utilize established models for the inphase and quadrature components, employing stochastic differential equations (SDEs) to capture the continuous-time statistical properties of the fading channel. We estimate the complementary cumulative distribution function (CCDF) of the fade duration in different fading environments using Monte Carlo simulations and analyze how various system parameters impact its behavior. To enhance the efficiency of our estimates, we leverage importance sampling (IS), a well-known variance-reduction technique, for accurately estimating the tail of the CCDF. The proposed IS scheme involves solving a high-dimensional controlled partial differential equation. To overcome the curse of dimensionality, we use Markovian projection to develop a novel one-dimensional SDE for signal envelope variations, enhancing the computational feasibility of IS. We present numerical results for the CCDF of fade duration in Rayleigh and Rice environments using our proposed IS estimators.