Effect of Time-Dependent Drift and Diffusion in Molecular Communication Systems

This letter presents analysis of a molecular communication (MC) system considering time-dependent drift and diffusion of molecules. The proportionality in diffusion and drift is considered, and by applying the method of images, the general solution for Fokker-Planck (FP) equation is provided. Two different functional forms of the time-dependent drift and diffusion, viz., power-law time dependence and periodic driver, are used to analyze the MC system. The expressions for cumulative distribution function (CDF), also known as first passage probability (FPP), corresponding to first passage time density function (FPTDF) are derived. Moreover, the expressions for pulse-peak time and pulse peak of FPTDF are obtained. Further, the impacts of time-dependent drift and diffusion are examined in terms of average bit-error-rate (BER). Monte-Carlo and particle-based simulations (PBS) have also been performed to validate the feasibility of the used analytical models.