Characterization of Stochastic Diffusivity-Based Information Particles in Molecular Communication Systems

This work considers a three-dimensional mobile molecular communication (MC) via an anomalous-diffusion-based system. The communicating devices in the considered MC system are identical and can move anomalously with emitted information-carrying molecules. We propose a stochastic diffusivity-based anomalous diffusion model which considers the non-Gaussian Brownian displacement of the molecules using the subordination approach. The proposed stochastic diffusivity model for mobile MC channels is characterized by the channel impulse response (CIR), and its mean is derived. We consider a discrete-time statistical channel model at a high inter-symbol interference regime and derive the bit error rate expressions. We also derive the asymptotic expression and upper bound of the capacity for the subordination approach. Furthermore, we show the degree of accuracy through root mean square error for the Poisson and Gaussian distributions.