On Anomalous Diffusion of Devices in Molecular Communication Systems

A one-dimensional (1-D) anomalous-diffusive molecular communication channel is considered, wherein the devices (transmitter (TX) and receiver (RX)) can move in either direction along the axis. For modeling the anomalous diffusion of information carrying molecules (ICM) as well as that of the TX and RX, the concept of time-scaled Brownian motion is explored. In this context, a novel closed-form expression for the first hitting time density (FHTD) is derived. Further, the derived FHTD is validated through particle-based simulation. For the transmission of binary information, the timing modulation is exploited. Furthermore, the channel is assumed as a binary erasure channel (BEC) and analyzed in terms of achievable information rate (AIR).