Molecular Communication with Passive Receivers in Anomalous Diffusion Channels

We consider anomalous diffusion for molecular communication with a passive receiver. We first consider the probability density function of molecules' location at a given time in a space of arbitrary dimension. The expected number of observed molecules inside a receptor space of the receiver at certain time is derived taking into account the life expectancy of the molecules. In addition, an implicit solution for the time that maximizes the expected number of observed molecules is obtained in terms of Fox's H-function. The closed-form expressions for the bit error rate of a single-bit interval transmission and a multi-bit interval transmission are derived. It is shown that lifetime limited molecules can reduce the inter-symbol interference while also enhancing the reliability of MC systems at a suitable observation time.