Distribution of first arrival position in molecular communication

In molecular communication systems, information is conveyed via nanoscale particles or molecules. Traditionally, the distribution of the first arrival time to the receiver is considered for system design and evaluation if nanoscale particles or molecules are diffused from the transmitter to the receiver in diffusion-based molecular communication systems. In this paper, we consider an extra information in the diffusion-based molecular communication system, namely the first arrival position at the receiver. A mathematical framework is developed to obtain the closed-form density function of the first arrival position for particles/molecules diffusing under constant net drift. The derived density function not only provides a novel analytical framework for existing molecular communication systems but may inspire novel molecular communication system design.