Spatially Distributed Molecular Communications: An Asynchronous Stochastic Model

This letter studies large-scale molecular communication systems by using point processes theory. A swarm of point transmitters randomly placed in a bounded space are considered in conjunction with a single fully absorbing receiver. The transmitters' positions are modeled by a spatial point process, but the global clock assumption, adopted by prior works, is here removed. More precisely, the emission times for each point transmitter are considered as random and are modeled by a non-stationary time-domain point process. We show that, if the intensity function is the same for all time point processes (thus taking the meaning of a distributed input), the average number of received molecules per time unit (receiving rate) can be computed through a convolution: the collective response to a one-molecule emission can be properly interpreted as the impulse response. This models unifies all the widely known transmitter models (exact concentration, Poisson concentration, and timing transmitter), which result as special cases. Analytical expressions for the receiving rate are provided and validated by Monte-Carlo simulations.