On Molecular Communications via Diffusion with Multiple Transmitters and Multiple Receivers

This paper analyzes distributed molecular communications with multiple transmitters and multiple receivers randomly placed in a 3D space. Receivers, whose positions are modeled by a homogeneous Poisson point process, are assumed to be passive and spherical. Since they are not dimensionless, their presence affects the statistics of transmitter points, resulting in a Poisson hole process, instead of the Poisson process usually adopted in previous works on multiple transmitters. Moreover, molecules emissions from different transmitters are considered asynchronous, according to a recently proposed stochastic model. Here, the intensity function of the time point processes modeling molecules emissions is given a further meaning; in particular, it is considered as the propensity function of a chemical reaction. The average amount of received molecules per time unit (receiving rate) is evaluated accordingly for each receiver. When the swarm of receivers is considered as an equivalent, single, spatially distributed receiver, the average amount of received molecules per time and volume units (receiving rate density) is introduced and analytically evaluated.