Noise properties of linear molecular communication networks

Molecular communication networks consist of transmitters and receivers distributed in a fluid medium. The communication in these networks is realised by the transmitters emitting signalling molecules, which are diffused in the medium to reach the receivers. This paper investigates the properties of noise, or the variance of the receiver output, in molecular communication networks. The noise in these networks come from multiple sources: stochastic emission of signalling molecules by the transmitters, diffusion in the fluid medium and stochastic reaction kinetics at the receivers. We model these stochastic fluctuations by using an extension of the master equation. We show that, under certain conditions, the receiver outputs of linear molecular communication networks are Poisson distributed. The derivation also shows that noise in these networks is a nonlinear function of the network parameters and is non-additive. Numerical examples are provided to illustrate the properties of this type of Poisson channels.