Spatially Distributed Molecular Communications via Diffusion: Second-Order Analysis

Unlike electromagnetic communications, where the noise is typically represented by a (Gaussian) independent source which is added to the useful signal (additive noise), molecular communications via diffusion are affected by a random disturbance which is intrinsically related to the random nature of emission, propagation (Brownian motion) and reception. In point-to-point molecular communications, the number of received molecules is generally a Poisson random variable. Thus, the evaluation of the signal-to-noise ratio (intended as the ratio between the squared mean value of the received molecules and its variance) is not a problem of interest, since its value simply equals the mean of such a random variable. However, in spatially distributed communications, where the point transmitters are randomly placed in the 3D space according to a point process, the number of received molecules derives from the contribution of a random sum of emissions, so that it is no more a Poisson random variable. Thus, the evaluation of the signal-to-noise ratio is not trivial. Here, we provide an analytical framework to evaluate the signal-to-noise ratio in spatially distributed molecular communications for both synchronous and asynchronous transmitters. The analysis is extended to the signal-to-interference-noise ratio when digital communications with intersymbol interference are considered.