Connectivity Properties of Free Diffusion-Based Molecular Nanoscale Communication Networks

The connectivity properties of nanonetworks that employ free diffusion-based molecular communication are analyzed by constructing a model based on Gilbert's disk graph. In free diffusion-based molecular communication, "path loss" has a different functional form compared with wireless propagation and the scenarios under consideration are not generally limited to 2-D environments as in the case of wireless networks. Hence, the constructed model takes into account the peculiarities of diffusion-based communication in 1-D, 2-D, and 3-D scenarios. The model incorporates particle-counting noise and is independent of the signaling mechanism employed. Analytical formulas are derived for the critical values of the signal strength-to-detection threshold ratio and the number of nodes that are required to achieve a connected or an almost-connected network. Monte Carlo simulations are used to validate model predictions and to suggest design guidelines for deploying nanonetworks. An empirical study is also conducted to evaluate the time required to broadcast an alarm in a connected nanonetwork of various sizes. The time to broadcast as a function of the number of nodes in a fixed region is observed to follow a power law, where the exponent depends on the dimensionality of the medium.