Optimal Transmitted Molecules and Decision Threshold for Drift-Induced Diffusive Molecular Channel With Mobile Nanomachines

We study a drift-induced diffusive mobile molecular communication system where source, destination and cooperative nanomachines follow the one-dimensional Brownian motion. For information exchange from source nanomachine to receiver nanomachine, both direct and decode-forward (DF) relay-assisted cooperative paths are considered. The closed-form expressions for the probabilities of detection and false alarm are derived at the cooperative and destination nanomachines considering the multiple-source interference (MSI) and the inter-symbol-interference (ISI). The closed-form expressions for end-to-end average probability of error, and maximum achievable rate are also obtained. Moreover, to achieve minimum expected probability of error the optimum number of molecules to be transmitted from transmitter and optimal detection threshold in receiver nanomachine are found. The analytical expressions are validated through particle-based and Monte-Carlo simulation methods.