Rescaled Brownian Motion of Molecules and Devices in Three-Dimensional Multi-User Mobile Molecular Communication Systems

This paper considers a three-dimensional anomalous-diffusive mobile molecular communication (MC) channel. Herein, the communicating devices, i.e., point transmitter (Tx) and passive receiver (Rx) can also move anomalously with the information-carrying molecule (ICM). In order to incorporate the anomalous diffusion phenomenon, the concept of rescaled-Brownian motion is explored. Two different scenarios, named point-to-point and multi-user MC systems, are considered for the analysis. First, considering the point-to-point scenario, the expressions for the channel impulse response (CIR) incorporating static and mobile Tx and Rx are derived. Further, the expressions for the peak time of CIR and the corresponding peak value are also derived. Furthermore, the point-to-point MC system is exploited in terms of bit-error-rate (BER), minimum BER, maximum mutual information, and throughput. A multi-user MC system is considered in the second scenario, and a molecular division multiple access (MDMA) method is used. The system is analyzed in terms of BER and throughput. Further, the system performance is optimized using two schemes known as min-max fairness for error probability and max-min fairness for throughput. Furthermore, we use best-to-best and best-to-worst assignment strategies to allocate different types of ICMs for each Rx. Subsequently, the optimal allocation for the number of ICMs is obtained when specific ICMs are assigned to all users/receivers for a two-user scenario. All the channel metrics are verified through particle-based and Monte-Carlo simulations.