Channel Parameter Estimation in a Molecular Communication System With Independent and Correlated Arrival Times

A timing-based molecular communication (MC) system with a zero drift-force for the transmission of molecules via an aqueous channel is considered in this letter. The first arrival times of the molecules with a degradation period are modeled by truncated Lévy distributions and for the cases of these propagation timings to be independent, uniformly, and exponentially correlated, the distance between the transmitter and the receiver and the diffusion coefficient of the aqueous medium are estimated using the maximum likelihood estimation technique. The Cramer-Rao Lower Bounds on the estimates of the system parameters are derived to obtain their normalized mean square errors, which show a predominant inverse dependency on the diffusion coefficient towards the estimation of the distance between the transmitter and the receiver. It is also observed that the estimation of the lower values of the diffusion coefficient is almost independent of the distance parameter. Further, the correlation of the propagation delays has a significant impact on the estimation of the system parameters for higher values of the diffusion coefficient.