Joint Clock Offset and Skew Estimation Based on Correlated Propagation Delays in Internet of Bio-Nano Things

The Internet of Bio-Nano Things (IoBNT) enables complex tasks like health monitoring and environmental sensing, requiring precise clock synchronization between nanomachines. In this article, we propose a clock synchronization method based on the arrival times of molecules that considers both clock offset and clock skew parameters in a timing-based diffusive channel. The timing-based diffusive channel requires a degradation factor to limit the lifespan of molecules. The existing methods assume ideal conditions for the synthesis time and arrival time of the molecules. However, we consider a practical scenario where the molecule synthesis time is nonzero and the first arrival times of the molecule are correlated for the joint estimation of the clock offset and clock skew. Individual estimation of clock offset requires prior knowledge of the clock skew. However, in practice, both parameters are unknown. Therefore, we address the synchronization issues that arise from individual estimation of the clock offset by jointly estimating both parameters. Using the transmission of molecules and their correlated arrival times, the receiver nanomachine (RN) employs the maximum likelihood (ML) estimator to estimate the synchronization parameters. Numerical results demonstrate that the proposed estimator outperforms the existing one.