  In Diffusion-based Molecular Communications, the channel between Transmitter
Nano-machine (TN) and Receiver Nano-machine (RN) can be modeled by Additive
Inverse Gaussian Channel, that is the first hitting time of messenger molecule
released from TN and captured by RN follows Inverse Gaussian distribution. In
this channel, a quantity-based modulation embedding message on the different
quantity levels of messenger molecules relies on a time-slotted system between
TN and RN. Accordingly, their clocks need to synchronize with each other. In
this paper, we discuss the approaches to make RN estimate its timing offset
between TN efficiently by the arrival times of molecules. We propose many
methods such as Maximum Likelihood Estimation (MLE), Unbiased Linear Estimation
(ULE), Iterative ULE, and Decision Feedback (DF). The numerical results shows
the comparison of them. We evaluate these methods by not only the Mean Square
Error, but also the computational complexity.
