On Timing Synchronization for Quantity-based Modulation in Additive Inverse Gaussian Channel with Drift

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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.