Probability Distribution of a Signal's Peak Time in a Molecular Diffusive Media

The peak time of a received signal in a molecular channel is random and generally assumed to follow the Normal distribution. However, the untested validity of the assumption motivates this letter. Considering an absorbing receiver placed in a free-diffusion molecular communication via diffusion (MCvD) system, we analyze the randomness in terms of the distribution of the peak time using simulated data and define one of the parameters. In addition, we derive the semi-analytical expressions of the distribution by using Poisson and Normal approximations of the absorbed molecules. Through numerical analysis, we evaluate the accuracy of the models and demonstrate that the Poisson model achieves a better fit. The key finding is that the distribution has extreme values resulting in a heavy right-tail and this information can be a useful tool to develop improved channel models.