Molecular Channel Fading Due to Diffusivity Fluctuations

Molecular communications via diffusion is sensitive to environmental changes, such as the diffusion coefficient (mass diffusivity). The diffusivity is directly related to a number of parameters, including the ambient temperature, which varies slowly over time. While molecular noise models have received significant attention, channel fading has not been extensively considered. Using experimental data, we show that the ambient temperature varies approximately according to a normal distribution. As a result, we analytically derive the fading distribution and validate it using numerical simulations. We further derive the joint distribution of the channel gain and the additive noise, and examine the impact of such interactions on the ISI distribution, which is shown to conform to a generalized extreme value distribution.