3-D Diffusive-Drift Molecular Channel Characterization for Active and Passive Receivers

The analytical characterization of a 3-D diffusion-drift fluid channel with various molecular receivers is an open problem in the study of molecular communication (MC). In the absence of closed-form expressions of the molecular receptivities for different receivers, the performance evaluation of a receiver relies heavily on time-consuming simulations. In this paper, channel characterizations for active and passive receivers are provided. The diffusion-drift kernel and probability distribution function (PDF) of a particle's location in a 3-D fluid environment are derived using the stochastic Fokker-Planck equation. Furthermore, the PDF of the absorbing point on an infinite absorbing wall in a 3-D geometry is obtained. Closed-form expressions for the molecular receptivities of the active and passive receivers are derived. Assuming interference at the molecular receiver, an error performance analysis of both types of receivers using a maximum-likelihood sequence detector with hard-decision Viterbi decoding is provided.