Stochastic Diffusivity With Time-Varying Trajectory in Mobile Molecular Communication: Performance Analysis and Channel Modeling

This work considers a three-dimensional mobile molecular communication (MC) with intra-body disease spread applications. The communicating devices in the considered mobile MC system are point transmitters and passive spherical receiver nano-machines (NMs) with emitted information-carrying molecules following the Gaussian Brownian motion. These NMs can be used to detect the presence of disease spread and for targeted drug delivery. We propose stochastic diffusivity models for both communicating devices and information-carrying molecules. Using the stochastic diffusivity model and considering initial distance as a reference, we derive the probability density function of the relative distance between the communicating devices. We allocate the time-varying trajectory to the information-carrying molecules moving towards receiver NM and obtain its diffusivity distribution. Through the proposed stochastic diffusivity model, we characterize the mobile MC channel by channel impulse response and derive its statistical mean. We consider the discrete-time statistical channel model at a high inter-symbol interference regime and analyze the channel performance in terms of error analysis and receiver operating characteristics. We also derive the channel for the considered system model. We show the degree of accuracy through root mean square error for the Poisson and Gaussian distribution models. Furthermore, the numerical results are verified through particle-based simulations.