Concentration-Encoded Subdiffusive Molecular Communication: Theory, Channel Characteristics, and Optimum Signal Detection

Impact of Anomalous Diffusion Phenomenon on Molecular Information Delivery in Bounded Environment

Through this paper, a three-dimensional molecular communication (MC) inside a cuboid container is considered. Instead of normal diffusion phenomenon, the anomalous diffusion phenomenon is incorporated which enhances the practicability of the model. The Fick's law is re-defined for the considering rectangular coordinate system in which information carrying molecules (ICMs) diffuse anomalously in the environment. The impact of flow of the fluid along the direction in the environment is also considered. Moreover, considering free propagator phenomenon, the expressions of spatio-temporal probability density function (PDF) of the ICMs is derived for the considered model. Further, the novel closed-form expressions for first arrival time density (FATD) of the ICM, survival probability (SP) at any time, and its corresponding first arrival probability (FAP) are also derived. Furthermore, the considered MC model is also analyzed in terms of minimum bit-error-rate (BER) using log-likelihood ratio test (LLRT) optimal detector. The derived expressions are verified using MATLAB based particle-based and Monte-Carlo simulations.

Impact of Evanescence Process on Three-Dimensional Sub-Diffusion-Based Molecular Communication Channel

In most of the existing works of molecular communication (MC), the standard diffusion environment is taken into account where the mean square displacement (MSD) of an information molecule (IM) scales linearly with time. On the contrary, this work considers the sub-diffusion motion that appears in crowded and complex (porous or fractal) environments (movement of the particles in the living cells) where the particle's MSD scales as a fractional order power law in time. Moreover, we examine an additional evanescence process resulting from which the molecules can degrade before hitting the boundary of the receiver (RX). Thus, in this work, we present a 3D MC system with a point transmitter (TX) and the spherical RX with the sub-diffusive behavior of an IM along with its evanescence. Furthermore, an IM's closed-form expressions for the arrival probability and the first passage time density (FPTD) are emulated in the above context. Additionally, we investigate the performance of MC by using the concentration-based modulation technique in a sub-diffusion channel. Finally, the considered MC channel is exploited in terms of the probability of detection, probability of false alarm, and probability of error for different parameters such as the reaction rate, fractional power, and radius of the RX.