# Diffusive Mobile MC with Absorbing Receivers: Stochastic Analysis and Applications

## TL;DR

This paper provides a comprehensive stochastic analysis of a diffusive mobile molecular communication system with absorbing receivers, deriving key statistical properties of the channel and applying them to optimize drug delivery and communication system performance.

## Contribution

It introduces the first analytical derivation of the CIR's distribution and absorption probability in a mobile MC system, enabling optimized system designs.

## Key findings

- Significant reduction in drug release compared to constant schemes.
- Improved bit error rate and molecule efficiency with optimized parameters.
- Demonstrated importance of accounting for mobility in system design.

## Abstract

This paper presents a stochastic analysis of the time-variant channel impulse response (CIR) of a three dimensional diffusive mobile molecular communication (MC) system where the transmitter, the absorbing receiver, and the molecules can freely diffuse. In our analysis, we derive the mean, variance, probability density function (PDF), and cumulative distribution function (CDF) of the CIR. We also derive the PDF and CDF of the probability p that a released molecule is absorbed at the receiver during a given time period. The obtained analytical results are employed for the design of drug delivery and MC systems with imperfect channel state information. For the first application, we exploit the mean and variance of the CIR to optimize a controlled-release drug delivery system employing a mobile drug carrier. We evaluate the performance of the proposed release design based on the PDF and CDF of the CIR. We demonstrate significant savings in the amount of released drugs compared to a constant-release scheme and reveal the necessity of accounting for the drug-carrier's mobility to ensure reliable drug delivery. For the second application, we exploit the PDF of the distance between the mobile transceivers and the CDF of p to optimize three design parameters of an MC system employing on-off keying modulation and threshold detection. Specifically, we optimize the detection threshold at the receiver, the release profile at the transmitter, and the time duration of a bit frame. We show that the proposed optimal designs can significantly improve the system performance in terms of the bit error rate and the efficiency of molecule usage.