Asymptotic MIMO Channel Model for Diffusive MC with Fully-absorbing Receivers

TL;DR

This paper develops an asymptotic analytical model for the number of molecules absorbed in diffusive MIMO molecular communication systems with fully-absorbing spherical receivers, accounting for mutual interactions.

Contribution

It introduces a novel asymptotic model using fictitious negative sources to describe receiver interactions, aligning well with numerical solutions for long times.

Findings

Model agrees with numerical solutions for long times

Barycenter tends to the receiver center asymptotically

Provides a practical approach where exact solutions are unavailable

Abstract

This letter introduces an analytical model that gives the asymptotic cumulative number of molecules absorbed by spherical receivers in a diffusive multiple-input multiple-output (MIMO) molecular communication (MC) system with pointwise transmitters. In the proposed model, the reciprocal effect among the fully absorbing (FA) receivers is described by using the concept of fictitious pointwise negative source of molecules, the best position of which for each spherical receiver being defined by its absorption barycenter. We show that there is an agreement between the proposed asymptotic model and the numerical solution of the exact analytical model from the literature that describes the interaction among the receivers, which is solved for a sufficient long time. We resort to numerical solution because for the exact model there is no analytical solution apart for the case of one transmitter and two receivers. We demonstrate that the barycenter tends to coincide with the center of the FA receivers in the temporal asymptotic case.