Asymptotic MIMO Channel Model for Diffusive MC With Fully-Absorbing Receivers

Abstract

In a recent paper it has been shown that to model a diffusive molecular communication (MC) channel with multiple fully absorbing (FA) receivers, these can be interpreted as sources of negative particles from the other receivers' perspective. The barycenter point is introduced as the best position where to place the negative sources. The barycenter is obtained from the spatial mean of the molecules impinging on the surface of each FA receiver. This paper derives an expression that captures the position of the barycenter in a diffusive MC channel with multiple FA receivers. In this work, an analytical model inspired by Newton's law of gravitation is found to describe the barycenter, and the result is compared with particle-based simulation (PBS) data. Since the barycenter depends on the distance between the transmitter and receiver and the observation time, the condition that the barycenter can be assumed to be at the center of the receiver is discussed. This assumption simplifies further modeling of any diffusive MC system containing multiple FA receivers. The resulting position of the barycenter is used in channel F. Vakilipoor and M. Magarini are with the

Heuristic Barycenter Modeling of Fully Absorbing Receivers in Diffusive Molecular Communication Channels

“…Those points are also the center of each ring. We can take the weighted sum of the coordinate of the circles' centers on the diameter of the sphere aligned with the transmitter as (24). The numerator of ( 24) is the weighted sum of the points on the diameter of the receiver, which includes the radius of the receiver in the direction of the transmitter.…”

“…Fig. 2 compares the empirical γ obtained from the PBS based on different simulation step times with the analytical γ from (24). The PBS data was obtained through a Monte Carlo simulation for 100 trials with simulation step time {10 −7 , 10 −5 , 10 −4 , 10 −3 } 1 s and diffusion coefficient 79.4 µm 2 /s.…”

Localizing the Unknown Receiver in a Diffusive SIMO Molecular Communication System

“…where L {f } = f and L {N } = N . Next, we use the final value theorem to achieve the temporal asymptotic behavior, as t → ∞, of FA receivers' observation [9] …”

“…Thus, barycenters of receivers are assumed to be at the centers of the spherical FA receivers, as t → ∞. Hence, d i,j is approximated as the distance between the center of R i and R j [9].…”

“…In this paper, we rely on the single-input multiple-output (SIMO) asymptotic model proposed in [9]. According to the model, the asymptotic behavior can be estimated as a longtime observation 1 that depends on the physical properties of the system such as diffusion coefficient, distance, etc.…”