Conference PaperPDF Available

Abstract and Figures

Information delivery using chemical molecules is an integral part of biology at multiple distance scales and has attracted recent interest in bioengineering and communication. The collective signal strength at the receiver (i.e., the expected number of observed molecules inside the receiver), resulting from a large number of transmitters at random distances (e.g., due to mobility), can have a major impact on the reliability and efficiency of the molecular communication system. Modeling the collective signal from multiple diffusion sources can be computationally and analytically challenging. In this paper, we present the first tractable analytical model for the collective signal strength due to randomly-placed transmitters, whose positions are modelled as a homogeneous Poisson point process in three-dimensional (3D) space. By applying stochastic geometry, we derive analytical expressions for the expected number of observed molecules and the signal-to-interference ratios (SIRs) at a fully absorbing receiver and a passive receiver. Our results reveal that the collective signal strength at both types of receivers increases proportionally with increasing transmitter density. The SIR of a fully absorbing receiver is greater than that of a passive receiver, which suggests greater reliability at the fully absorbing receiver. The proposed framework dramatically simplifies the analysis of large-scale molecular systems in both communication and biological applications.
Content may be subject to copyright.
arXiv:1605.08311v2 [cs.IT] 3 Aug 2016
3D Stochastic Geometry Model for Large-Scale
Molecular Communication Systems
Yansha Deng, Adam Noel, Weisi Guo, Arumugam Nallanathan, and Maged Elkashlan§
Department of Informatics, King’s College London, UK
School of Electrical Engineering and Computer Science, University of Ottawa, Canada
School of Engineering, University of Warwick, UK
§School of Electronic Engineering and Computer Science, Queen Mary University of London, UK
Abstract—Information delivery using chemical molecules is an
integral part of biology at multiple distance scales and has
attracted recent interest in bioengineering and communication.
The collective signal strength at the receiver (i.e., the expected
number of observed molecules inside the receiver), resulting from
a large number of transmitters at random distances (e.g., due to
mobility), can have a major impact on the reliability and efficiency
of the molecular communication system. Modeling the collective
signal from multiple diffusion sources can be computationally
and analytically challenging. In this paper, we present the first
tractable analytical model for the collective signal strength due
to randomly-placed transmitters, whose positions are modelled
as a homogeneous Poisson point process in three-dimensional
(3D) space. By applying stochastic geometry, we derive analytical
expressions for the expected number of observed molecules at
a fully absorbing receiver and a passive receiver. Our results
reveal that the collective signal strength at both types of receivers
increases proportionally with increasing transmitter density. The
proposed framework dramatically simplifies the analysis of large-
scale molecular systems in both communication and biological
applications.
Index Terms—molecular communications, absorbing receiver,
passive receiver, stochastic geometry, interference modeling.
I. INTRODUCTION
Molecular communication via diffusion has attracted sig-
nificant bioengineering and communication engineering re-
search interest in recent years [1]. Messages are delivered
via molecules undergoing random walks [2], a prevalent phe-
nomenon in biology [3]. In fact, molecular communication
exists in nature at both the nano- and macro-scales, offering
transmit energy and signal propagation advantages over wave-
based communications [4,5]. One application example is that
swarms of nano-robots can track specific targets, such as a
tumour cells, to perform operations such as targeted drug
delivery [6]. In order to do so, energy efficient and tether-less
communications between the nano-robots must be established
in biological conditions [7], and possibly additional nano-bio-
interfaces need to be implemented [8].
Fundamentally, molecular communications involves modu-
lating information onto the property of a single or a group
of molecules (e.g., number, type, emission time). When mod-
ulating the number of molecules, each messenger node will
transmit information-bearing molecules via chemical pulses. In
a realistic environment with a swarm of robots (i.e., messenger
nodes) operating together, they are likely to transmit molecular
messages simultaneously. Due to limitations in transmitter de-
sign and molecule type availability, it is likely that many trans-
mitters will transmit the same type of information molecule.
Thus, it is important to model the collective signal strength due
to all transmitters with the same type of information molecule,
and to account for random transmitter locations due to mobility.
Existing works have largely focused on modeling: 1) the
signal strength of a point-to-point communication channel by
considering the self-interference that arises from adjacent sym-
bols (i.e., inter-symbol-interference (ISI)) at a passive receiver
[9], at a fully absorbing receiver [10], and at a reversible
adsorption receiver [11]; and 2) the collective signal strength of
a multi-access communication channel at the passive receiver
due to co-channel transmitters (i.e., transmitters emitting the
same type of molecule) with the given knowledge of their total
number and location [9].
The first work to consider randomly distributed co-channel
transmitters in 3-D space according to a spatial homogeneous
Poisson process (HPPP) is [12], where the probability density
function (PDF) of the received signal at a point location was
derived based on the assumption of white Gaussian transmit
signals. Since the receiver size was negligible, the placement
of transmitters did not need to accommodate the receiver’s
location. More importantly, only the Monte Carlo simulation,
and not particle-based simulation, was performed to verify the
derived PDF.
From the perspective of receiver type, many works have
focused on the passive receiver, which can observe and count
the number of molecules inside the receiver without interfering
with the molecules [9,12]. In nature, receivers commonly
remove information molecules from the environment once they
bind to a receptor. One example is the fully absorbing receiver,
which absorbs all the molecules hitting its surface [10, 11].
However, no work has studied the channel characteristics and
the received signal at the fully absorbing receiver in a large-
scale molecular communication system, let alone its compari-
son with that at the passive receiver.
In this paper, we model the collective signal strength at the
passive receiver and fully absorbing receiver due to a swarm
of mobile point transmitters that simultaneously emit a given
number of information molecules. Unlike [12], which focused
on the statistics of the received signal at any point location,
we focus on examining and deriving exact expressions for
the expected number of molecules observed inside two types
of receiver for signal demodulation. This is achieved using
stochastic geometry, which has been extensively used to model
and provide simple and tractable results for wireless systems
[13]. Our contributions can be summarized as follows:
1) We use stochastic geometry to model the collective signal
at a receiver in a large-scale molecular communication
system, where the receiver is either passive or fully
absorbing. We distinguish between the desired signal due
to the nearest transmitter and the interfering signal due
to the other transmitters.
2) We derive a simple closed-form expression for the ex-
pected number of molecules absorbed at the fully absorb-
ing receiver, and a tractable expression for the expected
number of molecules observed inside the passive receiver
at any time instant.
3) We define and derive tractable analytical expressions for
the fraction of molecules due to the nearest transmitter
and the fraction of molecules due to the other transmit-
ters.
4) We verify our results using particle-based simulation and
Monte Carlo simulation, which prove that the expected
number of molecules observed at both types of receiver
increases linearly with increasing transmitter density.
II. SYSTEM MODEL
We consider a large-scale molecular communication system
with a single receiver in which a swarm of point transmitters are
spatially distributed outside the receiver in R3/Vrraccording
to an independent and HPPP Φwith density λ, where Vrr
is the volume of receiver rr. This spatial distribution, which
was previously used to model wireless sensor networks [14],
cellular networks [13] and heterogenous cellular networks [15],
has also been applied to model bacterial colonies in [16] and
the interference sources in a molecular communication system
[12]. We consider a fluid environment in the absence of flow
currents: the extension for flow currents will be treated in future
work.
At any given time instant, a number of transmitters will
be either silent or active. Thus, we define the activity prob-
ability of a transmitter that is triggered to transmit data as
ρa(0 < ρa<1). This activity probability is independent of the
receiver’slocation. Thus, the active point transmitters constitute
independent HPPPs Φawith intensities λa=λρa. Each
transmitter transmits molecular signal pulses with amplitude
NFA
tx (NPS
tx ) to the absorbing receiver (the passive receiver). We
assume the existence of a global clock such that all molecule
emissions can only occur at t= 0.
We consider two types of spherical receiver with radius rr:
1) Fully absorbing receiver [17], and 2) Passive receiver [4,
18]. To equivalently compare them, we assume both types of
receiver are capable of counting the number of information
molecules within the receiver volume at any time instant for
information decoding.
It is well known that the distance between the transmitter and
the receiver in molecular communication is the main contributor
Receiver
k th Point!
Transmitter
T
t
P
T
t
P
T
t
P
T
t
P
T
t
P
T
t
P
T
t
P
rr
Fig. 1. Illustration of a receptor receiving molecular pulse signals from point
transmitters at different distances.
to the degradation of the signal strength (i.e., the number of
molecules observed at the receiver). Instinctively, we assume
that the receiver is associated with the nearest transmitter to
obtain the strongest signal. Thus, the messenger molecules
transmitted by other active point transmitters act as interference,
which impairs the correct reception at the receiver. To measure
this impairment, we formulate the desired signal, the interfering
signal for the absorbing receiver and the passive receiver in the
following subsections.
A. Absorbing Receiver
In our proposed large-scale molecular communication sys-
tem, let us consider the center of an absorbing receiver located
at the origin. Using the Slivnyak-Mecke’s theorem [13], the
fraction FFA of molecules absorbed at the receiver until time
Tdue to an arbitrary point transmitter xat the location xwith
molecule emission occurring at t= 0 can be represented as
[17]
FFA ( rr, T |kxk) = rr
kxkerfc nkxk − rr
4DT o,(1)
where kxkis the distance between the point transmitter and the
center of the receiver where the transmitters follow a HPPP,
and Dis the constant diffusion coefficient, which is usually
obtained via experiment as in [19, Ch. 5]. The fraction FFA
uof
molecules absorbed inside the receiver until time Tdue to a
single pulse emission by the nearest active transmitter can be
represented as
FFA
u(rr, T | kxk) = rr
kxkerfc nkxk − rr
4DT o,(2)
where kxkdenotes the distance between the receiver and the
nearest transmitter,
x= arg min
xΦakxk,(3)
xdenotes the nearest point transmitter for the receiver, and
Φadenotes the set of active transmitters’ positions.
The fraction of molecules absorbed at the receiver until
time Tdue to single pulse emissions at each active interfering
transmitter FFA
Iand that due to a single pulse emission at each
active transmitter FFA
all is represented as
FFA
I(rr, T | kxk) = X
Φa/x
rr
kxkerfc nkxk − rr
4DT o,(4)
and
FFA
all (rr, T | kxk) = X
Φa
rr
kxkerfc nkxk − rr
4DT o,(5)
respectively.
The expected number of molecules absorbed at the receiver
by time Tdue to all active transmitters is equivalently the
expected number of molecules absorbed at the receiver until
time T, which can be calculated as
ENFA
all (Ωrr, T )=NFA
tx FFA
all (rr, T | kxk)
=NFA
tx FFA
u(rr, T | kxk)
|{z }
EFA
u
+NFA
tx FFA
I(rr, T | kxk)
|{z }
EFA
I
,(6)
where FFA
all (rr, T | kxk)is given in (5), EFA
uis the fraction of
absorbed molecules at the absorbing receiver until time Tdue
to the nearest transmitter, and EFA
Iis the fraction of absorbed
molecules at the absorbing receiver until time Tdue to the
other (interfering) transmitters.
B. Passive Receiver
In a point-to-point molecular communication system with a
single point transmitter located distance kxkaway from the
center of a passive receiver with radius rr, the local point
concentration at the center of the passive receiver at time T
due to a single pulse emission by the transmitter is given as
[20, Eq. (4.28)]
C( Ωrr, T |kxk) = 1
(4πD T )3/2 exp kxk2
4DT .(7)
The fraction of information molecules observed inside the
passive receiver with volume Vrrat time Tis denoted as
FPS (rr, T | kxk) = Z
Vrr
C(rr, T | kxk)dVrr,(8)
where Vrris the volume of the spherical passive receiver.
According to (8) and Theorem 2 in [21], the fraction FPS of
information molecules observed inside the passive receiver at
time Tdue to a single pulse emission by a transmitter at time
tis derived as
FPS ( Ωrr, T |kxk) = 1
2erfrr− kxk
2DT + erfrr+kxk
2DT
+DT
πkxk"exp (rr+kxk)2
4DT exp (kxk − rr)2
4DT #,
(9)
which does not assume that the molecule concentration inside
the passive receiver is uniform. This is unlike the common as-
sumption that the concentration of molecule inside the passive
receiver is uniform. Although that assumption is commonly
applied, it relies on the receiver being sufficiently far from the
transmitter (see [21]), which we cannot guarantee here since
the transmitters are placed randomly.
In the large-scale molecular communication system with a
passive receiver centered at the origin, the expected number of
molecules observed inside the receiver at time Tdue to a single
pulse emission at all active transmitters at t= 0 is given as
ENPS
all (Ωrr, T )=E(X
Φa
NPS
tx FPS ( Ωrr, T |kxk))
=NPS
tx FPS
u(rr, T | kxk)
|{z }
EPS
u
+NPS
tx FPS
I(rr, T | kxk)
|{z }
EPS
I
,
(10)
where FPS ( Ωrr, T | kxk)is given in (9), EPS
uis the fraction
of molecules observed inside the receiver at time Tdue to the
nearest transmitter, and EPS
Iis the fraction of molecules ob-
served inside the receiver at time Tdue to the other (interfering)
transmitters.
III. RECEIVER OBSERVATIONS
In this section, we first derive the distance distribution
between the receiver and the nearest point transmitter. By doing
so, we derive exact expressions for the expected number of
molecules observed inside the receiver due to the nearest point
transmitter and that due to the interfering transmitters.
A. Distance Distribution
Unlike the stochastic geometry modelling of wireless net-
works, where the transmitters are randomly located in the un-
bounded space, the point transmitters in a large-scale molecular
communication system can only be distributed outside the sur-
face of the spherical receiver. Taking into account the minimum
distance rrbetween point transmitters and the receiver center,
we derive the probability density function (PDF) of the shortest
distance between a point transmitter and the receiver in the
following proposition.
Proposition 1. The PDF of the shortest distance between any
point transmitter and the receiver in 3D space is given by
fkxk(x) = 4λaπx2eλa(4
3πx34
3πrr
3),(11)
where λa=λρa.
Proof. See Appendix A.
Based on the proof of Proposition 1, we also derive the PDF
of the shortest distance between any point transmitter and the
receiver in 2D space in the following lemma.
Corollary 1. The PDF of the shortest distance between any
point transmitter and the receiver in 2D space is given by
fkxk(x) = 2λaπreλa(πr 2πrr
2),(12)
where λa=λρa.
B. Absorbing Receiver Observations
In this subsection, we derive a closed-form expression for the
expected number of molecules observed inside the absorbing
receiver in 3D space.
Using Campbell’s theorem, we derive the expected number
of absorbed molecules due to the nearest transmitter and that
due to the interfering transmitters until time tas
EFA
u=NFA
tx Z
rr
Πt
0(x) 4λaπx2eλa(4
3πx34
3πrr
3)dx, (13)
and
EFA
I=NFA
tx (4πλa)2Z
rrZ
x
Πt
0(r)r2drx2eλa(4
3πx34
3πrr
3)dx,
(14)
respectively.
Theorem 1. The expected net number of molecules absorbed
at the absorbing receiver in 3D space during any sampling
time interval [t, t +Tss ]is derived as
ENFA
all (Ωrr, t, t +Tss )
= 4NFA
tx πλarrhDπTss + 2DrrpTss +tti.
(15)
The expected number of molecules observed inside the fully
absorbing receiver in 3D space until time tis derived as
ENFA
all (Ωrr, t)= 4NFA
tx πλarrhDπt + 2rrDti.
(16)
Proof. See Appendix B.
From Theorem 1, we find that the expected number of
molecules absorbed at the absorbing receiver at time tis
linearly proportional to the density of active transmitters,
and increases with increasing diffusion coefficient or receiver
radius. As expected, we find that the expected number of
molecules absorbed at the receiver until tis always increasing
with time t.
C. Passive Receiver Observations
In the following theorem, we derive the expected number of
molecules observed inside the passive receiver in 3D space.
Using Campbell’s theorem, we derive the expected number
of observed molecules due to the nearest transmitter and that
due to the interfering transmitters at time tas
EPS
u= 4λaπN PS
tx e4
3πrr
3λaZ
rr
Φ (x)x2exp n4
3πx3λaodx,
(17)
and
EPS
I=(4πλa)2e4
3πrr
3λaNPS
tx Z
rrZ
x
Φ (r)r2dr
x2e4
3πx3λadx, (18)
respectively. In (17) and (18), Φ (r) = FPS ( rr, t|r).
Theorem 2. The expected net number of molecules observed
inside the passive receiver during any sampling time interval
[t, t +Tss ]in 3D space is derived as
ENPS
all ( Ωrr, t, t +Tss |kxk)= 4NPS
tx πλa
Z
rr
FPS (rr, t +Tss |r)r2dr Z
rr
FPS (rr, t|r)r2dr,
(19)
where FPS (rr, t|r)is given in (9).
The expected number of molecules observed inside the pas-
sive receiver at time tin 3D space is derived as
ENPS
all (rr,0, t|kxk)=
4NPS
tx πλaZ
rr
FPS (rr, t|r)r2dr. (20)
Proof. Analogous to Appendix B without solving the integrals.
In Theorem 2, we observe that the expected number of
molecules observed inside the passive receiver also increases
proportionately with the density of active transmitters.
IV. NUMERICAL AND SIMULATION RESULTS
In this section, we examine the expected number of
molecules observed at the absorbing receiver and the passive
receiver due to simultaneous single pulse emissions at all active
point transmitters. In all figures of this section, we set the
parameters as follows: rr= 5 µm and NFA
tx =NPS
tx = 104.
In all figures, the analytical curves of the expected number
of molecules absorbed at the absorbing receiver due to all
the transmitters, the nearest transmitter, and the interfering
transmitters are plotted using Eqs. (15), (13), and (14), and
are abbreviated as “Absorbing All”, “Absorbing Nearest”, and
Absorbing Aggregate”, respectively. The analytical curves of
the expected number of molecules observed inside the passive
receiver due to all the transmitters, the nearest transmitter, the
interfering transmitters are plotted using (19), (17), and (18),
and are abbreviated as “Passive All”, “Passive Nearest”, and
“Passive Aggregate”, respectively.
A. Particle-Based and Pseudo Simulation Validation
In Fig. 2, we set D= 80 ×1012 m2
s, and assume that the
transmitters are placed up to R= 50 µm from the center of the
receiver at a density of λa= 104transmitters per µm3(i.e.,
52 average number of transmitters, including the subtraction of
the receiver volume). The receiver takes samples every Tss =
0.01 s and calculates the net change in the number of observed
molecules between samples. The default simulation time step
is also 0.01 s. Unless otherwise noted, all simulation results
were averaged over 104transmitter location permutations, with
each permutation simulated at least 10 times.
In Fig. 2, we verify the analytical expressions for the
expected net number of molecules observed during [t, t +Tss ]
at the absorbing receiver in Eq. (13) and Eq. (14), and that
inside the passive receiver in Eq. (17) and Eq. (18) by com-
paring with the particle-based simulations and the Monte Carlo
10−1 100
0
0.2
0.4
0.6
0.8
1
0.01 0.02 0.03
0
0.2
0.4
0.6
0.8
1
Absorbing Nearest
Absorbing Aggregate
Absorbing Nearest
Absorbing Aggregate
Passive Aggregate
Passive Nearest
Analytical
Particle−Based Sim.
Monte Carlo Sim.
Time (s) Time (s)
Net Number of Observed Molecules
Fig. 2. Net number of observed molecules inside the receiver as a function of
time. All curves are scaled by the maximum value of the analytical curves in
the right subplot.
TABLE II
THE S IMUL ATI ON PARA METERS A ND SCA LING VALUE S APP LIED IN FIG. 2.
Transmitter Receiver Realizations Time Scaling
Step [s] Value
Nearest Passive 104102149.57
Nearest Active 104102354.52
Aggregate Passive 1041029.252
Aggregate Active 10310359.42
simulations. The particle-based simulations were performed by
tracking the progress of individual particles to obtain the net
number of observed molecules during [t, t +Tss]using the
AcCoRD simulator (Actor-based Communication via Reaction-
Diffusion) [22]. The pseudo simulations rely on the Monte
Carlo simulation method, which were performed by averaging
the expected number of observed molecules due to all active
transmitters with randomly-generated location, as calculated
from Eq. (1) and Eq. (9), over 104realizations.
In the right subplot of Fig. 2, we compare passive and absorb-
ing receivers and observe the expected net number of observed
molecules during [t, t +Tss ]due to the nearest transmitter and
due to the aggregation of the interfering transmitters. In the
left subplot of Fig. 2, we lower the simulation time step to
104s for the first few samples of the two absorbing receiver
cases, in order to demonstrate the corresponding improvement
in accuracy. All curves in both subplots are scaled by the max-
imum value of the corresponding analytical curve in the right
subplot; the scaling values and other simulation parameters are
summarized in Table II.
1) Particle-Based Simulation Validation: Overall, there is
good agreement between the analytical curves and the particle-
based simulations in the right subplot of Fig. 2. The analytical
results for the net number of molecules observed inside the
passive receiver during [t, t+Tss]due to the nearest transmitter
is highly accurate, and even captures the net loss of molecules
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
0.5
1
1.5
2x 105
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
2000
4000
6000
8000
Analytical
Monte Carlo Sim.
Passive All
Absorbing All
Passive Nearest
Passive Aggregate
Absorbing Aggregate
Absorbing Nearest
Number of Observed Molecules
Time (s)
Fig. 3. Expected number of molecules observed inside the receiver as a
function of time.
observed after t= 0.1s. There is a slight deviation in the
particle-based simulation for the “passive aggregate” curve,
particularly as time approaches t= 1 s, which is primarily due
to the very low number of molecules observed at this time (note
that the scaling factor in this case is only 9.252; see Table II).
There is less agreement between the particle-based simula-
tions and the analytical expressions for the absorbing receiver,
and this is primarily due to the large simulation time step (even
though we used a smaller time step for the aggregate transmitter
case in the right subplot; see Table II). To demonstrate the
impact of the time step, the left subplot shows much better
agreement for the absorbing receiver model by lowering the
time step to 104s. This improvement is especially true in the
case of the nearest transmitter, as there is significant devia-
tion between the particle-based simulation and the analytical
expression for very early times in the right subplot.
2) Monte Carlo Simulation Validation: There is a good
match between the analytical curves and the Monte Carlo
simulations for the net number of molecules observed at both
types of receiver during [t, t+Tss ]due to the nearest transmitter,
which can be attributed to the large number of molecules and
the shortest distance value compared with R= 50 µm (as
shown in Table II). There is slight deviation in the Monte Carlo
simulations for the expected number of molecules observed
inside both types of receiver due to the interfering transmitters,
and this is primarily due to the restricted placement of trans-
mitters to the maximum distance R= 50 µm. In Figs. 3, better
agreement between the analytical curves and pseudo simulation
is achieved by increasing the maximum placement distance R.
Due to the extensive computational demands to simulate
such large molecular communication environments, we assume
that the particle-based simulations have sufficiently verified the
analytical models. The remaining simulation results in Fig. 3
is only generated via Monte Carlo simulation.
B. Performance Evaluation
From Fig. 2 and the scaling values in Table II, we see
that the expected net number of molecules absorbed at the
absorbing receiver is much larger than that inside the passive
receiver, since every molecule arriving at the absorbing receiver
is permanently absorbed. We also notice that the expected net
number of absorbed molecules due to the nearest transmitter is
much larger than that due to the interfering transmitters, which
may be due to a relatively low transmitter density.
Interestingly, the concurrent single pulse transmission by the
transmitters at time t= 0 results in a longer and stronger
channel response at the absorbing receiver than that at the
passive receiver. If the demodulation is based on the number of
observed molecules during each bit interval, the longer channel
response at the absorbing receiver may contribute to higher ISI
than at a passive receiver for the same bit interval, whereas its
stronger channel response may benefit signal detection.
In Fig. 3, we set the parameters: D= 120 ×1012 m2
s,
R= 100 µm, and Tss = 0.1s. Fig. 3 plots the expected
number of molecules observed at the absorbing receiver and
the passive receiver at time t. We set the density of active
transmitters as λa= 103m3. As shown in the lower subplot
of Fig. 3, the channel responses of the receivers due to the
nearest transmitter in this large-scale molecular communication
system are consistent with those observed at the absorbing
receiver in [11, Fig. 4] and the passive receiver in [4, Fig. 2]
and [18, Fig. 1] for a point-to-point molecular communication
system.
In Fig. 3, we notice that the expected number of observed
molecules at time tdue to all the transmitters is dominated by
the interfering transmitters, rather than the nearest transmitter,
which is due to the higher density of transmitters. Furthermore,
as we might expect, the expected number of molecules observed
inside the passive receiver at time tstabilizes after t= 0.8s,
whereas that at the absorbing receiver increases linearly with
increasing time. This reveals the potential differences in optimal
demodulation and interference cancellation design for these two
types of receiver.
V. CONCLUSIONS AND FUTURE WORK
In this paper, we provided a general model for the transmitter
modelling in a large-scale molecular communication system
using stochastic geometry. The collective signal strength at a
fully absorbing receiver and a passive receiver are modelled
and examined. We derived tractable expressions for the ex-
pected number of observed molecules at the fully absorbing
receiver and the passive receiver, which were shown to increase
with transmitter density. Our analytical results were validated
through particle-based simulation and Monte Carlo simulation.
The analytical model presented in this paper can also be applied
for the performance evaluation of other types of receiver
(e.g., partially absorbing, reversible adsorption receiver, ligand-
binding receiver) in large-scale molecular communication sys-
tems by substituting its corresponding channel response.
REFERENCES
[1] T. Nakano, A. Eckford, and T. Haraguchi, Molecular communication.
Cambridge University Press, 2013.
[2] E. Codling, M. Plank, and S. Benhamous, “Random walk models in
biology,Journal of The Royal Society Interface, vol. 5, no. 25, pp. 813–
834, Aug. 2008.
[3] S. Atkingson and P. Williams, “Quorum sensing and social networking
in the microbial world,Journal of The Royal Society Interface, vol. 6,
no. 40, pp. 959–978, Aug. 2009.
[4] I. Llatser, A. Cabellos-Aparicio, and M. Pierobon, “Detection techniques
for diffusion-based molecular communication,IEEE Journal on Selected
Areas in Communications (JSAC), vol. 31, pp. 726–734, Dec. 2013.
[5] W. Guo, C. Mias, N. Farsad, and J. Wu, “Molecular versus electromag-
netic wave propagation loss in macro-scale environments,” IEEE Trans.
Mol. Biol. Multi-Scale Commun., vol. 1, Mar. 2015.
[6] S. M. Douglas, I. Bachelet, and G. M. Church, “A logic-gated nanorobot
for targeted transport of molecular payloads,Science, vol. 335, no. 6070,
pp. 831–834, Feb. 2012.
[7] A. Cavalcanti, T. Hogg, B. Shirinzadeh, and H. Liaw, “Nanorobot
communication techniques: a comprehensive tutorial,” in Proc. IEEE Int.
Conf. Control, Autom., Robot., Vis., Dec. 2006, pp. 1–6.
[8] C. J. Kirkpatrick and W. Bonfield, “Nanobiointerface: a multidisciplinary
challenge,Journal of The Royal Society Interface, vol. 7, no. Suppl 1,
pp. S1–S4, Dec. 2009.
[9] A. Noel, K. C. Cheung, and R. Schober, “A unifying model for external
noise sources and isi in diffusive molecular communication,” IEEE J. Sel.
Areas Commun., vol. 32, no. 12, pp. 2330–2343, Dec 2014.
[10] H. B. Yilmaz and C.-B. Chae, “Simulation study of molecular communi-
cation systems with an absorbing receiver: Modulation and ISI mitigation
techniques,Simulat. Modell. Pract. Theory, vol. 49, pp. 136–150, Dec.
2014.
[11] Y. Deng, A. Noel, M. Elkashlan, A. Nallanathan, and K. C. Cheung,
“Modeling and simulation of molecular communication systems with
a reversible adsorption receiver,arXiv, 2016. [Online]. Available:
http://arxiv.org/abs/1601.00681
[12] M. Pierobon and I. F. Akyildiz, “A statistical–physical model of interfer-
ence in diffusion-based molecular nanonetworks,” IEEE Trans. Commun.,
vol. 62, no. 6, pp. 2085–2095, Jun. 2014.
[13] F. Baccelli and B. Blaszczyszyn, Stochastic geometry and wireless
networks: Volume 1: Theory. Now Publishers Inc, 2009, vol. 1.
[14] Y. Deng, L. Wang, M. Elkashlan, A. Nallanathan, and R. K. Mallik,
“Physical layer security in three-tier wireless sensor networks: A stochas-
tic geometry approach,IEEE Trans. Inf. Forensics Security, vol. 11,
no. 6, pp. 1128–1138, Jun. 2016.
[15] Y. Deng, L.Wang, M. Elkashlan, M. Direnzo, and J. Yuan, “Modeling and
analysis of wireless power transfer in heterogeneous cellular networks,”
IEEE Trans. Commun., 2016.
[16] S. Jeanson, J. Chadoeuf, M. Madec, S. Aly, J. Floury, T. F. Brocklehurst,
and S. Lortal, “Spatial distribution of bacterial colonies in a model
cheese,Applied and Environmental Microbiology, vol. 77, no. 4, pp.
1493–1500, Dec. 2010.
[17] H. B. Yilmaz, A. C. Heren, T. Tugcu, and C.-B. Chae, “Three-
Dimensional channel characteristics for molecular communications with
an absorbing receiver,” IEEE Communications Letters, vol. 18, no. 6, pp.
929–932, Jun. 2014.
[18] A. Noel, K. C. Cheung, and R. Schober, “Improving receiver perfor-
mance of diffusive molecular communication with enzymes,” IEEE Trans.
Nanobiosci., vol. 13, no. 1, pp. 31–43, Mar. 2014.
[19] E. L. Cussler, Diffusion: mass transfer in fluid systems. Cambridge
university press, 2009.
[20] P. Nelson, Biological Physics: Energy, Information, Life, updated 1st ed.
W. H. Freeman and Company, 2008.
[21] A. Noel, K. C. Cheung, and R. Schober, “Using dimensional analysis
to assess scalability and accuracy in molecular communication,” in Proc.
IEEE ICC MoNaCom, Jun. 2013, pp. 818–823.
[22] A. Noel. (2016) Actor-based communication via reaction-diffusion.
[Online]. Available: https://github.com/adamjgnoel/AcCoRD
... Other researchers propose new ideas such as using ion protein channels to control molecules release [Arjmandi et al., 2016], a ratio shift between two types of molecules [Mosayebi et al., 2016] or the dynamic properties of propagation patterns in molecules' concentration [Nakano and Suda, 2017]. In the second class of works, the researchers modeled molecular communication channels to study the dynamic distribution of information in the medium [Chahibi et al., 2016;Deng et al., 2016]. They use discrete-time channels [Damrath et al., 2017], or continuous stochastic models for constant [Bicen et al., 2016] and mobile transmitters and receivers [Ahmadzadeh et al., 2017]. ...
... Instead of using electromagnetic waves, molecules are used as wireless carriers of information between the transmitter and the receiver[Pierobon and Akyildiz, 2010]. However, the achievable throughput with molecular communications is still very low and the delay is very high, despite the efforts reported in the literature to enhance both of them and to decrease the inter-symbol interference[Ahmadzadeh et al., 2017;Akdeniz et al., 2018;Ardeshiri et al., 2017;Arjmandi et al., 2016;Assaf et al., 2017;Barros, 2017;Bicen et al., 2016;Chahibi et al., 2016;Chang et al., 2018;Cho et al., 2017; Cherkaoui, 2018, 2019;Damrath et al., 2017;Deng et al., 2016;Einolghozati et al., 2016;Enomoto et al., 2011;Farsad et al., 2016;Kim et al., 2014;Mosayebi et al., 2016;Nakano and Suda, 2017;Noel et al., 2014; Tavakkoli et al., 2017a,b; Tepekule et al., 2015a,b;Unluturk and Akyildiz, 2017]. ...
... The most studied methods proposed for molecular communication are based on the principle of molecular diffusion, where molecules move randomly, because of the thermal fluctuations of the medium, until they reach the receiver. The work on molecular communication in the literature can be categorized into five classes; a) modulation techniques[Arjmandi et al., 2016;Farsad et al., 2016;Mosayebi et al., 2016;Nakano and Suda, 2017], b) channel modeling studies[Ahmadzadeh et al., 2017;Bicen et al., 2016;Chahibi et al., 2016;Damrath et al., 2017;Deng et al., 2016], c) relay assistance methods[Ardeshiri et al., 2017; Tavakkoli et al., 2017a,b], d) ISI avoidance[Akdeniz et al., 2018;Assaf et al., 2017;Chang et al., 2018;Cho et al., 2017; Cherkaoui, 2018, 2019; Kim 5.4. STATE-OF-THE-ART 77 et al., 2014;Noel et al., 2014; Tepekule et al., 2015a,b] and e) end-to-end communication system designs ...
Thesis
Full-text available
The field of nanotechnology has undergone very rapid and fascinating development in recent years. This rapid and impressive advance has led to new applications of nanotechnology in the biomedical and military industries, making it a key area of research in multidisciplinary fields. However, the individual processing capacity of nanodevices is very limited, hence the need to design nanonetworks that allow the nanodevices to share information and to cooperate with each other. There are two solutions to establish a nanocommunication system: either by adapting the classical electromagnetic communication to the requirements of nano scale, or by using biological nanosystems inspired by nature such as the molecular communication proposed in the literature. In this thesis, we are interested in the second solution, which is exploiting the potential of biological nanosystems used by nature since billions of years to design biocompatible nanonetworks that can be used inside the human body for medical applications. Nevertheless, the use of this new paradigm is not without challenges. The very low achievable throughput and the Inter-Symbol Interference (ISI) are the most influential problems on the quality of molecular communication. The main objective of this thesis is to design and evaluate new methods inspired by nature in order to enhance the performance of nano-communication systems. To do this, the work is divided into three main parts. In the first part, we enhance the performance of molecular communication by proposing a new method that uses a photolysis-reaction instead of using enzyme to better attenuate ISI. We also propose an optimization of the receiver used in MIMO systems by judiciously choosing the parameters used in its design to reduce the influence of path loss on the quality of the system. The second part proposes a new wired nano-communication system based on self-assembled polymers that build an electrically conductive nanowire to connect the nanodevices to each other. The use of electrons as information carriers drastically increases the achievable throughput and reduces the delay. We study the dynamic process of self-assembly of the nanowire and we propose a bio inspired receiver that detects the electrons sent through the conductive nanowire and converts them into a blue light. The third part applies the proposed wired nano-communication system to design an architecture of Wired Ad hoc NanoNETworks (WANNET) with a physical layer, Medium Acess Control (MAC) layer and application layer. We also calculate the maximum throughput and we evaluate the performance of the system.
... This paper was presented in part at the IEEE Global Telecommunications Conference, Singapore, December 2017 [1]. reactions may occur during molecule propagation via enzyme reaction [7], or at the reception of molecule via reversible absorption reaction [8] or ligand binding reaction [9]. To capture the molecule behaviour at any time, existing research has mainly focused on mathematically modelling and theoretical analysis of these physical and chemical processes, such as the channel response modelling [8], [10], channel capacity calculation [11], [12], and bit error probability derivation [7], [13]. ...
... reactions may occur during molecule propagation via enzyme reaction [7], or at the reception of molecule via reversible absorption reaction [8] or ligand binding reaction [9]. To capture the molecule behaviour at any time, existing research has mainly focused on mathematically modelling and theoretical analysis of these physical and chemical processes, such as the channel response modelling [8], [10], channel capacity calculation [11], [12], and bit error probability derivation [7], [13]. ...
... For one type of molecular species flowing in a 3D straight convection-diffusion channel with rectangular cross section, its concentration C(x, y, z, t) can be described by the 3D convection-diffusion equation as [37] ∂C(x, y, z, t) ∂t = D∇ 2 C(x, y, z, t) − v · ∇C(x, y, z, t), (8) where ∇ is the Nabla operator, and v is the flow velocity described by (7). When the flow falls into dispersion regime, the interaction between cross-sectional diffusion and nonuniform convection can lead to a uniform molecule distribution along the cross-section, i.e., ∂C(x,y,z,t) ∂y = ∂C(x,y,z,t) ∂z = 0, such that (8) can be simplified into a 1D convection-diffusion equation [38] ∂C(x, t) ∂t ...
Article
Full-text available
The design of communication systems capable of processing and exchanging information through molecules and chemical processes is a rapidly growing interdisciplinary field, which holds the promise to revolutionize how we realize computing and communication devices. While molecular communication (MC) theory has had major developments in recent years, more practical aspects in designing components capable of MC functionalities remain less explored. This paper designs chemical reactions-based microfluidic devices to realize binary concentration shift keying (BCSK) modulation and demodulation functionalities. Considering existing MC literature on information transmission via molecular pulse modulation, we propose a microfluidic MC transmitter design, which is capable of generating continuously predefined pulse-shaped molecular concentrations upon rectangular triggering signals to achieve the modulation function. We further design a microfluidic MC receiver capable of demodulating a received signal to a rectangular output signal using a thresholding reaction and an amplifying reaction. Our chemical reactions-based microfluidic molecular communication system is reproducible and its parameters can be optimized. More importantly, it overcomes the slow-speed, unreliability, and non-scalability of biological processes in cells. To reveal design insights, we also derive the theoretical signal responses for our designed microfluidic transmitter and receiver, which further facilitate the transmitter design optimization. Our theoretical results are validated via simulations performed through the COMSOL Multiphysics finite element solver. We demonstrate the predefined nature of the generated pulse and the demodulated rectangular signal together with their dependence on design parameters.
... The distance r d = x d from the typical RBN can be a constant or a random variable. In addition to the tagged TBN, there are interfering transmitters in 3D fluid medium whose locations can be modeled by 3D homogeneous PPP Φ [17], [20], [22]. Since the receiver occupies the space B(0, a), the support of PPP is taken as R 3 \ B(0, a) [17], [22]. ...
... In addition to the tagged TBN, there are interfering transmitters in 3D fluid medium whose locations can be modeled by 3D homogeneous PPP Φ [17], [20], [22]. Since the receiver occupies the space B(0, a), the support of PPP is taken as R 3 \ B(0, a) [17], [22]. ...
Preprint
Full-text available
In this paper, we present an analytical framework to derive the performance of a molecular communication system where a transmitter bio-nano-machine (TBN) is communicating with a fully-absorbing spherical receiver bio-nano-machine (RBN) in a diffusive propagation medium in the presence of other TBNs. We assume that transmit bits at each TBN is random and different than transmit bits at other TBNs. We model the TBNs using a marked Poisson point process (PPP) with their locations as points of PPP and transmit symbols as marks. We consider both inter-symbol interference (ISI) and co-channel interference (CCI). ISI is caused by molecules transmitted in the previous slots while CCI is due to the molecules emitted from other TBNs. We derive the bit error probability of this system by averaging over the distribution of the transmit bits as opposed to the past approaches consisting of conditioning on previous transmit bits and/or assuming the transmit bits of every TBN are the same. Using numerical results, we validate our analysis and provide various design insights about the system, for example, the impact of detection threshold on the system performance. We also show the importance of accurately incorporating the randomness of transmit bits in the analysis.
... Meanwhile, chemical reactions may occur during molecule propagation via enzyme reaction [6], or at the reception of molecule via reversible absorption reaction [7] or ligand binding reaction [8]. To capture the molecule behaviour at any time, existing research has mainly focused on mathematically modelling and theoretical analysis of these physical and chemical processes, such as the channel response modelling [7], [9], channel capacity calculation [10], [11], and bit error probability derivation [6], [12]. ...
... Meanwhile, chemical reactions may occur during molecule propagation via enzyme reaction [6], or at the reception of molecule via reversible absorption reaction [7] or ligand binding reaction [8]. To capture the molecule behaviour at any time, existing research has mainly focused on mathematically modelling and theoretical analysis of these physical and chemical processes, such as the channel response modelling [7], [9], channel capacity calculation [10], [11], and bit error probability derivation [6], [12]. ...
Preprint
Full-text available
The design of communication systems capable of processing and exchanging information through molecules and chemical processes is a rapidly growing interdisciplinary field, which holds the promise to revolutionize how we realize computing and communication devices. While molecular communication (MC) theory has had major developments in recent years, more practical aspects in designing components capable of MC functionalities remain less explored. Motivated by this, we design a microfluidic MC system with a microfluidic MC transmitter and a microfluidic MC receiver based on chemical reactions. Considering existing MC literature on information transmission via molecular pulse modulation, the proposed microfluidic MC transmitter is capable of generating continuously predefined pulse-shaped molecular concentrations upon rectangular triggering signals using chemical reactions inspired by how cells generate pulse-shaped molecular signals in biology. We further design a microfluidic MC receiver capable of demodulating a received signal to a rectangular output signal using a thresholding reaction and an amplifying reaction. Our chemical reactions-based microfluidic molecular communication system is reproducible and well-designed, and more importantly, it overcomes the slow-speed, unreliability, and non-scalability of biological processes in cells. To reveal design insights, we also derive the theoretical signal responses for our designed microfluidic transmitter and receiver, which further facilitate the transmitter design optimization. Our theoretical results are validated via simulations performed through the COMSOL Multiphysics finite element solver. We demonstrate the predefined nature of the generated pulse and the demodulated rectangular signal together with their dependence on design parameters.
... Meanwhile, chemical reactions may occur during molecule propagation via enzyme reaction [7], or at the reception of molecule via reversible absorption reaction [8] or ligand binding reaction [9]. To capture the molecule behaviour at any time, existing research has mainly focused on mathematically modelling and theoretical analysis of these physical and chemical processes, such as the channel response modelling [8], [10], channel capacity calculation [11], [12], and bit error probability derivation [7], [13]. ...
... Meanwhile, chemical reactions may occur during molecule propagation via enzyme reaction [7], or at the reception of molecule via reversible absorption reaction [8] or ligand binding reaction [9]. To capture the molecule behaviour at any time, existing research has mainly focused on mathematically modelling and theoretical analysis of these physical and chemical processes, such as the channel response modelling [8], [10], channel capacity calculation [11], [12], and bit error probability derivation [7], [13]. ...
Article
Full-text available
The design of communication systems capable of processing and exchanging information through molecules and chemical processes is a rapidly growing interdisciplinary field, which holds the promise to revolutionize how we realize computing and communication devices. While molecular communication (MC) theory has had major developments in recent years, more practical aspects in designing components capable of MC functionalities remain less explored. Motivated by this, we design a microfluidic MC system with a microfluidic MC transmitter and a microfluidic MC receiver based on chemical reactions. Considering existing MC literature on information transmission via molecular pulse modulation, the proposed microfluidic MC transmitter is capable of generating continuously predefined pulse-shaped molecular concentrations upon rectangular triggering signals using chemical reactions inspired by how cells generate pulse-shaped molecular signals in biology. We further design a microfluidic MC receiver capable of demodulating a received signal to a rectangular output signal using a thresholding reaction and an amplifying reaction. Our chemical reactions-based microfluidic molecular communication system is reproducible and well-designed, and more importantly, it overcomes the slow-speed, unreliability, and non-scalability of biological processes in cells. To reveal design insights, we also derive the theoretical signal responses for our designed microfluidic transmitter and receiver, which further facilitate the transmitter design optimization. Our theoretical results are validated via simulations performed through 2 the COMSOL Multiphysics finite element solver. We demonstrate the predefined nature of the generated pulse and the demodulated rectangular signal together with their dependence on design parameters.
... Other researchers propose new ideas such as; using ion protein channels to control molecules release [24], a ratio shift between two types of molecules [25] or the dynamic properties of propagation patterns in molecules' concentration [26]. In the second class of works, the researchers modeled molecular communication channels to study the dynamic distribution of information in the medium [27], [28]. They use discrete-time channels [29], or continuous stochastic models for constant [30] and mobile transmitters and receivers [31]. ...
Preprint
Full-text available
In this paper, we propose a new end-to-end system for wired nano-communication networks using a self-assembled polymer. The self-assembly of a polymer creates a channel between the transmitter and the receiver in the form of a conductive nanowire that uses electrons as carriers of information. We derive the channel's analytical model and its master equation to study the dynamic process of the polymer self-assembly. We validate the analytical model with numerical and Monte-Carlo simulations. Then, we approximate the master equation by a one-dimensional Fokker-Planck equation and we solve this equation analytically and numerically. We formulate the expressions of the polymer elongation rate, its diffusion coefficient and the nullcline to study the distribution and the stability of the self-assembled nanowire. This study shows promising results for realizing stable polymer-based wired nanonetworks that can achieve high throughput.
... Furthermore, we follow the global synchronization assumption as [11,12,20], where all transmitters are assumed with synchronous transmission. This facilitates simple analysis and leads to tractable results. ...
Article
Full-text available
In recent years, communicating information using molecules via diffusion has attracted significant interest in bio-medical applications. To date, most of research have concentrated on point-to-point molecular communication (MC), whereas in a realistic environment, multiple MC transmitters are likely to transmit molecular messages simultaneously sharing the same propagation medium, resulting in significant performance variation of the MC system. In this type of large-scale MC system, the collective signal strength at a desired receiver can be impaired by the interference caused by other MC transmitters, which may degrade the system reliability and efficiency. This paper presents the first tractable analytical framework for the collective signal strength at a partially absorbing receiver due to a desired transmitter under the impact of a swarm of interfering transmitters in a three-dimensional (3D) large-scale MC system using stochastic geometry. To combat the multiuser interference (MUI) and the intersymbol interference (ISI) in the multiuser environment, we propose Reed Solomon error correction coding, due to its high effectiveness in combating burst and random errors, as well as the two types of information molecule modulating scheme, where the transmitted bits are encoded using two types of information molecules at consecutive bit intervals. We derive analytical expressions for the bit error probability (BEP) of the large-scale MC system with the proposed two schemes to show their effectiveness. The results obtained using Monte Carlo simulations, matched exactly with the analytical results, justifying the accuracy of the derivations. Results reveal that both schemes improve the BEP by 3 to 4 times compared to that of a conventional MC system without using any ISI mitigation techniques. Due to the implementation simplicity, the two-types molecule encoding scheme is better than the RS error correction coding scheme, as the RS error correction coding scheme involves additional encoding and decoding process at both transmitter and receiver nodes. Furthermore, the proposed analytical framework can be generalized to the analysis of other types of receiver designs and performance characterization in multiuser large-scale MC systems. Also, the two types of information molecule modulating scheme, can be extend to M-type of information molecule modulating scheme without loss of generality. Index Terms Large-scale molecular communication system, partially absorbing receiver, intersymbol interference, multiuser interference, 3D stochastic geometry, Reed Solomon Codes. 2
Article
In this paper, we present an analytical framework to derive the performance of a molecular communication system where a transmitter bio-nano-machine (TBN) is communicating with a fully-absorbing spherical receiver bio-nano-machine (RBN) in a diffusive propagation medium in the presence of other TBNs. We assume that transmit bits at each TBN is random and different than transmit bits at other TBNs. We model the TBNs using a marked Poisson point process (PPP) with their locations as points of PPP and transmit symbols as marks. We consider both inter-symbol interference (ISI) and co-channel interference (CCI). ISI is caused by molecules transmitted in the previous slots while CCI is due to the molecules emitted from other TBNs. We derive the bit error probability of this system by averaging over the distribution of the transmit bits as opposed to the past approaches consisting of conditioning on previous transmit bits and/or assuming the transmit bits of every TBN are the same. Using numerical results, we validate our analysis and provide various design insights about the system, for example, the impact of detection threshold on the system performance. We also show the importance of accurately incorporating the randomness of transmit bits in the analysis.
Article
Unlike electromagnetic communications, where the noise is typically represented by a (Gaussian) independent source which is added to the useful signal (additive noise), molecular communications via diffusion are affected by a random disturbance which is intrinsically related to the random nature of emission, propagation (Brownian motion) and reception. In point-to-point molecular communications, the number of received molecules is generally a Poisson random variable. Thus, the evaluation of the signal-to-noise ratio (intended as the ratio between the squared mean value of the received molecules and its variance) is not a problem of interest, since its value simply equals the mean of such a random variable. However, in spatially distributed communications, where the point transmitters are randomly placed in the 3D space according to a point process, the number of received molecules derives from the contribution of a random sum of emissions, so that it is no more a Poisson random variable. Thus, the evaluation of the signal-to-noise ratio is not trivial. Here, we provide an analytical framework to evaluate the signal-to-noise ratio in spatially distributed molecular communications for both synchronous and asynchronous transmitters. The analysis is extended to the signal-to-interference-noise ratio when digital communications with intersymbol interference are considered.
Article
Full-text available
In this paper, we model and analyze the downlink (DL) wireless power transfer and uplink (UL) information transmission of K-tier heterogeneous cellular networks (HCNs) with randomly located base stations (BSs) and mobile terminals (MTs). In the DL and UL, each energy-constrained MT pairs up with its corresponding BS, which provides the maximum received power at MT. Due to the densely located BSs and universal frequency reuse between all tiers in HCNs, the typical MT is allowed to harvest energy from the serving BS by direct beamforming, as well as from the other interfering BSs. Equipped with large storage battery, the typical MT utilizes the harvested energy to provide constant transmit power for the UL information transmission. Stochastic geometry is used to model and evaluate the intrinsic relationship between the energy harvested from the BSs in the DL and the information transmission performance in the UL. To well evaluate the system performance, we first derive exact expressions for the maximum transmit power at MT, the UL outage probability, and the UL average ergodic rate per MT.As the number of BS antennas goes to infinity, we further derive asymptotic expressions for the maximum transmit power at MT, the UL outage probability, and the UL average ergodic rate per MT. Our results show that the UL outage probability per MT first decreases and then increases with increasing the time allocation factor (the fraction of time allocated to the DL), and the UL outage probability and the UL average ergodic rate per MT can be largely improved by using the massive antenna arrays at the BSs.
Research
Full-text available
In this paper, we present an analytical model for the diffusive molecular communication (MC) system with a reversible adsorption receiver in a fluid environment. The widely used concentration shift keying (CSK) is considered for modulation. The time-varying spatial distribution of the information molecules under the reversible adsorption and desorption reaction at the surface of a receiver is analytically characterized. Based on the spatial distribution, we derive the net number of newly-adsorbed information molecules expected in any time duration. We further derive the number of newly-adsorbed molecules expected at the steady state to demonstrate the equilibrium concentration. Given the number of newly-adsorbed information molecules, the bit error probability of the proposed MC system is analytically approximated. Importantly, we present a simulation framework for the proposed model that accounts for the diffusion and reversible reaction. Simulation results show the accuracy of our derived expressions, and demonstrate the positive effect of the adsorption rate and the negative effect of the desorption rate on the error probability of reversible adsorption receiver with last transmit bit-1. Moreover, our analytical results simplify to the special cases of a full adsorption receiver and a partial adsorption receiver, both of which do not include desorption.
Article
Full-text available
In this paper, we present an analytical model for a diffusive molecular communication (MC) system with a reversible adsorption receiver in a fluid environment. The time-varying spatial distribution of the information molecules under the reversible adsorption and desorption reaction at the surface of a bio-receiver is analytically characterized. Based on the spatial distribution, we derive the number of newly-adsorbed information molecules expected in any time duration. Importantly, we present a simulation framework for the proposed model that accounts for the diffusion and reversible reaction. Simulation results show the accuracy of our derived expressions, and demonstrate the positive effect of the adsorption rate and the negative effect of the desorption rate on the net number of newly-adsorbed information molecules expected. Moreover, our analytical results simplify to the special case of an absorbing receiver.
Article
Full-text available
Molecular communications (MC) has been studied as a bio-inspired information carrier for micro-scale and nano-scale environments. On the macro-scale, it can also be considered as an alternative to electromagnetic (EM) wave based systems, especially in environments where there is significant attenuation to EM wave power. This paper goes beyond the unbounded free space propagation to examine three macro-scale environments: the pipe, the knife edge, and the mesh channel. Approximate analytical expressions shown in this paper demonstrate that MC has an advantage over EM wave communications when: 1) the EM frequency is below the cut-off frequency for the pipe channel, 2) the EM wavelength is considerably larger than the mesh period, and 3) when the receiver is in the high diffraction loss region of an obstacle.
Article
Full-text available
Molecular nanonetworks stand at the intersection of nanotechnology, biotechnology, and network engineering. The research on molecular nanonetworks proposes the interconnection of nanomachines through molecule exchange. Amongst different solutions for the transport of molecules between nanomachines, the most general is based on free diffusion. The objective of this paper is to provide a statistical–physical modeling of the interference when multiple transmitting nanomachines emit molecules simultaneously. This modeling stems from the same assumptions used in interference study for radio communications, namely, a spatial Poisson distribution of transmitters having independent and identically distributed emissions, while the specific molecule emissions model is in agreement with a chemical description of the transmitters. As a result of the property of the received molecular signal of being a stationary Gaussian Process (GP), the statistical–physical modeling is operated on its Power Spectral Density (PSD), for which it is possible to obtain an analytical expression of the log-characteristic function. This expression leads to the estimation of the received PSD probability distribution, which provides a complete model of the interference in diffusion-based molecular nanonetworks. Numerical results in terms of received PSD probability distribution and probability of interference are presented to compare the proposed statistical–physical model with the outcomes of simulations.
Article
Full-text available
Within the domain of molecular communications, researchers mimic the techniques in nature to come up with alternative communication methods for collaborating nanomachines. This work investigates the channel transfer function for molecular communication via diffusion. In nature, information-carrying molecules are generally absorbed by the target node via receptors. Using the concentration function, without considering the absorption process, as the channel transfer function implicitly assumes that the receiver node does not affect the system. In this letter, we propose a solid analytical formulation and analyze the signal metrics (attenuation and propagation delay) for molecular communication via diffusion channel with an absorbing receiver in a 3-D environment. The proposed model and the formulation match well with the simulations without any normalization.
Article
This paper introduces AcCoRD (Actor-based Communication via Reaction-Diffusion). AcCoRD is a sandbox reaction-diffusion solver designed for the study of molecular communication systems. It uses a hybrid of microscopic and mesoscopic simulation models that enables scalability via user control of local accuracy. AcCoRD is developed in C as an open source command line tool and includes utilities to process simulation output in MATLAB. The latest code and links to user documentation can be found at https://github.com/adamjgnoel/AcCoRD/. This paper provides an overview of AcCoRD's design, including the motivation for developing a specialized reaction-diffusion solver. The corresponding algorithms are presented in detail, including the computational complexity of the microscopic and mesoscopic models. Other novel derivations include the transition rates between adjacent mesoscopic subvolumes of different sizes. Simulation results demonstrate the use of AcCoRD as both an accurate reaction-diffusion solver and one that is catered to the analysis of molecular communication systems. A link is included to videos that demonstrate many of the simulated scenarios. Additional insights from the simulation results include the suitability of hybrid model parameters, the impact of reactive surfaces in the proximity of a hybrid interface, and the size of a bounded environment that is necessary to assume that it is unbounded. Development of AcCoRD is ongoing, so its future direction is also discussed in order to highlight improvements that will expand its potential areas of application. Planned improvements include a fluid flow model and more complex actor behavior.
Article
This paper develops a tractable framework for exploiting the potential benefits of physical layer security in three-tier wireless sensor networks using stochastic geometry. In such networks, the sensing data from the remote sensors are collected by sinks with the help of access points, and the external eavesdroppers intercept the data transmissions.We focus on the secure transmission in two scenarios: i) the active sensors transmit their sensing data to the access points, and ii) the active access points forward the data to the sinks. We derive new compact expressions for the average secrecy rate in these two scenarios. We also derive a new compact expression for the overall average secrecy rate. Numerical results corroborate our analysis and show that multiple antennas at the access points can enhance the security of three-tier wireless sensor networks. Our results show that increasing the number of access points decreases the average secrecy rate between the access point and its associated sink. However, we find that increasing the number of access points first increases the overall average secrecy rate, with a critical value beyond which the overall average secrecy rate then decreases. When increasing the number of active sensors, both the average secrecy rate between the sensor and its associated access point and the overall average secrecy rate decrease. In contrast, increasing the number of sinks improves both the average secrecy rate between the access point and its associated sink, as well as the overall average secrecy rate.
Article
This comprehensive guide, by pioneers in the field, brings together, for the first time, everything a new researcher, graduate student or industry practitioner needs to get started in molecular communication. Written with accessibility in mind, it requires little background knowledge, and provides a detailed introduction to the relevant aspects of biology and information theory, as well as coverage of practical systems. The authors start by describing biological nanomachines, the basics of biological molecular communication and the microorganisms that use it. They then proceed to engineered molecular communication and the molecular communication paradigm, with mathematical models of various types of molecular communication and a description of the information and communication theory of molecular communication. Finally, the practical aspects of designing molecular communication systems are presented, including a review of the key applications. Ideal for engineers and biologists looking to get up to speed on the current practice in this growing field.
Article
The research activities on Molecular Communication via Diffusion (MCvD) that can interconnect nanomachines, heavily depend on simulations to verify and evaluate the new communication paradigm. The existing simulation tools cannot be directly used for MCvD systems since the diffusion channel has different characteristics compared to classical communication channels. In an MCvD system, diffusion and demodulation processes have their own constraints and characteristics due to the impossibility of sending a negative number of molecules, the random movement of molecules, and a reception process of molecules that determines the signal. Therefore, a custom end-to-end MolecUlar CommunicatIoN (MUCIN) simulator for MCvD systems is presented. Compared to other simulators available in the literature, MUCIN simulator is an end-to-end simulator that considers first hitting process for the signal reception. It supports 1-D to 3-D environments, sending consecutive symbols, imperfect molecule reception, extendable modulation, and filtering modules. MUCIN simulator source code is available under BSD licensing for contributors from the nanonetworking community. Following the simulator analysis, a case study of inter-symbol-interference mitigation that utilizes the decision in one previous slot is introduced. The contribution of this paper is twofold; one is the modeling and the development of an end-to-end MCvD simulator, the other is the performance evaluation of the proposed inter-symbol interference filtering and demodulation techniques.