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Modeling and Performance Analysis of Multihop Underwater Optical Wireless Sensor Networks

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Journal Version: End-to-End Performance Analysis of Underwater Optical Wireless Relaying and Routing Techniques Under Location Uncertainty ____________________________________________________________________ Underwater optical wireless networks (UOWNs) have recently gained attention as an emerging solution to the growing demand for broadband connectivity. Even though it is an alternative to low-bandwidth and high-latency acoustic systems, underwater optical wireless communications (UOWC) suffers from limited range and require effective multi-hop solutions. Therefore, this paper analyzes and compares the performance of multihop underwater optical wireless networks under two relaying schemes: Decode & Forward (DF) and Amplify & Forward (AF). Noting that nodes close to the surface station (SS) are required to relay more information, these nodes are enabled for retro-reflective communication, where SS illuminates these nodes with a continuous-wave beam which is then modulated and reflected back to the SS receivers. Accordingly, we analytically evaluate important performance metrics including end-to-end bit error rate, achievable multihop data rates, and communication ranges between node pairs. Thereafter, we develop routing algorithms for DF and AF schemes in order to maximize the end-to-end performance metrics. Numerical results demonstrate that multi-hop transmission can significantly enhance the network performance and expand the communication range. I. INTRODUCTION The recent demand on high quality of service communications for commercial, scientific and military applications of underwater exploration necessitates a high data rate, low latency, and long range networking solutions [1], [2]. Meeting these demands is a formidable challenge for most electromagnetic frequencies due to the highly attenuating aquatic medium. Therefore, acoustic systems have received a considerable attention in the past decades. Because of surface-induced pulse spread and frequency-dependent attenuation, however, acoustic communication data rates are restrained to around tens of thousands of kbps for ranges of a kilometer, and less than a thousand kbps for longer ranges [3]. Moreover, the low propagation speed of acoustic waves (1500 m/s) induces a high latency [4], especially for long range applications where real-time communication and synchronization are challenging. On the other hand, underwater optical communication (UOWC) has the advantages of higher bandwidth, lower latency and enhanced security [5]. Nevertheless, light pulses propagating in seawater undergo hostile channel impairments including absorption and scattering. It is also susceptible to many noise sources at the receiver side such as sunlight, background, thermal, and dark current noises [6]. Broadband communication at far distances can be realized employing sufficiently dense network deployments where information can be traversed through a series of relays. Hence, end-to-end (E2E) path characterization and developing efficient routing mechanisms are necessary in practice.
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Modeling and Performance Analysis of Multihop
Underwater Optical Wireless Sensor Networks
Abdulkadir Celik, Nasir Saeed, Tareq Y. Al-Naffouri, and Mohamed-Slim Alouini
Computer, Electrical, and Mathematical Sciences and Engineering Division (CEMSE)
King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900, KSA.
Abstract—Underwater optical wireless networks (UOWNs)
have recently gained attention as an emerging solution to the
growing demand for broadband connectivity. Even though it is an
alternative to low-bandwidth and high-latency acoustic systems,
underwater optical wireless communications (UOWC) suffers
from limited range and requires effective multi-hop solutions.
Therefore, this paper analyzes and compares the performance
of multihop underwater optical wireless networks under two
relaying schemes: Decode & Forward (DF) and Amplify &
Forward (AF). Noting that nodes close to the surface sink (SS)
are required to relay more information, these nodes are enabled
for retro-reflective communication, where SS illuminates these
nodes with a continuous-wave beam which is then modulated and
reflected back to the SS receivers. Accordingly, we analytically
evaluate important performance metrics including end-to-end bit
error rate, achievable multihop data rates, and communication
ranges between node pairs. Thereafter, we develop routing
algorithms for DF and AF schemes in order to maximize the end-
to-end performance metrics. Numerical results demonstrate that
multi-hop transmission can significantly enhance the network
performance and expand the communication range.
I. INTRODUCTION
The recent demand on high quality of service communica-
tions for commercial, scientific and military applications of un-
derwater exploration necessitates a high data rate, low latency,
and long range networking solutions [1], [2]. Meeting these
demands is a formidable challenge for most electromagnetic
frequencies due to the highly attenuating aquatic medium.
Therefore, acoustic systems have received a considerable at-
tention in the past decades. Because of frequency-dependent
attenuation, however, acoustic communication data rates are
restrained to around tens of kbps for ranges of a kilometer, and
less than a thousand kbps for longer ranges [3]. Moreover, the
low propagation speed of acoustic waves (1500 m/s) induces a
high latency [4], especially for long range applications where
real-time communication and synchronization are challenging.
On the other hand, underwater optical communication
(UOWC) has the advantages of higher bandwidth, lower
latency and enhanced security [5]. Nevertheless, light pulses
propagating in seawater undergo hostile channel impairments
including absorption and scattering. It is also susceptible to
many noise sources at the receiver side such as sunlight,
background, thermal, and dark current noises [6]. Broadband
communication at far distances can be realized employing
sufficiently dense network deployments where information can
be traversed through a series of relays. Hence, end-to-end
(E2E) path characterization and developing efficient routing
mechanisms are necessary in practice.
Recent efforts on UOWC can be exemplified as follows: The
work in [7] presented the modeling of an UOWC channel using
the vector radiative transfer theory. Arnon modeled three types
of UOWC links: line-of-sight (LoS), modulating retroreflector,
and reflective links [8]. Based on Poisson point process
based spatial distribution of nodes,Vavoulas et. al. analyzed
the k-connectivity of underwater optical wireless networks
(UOWNs) under different channel conditions and network
density [9]. Akhoundi et. al. introduced and investigated a
potential adaptation of cellular code division multiple access
(CDMA) for UOWNs [6], [10]. In [11], authors characterized
the performance of relay-assisted underwater optical CDMA
system where multihop communication is realized by chip
detect-and-forward method. Similarly, Jamali et. al. consider
the performance anaylsis of multihop UOWC using DF relay-
ing [12]. Performance of UOWC closely related to establish-
ing a constant link via precise pointing, acquisitioning, and
tracking (PAT) mechanisms which requires accurate UOWN
localization schemes [13]–[15]. On the other hand, localization
performance heavily depends on the UOWN network con-
nectivity which is shown to be a function of node density,
divergence angle, and transmission range [16].
Our main contributions can be summarized as follows: We
consider an UOWN where sensor nodes are required to deliver
measurements to a sink/station located at the sea surface as
shown in Fig. 1. As the surface sink/station (SS) can have
a number of sophisticated and powerful optical transceivers,
nodes in the proximity of the SS are assumed to be capable
of retro-reflection (RR) transmission which is quite similar to
the backscatter communication. Two operational modes are
defined for the retro-reflection (RR) communication: passive
and active. In the passive mode, the sink illumines the RR
capable nodes with a continuous-wave beam which is then
backscatter modulated and reflected by the retro-reflectors. In
the active mode, on the other hand, sensors either intensify
the reflected signal by their own power in DF relaying or
amplify the signal received from previous hope in AF relaying.
Accordingly, we analyze and compare the performance of
multi-hop underwater optical wireless networks under DF and
AF relaying schemes. We analytically evaluate their important
performance metrics including E2E bit error rate (BER),
achievable multi-hop data rates, and communication ranges
between node pairs. Thereafter, we develop routing algorithms
for DF and AF schemes in order to maximize the E2E data
rates.
The remainder of the paper is organized as follows: Section
II introduces the system model. Section III and Section IV
analyzes the performance of DF and AF transmission, respec-
tively. Section V addresses the routing algorithms for DF and
AF schemes. Section VI presents the numerical results and
Section VII concludes the paper with a few remarks.
II. SYSTEM MODEL
A. Network Model
We consider a two-dimensional underwater optical wireless
network (UOWN) which consists of a single surface sta-
tion/sink with Moptical transceivers and Nnodes/sensors
each with a single optical transceiver. The surface sink is
responsible for receiving the data collected from sensors and
disseminating this information to mobile or onshore sinks.
While seabed sensors are fixed to the ground, others are either
moored or buoyed as shown in Fig. 1 where red-colored
buoyed nodes closer to the surface are required to relay all
the uplink information to the sink.
Fig. 1: Illustration of UOWNs with retro-reflection capable nodes.
According to the Beer’s law, aquatic medium can be char-
acterized for wavelength as a combination of absorption and
scattering effects, i.e., epq“apq`bpqwhere apq,bpq
and epqare absorption, scattering and extinction coefficients
respectively. Node iis defined with its location `i“pxi,y
iq
and directivity/rotation i,@iwhich is determined based on the
assumption that transmitter axis of all nodes are intersecting
with the center point of the surface sink. As illustrated in Fig.
2, we consider two types of optical channels: LoS and RR.
The propagation loss factor between nodes iand jis defined
as follows
Lj
iexp #´epqdij
cosp'j
iq+,(1)
where dij k`i´`jkis the Euclidean distance and j
i
is the angle between the receiver plane and the transmitter-
receiver trajectory. On the other hand, geometric loss of the
LoS channel is given as [17]
gij
LoS $
&
%
Aj
d2
ij
cosp'j
iq
2r1´cospiqs cp j
iq,´{2§'j
i§{2
0,otherwise
,(2)
Long Range
Narrow Beam
Divergence Angle
n
2
Short Range
Wide Beam
Divergence Angle
sw
2
A
B
C
D
C
B
A
D
D
C
B
LoS Link Cont. Light Beam LoS+RR Link
Surface Station
Fig. 2: Demonstration of LoS and LoS+RR Links.
where Ajis the receiver aperture area of node j,iis the laser
beam divergence angle of node i, and gp j
iqis the concentrator
gain, which is defined as
cp j
iq“#n2
sin2p jq,0§ j
i§ j
0,
j
i° j
,(3)
j
iis the angle of incidence w.r.t. the receiver axis, jis
the concentrator field-of-view (FoV) which can be {2and
down to {6for hemisphere and parabolic concentrators,
and nis the internal refractive index. In case of backscatter
communication, geometric loss of the reflection channel from
RR capable node jto the sink receiver s,1§s§M, is given
as [8]
gjs
RR #Ascosp's
jq
rdjs tanpjqs2cp s
jq,´{2§'s
j§{2
0,otherwise
.(4)
B. Power Consumption Model
The total power consumption of a DF node is given as
Pi
DF POEC `PADC `PDE `PDAC `Pi
PA `PEOC
where terms respectively represent the circuit power consump-
tion of optical-to-electrical converter, analog-to-digital con-
verter, detector, digital-to-analog converter, power amplifier,
and optical-to-electrical converter. The amplifier consumption
is modeled as Pi
PA
Pt
iwhere is the peak-to-average-
ratio (PAR), is the drain efficiency and Pt
iis the transmission
power of node i[18]. In a similar fashion, the total power
consumption of an AF node is given by Pi
AF POEC `
Pi
PA`PEOC . In order to establish a fair comparison between
DF and AF cases, we assume Pi
DF Pi
AF ,@i.
III. PERFORMANCE ANALYSIS OF DF RELAYING
We consider E2E performance analysis of an arbitrary multi-
hop path from an origin node to the sink. Such a path is defined
as an ordered set of nodes, i.e., Hoùs“th|0§h§Hu
where H“|Hoùs|is the number of hops and h0
(hH) represents the source (sink) node. In DF transmission,
the received optical signal at each hop is converted into
electrical signal, then decoded, and finally re-encoded before
retransmission for the next hop. Although DF greatly improves
performance as it limits background noise propagation, it intro-
duces significant power consumption and encoding/decoding
delay to the system. The most common detection technique for
OWC is intensity-modulation/direct-detection (IM/DD) with
Dij
LoS 2 cospj
iq
epqW0¨
˚
˚
˝
epq
2 cospj
iq
Pt
it
ir
jAjcospj
iqgp j
iqd
j
2r1´cospiqs ¯
Rj
iThc´erfc´1p2¯
Pe
i,j qaT{2`bp0
j¯2
´p0
j˛
1{2,{2sp'j
iq(5)
D,j
RR »2 cospj
iq
epqW0¨
˚
˚
˝
epq
2 cospj
iq´M
s1
Pt
st
sAjcospj
sqgp j
sq1{2,{2sp'j
sq
2r1´cospsqs ¯RR
j
j´M
s1
Ascosps
jqgp s
jq1{2,{2sp's
jq
tan2psq¯d
j
¯
Rj
iThc´erfc´1p2¯
Pe
i,j qaT{2`bp0
j¯2
´p0
j˛
(6)
on-off keying (OOK). Assuming that photon arrivals follows
a Poisson Process, photon arrival rate of node his given as
[19]
phPr
hd
h
Rh
h´1T}c,(7)
where Pr
his the received power at node has formulated below,
d
his the detector counting efficiency, Rh
h´1is the data rate of
the hop ph´1,hq,Tis pulse duration, }is Planck’s constant,
and cis the vacuum speed of light.
For a LoS hop, received power at node his given as
Pr
hPt
h´1t
h´1r
hGh´1,h
LoS ,1§h§H´1,(8)
where Pt
h´1is the average optical transmitter power of previ-
ous node, t
h´1is the transmitter efficiency of node h´1,r
his
the receiver efficiency of node h, and Gh´1,h
LoS Lh
h´1gh´1,h
LoS is
the composite channel gain. On the other hand, for an active
mode RR node, reception power at the destination node is
derived as
Pr
H˜M
ÿ
s1
Pt
st
sGs,H´1
LoS ¸
H´1rr
H´1˜M
ÿ
s1
GH´1,s
RR r
s¸,
(9)
where the first term is the total power received from all light
sources at the sink, Gs,H´1
LoS is the incoming composite channel
gain,
H´11is the amplifier factor of active mode (which
is unity for the passive mode), rr
H´1is the RR efficiency
of the node before the sink (which is zero for RR incapable
nodes), the last term accounts for cumulative received power
at all receivers of the sink, and GH´1,s
RR Ls
H´1gH´1,s
RR is the
reflection composite channel gain.
If a large number of photon reception is assumed, the
Poisson distribution can be approximated by a Gaussian distri-
bution as per the central limit theorem. For a given data rate,
¯
R, the BER of a single hop is given by [8]
Pe
h´1,h 1
2erfc ˜cT
2ˆbp1
h´bp0
h˙¸(10)
where p1
hph`pdc `pbg and p0
hpdc `pbg are the
numbers of photon arrivals when binary 1 and binary 0 are
transmitted respectively, pdc Pdcd
h
{Rh
h´1T}cis the additive
noise due to dark counts, Pdc dark current noise power, pbg
Pbgd
h
{Rh
h´1T}cis the background illumination noise, and Pbg
is the background noise power. For a certain BER threshold,
¯
Pe
i,j , data rate of the hop ph´1,hqis derived from (10) as
Rh
h´1Pr
hd
h
T}c´erfc´1p2¯
Pe
h´1,hqa2{T`ap0
h¯2
´p0
h,
(11)
which is inversely proportional to the BER. We should note
that data rate and BER performance of each hop heavily
depends on accurate PAT mechanisms which requires precise
UOWN localization algorithms [13]–[15].
For a given error and data rate, communication ranges
between two generic nodes (i, j) are derived in (5) and (6)
for LoS and active RR cases respectively, where W0p¨q is
the principal branch of product logarithm function. Range
expressions of LoS and active RR schemes can be derived
by substituting (8) and (9) into (11), respectively. After some
algebraic manipulations, LoS case (i.e., (8)Ñ(11)) can be put
in the form of ab
x2expcxuwhich has the following root
x2
cW0´c
2bb
a¯where a,b,care constants, and nis an
integer. For the sake of tractability in RR cases, we treated
distance and angle from/to sink transceivers identical within
the propagation loss expressions. Accordingly, active RR case
(i.e., (9)Ñ(11)) is put in the form of ab
x4exp2cxuwhich
has the following root x2
cW0´c
2
4
bb
a¯. For the passive
mode, the range can be obtained from (6) by setting
j1.
Denoting Xhas the Bernoulli random variable which rep-
resent the erroneous decision of node h, total number of
incorrect decision made along the path is given as X
H
h1Xh. Assuming Xh’s are independent but non-identically
distributed, Xis a Poisson-Binomial random variable. Noting
that a transmitted bit is received correctly at the sink if the
error events take place in even numbers of nodes, E2E BER
is derived as
Poùs
E2Eÿ
jPAÿ
BPFjπ
kPB
Pe
k´1,k π
lPBc`1´Pe
l´1,l˘(12)
where A“t1,3,...,Huis the set of odd numbers and Fjis
the set of all subsets of jintegers that can be selected from
A.Poùs
E2Ecan be expeditiously calculated from polynomial
coefficients of the probability generating function of Xin
OpAlog Aqwhere Ais the cardinality of A[20]. Notice that X
reduces to a Binomial variable if all hops are identical, which
is hardly the case in practice. Finally, the achievable multi-hop
h
h
H1
t
h
P1
r
h
n
h
P
PA
P
ASE
h
P
h
A
r
h
P
t
h
P
t
h1
Receiver
Efficiency
Receiver
Noise Amplifier
ASE
Noise
Transmitter
Efficiency
Channel
Gain
Tx Power of
Node h-1
Tx Power of
Node h
NODE h
Fig. 3: Illustration of considered AF Transmission.
rate is determined by the minimum of the data rates along the
path, i.e.,
Roùsmin
1§h§H`Rh
h´1˘(13)
IV. PERFORMANCE ANALYSIS OF AF RELAYING
AF transmission is obtained by executing optical-to-
electrical conversion at each node, amplifying the received
electrically, and then re transmitting the amplified signal for
the next hop as shown in Fig. 3. The main drawback of
the AF transmission is propagation of noise added at each
node, which is amplified and accumulated through the path.
Accordingly, received and transmitted power at intermediate
node 1§h§H´1can be modeled as
Pr
hPt
h´1t
h´1r
hGh´1,h
LoS `Pn
h,(14)
Pt
hAhPr
h`PASE
h,(15)
where Ahis the amplifier gain, Pn
his the local noise at the
receiver, and PASE
his the amplified spontaneous emission
(ASE) noise of the amplifier. Based on the recursion of (14)
and (15), received and transmitted powers at node hcan be
respectively written in a generic form as
Pr
hP0
t
h´1
π
i1
Ai
h´1
π
j0
t
j
h
π
k1
r
k
h
π
l1
Gl´1,l
LoS
`
h
ÿ
i1
Pn
i
h´1
π
ji
Aj
h´1
π
ki
t
k
h
π
li`1
r
l
h
π
mi`1
Gm´1,m
LoS
`
h´1
ÿ
i1
PASE
i
h´1
π
ji`1
Aj
h´1
π
ki
t
k
h
π
li`1
r
l
h
π
mi`1
Gm´1,m
LoS ,
(16)
Pt
hP0
t
h
π
i1
Ai
h´1
π
j0
t
j
h
π
k1
r
k
h
π
l1
Gl´1,l
LoS
`
h
ÿ
i1
Pn
i
h
π
ji
Aj
h´1
π
ki
t
k
h
π
li`1
r
l
h
π
mi`1
Gm´1,m
LoS
`
h
ÿ
i1
PASE
i
h
π
ji`1
Aj
h´1
π
ki
t
k
h
π
li`1
r
l
h
π
mi`1
Gm´1,m
LoS ,
(17)
which follows by assuming independent signals, hops, and
noises. Based on power consumption model given in Section
II-B, the amplifier gain of each node can be derived as follows
Ah1
Pr
hˆPAF ´POEC ´PEOC
{´PASE ˙.(18)
Remarking that the node before the sink is RR capable, total
received power at the destination node is given as
Pr
HPt
H´1t
H´1˜M
ÿ
s1
GH´1,s
LoS r
s¸
`˜M
ÿ
s1
Pt
st
sGs,H´1
LoS ¸
H´1rr
H´1˜M
ÿ
s1
GH´1,s
RR r
s¸,
(19)
where the first and second terms are amplified and reflected
signals received from previous node and sink, respectively.
Separating the signal and propagated noise part of (19) as Psig
H
and Ppn
H, i.e., Pr
HPsig
H`Ppn
H, E2E BER can be calculated
as
Poùs
E2E1
2erfc ˜cT
2ˆbp1
H´bp0
H˙¸(20)
where p1
Hpsig `ppn `pdc `pbg,p0
Hppn `pdc `pbg,
psig Psig
Hd
H
{RoùsT}c, and ppn Ppn
Hd
H
{RoùsT}c. From
(20), achievable E2E data rate of AF scheme is derived as
RoùsPsig
Hd
H
T}c´erfc´1p2¯
Poùs
E2Eqa2{T`ap0
H¯2
´p0
H.
(21)
V. ROUTING FOR DF AND AF RELAYING
Let us consider the network graph GpV,E,qwhere Vis
the set of sensor nodes, Eis the set of edges, and PRNˆNis
the edge weight matrix whose metric can be distance, rate, etc.
The optimal route for a source node is defined as the multi-hop
path with the maximum E2E data rate. For a certain data rate
request of the source, we first update the graph by removing
the infeasible edges between nodes pi, jqif dj
iDj
ibased
on (5) and (6) according to link type. On the remaining edges
which are weighted by single-hop data rates, we need to find
the following optimal route
oÑsargmin
@poùsqˆmin
hPH`Rh
h´1˘˙(22)
where oùsdenotes an arbitrary path. The problem
defined in (22) is known as widest path or bottleneck shortest
path problem and can expeditiously be solved by Dijkstra’s
algorithm by modifying the cost updates [21]. For minimum
E2E-BER routing, we consider the maximization of the E2E
bit success rate (BSR) , BSR ±H
h1p1´Pe
h´1,hq, assuming
that the SS can correctly detect a bit iff it is successfully
detected at each hop Here, we neglect the fortunate events
of correction at even number of errors. Since the shortest
path algorithms are only suitable to additive costs, BER
maximization can be transformed from multiplication into
summation by taking the logarithm
oÑsargmax
@poùsq˜H
ÿ
h1
´log `1´Pe
h´1,h˘¸(23)
where edge weights are set to j
i“´log ´1´Pe
h´1,h¯.
On the other hand, routing for AF scheme is determined by
10 15 20 25 30 35 40
Total # Sensors
101
102
103
E2E Data Rate [Mbps]
DF
AF
(a)
10 15 20 25 30 35 40
Total # Sensors
10-9
10-8
10-7
E2E BER
AF
DF
(b)
10 15 20 25 30 35 40
Total # Sensors
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
# Outage Sensors / # Hops
AF # Outage Sensors
DF # Outage Sensors
Avg. # Hops
(c)
Fig. 4: Performance Comparison of DF and AF schemes: a) E2E data rates, b) E2E-BER, and b) Number of outage sensors and hops.
both received signal power and noise propagation. Therefore,
we consider the route with the highest signal-to-noise-ratio
(SNR) product which can also be calculated by shortest
path algorithms using logarithmic transformation. It is worth
mentioning that performance of potential routing techniques
depends on the connectivity of the UOWNs which is shown
to be a function of number of nodes, divergence angle, and
communication range [16].
VI. NUMERICAL RESULTS
We consider a 200mˆ200msimulation area where the SS is
located at the origin. The RR capable nodes are symmetrically
located 30mbelow the SS and their numbers are the same
with the number of SS transceivers. W.l.o.g., all efficiency
parameters are set to 0.9. Circuit power consumption is set to
30,7,40,15.4,23 milliwatts for POEC ,P
ADC ,P
DE,P
DAC,
and POEC , respectively. Notice that residual power of the total
sensor power is used by the power amplifier to increase the
transmission power for the best performance. Unless it is stated
explicitly otherwise, we use the parameters listed in Table I
which is mainly drawn from [8], [18].
TABLE I: Table of Parameters
Par. Value Par. Value Par. Value
M2}6.62E ´34 ¯
Pe
h´1,h 1E ´5
n1.33 c2.25E8 ms´1¯
R1Mbps
10˝PDF 0.125 W1
90˝PSS 10 W0.35
We should first note that directivity of the sensors and FoV
of the receivers mainly determine the link availability between
the nodes. To illumine, Fig. 5 shows the photon arrival rate
w.r.t. xy-coordinates for a sensor fixed at origin and pointing
in positive x-axis direction while the receiver is located at
different location and its receiver directed to the origin.
Performance comparison of DF and AF schemes are shown
in Fig. 4 which is obtained by averaging ten thousand network
scenarios where nodes are uniformly distributed over the
simulation area. Fig. 4a compares the average E2E data rate
performances w.r.t. increasing total number of sensors. For
each node excluding the RR capable ones as they serve as
Fig. 5: Photon arrival rates w.r.t. coordinates.
pure relays, E2E data rate of each node is calculated and then
averaged. AF scheme obviously has a superior performance
which is due to the following reasons: First, AF scheme
has more transmission power availability since it does not
consume power on digital processing circuitry as in the DF
scheme. Second, E2E capacity of the DF scheme is primarily
determined by the bottleneck hope. Thus, even if most of the
hops are in a desirable state, the bottleneck can degrade entire
performance of the source node. For some scenarios, we have
also observed that certain bottleneck hops are exploited by
cluster of sensors as a gateway toward the SS. In such cases,
E2E performance of entire cluster is degraded. However, AF
scheme is not directly affected from these issues, as it has
more transmission power and weak channels can be mitigated
by amplification in the remaining hopes.
On the other hand, it is shown that DF provides a better
performance for the E2E-BER as shown in Fig. 4b. The
intuition behind this change is due to the following reasons:
Unlike the AF scheme, decoding the received signal at each
hop eliminates the propagation of the noise along the path.
Moreover, detection errors can be reversed by even numbered
of errors as explained above. Finally, average number of outage
sensors in DF and AF schemes are shown in Fig. 4c which is
normalized to total number of sensors. Outage occurs when a
sensor has an E2E data rate less than ¯
R. Accordingly, we have
observed that DF scheme observe more outage which is due
to the reasons mentioned for Fig. 4a. Moreover, the average
number of hops to reach the SS starts from around 3.5 and
converges to 6 as number of nodes increases.
Since we do not have an omnidirectional radiation as in
acoustic channels, increasing the number of nodes does not
have a direct effect on the performance as the channel gain is
determined with angles along with the distance. Therefore, an
intelligent sensor deployment is crucial to improve the overall
network performance.
VII. CONCLUSIONS
Thanks to its high bandwidth and low latency, UOWC is
an alternative to traditional underwater acoustic communica-
tions. However, UOWC has limited transmission range and
necessitates efficient multihop communication techniwues to
realize UOWNs. Therefore, this paper considered modeling
and performance analysis of multihop UOWNs by using DF
and AF relaying schemes and deriving the closed-form E2E
data rate, BER, and communication ranges. Thereafter, routing
algorithms for E2E performance maximization is developed.
Finally, merits and drawbacks of each scheme is discussed,
which is followed by some potential future research direction.
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