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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

i“exp #´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

2⇡r1´cosp✓iqs 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

A

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 tanp✓jqs2cp 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 h“0

(h“H) 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 cosp✓j

iq

epqW0¨

˚

˚

˝

epq

2 cosp✓j

iq

Pt

i⌘t

i⌘r

jAjcospj

iqgp j

iq⌘d

j

2⇡r1´cosp✓iqs ¯

Rj

iThc„´erfc´1p2¯

Pe

i,j qaT{2`bp0

j¯2

´p0

j⇢˛

‹

‹

‚

1r´⇡{2,⇡{2sp'j

iq(5)

D↵,j

RR »2 cosp✓j

iq

epqW0¨

˚

˚

˝

epq

2 cosp✓j

iq´∞M

s“1

Pt

s⌘t

sAjcospj

sqgp j

sq1r´⇡{2,⇡{2sp'j

sq

2⇡r1´cosp✓sqs ¯⌘RR

j⌘↵

j´∞M

s“1

Ascosps

jqgp s

jq1r´⇡{2,⇡{2sp's

jq

⇡tan2p✓sq¯⌘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]

ph“Pr

h⌘d

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

h“Pt

h´1⌘t

h´1⌘r

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

s“1

Pt

s⌘t

sGs,H´1

LoS ¸⌘↵

H´1⌘rr

H´1˜M

ÿ

s“1

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´1•1is 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

h“ph`pdc `pbg and p0

h“pdc `pbg are the

numbers of photon arrivals when binary 1 and binary 0 are

transmitted respectively, pdc “Pdc⌘d

h

{Rh

h´1T}cis the additive

noise due to dark counts, Pdc dark current noise power, pbg “

Pbg⌘d

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´1“Pr

h⌘d

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 a“b

x2expt´cxuwhich has the following root

x“2

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 a“b

x4expt´2cxuwhich

has the following root x“2

cW0´c

2

4

bb

a¯. For the passive

mode, the range can be obtained from (6) by setting ⌘↵

j“1.

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

h“1Xh. 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

E2E“ÿ

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.,

Roùs“min

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

h“Pt

h´1⌘t

h´1⌘r

hGh´1,h

LoS `Pn

h,(14)

Pt

h“AhPr

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

h“P0

t

h´1

π

i“1

Ai

h´1

π

j“0

⌘t

j

h

π

k“1

⌘r

k

h

π

l“1

Gl´1,l

LoS

`

h

ÿ

i“1

Pn

i

h´1

π

j“i

Aj

h´1

π

k“i

⌘t

k

h

π

l“i`1

⌘r

l

h

π

m“i`1

Gm´1,m

LoS

`

h´1

ÿ

i“1

PASE

i

h´1

π

j“i`1

Aj

h´1

π

k“i

⌘t

k

h

π

l“i`1

⌘r

l

h

π

m“i`1

Gm´1,m

LoS ,

(16)

Pt

h“P0

t

h

π

i“1

Ai

h´1

π

j“0

⌘t

j

h

π

k“1

⌘r

k

h

π

l“1

Gl´1,l

LoS

`

h

ÿ

i“1

Pn

i

h

π

j“i

Aj

h´1

π

k“i

⌘t

k

h

π

l“i`1

⌘r

l

h

π

m“i`1

Gm´1,m

LoS

`

h

ÿ

i“1

PASE

i

h

π

j“i`1

Aj

h´1

π

k“i

⌘t

k

h

π

l“i`1

⌘r

l

h

π

m“i`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

Ah“1

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

H“Pt

H´1⌘t

H´1˜M

ÿ

s“1

GH´1,s

LoS ⌘r

s¸

`˜M

ÿ

s“1

Pt

s⌘t

sGs,H´1

LoS ¸⌘↵

H´1⌘rr

H´1˜M

ÿ

s“1

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

H“Psig

H`Ppn

H, E2E BER can be calculated

as

Poùs

E2E“1

2erfc ˜cT

2ˆbp1

H´bp0

H˙¸(20)

where p1

H“psig `ppn `pdc `pbg,p0

H“ppn `pdc `pbg,

psig “Psig

H⌘d

H

{RoùsT}c, and ppn “Ppn

H⌘d

H

{RoùsT}c. From

(20), achievable E2E data rate of AF scheme is derived as

Roùs“Psig

H⌘d

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

i•Dj

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

oÑs“argmin

@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 ﬁ±H

h“1p1´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

oÑs“argmax

@poùsq˜H

ÿ

h“1

´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 W⇠1

90˝PSS 10 W⇣0.35

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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