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TRANSCRIPT
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Effects of Wind-induced Near-surface Bubble
Plumes on the Performance of Distributed
Underwater Acoustic Sensor Networks
AbstractThis paper analyzes the effect of the presence ofnear-surface oceanic bubble plumes on the overall performanceof distributed Underwater Wireless Acoustic Sensor Networks(UWASNs). The existence of bubble plumes in surface and sub-surface ocean water columns is inevitable in most windy oceanicenvironments. There exists studies reporting the degradationof acoustic signal propagating through oceanic bubble plumes.However, most of the existing network protocols designed foruse in underwater sensor networks are ignorant of these effects.In this paper, we study these effects and observe how bubbleplumes have impact on the overall performance of UWASNs,
with respect to different parameters such as the bit error rate(BER), delay, and signal-to-interference-plus-noise-ratio (SINR).Simulation studies show that in the presence of bubble plumes,SINR decreases by approximately 29 %, BER increases by 71 %,and delay increases by 56 %, approximately.
Keywords-Shallow-water, acoustics signal, multipath-
reflection, acoustic sensor network, bubble plumes
I. INTRODUCTION
This paper presents an analysis of the effect of oceanic
bubble plumes on the performance of distributed UWASNs.
UWASNs are envisioned to enable applications such as
oceanographic data collection, pollution monitoring, offshore
exploration, disaster prevention, and assisted navigation [1][2].
Large volume of research literature (e.g., [3], [4], [5], [6],
[7]) exists on UWASNs. However, most studies ignored the
effect of bubble plumes on the overall network performance,
despite the fact that the existence of near-surface bubble
plumes is inevitable in most windy oceanic environments. This
work is an attempt towards addressing this important research
lacuna.
A UWASN consists of variable number of sensor nodes,
which are capable of sensing, processing, and communicating,
and are deployed over a given area of interest to perform
application-centric collaborative monitoring tasks [8]. Under
the surface of water, electromagnetic signals (RF) cannot beused efficiently, primarily due to the absorption by the conduc-
tive sea water. Similarly, optical signals cannot be used in the
underwater column, as they suffer from increased scattering
effects. Additionally, the precision for sending optical signal
should be high. On the contrary, in an underwater column,
acoustic signal can traverse significant distance without atten-
uation. So, for reliable communication in such an environment,
acoustic signal is normally used.
Unlike terrestrial wireless sensor networks, UWASNs suffer
from multiple challenges. Some of the key inherent character-
istics [9] in designing a UWASN are listed below.
The available acoustic bandwidth under the surface of wa-
ter depends on the transmission range [10] and frequency.
Due to high environmental noise at low frequency [11],
communication quality also degrades.
UWASNs are highly dynamic in nature. Except for the
nodes anchored with surface buoys, the other nodes have
mobilities ranging from minimum to a finite value. The
relative mobility between the source and receiver nodesleads to Doppler spread. Additionally, nodes mobility
leads to deformation in architecture of a sensor network,
which, in turn, affects its communication performance.
In UWASNs, internode communication is affected for the
acoustic signal fluctuation caused by many factors such
as path loss, noise, and multi-path fading [12].
End-to-end delay in underwater environments is very
high [13]. The acoustic signal propagation speed in such
environments is five orders of magnitude higher than the
propagation speed in terrestrial environment. Propagation
speed of wireless acoustic signal in underwater environ-
ment is about 1500 m/s, which is five orders of magnitude
lower than propagation speed of signal used in terrestrial
sensor network.
Due to the adverse channel condition, there is a probabil-
ity of having high Bit Error Rate (BER) and temporary
losses of connectivity, thereby affecting the overall net-
work performance.
Battery power of sensor nodes is limited and remote
replenishment of power source is nearly impossible. Also,
solar power cannot be exploited as an energy source under
water. Therefore, energy consumption per node in the
network is crucial aspect of study to increase the overall
network lifetime.
Power attenuation of the signal depends primarily onfrequency and distance.
There is a probability of hardware failure due to foul-
ing and corrosion. Failure rate of nodes in underwater
environments is more than that in the terrestrial sensor
network.
An ocean column is typically segmented into three lay-
ers mixed, thermocline, and deep isothermal. Among all
these layers, the mixed layer is normally the most turbu-
lent. The upper surface of this layer is directly subjected
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to tangential stress due to surface winds. In other words,
transfer of momentum takes place from wind to the water
surface, which often results in splashing/breaking of the waves.
This phenomenon creates concentrated layers of micro-bubbles
underlying the ocean surface, typically up to a depth of 10
meters [14]. The layers of bubble plumes have been observed
to vary not only in depth, but also in range and time [15].
Their evolution in density, radius, and spatial distribution has
profound influence on the quality of acoustic communication
[16].
A. Contribution
As mentioned above, the communication performance of
distributed UWASN systems is very sensitive to the presence
of near-surface bubble plumes. Again, wind has an important
role on the nature and intensity of plumes at subsurface region.
So, it is also important to study the effect of wind velocity on
the overall performance of distributed UWASN.
In sum, the contributionsof this work is cataloged as below.
We have analyzed the variation of plume depth with the
variation of wind speeds. We have also studied how the spatial distribution of
bubble plumes varies as a function of wind velocity.
We have analyzed the effect of individual bubble, as
well as the combined effect of bubble plumes, on the
propagation characteristics of the acoustic signal.
Finally, we have analyzed the performance of the network
in terms of three metrics: SINR, BER, and delay.
I I . RELATED WORK
The unique characteristics of acoustic signal propagation in
underwater environment makes UWASNs distinct from those
of the terrestrial wireless sensor networks. There exist studies
on the performance analysis of UWASNs in the physicallayer. Most of these studies are focused on the physical
characteristics of acoustic signal. There is deficiency of work
analyzing the performance of UWASNs by considering the
interaction of wireless acoustic signals in realistic physical
phenomena occurring in the ocean, especially in the surface
and subsurface regions.
Ismail et al. [17] analyzed the performance of UWASNs in
terms of propagation loss by considering the acoustic signal to
be propagated through underwater ocean channel. The authors
considered only the inherent characteristics of the underwater
channel from the communication point of view. Stefanov
and Stojanovic [18] analyzed the performance of underwater
acoustic ad-hoc networks in the presence of interference.They have assumed the uniform distribution of nodes in the
entire channel. They have modeled path loss in inter-node
communication to be frequency dependent, and have assumed
Rician distribution of acoustic fading.
Fox et al. [19] proposed a methodology for predicting
the underwater acoustic communication performance. They
showed how performance varies with respect to the variation
in relative locations of source and receiver nodes in the per-
spective of acoustic speed profile in the channel. The authors
have taken parameters such as variable sound speed profiles
as a function of environment variables between the source
and the receiver nodes. These parameters help in assessing
the overall communication performance of UWASNs. Llor
and Malumbes [20] studied how physical layer modeling
affects the performance of higher layer protocols. Zhang et
al. [21] considered a linear multihop communication architec-
ture to model acoustic propagation. They took into account
frequency-dependent signal attenuation, interhop interference,
and propagation delay.
A synthesis from the review of existing works reveals that
the effect of near-surface bubble plumes on overall network
performance needs investigation.
Fig. 1: Architecture profile of UWASN
Fig. 2: Link establishment between any two nodes in the
network
III. COMMUNICATION ARCHITECTURE
We have considered a 3-D architecture where large number
of nodes are randomly distributed in space in the ocean
column, as shown in Figure 1. Due to the several advantages
of single-hop communication over multi-hop [22], we have
considered the multi-hop communication architecture between
the source and the surface sink node. We have neglected the
vertical movement of nodes, as their deviation with respect to
their equilibrium position is very small.
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Typically, nodes in UWASN are equipped with acoustic
transceivers, whereas the surface sink nodes are equipped
with both acoustic and electromagnetic transceivers. The nodes
placed in between the source and surface sink nodes act as
the relay nodes. The relay nodes help in routing informa-
tion from the source node to the surface sink. The nodes
communicate with one another in the wireless medium using
acoustic signal. In this paper, we have not considered inter-
sink communication. Nodes are assumed to be homogeneous
in nature with respect to their transmission capability. One of
the challenging aspects of network modeling is establishing
connectivity amongst the sensor nodes. Connectivity between
any two nodes is established when they come in the transmis-
sion range of each other. In this paper, the network model is
presented in terms of a graph
G= (N, Cl) (1)
In Equation (1), N=N1, N2,....,Nn is the number of nodesdeployed over the particular region of interest, and Cl is thelink established between two nodes. The term, Cl, can be
expressed as:(ni, nj) Cl (2)
The scenario is depicted in Figure 2.
IV. CHARACTERIZATION OF NEAR-SURFACE WIND
INDUCED BUBBLE PLUMES
A. Categorization of bubble plumes
The physical unit formed by the combination of many
discrete bubbles is termed as bubble plume or bubble clouds
[23]. Based on Thorps measurements and observations [23],
Monohan [24] classified bubble plumes into three categories:
, , and . These plumes bear their names on the basis oftheir individual lifetime during active bubble generation pro-
cess induced by wind action on the ocean surface. Whitecaps
[15] are associated with two stages, Stage-A and Stage-B, due
to wave breaking. Stage-A is involved with the crest of spilling
breaker and Stage-B with the foam patch. Theplume is thesubsurface extension of Stage-A whitecap [15], and it contains
the highest void fraction ranging from 101 to 102. They
have very short lifetime, typically in the order of less than
1 second. Due to the dissipation of momentum of downward
moving jets that originate due to wave-breaking, plumesdecay into plumes. The plumes have less void fraction(ranging from 104 to 103 ) than plumes, and they
remain attached with the Stage-B foam patch. They, typically,persist only upto 4 seconds. In course of time, theplumesevolve into plumes, and gradually become detached fromthe originating whitecap. Among the three plume categories,
plumes have the lowest void fraction ranging from 106 to107 with a time span 10-100 times greater than plumes.Due to their high longevity and size, the plumes areaffected by the local circulation process, and finally decay to
a weak-stratified background layer. Even if,m plume hashigh void fraction, due to their very short lifetime with respect
to andplume, we have omitted the analysis of the theireffect on the performance of distributed UWASNs.
B. Physical characterization of bubble plumes
This section discusses the spatial distribution of bubble
plumes and the quantification of their population. Monahan
[24] extensively studied the characteristics of oceanic bubbles,
and their importance in the gas exchange between air-sea
interface. As proposed by Hall [25], the Bubble Population
Spectral Density (BPSD), , for any level of bubble plume ismathematically expressed in the functional form as:
(r,z,w10) = N0(r, z)Z(z, w10)W(w10) (3)
In Equation (3), r is the bubble radius, z is the depth fromocean surface, w10 is the wind speed 10 m above the seasurface, W is a wind-dependent factor, and N0 is a constanthaving value corresponding to a particular value of, which isobtained for particular values of radius (r), depth (z), and wind
velocity (w10). The term (r, z) denotes the spectral shapefunction,Z(z) is the depth dependent function signifying the
e-folding depth [26] for each level of bubble plumes. The e-folding depth is normalized with respect to the reference depth
z = 0. Thus, the general form of Equation (3) is written as:
(r,z,w10) = N0(r)Z(z)W(w10) (4)
C. Wind dependent factor
As observed by Monahan [24], the rate of generation of
bubble plumes is equal to the rate of formation of whitecaps.
The study of the relation between the fraction of whitecaps
on the sea surface and the wind velocity was undertaken by
Monahan and Muircheartaigh [27]. After a couple of decades,
Andreas and Monahan [28] presented a premier work, which
states that the fraction of whitecaps present on the sea surface
can be approximated to be proportional to the third power
of wind speed. Hall [25] undertook an integrated study on
several research works done on the dependence of BPSD on
wind velocity (w10). Finally, the author proposed a functionalrelation, which is given below [15]:
W(w10) = (w1013
)3 (5)
In Equation (5), w10 is the wind velocity 10 m above thesurface. As it is assumed that wind is the main factor to
induce the formation of all bubbles, the function W(w10)is regarded the same for all stages of plume development,
including the last stage, i.e., the background layer at any
instant of time.
D. Nature of spectral shape function
Based on the analysis of several experimental data using
multiple measuring techniques, Hall [25] postulated that the
spectral shape function follows power law with an exponent
close to -4. It has been observed that this power law is valid
for bubbles having radii in the range 20-30 m upto 50-80m.Again, on the basis of the report presented by Hall [25], it can
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be stated that the power law for spectral shape function holds
good for small and intermediate shaped bubbles. Therefore,
power law of spectral shape function is invariant for small
and intermediate shaped bubbles, except for the changes in
population size. Therefore, the generalized form of the spectral
shape function forplumes,plumes, and the backgroundlayer is expressed as [25]:
(r) =
0, forrref =rmin
(rrefr1
)3, forrmin rref< r1
1.0, forr1 rref r2
( r2rref
)4, forr2 > rref r3
(6)
In Equation (6), rmin = 10 m, r1 = 15 m, r2 = 20 m, r3= 54.4 + (1.984)z m, and z is in meter. In the subsequentsections, BPSD for different types of bubble plumes is
discussed.
1) Form of BPSD for Plume: From the previoussection, it has been observed that the spectral slope of
the power law is a function of bubble size. Higher slopes
correspond to bubbles of larger radii. As the lifetime of a
plume is comparatively shorter than that of plume,the spectral slope for a plume is set as -4, whereas forplume and background layer a slightly higher value of -2.6is taken. Again, in our study it has been assumed that bubbles
of larger radii exist near to the surface, and with increasing
depth, the population density decreases. Considering all
the aspects stated above, the functional form of BPSD for
plumes is expressed as follows [15].
(r,z,w10) = N0(r)Z(z)W(w10) (7)
In Equation (7), the value of the constant, N0 , is taken tobe 2.0107 m3m1 [26]. The functional form for spectralshape function, (r), for plume can be expressed as:
(r) =
0, forrref > rmin
(rrefr1
)3, forrmin rref < r1
1.0, forr1 rref r2
( r2rref
)4, forr2 < rref r3
( r2r3
)4( r3rref
)2.6, forrref > r3
(8)
Following the work by Monahan and Lu [29], which considers
uniform distribution of plume as a function of e-folding
depth, the general form of depth dependent function is math-ematically expressed as:
Z(z) =
1.0, forzref zmax
0, forz > zmax(9)
In Equation (9), the parameter,Zmax, refers to the maximumpenetration depth of a plume, and it is related to orbitalmotion of breaking wave. Therefore, it controls the vertical
axis of plume. Normally, the penetration depth ofplume extends to one half of the significant wave height
[26]. The expression of maximum penetration depth for
plume,Zmax, is presented as [15]:
Zmax = (1.23 102)w210 (10)
2) BPSD for plume: Mathematically, bubble densityspectrum for plume can be expressed in a manner similarto that in Equation (7) for plume. Therefore, consideringvarious parameters associated with the plume, the densityspectrum is expressed as:
(r,z,w10) = N0(r)Z(z)W(w10) (11)
Asplumes are the transformed products ofplumes, thespectral shape function ofplumes,(r), for small and in-termediate shaped bubbles remains unchanged. However, their
concentration gets weaker. During the transformation phase
from plume to plume, a significant change is observedin bubble population size. The spectral shape function for
plume is expressed as:
(r) =
0, forrref< rmin
(rrefr1
), forrmin rref < r1
1.0, forr1 rref r2
( r2rref
)4, forr2 < rref r3
( r2r3
)4( r3rref
)p(z), forrref> r3
(12)
In Equation (12),p(z)is the spectral slope, which has a steepervalue for the bubbles having radius larger than 60m, and itis expressed as:
p(z) = 4.37 + ( z
2.55)2 (13)
The representative values forr1,r2, andr3 are taken the sameas in Equation (7). Majority of the experimental observations
show that the depth dependent function Z(z) in Equation(12) is expressed as:
Z(z) = exp(z/d) (14)
In Equation (14), d is the the e-folding depth for plume.The e-folding depth as a function of wind speed, w10, isexpressed as:
d(w10) = davg(w10)
ln(Mv(atz=0)Mn
)(15)
In Equation (15), davg is the average penetration depth, Mvis the back-scattering cross-section per unit volume, and Mnis the average noise level. The parameter, davg , is expressedas:
davg(w10) = 0.6(w10 5) + 3.5 (16)
Equation (16) is valid for any value ofw10 greater than 5 m/s.The parameter, Mv, used in Equation (15) is expressed as:
0
n(r)bsdr (17)
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(a) BPSD for small and intermediate bubbles (b) BPSD for near-large bubbles
(c) BPSD for large bubbles
Fig. 3: Distribution of BPSD for andplumes
Fig. 4: Variation of penetration depths of plumes with the variation in wind speed
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0
50
100
150
200
250
10 15 20 25 30 35 40
(Ceff)[m/s]
Frequency [kHz]
w10= 11m/sw10= 12m/sw10= 13m/s
(a) Effective speed, (Ceff), of acoustic signal throughGamma plume
0
20
40
60
80
100
120
10 15 20 25 30 35 40
((C
eff)+(Ceff))avg
[m/s]
Frequency [kHz]
w10= 11m/sw10= 12m/sw10= 13m/s
(b) Effective speed of acoustic signal through Beta as well asGamma-plume
Fig. 5: Acoustic signal propagation through Beta and Gamma plume induced region
0
0.05
0.1
0.15
0.2
0.25
0.3
10 15 20 25 30 35 40
(s
)[dB/m]
Frequency [kHz]
w10= 11m/sw10= 12m/sw10= 13m/s
(a) Attenuation, (s) of acoustic signal through Gammaplume
0
0.1
0.2
0.3
0.4
0.5
0.6
10 15 20 25 30 35 40
(s
)+
[dB/m]
Frequency [kHz]
w10= 11m/sw10= 12m/sw10= 13m/s
(b) Attenuation of acoustic signal due to combined effect ofBeta and Gamma plume
Fig. 6: Attenuation of acoustics signal through Beta and Gamma plume
In the Equation (17), bs is the back scattering cross-sectionfor a single bubble.
Figures 3 (a), (b), (c) depict the distribution of BPSD
for both the plumes. From the figures, we observe that the
distribution curves get shifted upward for plume withrespect to the plume.
E. Nature of penetration of andPlumes
Wind velocity is an important factor in deciding the pen-
etration depth of a particular type of plume. It is usuallyseen that the penetration depth ofplume is lower than thatof the plume for a particular wind velocity. Variation ofpenetration depth for both types of aforementioned plumes
is shown in Figure 4. From Figure 4, we infer that in the
near-surface bubble-induced region, wireless acoustic signal
propagates partly through the plume induced region andpartly through the andplume induced regions, together.Figure 7 shows the bubble induced regions under different
wind speeds.
0
2
4
6
8
10
11 12 13
PenetartionDepth(m)
Wind speed w10(m/s)
- and -plume induced region
-plume induced region
Fig. 7: Bubble induced regions under different wind speed
V. ANOMALOUS BEHAVIOR OF ACOUSTIC SIGNAL IN THE
PRESENCE OF BUBBLE PLUMES
During propagation through oscillating bubble clouds,
acoustic signal gets attenuated. To calculate the attenuation
and perturbation caused by the bubble plumes, we followed
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the approach used by Norton and Novarini [15] and Hall [25].
The assumptions made in this approach are as follows:
The compressional speed of acoustic signal is assumed
to be approximately constant throughout the medium.
There is no interaction between any pair of bubbles.
Due to the oscillation mechanism, the medium becomes
dispersive.
Multiple scattering among the bubbles is negligible.The steps to be followed to calculate the sound perturbation
are:
Compressibility is first calculated for a single bubble.
Total change in compressibility (K) is calculated byintegrating the result obtained for a single bubble, for
sizes of bubbles ranging in radius from maximum (rmax)to minimum (rmin).
Then, the effective speed of acoustic signal (Ceff) isexpressed in terms ofK.
Under the condition when typical square distance between
bubbles is larger than the scattering strength, the effective
compressibility, Keff, of the bubble mixture is expressed asfollows:
Keff = (1 Vfrac)K0+ K (18)
In Equation (18), K0 is the compressibility of ocean waterin the absence of bubbles, and Vfrac is the fractional volumeoccupied by the bubbles. Assuming kr < 1, where k is thepropagation vector of acoustic signal, Kis expressed as:
K(f, z) = N
0f2r
(frf 1 +i)
(19)
For a distribution of plumes, the expression is written as:
K(f, z) = 1
0f2
rmaxrmin
[ r(r)
((frf
)2 1 +i) ] dr (20)
In Equation (19), the physical parameter, fr, is the resonancefrequency. Under adiabatic oscillation and no viscous effect,
for a spherical air-bubble in water, the resonance frequency is
expressed as:
fr = (1 + z
10)0.5(
3.25 106
r ) (21)
where, fr is expressed in Hz, and the radius r is in m.The parameter, , in Equation (19), is the damping constant.Damping is observed in three formsdue to radiation,r, dueto shear viscosity, , and due to thermal conductivity, t.Damping constant, , in terms of these three components isexpressed as:
= r++ t (22)
Mathematical calculation shows that out of these three, damp-
ing due to viscosity and temperature can be neglected as
compared to damping due to radiation. So, the effective
damping is expressed as:
= r =2f r
C0(23)
where,C0 is the velocity of acoustic signal in the absence ofbubble plumes.
For low void fraction, the effective sound speed, Ceff, isexpressed as [15]:
1
C2eff=
1
C20+
1
f2
rmaxrmin
[ r(r)
((frf
)2 1 +i)] dr (24)
Equating the numerator and the denominator of Equation (24),
we have:
1
C2eff=
1
C20+
1
f2
rmaxrmin
r(r)[((frf
)2 1) ir]
[((frf
)2 1)2 +2r ]dr (25)
By putting the value of r from Equation (23) in Equation(25), and writing the real and imaginary part separately, we
have:
1
C2eff=
1
C20+
1
f2
rmaxrmin
r(r)[((frf
)2 1)]
[((frf
)2 1)2 +2r ]dr (26)
1
C2eff=
1
C20+
1
f2
rmax
rmin
r(r)(r)
[((frf
)2 1)2 +2r ]dr (27)
Equations (26) and (27), respectively, represent the real and
imaginary parts. Next, we analyze the sound speed modified
during propagation through and plumes.
A. Sound speed perturbation by andplume
Sound perturbation due to bubble plume depends on the
wind speed and the type of plume. In this section, we have
computed the effective sound speed caused due to only the
and
plumes.1) Perturbation byplume: On the basis of their sizes,
we have classified the plumes into three subtypes: small-and-intermediate, near-large, and large. Contribution to the
effective sound speed, Ceff, through plume comes fromthese three subtypes. The parameter, Ceff, for plume isexpressed as:
( 1
Ceff) =
1
C20 I (28)
In the Equation (28), the quantity I is known as the integra-tion term and it can be expressed as:
I = 1
f2
rmaxrmin
r(r)
[((fr
f )2 +2r 1)
2 +2r ]dr (29)
In the Equation (29), fr is known as the resonance frequencyofplume. It is a function of bubble radius and the depthof influence of plume. It has also a implicit dependency on
the wind speed. For three values of wind speed, namely, 11
m/s, 12 m/s, 13 m/s, values of resonance frequency are given
in the set of Equations (30) as:
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fr =3.47 106
r (30a)
fr =3.53 106
r (30b)
fr =3.58 106
r (30c)
Now, putting the values of BPDS, , of plume, fordifferent bubble sub-categories, we have calculated the inte-
gral, I for these plume subtypes. Depending on the bubblesubtypes, integration limits have been varied. For small-and-
intermediate, rmin = rmin and rmax = r1, for near-large,rmin = r1 and rmax = r2, for large, rmin = r2 andrmax= r3.As an example, we have evaluated the integral, I, for small-and-intermediate bubbles which we have denoted as Is fora particular wind speed, w10, as parameter. Here, for windspeed, w10 = 11m/s, we have calculated I for small-and-intermediate bubbles. We have denoted it as Is, the calculation
is given below as:
Small and intermediate bubbles
Wind speed w10 = 11 m/s
Is= (1.51 1016)f3
r1
rmin
r9
[((134.39 106)2 f2C0r2 106)2+ (2f3r3 109)2]
dr (31)
Next we have calculated Is for other two values of w10,namely, 12 m/s and 13 m/s.
In the same way as above, we have calculated I for near-large and large bubbles for three wind speeds.
2) Perturbation by Plume: Like the plume,the plume is further classified into three categories.Contribution to the effective sound speed under variable
wind speed for each of these categories has been taken into
consideration.
The effective sound speed, Ceff, through plume isexpressed as:
( 1
Ceff)=
1
C20 I (32)
The integration term, I, for plume for three kinds ofplumes is expressed in the Equation (33) as:
fr =4.25 106
r (33a)
fr =4.32 106
r (33b)
fr =4.40 106
r (33c)
Now, for different values of BPDS, , of plume, wehave carried out the integration, I for different bubblesubtypes. Depending on the bubble subtypes, integration
limits have been varied.
For instance, we have evaluated the integral, Is, for small-and-intermediate bubbles under the wind speed, w10. Here,for wind speed, w10 = 11m/s, we have calculated I forsmall-and-intermediate bubbles. We have represented the
integration, Is, as:Small-and-intermediate bubbles
Wind speed w10 = 11 m/s
The integration term, Is, is expressed as:
Is = (5.61 1017)f3
r1rmin
r7
[((164.60 106)2 f2C0r2 106)2
+ (2f3r3 109)2]
dr (34)
Again, we have calculated I for near-large and largebubbles for other values of wind speed.
B. Acoustic signal attenuation by near-surface bubble plumes
In Section A, we have the effective sound speed, Ceff, in
the presence of both types of plumes: as well as . Theterm, Ceff, is expressed in terms of the real and imaginarycomponents as:
Ceff=Cs+is (35)
In Equation (35), the real component, Cs, represents theacoustic phase speed, and the imaginary component, s,represents the attenuation of the acoustic signal due to the
presence of bubble plumes. Equation (24) is derived under
the condition where multiple scattering among the bubbles is
neglected. The two terms on the right side of Equation (35),
can be, respectively, written as:
Cs = Re(Ceff) (36)
s(dB/m) = 20
In(10)Im(
1
Ceff) (37)
In Figure 5, we have shown the variation of signal propagation
through the and plume induced underwater region.From the two figures, we can infer that with the same
increment in frequency, the acoustic signal is subjected to less
resistance from theplume induced region, compared to theregion induced by both the andplumes. Alternatively,we can say that the acoustic signal propagates faster through
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TABLE I: Simulation Parameters
Parameters Values
Deployment Region 100m 100m 100mBubbles Penetration Depth plume: 1.4m - 2.1m; plume: 7.1m - 8.3m
Signal frequencies 10 kHz, 15 kHz, 20 kHz, 25 kHz, 30 kHz, 35 kHz, 40 kHz
Data rate 500 bps
Packet interval 10 sec
Modulation scheme 64-QAM
Number of nodes (N) 150Spreading co-efficient 1.5
Wind Speed (w10) 11 m/s, 12 m/s, 13 m/s
the plume induced region. In Figure 6, we show theacoustic signal attenuation during propagation through andplume induced region. From the two figures, we infer thatthe attenuation rate of acoustic signal is higher in the and plume induced region, than in the region with onlyplume.
VI . PERFORMANCE EVALUATION
In this Section, we present the result of simulation-based
UWASN in terms of different metrics, which are explainedbelow.
A. Simulation settings
Settings of the simulation parameters are shown in Table
I. We have used the NS-3 simulator for our work. We have
considered the network to be consisting of 150 nodes. We have
considered shallow region for the deployment of network. The
nodes are deployed in a region of dimension 100m100m100m. The nodes are deployed randomly at different depths inbetween 0 to 100 m. The sink node is placed at the sea-surface.
We have used the Meandering-current mobility model [30].
Packets are transmitted from the source node to the sink node
via the intermediate relay nodes. We have considered seven
operating frequencies, namely, 10, 15, 20, 25, 30, 35, and 40
kHz.
B. Performance metrics
The performance of UWASN is assessed using the
following metrics.
Signal-to-Interference-Plus-Noise-Ratio (SINR): In any
communication system, signal gets affected due to the
presence of noise generated by system itself or injected from
outside. Like the Signal-to-Noise-Ratio (SNR), SINR is an
important metric for estimating the link quality in wireless
communication among nodes. Interference occurs when
signals from transmitters, other than the desired source, arrive
at the receiver coincidentally with the desired signal [31].
Mathematically, SINR is expressed as:
SINR= SiI+N
(38)
In the Equation (38), Si indicates the signal from the ith
source,I indicates the interference between the signals at thereceiving end, and N is noise in the channel.
Bit Error Rate (BER): In digital transmission, BER is
defined as:
BE R=Percentage of bits with errors
Total no of bits sent (39)
BER and SNR are interrelated with each other, but they
are distinct. In our experiment, we have used the 64-QAM
modulation scheme for evaluating BER. We have:
BE R= 7
12 (0.5 erfc(z)) (40)
Different topologies may exhibit different BER in the same
situation.
Delay (Latency):
Delay is defined as the time taken by a packet to reach the
destination node from the source node [32]. In our work, we
have defined delay in terms of the propagation time, i.e., the
time for a message to reach the sink node from the source
node. Mathematically, it is expressed as:
Delay= Distance covered by the signal
Speed of acoustic signal through channel(41)
In propagating through the underwater channel, the acoustic
signal traverses through bubble-free and bubble-induced en-
vironments. Regarding speed, there will be combination of
ideal channel propagation speed, which is C0 (1500 m/s), andanother, the effective speed, Ceff, through the bubble plume.
C. Benchmark
We have compared the simulated results with the existing
Thorp propagation [33] model in underwater environment.
In Thorp model, internode communication is affected due toattenuation of acoustic signal by conductive and saline ocean
water. So, in this case, it is observed that the performance
of the network is solely dependent on the underwater oceanic
channel characteristics. In our study, part of the channel is
induced by bubble plume. So, in such a scenario, the perfor-
mance of the network differs from that using the Thorp model.
As the Thorp model includes the ideal channel scenario, we
have compared our simulation results with the results obtained
using the Thorp model.
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0
10
20
30
40
50
60
70
80
10 15 20 25 30 35 40
SINR[
dB]
Frquency [kHz]
Bubble Plume, N = 30Bubble Plume, N = 90
Bubble Plume, N = 150
Thorpe, N = 30Thorpe, N = 90
Thorpe, N = 150
(a) SINR for wind speed 11 m/s
0
10
20
30
40
50
60
70
80
10 15 20 25 30 35 40
SINR[
dB]
Frquency [kHz]
Bubble Plume, N = 30Bubble Plume, N = 90
Bubble Plume, N = 150
Thorpe, N = 30Thorpe, N = 90
Thorpe, N = 150
(b) SINR for wind speed 12 m/s
Fig. 8: SINR for bubble induced and bubble free channel
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
10 15 20 25 30 35 40
BER
Frquency [kHz]
Bubble Plume, N = 30Bubble Plume, N = 90
Bubble Plume, N = 150
Thorpe, N = 30Thorpe, N = 90
Thorpe, N = 150
(a) BER for wind speed 11 m/s
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
10 15 20 25 30 35 40
BER
Frquency [kHz]
Bubble Plume, N = 30Bubble Plume, N = 90
Bubble Plume, N = 150
Thorpe, N = 30Thorpe, N = 90
Thorpe, N = 150
(b) BER for wind speed 12 m/s
Fig. 9: BER for bubble induced and bubble free channel
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
10 15 20 25 30 35 40
DELAY
[sec]
Frquency [kHz]
Bubble Plume, N = 30Bubble Plume, N = 90
Bubble Plume, N = 150
Thorpe, N = 30Thorpe, N = 90
Thorpe, N = 150
(a) Delay for wind speed 11 m/s
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
10 15 20 25 30 35 40
DELAY
[sec]
Frquency [kHz]
Bubble Plume, N = 30Bubble Plume, N = 90
Bubble Plume, N = 150
Thorpe, N = 30Thorpe, N = 90
Thorpe, N = 150
(b) Delay for wind speed 12 m/s
Fig. 10: Delay for bubble induced and bubble free channel
D. Result and discussion
The results obtained with respect to the three metrics defined
in Section VI-B are discussed below.
1) SINR: Figure 8 shows how SINR varies with frequencyfor different number of nodes under variable wind speed. We
see from the figure that for the same number of nodes at the
same frequency, SINR is higher using the Thorp model than in
the case where bubble plume is considered. Again, we observe
from the figure that towards the higher frequency region, SINR
increases with the increase in the number of nodes. In case of
Thorp, we observe that the distribution of SINR is frequency-
independent. This is due to the fact that even if signal and noise
values are different, the ratio is the same for all the cases. Our
study reveals that the overall SINR for bubble plume decreases
by 28.80% for wind speed 11 m/s and 29.80 %for wind speed12 m/s.
2) BER: Variation of BER with the variation in frequencyis shown in Figure 9. A close observation reveals that,
compared to Thorp, BER is higher in the bubble-induced
channel. Again, we see that BER gradually decreases with
the increase in frequency. Additionally, a comparative analysis
directs that as wind velocity shifts from 11 m/s to 12 m/s,
there is significant increase in the BER. This is due to the
fact that as the wind velocity increases, the bubble plumes
penetrate more deeper region. So, the signal traverses more
distance to reach the surface sink. As expected, the bubble-
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induced channel invokes more errors in bits than the bubble-
free channel. In sum, we infer that compared to Thorp, BER
increases by 69.27% for wind speed 11 m/s, and 71.72 % forthe wind speed 12 m/s.
3) Delay: Figure 10 shows the average time taken by a
packet to reach the destination from the source node. As seen
from the figure, in the bubble-induced channel, it takes longer
time for a packet to reach the destination from the source
node than in the bubble-free channel. Again, we observe
that with the increase in the number of nodes N, the delay
decreases. As the number of nodes increases, the number of
hops also increases. As a consequence, a packet takes lesser
propagation time. Another noticeable observation is that, with
the increase in wind speed, the delay also increases. As wind
speed increases, bubbles penetration depth also increases.
Therefore, the depth of near-surface bubble-induced region
increases, and the duration of interaction with bubbles also
increases. Simulation results show that delay for bubble plume
induced region increases by 47.21 %for wind speed of 11 m/s,and 64.34 % for wind speed of 12 m/s.
VII. CONCLUSION
Increased wind speed near the ocean surface induces the
generation of bubble plumes. Bubble plumes are important
physical entities that persist near to the ocean surface. In
UWASNs, we have studied the effect of near-surface bubble-
induced region on network performance. Simulation-based
network performance was undertaken in terms of three per-
formance metricsSINR, BER, and delay. The simulation
results were compared with the results obtained using the
Thorp model. Performance comparison shows that there is an
increase in SINR by 29.3 %, whereas, for BER and delay, itis increased by 70.5 % and 55.78 % respectively.
In this work, bubble-plumes were considered to be station-
ary. However, situations may arise where there is collective
motion of bubble plumes. In future, we want to observe the
effect of near-surface moving bubble plumes on the perfor-
mance of distributed UWASNs.
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