Underwater Channel Simulation

UNDERWATER

CHANNEL

SIMULATION

PRATHEEK PRAVEEN KUMAR

RUCHIR BHAGAT

SHIKSHA SUVARNA

PUBLISHED WORKS OF PRATHEEK PRAVEEN KUMAR

CALM REFLECTIONS

INCLUSIVE GROWTH

MY TIME, MY WORLD

INCLUSIVE GROWTH Enlarged 2 ED

Co-authored

UNDERWATER CHANNEL SIMULATION

STEGANOGRAPHY USING VISUAL CRYPTOGRAPHY

CONTENTS

CHAPTER 1 INTRODUCTION 1

CHAPTER 2 THEORY AND FUNDAMENTALS 3

CHAPTER 3 SYSTEM DESCRIPTION 25

CHAPTER 4 OBSERVATION AND RESULTS 28

CHAPTER 5 SUMMARY AND CONCLUDING REMARKS 41

REFERENCES 43

INDEX

CHAPTER 1

INTRODUCTION

The need for underwater wireless communications exists in applications such as

remote control in off-shore oil industry, pollution monitoring in environmental systems,

collection of scientific data recorded at ocean-bottom stations, speech transmission

between divers, and mapping of the ocean floor for detection of objects, as well as for the

discovery of new resources. Wireless underwater communications can be established by

transmission of acoustic waves.

Underwater communications, which once were exclusively military, are extending into

commercial fields. The possibility to maintain signal transmission, but eliminate physical

connection of tethers, enables gathering of data from submerged instruments without

human intervention, and unobstructed operation of unmanned or autonomous underwater

vehicles (UUVs , AUVs).

Underwater communications in general mainly gets affected due to

• Channel Variations

Channel variations are variations in: - Temperature - Salinity of water - pH of water -

Depth of water column or pressure and - Surface/bottom roughness.

• Multipath Propagation The channel can be considered as a wave guide and due to the

reflections at surface and bottom we have the consequence of multipath propagation of

the signal.

• Attenuation Acoustic energy is partly transformed into heat and lost due to sound

scattering by inhomogeneities.

• Doppler Shift - Due to the movement of the water surface, the ray getting reflected from

surface can be seen as a ray actually getting transmitted from a moving transmitter, and

thereby, having Doppler shift in the received. When the receiver and transmitter are

moving with respect to each other, the emitted signal will either be compressed or

expanded at the receiver. Thereby, Doppler effect is observed.

Channel variations and multipath propagation keep a lot of hurdles for the achievement

of high data rates and robust communication links. Moreover, the increasing absorption

towards higher frequencies limits the usable bandwidth typically to only a few kHz at

large distances.

The channel has been modeled by considering multipath propagation, surface and bottom

reflection coefficients. In order to achieve high data rates it is natural to employ

bandwidth efficient modulation. In our case Quadrature Phase-Shift Keying (QPSK,


1

which is equivalent to 4-QAM) modulation techniques have been used for transmitter and

receiver.

A random bit generator is employed as the bit source. The transmitter converts the bits

into QPSK symbols and the output from transmitter is fed into “Underwater Acoustic

Channel”. The receiver block takes the output from the channel, estimates timing and

phase offset, and demodulates the received QPSK symbols into information bits.

The QPSK modulation technique is extensively being used in several applications like

CDMA (Code Division Multiple Access) cellular service, wireless local loop, Iridium (a

voice/data satellite system) and DVB-S (Digital Video Broadcasting-Satellite). In our

case the idea of receiver design has been taken from these applications.

We have considered in depth the channel variations and multipath propagation as our

investigation. Thus we present a reliable simulation environment for underwater acoustic

communication applications (reducing the need of sea trails) that models the sound

channel by incorporating multipath propagation, surface and bottom reflection

coefficients, attenuation, spreading and scattering losses as well as the

transmitter/receiver device employing Quadrature Phase-Shift Keying (QPSK)

modulation techniques.

To express the quality of the simulation tool various simulation results for exemplary

scenes are presented. In the following, chapters 2 and 3 describe completely about

underwater acoustic channel, its variations and effects, the multipath propagation

phenomenon, the channel design, etc. Chapters 4 and 5 present a detailed description

about the QPSK modulation techniques used in this, and the complete communication

part of the system.


2

CHAPTER 2

THEORY AND FUNDAMENTALS

2. Fundamentals of Ocean acoustics

The ocean is an extremely complicated acoustic medium. The most characteristic

feature of the oceanic medium is its inhomogeneous nature. There are two kinds of

inhomogeneities: regular and random. Both strongly influence the sound field in the

ocean. The regular variation of the sound velocity with depth leads to the formation of the

“underwater sound channel” and, as a consequence, to long-range sound propagation.

The random inhomogeneities give rise to “scattering of sound” waves and, therefore, to

fluctuations in the sound field.

2.1 Sound Velocity in the Ocean

Variations of the sound velocity c in the ocean are relatively small. As a rule, c

lies between 1450 and 1540 m/s. But even, small changes of c significantly affect the

propagation of sound in the ocean.

Numerous laboratory and field measurements have now shown that the sound speed

increases in a complicated way with increasing temperature, hydrostatic pressure (or

depth), and the amount of dissolved salts in water. A simplified formula for the speed in

m/s was given by Medwin in [3]:

C=1449.2+4.6T- 0.055T2

+0.00029T2

+(1.34-0.01T)(S-35)+0.016z (2.1)

Here the temperature T is expressed in ° C, salinity S in parts per thousand ,depth z in

metres d velocity c in meters per second. Eq. (2.1) is valid for:

00 ≤T≤35

0 C

00 ≤S≤45 ppt

and 00 ≤z≤1000m

The Eq. (2.1) is sufficiently accurate for most cases. However, when the propagation

distances have to be derived from time-of-flight measurements, more accurate sound

speed formulae may be required (i.e. ≤ 0.1 m/s). These are provided by accurate

velocitometers.

2.2 Dependence of c on T, S and z

Fig. 1 shows the typical Temperature profile with surface of the sea at higher

temperature than the temperature at the sea bed. Here we can see, temperature decreases

with depth till some depth value 300 z = m and after that getting constant. This

corresponds to a summer profile of a typical sea.


3

Fig. 1: Temperature vs. Depth

Sound velocity varies with temperature, salinity and depth. The impact of temperature

and pressure upon the sound velocity, c is shown in Fig. 2. This can be viewed in three

domains. In the first domain, temperature is the dominating factor upon the velocity of

sound. In the second domain or transition domain, both the temperature and depths are

dominating upon the velocity of sound. In the third domain, sound velocity purely

depends on depths. These three domains can be seen in Fig. 2, first domain is till depths

of 200 m, transition domain is from 200-400 m and the third domain is above 400 m.


4

Fig. 2: Sound velocity vs. Depth

Dependence of c on salinity, S is shown in Fig. 3. Here, with the increase of S, velocity

of sound, c, also increases keeping the shape of the profile unaffected.


5

Fig. 3: Sound velocity vs. Salinity

2.3 Typical Vertical Profiles of Sound Velocity

The shape of the sound velocity profile

C(z)=c(T(z),S(z),z) (2.2)

is the most important for the propagation of sound in the ocean.

The c(z) profiles

-are different in the various regions of the ocean and

-vary with time (seasons).

At depths below 1 km variations of T and S are usually weak and the increase of sound

velocity is almost exclusively due to the increasing hydrostatic pressure. As a

consequence sound velocity increases almost linearly with depth.

2.3.1 Underwater Sound Channel (USC)

In the deep water regions typical profiles possess:

- Velocity minimum at a certain depth, zm(Fig. 4a)

- zm defines the axis of underwater sound channel

- above zm sound velocity increases mainly due to temperature and

- below it sound velocity increases due to hydrostatic pressure

If a sound source is on the access of the USC or near it, some part of the sound energy is

trapped in the USC and propagates within it, not reaching the bottom or surface, and,

therefore, not undergoing scattering or absorption at these boundaries, cf. [6].

Underwater Sound Channel of the first kind, co < ch

co – velocity at the surface, ch – velocity at a depth

Fig. 4: Underwater sound channel of the first kind (co < ch). (a) profile c(z), (b) ray diagram


6

Waveguide propagation can be observed in the interval depths of 0<z< zc . The depth z=0

and z=c are the boundaries of the USC. The channel traps all sound rays that leave a

source located on the USC axis at grazing angles:

(2.3)

where cm and c0 are the sound velocities at the axis and boundaries of the channel,

respectively. Hence, the greater the difference, c0 - cm the larger is the interval of angles

in which the rays are trapped, i.e. the waveguide is more effective, cf. [6].

Underwater Sound Channel of the second kind, c0 > ch

c0– velocity at the surface, ch – velocity at a depth ‘h’

Fig.5 : Underwater channel of the second kind (co > ch). (a) profile c(z), (b) ray diagram

Here, the USC extends from the bottom up to the depth zc where the sound velocity

equals ch . Two limiting rays are shown in Fig. 5b for this case. Trapped rays do not

extend above the depth zc. Only the rays reflected from the bottom reach this zone.

The depth of the USC axis in deep ocean is usually 1000-1200 m. In the tropical areas it

can range down to 2000 m. The sound velocity ranges from, cf. [6]:

- 1450 m/s to 1485 m/s in the Pacific Ocean.

- 1450 m/s to 1500 m/s in the Atlantic Ocean.

2.3.2 Surface Sound Channel

This channel is formed when the axis is at the surface. A typical profile for this

case is shown in Fig. 6a. The sound velocity increases down to depth z = h and then

begins to decrease. Rays leaving the source at grazing angles propagate with

multiple reflections in the surface sound channel, cf. [6].


7

Fig. 6: Surface sound channel. (a) profile c(z), (b) ray diagram

In the case of a rough ocean surface, the sound energy is partly scattered into angles

, at each interaction with the surface, i.e.

- rays leave the sound channel

- sound level decays in the surface sound channel and increases below the surface sound

channel.

Surface sound channels frequently occur

- in tropical and moderate zones of the ocean, where T and S are constant due to

mixing in the upper ocean layer. c increases due to hydrostatic pressure gradient.

-if the temperature on the surface decays due to seasonal changes, i.e. summer → autumn

→ winter

-in Arctic and Antarctic regions, where a monotonically increasing sound velocity profile

from the surface to the bottom can be observed.

2.3.3 Antiwaveguide Propagation

Antiwaveguide propagation is observed when the sound velocity monotonically

decreases with depth (Fig. 7a). Such sound velocity profiles are often a result of intensive

heating by solar radiation of the upper ocean layer.


8

Fig. 7: Formation of a geometrical shadow zone when the velocity

monotonically decreases with depth.

All rays refract downwards. The ray tangent to the surface is the limiting one. The shaded

area represents the geometrical shadow zone (Fig. 7b). The geometrical shadow zone is

not a region of zero sound intensity, cf. [6].

2.3.4 Sound Propagation in Shallow Water

This type of propagation corresponds to the case where each ray from the source,

when continued long enough is reflected at the bottom. A typical profile is shown in Fig.

8a. It is observed in shallow seas and the ocean shelf, especially during summer-autumn

period when the upper water layers get well heated, cf. [6].

Fig. 8: Sound propagation in a shallow sea. (a) profile c(z), (b) ray diagram

2.4 Propagation Loss of Sound

2.4.1 Spreading Loss

Spreading loss is a measure of signal weakening due to the geometrical spreading

of a wave propagating outward from the source. Two geometries are of importance in

underwater acoustics:


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1. Spherical Spreading

In a homogenous and infinitely extended medium, the power generated by a point source

is radiated in all directions on the surface of a sphere. This is called spherical spreading.

Since intensity equals power per area, we obtain at ranges r0 and r, cf. [2]

(2.4)

(2.5)

Incase of spherical spreading, the intensity decreases by r2

. The spreading loss is given

by

(2.6)

2. Cylindrical Spreading

Cylindrical spreading exists when the medium is confined by two reflecting planes. The

distance between the planes is supposed to be 10 h >10 λ . Where, λ denotes the

wavelength of the sound wave. Since intensity equals power per area, we obtain at ranges

with r0 and r with (r>>h).cf.[2].

(2.7)

The loss due to cylindrical spreading is

(2.8)

The intensity decreases linearly with distance r. In logarithmic notation, for cylindrical

spreading, the spreading loss is

(2.9)

Taking n as the exponent, we can express the spreading loss for geometric spreading in

logarithmic notation


10

(2.10)

where exponent n = 1 for cylindrical spreading; n = 2 for spherical spreading.

2.4.2 Sound Attenuation in water

The acoustic energy of a sound wave propagating in the ocean is partly: -

absorbed, i.e. the energy is transformed into heat. - lost due to sound scattering by

inhomogeneities.

Remark: It is not possible to distinguish between absorption and scattering effects in real

ocean experiments. Both phenomena contribute to the sound attenuation in sea water.

On the basis of extensive laboratory and field experiments the following empirical

formulae for attenuation coefficient in sea water have been derived.

a) Thorp formula, valid frequency domain see Fig. 9a

(2.11)

where, f is frequency [kHz]

b.) Schulkin and Marsh, valid frequency domain see Fig. 9b

(2.12)

where

A=2.34x10-6

, B =3.38x10-6

,

S is the salinity in [ppt],

P is the hydrostatic pressure [kg/cm2

]

F is the frequency [kHz], and

fT = 21.9x106-1520/(T+273)

[kHz],

is the relaxation frequency with T the temperature in [o

C]. While the temperature range

from 0 to 30

o C, fT varies approximately from 59 to 210 kHz.

c.) Francois and Garrison, valid frequency domain see Fig. 9c

(2.13)

The first term in equatio (2.14) corresponds to:

• B(OH)3

(2.14)


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• Magnesium Sulphate Mg(SO4 )

(2.15)

The sound speed is approximately given by

(2.16)

• Pure water (H2 O)

(2.17)

with f in [kHz], T in [o

C], S in [ppt]. And where zmax , pH and c denote the depth in [m],

the pH-value and the sound speed in [m/s] respectively.

Fig.9: Diagram indicating Empirical formula for different frequency domain

General diagram showing the variation of α with the three regions of Boric acid,

Magnesium Sulphate and Pure water is depicted in Fig. 10.


12

Fig. 10: General Diagram indicating the three regions of B(OH)3 , Mg(SO4 ) and (H2 O).

From Fig. 10, it can be observed that for the Boric acid region, Attenuation is

proportional to f2

. And for the regions Magnesium sulphate and pure water also

Attenuation is proportional to f2. In the transition domains it is proportional to f .

Attenuation increases with increasing salinity and temperature, Fig. 11. Attenuation

increases with increasing frequency.

(a)


13

(b)

Fig.11: Attenuation for various salinities and temperature. a)20 o

C b)30 o

C

2.4.3 Sound Attenuation in sediment

The sound attenuation in sediment mainly varies with the bottom type. Bottom type,

in short represented by bt, defines the sediment material of the ocean. The following table

provides the values of bt for each sediment type.

Bottom Reflection Coefficients

Table 1


14

The following empirical formula is provided to find the sound attenuation in the

sediment depending on the bt.

(2.18)

where αs is attenuation of sediment.

The following table provides the values for K and n for four sediment types.

Table 2

2.4.4 Surface and Bottom Scattering

Scattering is a mechanism for loss, interference and fluctuation. A rough sea

surface or seafloor causes attenuation of the mean acoustic field propagating in the ocean

waveguide. The attenuation increases with increasing frequency. The field scattered

away from the specular direction, and, in particular, the backscattered field (called

reverberation) acts as interference for active sonar systems. Because the ocean surface

moves, it will also generate acoustic fluctuations. Bottom roughness can also generate

fluctuations when the source or receiver is moving. The importance of boundary

roughness depends on the sound-speed profiles which determine the degree of interaction

of sound with the rough boundaries.

Often the effect of scattering from a rough surface is thought of simply an additional loss

to the specularly reflected (coherent) component resulting from the scattering of energy

away from the specular direction. If the ocean bottom or surface can be modeled as

randomly rough surface, and if the roughness is small with respect to the acoustic

wavelength, the reflection loss can be considered to be modified in a simple fashion by

the scattering process. A formula often used to describe reflectivity from a rough

boundary is

(2.19)

where R(θ ) is the new reflection coefficient, reduced because of scattering at the

randomly rough interface. Γ is the Rayleigh roughness parameter defined as

(2.20)


15

where k = 2π λ is the acoustic wave number and σ is the rms roughness.The rough

seasurface reflection coefficient for the coherent field is

(2.21)

The roughness of the ocean surface is due to wind induced waves. It can be calculated

from the spectral density of ocean displacements. It is often modeled by the Neumann-

Pierson wave spectrum. The rms roughness or rms wave height of a fully developed

wind wavefield is then approximately

(2.22)

where, vw denotes the wind speed, [m/s].

For ocean bottom, σ is related to the particle size (particle refers to the material of the

sediment, further see section 2.4.3, Table 1) by,

(2.23)

Where

bt - represents the bottom type

2.4.5 Ambient Noise

An important acoustic characteristic of the ocean is its underwater ambient noise.

It contains a great bulk of information concerning the state of the ocean surface, the

atmosphere over the ocean, tectonic processes in the earth’s crust under the ocean, the

behaviour of marine animals and so on From, Fig. 13, different dominating levels of

ambient noise and total noise level can be observed and the individual formulae for all

these are as stated belo

For shipping noise (traffic) 10-300 Hz

(2.24)

Turbulence noise

(2.25)


16

Self noise of the vessel

(2.26)

where f and s v denote the frequency and vessel speed respectively.

Biological noise (fishes, scrimps etc.)

(2.27)

where f and S denote the frequency and seasonal dependence.

Sea state noise

(2.28)

The sea state noise can be determined as function of wind speed vw in [kn] and

frequency f in [kHz] by

(2.29)

Thermal noise

The thermal noise is due to molecular agitation (Brownian Motion). It can be

expressed as function of frequency f in [kHz] by

(2.30)

Thus the total noise level can be determined by:

(2.31)


17

Fig. 12: Ambient Noise Level for different domains at vw = 20 kn

2.5 Sound Propagation

2.5.1 Image or Mirror Method

The image method superimposes the free-field solution with the fields produced

by the

image sources.

Fig. 13 shows a schematic representation of a wave from the boundaries of a layer, and the image sources


18

(2.32)

(2.33)

(2.34)

(2.35)

(2.36)

(2.37)

The remaining terms are obtained by successive imaging of these sources to yield the

ray expansion for the total field,

(2.38)


19

(2.39)

(2.40)

(2.41)

(2.42)

And D being the vertical depth of the duct.

2.5.2 Grazing angles

The angle with which each ray grazes the boundaries is usually termed as grazing

angle.

This is quite important because of its influence on both the bottom and surface reflection

coefficients. With simple mathematics, the grazing angle for the four paths or for all the

rays can be computed, and is given by

(2.43)

(2.44)

(2.45)

(2.46)


20

Further, from Eq. (3.27), we can write down the influence of

• Wind speed, frequency and grazing angle on Surface reflection coefficient, R,

• Bottom type and grazing angle on Bottom reflection coefficient, R.

The functional dependence of wind speed w v , frequency f and grazing angle m φ on

Surface reflection coefficient is illustrated in Fig. 18.

2.5.3 Travel Times

The travel time of each ray is the time taken for it to reach the receiver. From the

above discussion it is vivid that, all the other paths need more time compared to the direct

path. Travel times for all the rays can be easily computed provided we know the length’s

or distances of all rays and the velocity of each ray. From Eq.(3.28), we know the

distances of all rays and the velocity of each ray is the speed of sound, c. Thereby, we can

write as


21

Fig. 14 Multipath propagation depicting delays in 2-D

Fig 15. Multipath propagation depicting delays in 3D view

Fig. 20 and Fig. 21 show the delay of rays in 2 dimensional and 3 dimensional views. It

can be clearly observed the delay of sinc pulse from ray 1 till ray 8. Here, sinc pulse is

just taken as an example to show the concept of delay.


22

2.5.4 Transmission loss for each ray

The transmission loss or sometimes referred as propagation loss is nothing but the

sum

of all the losses, a ray gets effected. So, transmission loss can be written as,

(2.47)

In the above equation the transmission loss is written only for ray 4, as an example. In

terms of Eq. (3.27), spreading loss is due to the terms

(as discussed in sec. 2.4.1). The attenuation or absorption is from the imaginary part of

the complex wave number k , as discussed in sec. 2.4.3, refer to Eq. (2.30). The Total

Reflection loss can be seen in this way. It is a sum of,

• reflection loss, loss which is caused when a ray travels from medium1 to medium2

due to the refraction of the ray, due to the reflection of the ray.

• scattering loss, loss which is caused by the roughness of the boundary. That is rays

get scattered in an un orderly fashion.

In Eq. (3.27), it is caused due to the terms .

The following figure illustrates the transmission loss phenomenon.

Fig 16 : Multipath propagation depicting transmission loss


23

As an example, a sinc pulse is taken to present the transmission loss phenomenon. In

Fig.16, one can observe clearly the degradation process in amplitude from ray 1 till

ray 8.


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CHAPTER 3

SYSTEM DESCRIPTION

A detailed description about the simulation of a continuous-time baseband system

is provided here.

Fig. 17: Underwater Acoustic Simulation system

The communication system considered is shown in Fig. 17. This is a typical set up which

can represent any kind of system using quadrature amplitude modulation (QAM). This

QPSK system is used in our investigations. A brief overview of the system now follows.

At the transmitting side, the sequence of symbols d (n) is converted to a continuous-time

baseband signal Sbb(t) by a pulse amplitude modulator (PAM). Note that d (n) takes the

values from discrete set of complex-valued symbols. Up-conversion is performed by

multiplying with ej2Πft

resulting in a bandpass signal s (t ), being transmitted over the

channel (refer chapters 2 and 3). In order to remove the carrier, the received signal r (t )

is processed by a down-converter which outputs the corresponding baseband equivalent

signal rbb(t). The down-converter is followed by a low pass and then by a matched filter.

The detector gives the estimates of the transmitted symbols. As we already said above,

baseband representation is useful in order to be able to simulate the system using, for

example, Matlab, where only time discrete signals can be represented. Fig. 37 represents

the baseband equivalent system.


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Fig. 18: The baseband Equivalent system

A simulation is often based on oversampled system, i.e. the sampling rate is higher than

the symbol rate. In general, a higher sampling rate will more accurately reflect the

original system. However, this comes at the cost of a longer simulation time since more

samples need to be processed. It is common to use an oversampling rate that is a multiple

of the symbol rate. The number of samples per symbols, here denoted by Q is then an

integer.

In order to arrive at the desired discrete time system, we will take the continuous-time

baseband equivalent system, introduce an ideal anti-alias filter at the output of the

matched filter and then oversample its output. This is depicted in Fig. 38, where also

down-sampling a factor Q is assumed to be chosen so large that the bandwidth of the

matched filter is smaller than the bandwidth Q 2T of the anti-alias filter. Consequently,

the anti-alias filter does not change the signal output from the matched filter. The signal

at the input of the detector is same as for the continuous-time system. Thus, this

oversampled system is equivalent to the original system.

Fig.19: Oversampling the system

3.1 Channel

The complete description of the channel can be understood from chapters. 1, 2

and 3. Nevertheless, a brief summary of it is again provided here. The main problems of

this channel are its multipath propagation, thereby a cause of interference. And next are

channel variations, variations in physical parameters of the ocean such as temperature,

pH, salinity, pressure or depth of water. All these are extensively discussed in the above

chapters mentioned. This report considers almost all the parameters into consideration

while modeling the channel. The simulation block diagram of the channel can be found in

Appendix of the report. Fig. 44 represents the Underwater acoustic channel model used in


26

this simulation h1(t), represents the direct path or first ray with zero delay (relative) and

hN(t) represents the Nth

ray with a delay of ƬN with respect to the direct path.

Fig. 20 : Underwater Acoustic channel model


27

CHAPTER 4

OBSERVATIONS AND RESULTS

This chapter presents you with some exemplary simulation results along with

some interesting observations. First we look into the Underwater Acoustic Channel then

we cover the Communication part of the system.

As discussed in the above chapters 2 and 3, the major impact in an underwater acoustic

channel would be its multipath propagation. Always our desired goal is to achieve high

data rates at a decent geometry of the transmitter and receiver (low BER is implied). Here,

the term geometry means the physical positioning of a transmitter and receiver in an

underwater acoustic channel of depth D and infinite length. At shorter distances the

multipath reaches the receiver at a much longer time compared to the direct path. This

statement may appear some what contrasting to what we think. But, it certainly makes

sense when we look into it in a deeper view. Here, we are not speaking about the time

taken for each ray to reach the receiver. But, instead we are referring to the “Relative

time” of all the other rays comparing to direct path.

Fig.21 presents the simulation results for a particular environmental scenario varying the

receiver location. This figure explains the impact of distances, (indirectly its grazing

angles which play a major role) on time delays of multipath propagation for the following

environmental scenario. Here, the wind speed and bottom type are not included as we are

representing only the time delay concept without any transmission loss phenomenon

included.


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Fig. 21: Simulation Results showing relative travel times for various receiver locations of a sinc pulse

without including any transmission loss phenomenon.

The relative times of all the 8 rays comparing to direct and the grazing angles for each

case are provided in the following.

T = [0 20.8207 20.8207 47.0817 47.0817 73.6106 73.6106 100.2081]

Angles = [0 75.9638 75.9638 82.8750 82.8750 85.2364 85.2364 86.4237]

T = [0 5.1355 5.1355 18.7083 18.7083 37.4700 37.4700 59.1197]

Angles = [0 21.8014 21.8014 38.6598 38.6598 50.1944 50.1944 57.9946]

T = [0 1.0650 1.0650 4.2397 4.2397 9.4656 9.4656 16.6508]


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Angles = [0 4.5739 4.5739 9.0903 9.0903 13.4957 13.4957 17.7447]

T = [0 0.5331 0.5331 2.1299 2.1299 4.7828 4.7828 8.4794]

Angles = [0 2.2906 2.2906 4.5739 4.5739 6.8428 6.8428 9.0903]

There is a huge difference in relative travel times for very shorter distances of 10 m, case

(a), compared to a desirable range of 1000 m, case (d). This can be understood when we

observe the corresponding grazing angles for each case. In case (a), the grazing angles are

very high due to shorter distances where, as in case (d) you observe very low grazing

angles. Another observation is the same, relative travel times and grazing angles for rays

hitting surface or bottom, surface-bottom-surface or bottom-surface-bottom, etc. This is

due to the location of both transmitter and receiver at exactly half of channels depth.

Here, we did not show any impact of Reflection loss and Spreading loss, only the time

delay concept has been focused. From now on, we refer mainly to grazing angles to

explain the behaviour of the system as the distance or lengths of each ray are included

when you calculate the grazing angle. The following simulation results are exclusively

presented to show the impact of transmission loss (including time delays) on multipath

propagation at various vertical depths of transmitter and receiver along with various

horizontal distances. Changing the vertical depths means, placing the receiver not exactly

at the half of the water channel depths but instead placing it, either nearer to the bottom

or nearer to the surface to look what exactly is happening for the bottom and surface

reflection coefficients.

When the separation between them is 10-200 m you don’t have that much impact of

multi-path propagation and thereby, receiver design complexity is much reduced. But,in

practical applications the distance between the transmitter and receiver is generally

desired beyond 500 m. So, all our simulation results are presented considering a 1000 m

separation between the transmitter and receiver. But, nevertheless, we do present some

simulation results when the receiver is at smaller distances from the transmitter. Another

criterion which is considered in the following simulation results is the change of

transmitter and receiver vertical depths. These are presented only to show the impact of

the distances between transmitter and receiver. For example, when we think of the water

channel depths to be 40 m and if the receiver is located at depths of 35 m, it signifies that

there would be certainly a more amount reflection of the signal from Surface compared to

Bottom. We always mean relative time delays with respect to the direct path when we

speak about time delays.


30

Fig. 22 presents, simulation results including the transmission loss phenomenon for two

transmitters and receivers at different locations. First we look into Fig. 49a and 49b. This

is for the case where the receiver is placed at a shorter distance of 200 m and vertical

depths of transmitter and receiver are swapped between 10 and 35 m. The complete

environmental scenario that has been chosen is given above. As said above, here, we

observe only the direct path and the multi-paths are completely suppressed. This is due to

the lower reflection coefficients at higher grazing angles and thereby, the transmission

loss of each ray becomes quite negligible. The transmission loss considers the number of

reflections (in turn reflection coefficients) when a ray hits the boundaries along with the

spreading loss (1/L ). So, the direct path will never have any reflection loss. Apart from

the direct path we observe the 3rd

ray in both the cases (a) and (b), but not the 2nd

ray.

This is due to zero reflection of the 2nd

ray when it hits the surface.

R1 – Surface reflection coefficient

R2 – Bottom reflection coefficient

Angles = [7.1250 12.6804 9.9262 15.3763 27.6995 32.0054 29.8989 34.0193]

R1 = [0.2766 0.0179 0.0835 0.0028 0.0000 0.0000 0.0000 0.0000]

R2 = [0.2002 0.0591 0.1084 0.0342 0.0427 0.0481 0.0457 0.0501]

Angles = [-7.1250 12.6804 9.9262 27.6995 15.3763 32.0054 29.8989 42.7688]


31

R1 = [0.2766 0.0179 0.0835 0.0000 0.0028 0.0000 0.0000 0.0000]

R2 = [0.9772 0.0591 0.1084 0.0427 0.0342 0.0481 0.0457 0.0559]

Fig. 22:Simulation results showing relative travel times for various transmitter and receiver locations of a

sinc-pulse including the transmission loss phenomenon.

Coming to Fig. 22c and 22d, we certainly see the impact of multipath growing to greater

extent as the separation between transmitter and receiver is more, i.e. 1000 m. In Fig. 22c,

the 4th

ray hits the surface 2 times and then bottom one time, i.e. S-B-S and the 5th ray hits

the surface one time and 2 times the bottom, i.e. B-S-B. From the following results, it is

observed that the 4th

ray grazes at an angle of 3.1481° and 5th

ray with 5.9941°. This leads

to lower reflection coefficients for 5th ray compared to 4th ray.

Similarly, in Fig. 22d, the 5th

ray hits the surface one time and 2 times the bottom, i.e. B-

S-B and the 4th

ray hits the surface 2 times and then bottom one time, i.e. S-B-S. From the

results provided in d), it is observed that the 5th

ray grazes at an angle of 3.1481° and 4th

ray with 5.9941°. This leads to lower reflection coefficients for 4th ray compared to

5th

ray.


32

Here, we see another interesting observation, i.e. in Fig. 22c, the 4th

ray has larger

amplitude compared to 5th

ray and exactly the opposite is seen in Fig. 22d. This is due to

the swapping of the vertical placements of transmitter and receiver from 10 to 35 m.

The simulation results for grazing angles and reflection coefficients:

Angles = [1.4321 2.5766 2.0045 3.1481 5.9941 7.1250 6.5602 7.6884]

R1 = [0.9492 0.8447 0.9028 0.7773 0.4021 0.2766 0.3361 0.2242]

R2 = [0.7191 0.5533 0.6306 0.4858 0.2568 0.2002 0.2266 0.1769]

Angles = [-1.4321 2.5766 2.0045 5.9941 3.1481 7.1250 6.5602 10.4812]

R1 = [0.9492 0.8447 0.9028 0.4021 0.7773 0.2766 0.3361 0.0630]

R2 = [0.9772 0.5533 0.6306 0.2568 0.4858 0.2002 0.2266 0.0960]

Fig.23 represents another simulation result to just show the impact of multi-path at a little

bit lower wind speed of 6 knots and with a bottom type value of 4.


33

Fig. 23: Simulation results showing relative time travels for two different vertical depths of transmitter and

receiver of a sinc pulse including the transmission

By now it is understood, multi-path dominates when the separation between the

transmitter and receiver increases and also varies with the vertical positions of the

transmitter and receiver. Added to this when you have a lower wind speed and a soft

bottom, it becomes more worse. The difference can be clearly observed from Fig. 49c,d

and Fig. 50. Here also the same behavior of amplitude difference is observed for 4th,

5th,

6th

, 7th

etc as the geometry is different for both cases.

Finally, you have the case of a constructive interference and destructive interference of

the multipath. When the multi-path gets added to the direct path in accordance with its

phase then we have a constructive interference otherwise a destructive one. So,

sometimes even if the multi-path is not dominative, you may still have a poor BER.

As we have discussed till now the multipath propagation in underwater acoustic channel

and all the channel effects, now we move to communications part of the system. Always

in communications the desired goal is to achieve maximum signal to noise ratio. In

underwater acoustic channel the noise is in two forms, one is the ambient noise discussed

in chapter 2 and the other is the multipath itself. We can also say, here the signal itself

acts as a noise as the multipath is nothing but (delayed versions of direct path) generated

from our signal only. So, here when ever we refer to SNR we imply that it the ratio

between the signal strengths of the direct path and multipath. The following are some

simulation results which show the Bit Error Ratio for only direct path and multi-path for

2 different wind speeds and bottom types.

DIRECT PATH


34

1. Environmental Scenario

Fig. 24 represents the BER plot only for direct path. As one can imagine, when we

transmit only the direct path, there will not be any noise present only you have

attenuation of the signal strength. So, the BER of direct path is 0.

Fig. 24: BER plot direct-path for the above Environmental scenario 1.


35

In the following two cases of multi-path propagation have been considered. One is at a

mud bottom type and lower wind speeds and the other is a bit higher wind speed and sand

bottom type. In case 1, the BER is much higher compared to case 2 as expected.

This is due to more reflections at lower wind speeds and softer bottom types.

MULTI-PATH PROPAGATION

Case 1



36

(a)

(b)

Fig. 25: BER plots multi-path propagation for the above Environmental scenario 2, case 1 a) linear scale

b) log scale.

Case 2


37


(a)


38

(b)

Fig. 26: BER plots multi-path propagation for the above Environmental scenario 2, case 2 a) linear scal

b) log scale.

From Fig’s. 25 and 26 it can observed that when you have higher wind speeds and rough

bottom types, the strengths of all the rays constituting multi-path propagation is getting

minimized. In these type of situations the communication aspect would become easy

compared to the acoustic channel. But, in practical applications, lower wind speeds are

present and thereby, making the communications design more hard. So, we should

always keep the range of wind speeds between 0-20 knots for our desired underwater

acoustic applications and the communication system should be designed robust even at

lower wind speeds.

Constellation Diagrams

From the following constellation diagrams, you can see an error free propagation for

direct path, Fig. 27 and errors for multi-path, Fig. 28


39

Fig. 27: Received QPSK states for direct path

Fig. 28: Received QPSK states for multi path


40

CHAPTER 5

SUMMARY AND CONCLUDING REMARKS

Some underwater acoustic applications like simple status reports or transfer time

position coordinates require a bit rate of 100 bits/s. But in several other applications like

sea floor mapping and in some military applications bit rates of several k bits/s are

required due to the transfer of high size images. As an initial step to explore systems for

communication that have the potential of transferring data at rates of multiple k bits/sec

over distances of several kilometres underwater, we have developed this simulation tool.

This simulation tool is designed for communication using Quadrature Phase Shift Keying

(QPSK) modulation techniques in an Underwater Acoustic Channel (UAC). It mainly

consists of a transmitter, UAC and a receiver. It provides a thorough insight into various

problems that are encountered by underwater sound channel and also explains the

degradation of bit error rate (BER) due to channel variations and presence of multipath

propagation.

All the oceanographic acoustic fundamentals have been considered in depth while

modelling the UAC. QPSK modulation techniques have been employed for the

transmitter and receiver. This tool works with a very low BER for the direct path even at

higher bit rates and is also robust for all channel variations. In short we can summarize

the following about what this simulation model provides:

• a thorough insight into the complexity of an underwater acoustic channel.

• the ability to design and analyse time invariant equalizers with sensitivity to equalizer

mismatch.

• gives the flexibility to change the carrier frequency.

This tool shows the practical poor BER for multi path propagation and it produces

satisfactory results in the bandwidths ranging 1-2 Kbps. The robustness of the system for

multipath propagation drastically decreases when the channel variations are getting worse.

The simulation tool developed here was for fixed transmitter and receiver locations. As

explained in this report, the presence of multipath causes an intersymbol interference

(ISI) that destroys the message, due to different travel times for different rays. Depending

on the particular sound underwater channel in question, the ISI can involve, in tens or

even hundreds of symbols. A solution for this problem might be to employ an adaptive

equalizer in the simulation tool (here, adaptive is used as we refer to a moving transmitter

and receiver). An equalizer can be viewed as an inverse filter to the channel. But,


41

nevertheless, in practical situations even the employment of an equalizer would not solve

the problem of transferring high bit rates. This can pose us to think of employing

modulation techniques like Orthogonal Frequency Division Multiplexing (OFDM). So,

our future outlook for the extension of this simulation tool would be:

• Incorporation of moving transmitter and receiver.

• Model validation with measurements.

• Investigation of adaptive single input multiple output (SIMO) equalization.

• Application of orthogonal frequency division multiplex (OFDM) communication.


42

REFERENCES

[1] F.B. Jensen, W.A. Kuperman, M.B. Porter and H. Schmidt, Computational Ocean

Acoustics (Springer- Verlag, New York, Inc., 2000).

[2] H.G. Urban, Handbook of Underwater Acoustic Engineering (STN Atlas Elektronik

GmbH, Bremen, 2002).

[3] H. Medwin and C.S. Clay, Fundamentals of Acoustical Oceanography (Academic

Press,San Diego, 1998).

[4] John. G. Proakis, Digital Communications, fourth edition (McGraw-Hill, NY, 2001).

[5] Johnny R. Johnson, Introduction to Digital Signal Processing (Prentice-Hall of India

Pvt.Ltd, New Delhi, 1996).

[6] L.M. Brekhovskikh and Yu. P. Lysanov, Fundamentals of Ocean Acoustics (Springer-

Verlag, second edition).

[7] Simon Haykin, An introduction to Analog & Digital Communications (John Wiley &

Sons, Singapore, 1994).

[8] www.complextoreal.com

[9] http://literature.agilent.com

[10] http://www.kth.se

[11] 51-st Open Seminar on Acoustic Program, Gdansk 2004

[12] R. E. Williams and H. F. Battestin, "Coherent recombination of acoustic multipath

signals propagated in the deep ocean," The Journal of the Acoustical Society of America,

vol. 50, pp. 1433- 1442, 1971.

[13] SOund NAvigation and Ranging, coined by Professor F.V. Hunt of Harvard.

[14] Fundamentals of Marine Acoustics, Chapter 1 – Jerald W. Caruthers, Elsevier

Scientific Publishing Company, 1977.

[15] Luke Godden, “Underwater Ultrasonic Communication”, 2002 Undergraduate

Thesis, The University of Queensland.

[16] C. E. Shannon, (1949) “A mathematical Theory of Communication”, proceedings of

IE 37 , pp. 10-21.

[17] Mari Carmen Domingo, (2008) “Overview of channel models for underwater

wireless communication Networks”, Elsevier Journal on Physical Communication , vol . 1,

issue 3, pp. 163-182.


43

[18] Donald R. Hummeu, (1972) “The Capacity of a model for the underwater acoustic

channel”, IEEE Transactions on Sonics and Ultrasonics , vol. SU-19, no. 3, pp. 350-353.

[19] Thomas J. Hayward and T. C. Yang, (2004) “Underwater Acoustic Communication

Channel Capacity: A Simulation Study,’ Proc. of AIP conference, vol. 728, pages 114-

124.

[20] Balakrishnan Srinivasan, (2008) “Capacity of UW acoustic OFDM Cellular

Networks”, MS Thesis,University of California.

[21] Milica Stojanovic, (2007) “On the relationship between capacity and distance in an

underwater acoustic communication channel”,’ Proc. of ACM SIGMOBILE MC2R , vol.

11, issue 4, pp. 34-43.

[22] James Preisig and Milica Stojanovic, (2009) “Underwater acoustic communication

channels: Propagation models and statistical characterization”, IEEE Communications

Magazine , vol. 47, no. 1, pp.84-89.

[24] M. Stojanovic “Recent Advances in high-rate underwater acoustic Communications”,

IEEE J. Oceanic Eng., pp.125-136, Apr. 1996.

[25] A. Kaya and S.Yauchi, “An acoustic communication system for subsea robot,” in

Proc. OCEANS’89, pp. 765-770, Seattle, Washington, Oct 1989.

[26] M. Suzuki and T. Sasaki, “Digital acoustic image transmission system for deep sea

research submersible,” in Proc. OCEANS’92, pp. 567-570, Newport, RI, Oct, 1992.

[27] M. Stojanovic, J.A. Catipovic and J.G. Proakis, “Adaptive multichannel combining

and equalization for underwater acoustic communications,” Journal of the Acoustical

Society of America, vol. 94 (3), Pt. 1, pp.1621-1631, Sept. 1993.


44

INDEX

A

Absorption 1, 6, 11, 23 Academic 43 Acoustic 1, 2, 3, 11, 15, 16, 25, 26, 27,

28, 34, 39, 41, 43, 44 Acoustical 43, 44 Acoustics 3, 9, 43 Ambient 16, 18, 34 America 43, 44 Amplitude 24, 25, 33, 34 Analog 43 Angle 20, 21, 30, 32 Angles 7, 8, 20, 28, 29, 30, 31, 33 Antarctic 8 Anti-alias 26 Antiwaveguide 8 Applications 1, 2, 30, 39, 41 Arctic 8 Atlantic 7 Atlas 43 Atmosphere 16 AUVs 1 Axis 6, 7

B

B-S-B 32 Backscattered 15 Balakrishnan 44 Bandpass 25 Bandwidth 1, 26 Bandwidths 41 Baseband 25, 26 Battestin 43 Behavior 34 Behaviour 16, 30 Biological 17 Bottom-surface-bottom 30 Brekhovskikh 43 Bremen 43

Broadcasting-satellite 2 Brownian 17

C

California 44 Capacity 44 Caruthers 43 Catipovic 44 CDMA 2 Channel 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,

12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44

Channels 8, 30, 44 Characteristic 3, 16 Clay 43 Coefficient 11, 15, 16, 21, 31 Coefficients 1, 2, 14, 20, 30, 31, 32,

33 Communication 1, 2, 25, 28, 39, 41,

42, 43, 44 Communications 1, 34, 39, 43, 44 Complex 23 Complex-valued 25 Continuous-time 25, 26

D

Data 1, 2, 28, 41 Degradation 24, 41 Delhi 43 Detection 1 Device 2 Diagram 6, 7, 8, 9, 12, 13, 26 Direct-path 35 Direction 15 Directions 10 Domain 4, 11, 12 Domains 4, 13, 18 Domingo 43 Donald 44 Doppler 1

Down-converter 25 Down-sampling 26 Duct 20 DVB-s 2

E

Elektronik 43 Elsevier 43 Empirical 11, 12, 15 Energy 1, 6, 8, 11, 15 Engineering 43 Environment 2 Environmental 1, 28, 31, 35, 36, 37,

38, 39 Equalization 42, 44 Equalizer 41, 42 Equalizers 41 Equation 23 Estimates 2, 25

F

Field 3, 11, 15, 16, 19 Fields 1, 18 Fluctuation 15 Fluctuations 3, 15 Formula 3, 11, 12, 15 Formulae 3, 11, 16 Francois 11 Free-field 18 Frequencies 1 Frequency 11, 12, 13, 15, 17, 21, 41,

42 Function 17 Functional 21 Fundamentals 3, 41, 43

G

Garrison 11

Gdansk 43 Geometric 10 Geometrical 9 Geometries 9 Geometry 28, 34 Godden 43 Gradient 8

H

Harvard 43 Haykin 43 Hayward 44 Horizontal 30 Hummeu 44

I

Idea 2 Ideal 26 IEEE 44 Image 18, 44 Images 41 Imaging 19 India 43 Industry 1 Inhomogeneities 1, 3, 11 Inhomogeneous 3 Integer 26 Interference 15, 26, 34, 41 Intersymbol 41 Investigation 2, 42 Investigations 25 Iridium 2 ISI 41

J

James 44 Jensen 43 Jerald 43

John 43 Johnny 43 Johnson 43 Journal 43, 44

K

Kaya 44 KBPS 41 KHZ 1, 11, 12, 17 Knots 33, 39 Kuperman 43 Laboratory 3, 11 Layer 8, 18 Layers 9 Logarithmic 10 Long-range 3 Luke 43 Lysanov 43

M

Magnesium 12, 13 Mapping 1, 41 Mari 43 Marine 16, 43 Marsh 11 McGraw-hill 43 Measurements 3, 42 Mechanism 15 Medwin 3, 43 Milica 44 Military 1, 41 Modulation 1, 2, 25, 41, 42 Modulator 25 Molecular 17 Monotonically 8, 9 Multi-path 30, 33, 34, 36, 37, 39 Multi-paths 31 Multichannel 44 Multipath 1, 2, 22, 23, 26, 28, 30, 32,

34, 41, 43 Multiple 2, 7, 26, 41, 42 Multiplex 42

Multiplexing 42 Multiplying 25

N

Navigation 43 Networks 43, 44 Neumann 16 Newport 44 Noise 16, 17, 18, 34, 35

O

Observation 30, 33 Observations 28 Ocean 1, 3, 6, 7, 8, 9, 11, 14, 15, 16,

26, 43 Ocean-bottom 1 Oceanic 3, 44 Oceanographic 41 Oceanography 43 OFDM 42, 44 Off-shore 1 Operation 1 Orthogonal 42 Output 2, 26, 42 Outputs 25 Oversample 26 Oversampled 26 Oversampling 26 Overview 25, 43

P

Pacific 7 Parameter 15 Parameters 26 Particle 16 Path 21, 27, 28, 30, 31, 34, 35, 39, 40,

41 Ph 1, 12, 26

Ph-value 12 Phase-shift 1, 2 Phenomena 11 Phenomenon 2, 23, 24, 28, 29, 31, 32 Pierson 16 Pollution 1 Prentice-hall 43 Proakis 43, 44 Proc 44 Propagation 1, 2, 3, 6, 7, 8, 9, 18, 22,

23, 26, 28, 30, 34, 36, 37, 39, 41, 44 Pulse 22, 24, 25, 29, 34

Q

Qam 2, 25 QPSK 1, 2, 25, 40, 41 Quadrature 1, 2, 25, 41 Queensland 43

R

Radiation 8 Rayleigh 15 Rays 7, 8, 9, 20, 21, 22, 23, 28, 29, 30,

39, 41 Receiver 1, 2, 15, 21, 28, 29, 30, 31,

32, 33, 34, 41, 42 Receivers 31 Recombination 43 Reflection 1, 2, 14, 15, 16, 20, 21, 23,

30, 31, 32, 33 Reflections 1, 7, 31, 36 Reflectivity 15 Refract 9 Refraction 23 Reverberation 15 RMS 16 Robot 44 Robust 1, 39, 41 Robustness 41 Roughness 1, 15, 16, 23

S

Salinities 14 Salinity 1, 3, 4, 5, 6, 11, 13, 26 Salts 3 Sasaki 44 Satellite 2 SBB 25 Schematic 18 Schmidt 43 Schulkin 11 Scientific 1, 43 Seasonal 8, 17 Seasurface 16 Sediment 14, 15, 16 Shannon 43 Sigmobile 44 Signal 1, 9, 25, 26, 30, 34, 35, 43 Signals 25, 43 Simo 42 Simon 43 Simulate 25 Simulation 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44

Sinc-pulse 32 Singapore 43 SNR 34 Solution 18, 41 Sonar 15 Sonics 44 Sound 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,

12, 14, 15, 18, 21, 41, 43 Sound-speed 15 Spherical 10, 11 Springer 43 Srinivasan 44 Stojanovic 44 Submersible 44 Subsea 44 Sulphate 12, 13 Summer-autumn 9 Surface 1, 2, 3, 6, 7, 8, 9, 10, 15, 16,

20, 21, 30, 31, 32 Surface-bottom-surface 30

Symbols 2, 25, 26, 41 System 2, 25, 26, 28, 30, 34, 39, 41,

44 Systems 1, 15, 41

T

Table 14, 15, 16 Tangent 9 Technique 2 Techniques 2, 41, 42 Tectonic 16 Temperature 1, 3, 4, 6, 8, 11, 13, 14,

26 Theory 3, 43 Thermal 17 Thomas 44 Thorp 11 Transition 4, 13 Transmission 1, 23, 24, 28, 29, 30, 31,

32, 34, 44 Transmitter 1, 2, 28, 30, 31, 32, 33,

34, 41, 42 Transmitters 31 Trapped 6, 7 Traps 7 Travel 21, 29, 30, 32, 41 Travels 23, 34 Tropical 7, 8 Turbulence 16

U

UAC 41 Ultrasonic 43 Ultrasonics 44 Underwater 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44

University 43, 44 Unmanned 1 Up-conversion 25

USC 6, 7 UUVS 1 UW 44

V

Validation 42 Value 3, 33 Values 14, 15, 25 Varies 4, 11, 14, 34 Velocities 7 Velocitometers 3 Velocity 3, 4, 5, 6, 7, 8, 9, 21 Verlag 43 Vertical 6, 20, 30, 31, 33, 34

W

Washington 44 Water 1, 3, 6, 9, 11, 12, 13, 26, 30 Wavefield 16 Waveguide 7, 15 Wavelength 10, 15 Waves 1, 3, 16 Wiley 43 Williams 43 Wind 16, 17, 21, 28, 33, 34, 36, 39 Wireless 1, 2, 43

Y

Yang 44 Yauchi 44 Yu 43

Z

Zero 9, 27, 31

Documents

Underwater Channel Simulation