Statistical Analysis of Acoustic Transmission Scintillation in the 2014 Nordic Seas
Experiment
ARCHIVES
T TUTE
MASSACHUF -:1
OF TECHNIOLOLGY
by
APR 15 2015
Guy Schory
LIBRARIES
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2015
2009 Massachusetts Institute of Technology. All rights reserved
Signature of Author:
Certified by:
Signature redacted
G
0
Department of Mechanical Engineering
Jan 20, 20 I5
Signature redacted
Director of the Laborator
Nicholas C. Makris
Underseaem e Senig
Signature redacted
Accepted by:
David E. Hart
Chairman, Department Committee on Graduate Students
1
2
Statistical Analysis of Acoustic Transmission Scintillation in the 2014 Nordic Seas
Experiment
by
Guy Schory
Submitted to the Department of Mechanical Engineering on
February, 2015 in Partial Fulfillment of the Requirements
for the Degree of Master of Science in Mechanical
Engineering
Abstract
The propagation of acoustic signals through an underwater waveguide adds randomness to the
received signal, called scintillation. For a fully saturated field, this scintillation features statistical
properties that can be measured and estimated. Many analyses were conducted in the past for
finding and estimating the characteristics of these statistical properties.
In February 2014, the 2014 Nordic Seas Experiment was conducted in Norway, in which acoustic
broadband signals were transmitted and received frequently, propagating through a waveguide on
the continental shelf, and large sets of acoustic data were gathered.
The work presented here shows analysis of the statistical properties of the data recorded in the
2014 Nordic Seas Experiment. We show that the received signals indeed comply with a fully
saturated field by analyzing the distribution of the intensity and of several representations of
energy. We also show how the number of coherent cells can be estimated and that the statistical
properties of it fit the theory and previous work.
3
Acknowledgements
First and foremost, I wish to thank my advisor, Nicholas Makris, for his guidance and mentoring
as I worked on this thesis as well as throughout my studies at MIT. His attentiveness to my
academic strengths and weaknesses, his teachings and explanations allowed me to advance my
understanding in acoustics and made me a much better scientist altogether.
I also wish to thank my colleagues in our group for helping me with both logistic and scientific
problems I encountered on the way and for making me feel that I fit in the group despite the short
time I was a part of it.
I owe many thanks to Themistocles Resvanis, who shared his vast knowledge and experience with
me many times and helped me greatly with administrative and logistics issues as well as in
acclimating to the Boston area and to the US in general. I also want to thank my friend Giovani
Diniz who not only helped me catch up with the basic mechanical engineering material that I
wasn't previously familiar with but also lent an ear and crucial advice with personal issues.
I would also like to show my deepest gratitude to my supervisors in the Israeli Navy for aiding me
whenever I needed and especially to the DC based administrative staff who helped me
continuously and efficiently. Special thanks are also due to Eran Naftali, who encouraged me to
study at MIT and who helped me pursue this goal.
Lastly but most importantly, I would like to thank my wife, Liat, for supporting me completely
throughout my studies and my family and friends, both back home and in Boston. Without your
unquestionable support I'm sure that my academic road would have been that much harder.
4
Contents
Ab stract ......................................................................................................................................
3
Acknow ledgem ents.....................................................................................................................4
1.
Introduction.........................................................................................................................7
2.
Conducting the experiment and Data Collection ...............................................................
3.
2 .1 .
O v e rv ie w ..................................................................................................................................
9
2 .2 .
D ata C o llectio n .........................................................................................................................
9
TLAnalysis .......................................................................................................................
3 .1 .
4.
5.
6.
7.
9
G e n e ra l..................................................................................................................................1
Data Processing .................................................................................................................
10
0
12
4.1 .
B asic A n a ly sis .........................................................................................................................
12
4 .2 .
M eth o d o lo gy .........................................................................................................................
12
4.3.
Signal Degradation .................................................................................................................
13
Fully Saturated Field Analysis .......................................................................................
18
5 .1 .
G e n e ra l..................................................................................................................................1
8
5.2.
The distribution of the received field.................................................................................
18
5.3.
The distribution of the average intensity .............................................................................
20
5.4.
The distribution of the energy............................................................................................
23
NU source and FORA array Properties ..........................................................................
32
6.1.
SPL measurements.................................................................................................................32
6.2.
OAW RS array desensitized hydrophone ............................................................................
33
6.3.
Signal correlation by sensor...............................................................................................
35
Additional Analyses..........................................................................................................37
7.1.
M atched filter degradation ................................................................................................
5
37
7.2.
Number of coherence cells....................................................................................
7.3.
Correlation between signals ..............................................................................................
8.
Conclusions.......................................................................................................................60
9.
Appendix A .......................................................................................................................
.....
46
57
62
9.1.
Averaged intensity distribution .........................................................................................
62
9.2.
Distribution of the PS energy ..............................................................................................
65
9.3.
Distribution of the M F energy ............................................................................................
69
9.4.
Distribution of the CF energy ...............................................................................................
73
9.5.
M atched filter degradation ................................................................................................
77
9.6.
Parseval's sum energy as a function of time window ..........................................................
81
10.
Bibliography ..................................................................................................................
6
84
1. Introduction
On February 2014, the 2014 Nordic Seas Experiment went underway, led by Prof. Nicholas C.
Makris from MIT, with the participation of numerous scientists and engineers from MIT,
Northeastern University, Penn State University, the Institute of Marine Research, the Naval
Research Laboratory, BAE and Woods Hole Oceanographic Institute as well as the Institute of
Marine Research and the Defense Research Establishment, Norway.
In the experiment, acoustic broadband signals were transmitted and received frequently, using the
Ocean Acoustic Waveguide Remote Sensing system (OAWRS). The OAWRS system was used in
several experiments in the past, and is an effective system for imaging large areas on the
continental shelf instantaneously (1) (2). The acoustic signals propagated through a waveguide,
and large sets of acoustic data were gathered, that allow for a thorough analysis, both for the
detection of fish and other scatterers and for acoustic propagation properties. In certain times in
the experiment, an auxiliary ship deployed a transmitter and a receiver, and the data collected using
them allowed for one way propagation analysis. The analysis shown here is conducted on the data
received on March
3 rd,
both by the OAWRS receiver array and by the receiver hydrophone
deployed by the auxiliary ship.
The propagation of acoustic signals in an underwater waveguide adds randomness to the signals,
known as scintillations. Knowing the properties of the scintillations is important both before
conducting an experiment, for better planning of the experiment and when analyzing the results,
for accounting for inherent randomness. Substantial research about the scintillation of fully
saturated fields was conducted in the past, for example in (3) (4) (5) and (6).
One of the most important conclusions of the analysis of fully saturated fields is that the standard
deviation of the TL can be estimated, and for large time-bandwidth products, is approximated by
4.34 1/pt (3), where it is the number of coherent cells - the number of independent fluctuations
through the propagation (3) (5) (4). The number of coherent cells is dependent on the bandwidth
7
and the central frequency of the signal, as shown in (5). In chapter 7 we show that the number of
coherent cells in the data used in this analysis comply with the conclusions reached in (5).
The statistical properties described above are relevant for a fully saturated field (6) (3) (7) (4),
which means that the received signal is fully randomized, which in turn can be described by a
Circular Complex Gaussian Random (CCGR) (3). Chapter 5 shows that the received signals used
in this analysis is indeed CCGR, by showing that the distribution of the received intensity and
energy comply with the analytical distribution of these values, which is the gamma distribution,
with the number of coherent cells as the parameter.
Two representations of received energy are the Parseval's Sum (PS) energy, which is the total
energy received in the signal, and the Matched Filter (MF) energy, which is proportional to the
correlation of the received signal with the transmitted signal. The MF energy is very important in
sonar applications, as the matched filter allow for advanced signal processing (8) (9). The
difference between the PS energy and the MF energy gives us a measure of the deterioration of
the signal through the propagation (4), and in chapter 7 we analyze the dependence of this
difference on the range.
Throughout this work, we reproduce some of the analysis conducted in (3), (5), (4), we compare
our results with the ones received there, and we show that results received here support the
conclusions of these works.
8
2. Conducting the experiment and Data
Collection
2.1.
Overview
The experiment was conducted between February 16th and March 8th 2014, in several locations
in the Nordic sea, and it consisted of transmissions of LFM signals in six different bands, with 50
Hz bandwidth and 1 sec pulse duration, and reception of echoes by the OAWRS system, both
deployed by the WHOI RV Knorr. In addition to the research vessel, a second ship was used in
the experiment, whose main purposes were to check points of interest using an echosounder, and
assist with calibration of the sonars and the acoustic models.
On certain times during the experiment, a transmitter (Lubell single hydrophone) and a receiver
(Reson single hydrophone) were deployed from the second ship, allowing for one way
propagation, both by receiving the signals transmitted from the Knorr, and by transmitting signals
received by the OAWRS system.
The Transmitted signal was an increasing 50Hz LFM over one second in one of the following
bands: 825-875Hz, 930-980Hz, 1100-1150Hz, 1310-1360Hz, 1440-1490Hz and 1575-1625Hz.
In order to estimate the sound speed profiles, XBTs were deployed frequently, while CTDs were
used occasionally to get a better estimation of the sound speed and to calibrate the salinity levels.
2.2.
Data Collection
The data we used for most of the analysis in this work is the data collected on March
3 rd,
both by
the OAWRS system and by the Reson hydrophone. The reasons that we used these sets of data is
that on that date there are sufficient measurements to have a reliable statistical analysis.
Furthermore, using the data from both sets allows us to compare the results from the two systems
at similar environment characteristics.
9
3. TL Analysis
3.1.
General
As sounds propagates through an underwater medium, the wave's energy decreases due to
spreading and attenuation (10) (11) and is called Transmission Loss (TL). The TL can be estimated
using different models, and the model used in this analysis is the Parabolic Equations (PE) model
(11), implemented by the RAM procedure (12). An example for the output of the RAM model,
can be seen in figure 3.1.
1 runs, Source bot depth = 70 m; Freq. avg. 955 Hz
0
-50
50
-60
100
-70
-80
150
-90
200
-100
250
-110
300
-120
0
2
4
6
8
Range (km)
10
12
Figure 3.1: TL map, source depth 70 m, central frequency 955 Hz
The PE model uses the sound speed profiles to calculate the TL. As mentioned above, the sound
speed was estimated using frequently deployed XBTs and CTDs, and figure 3.2 shows the
estimated sound speed profiles measured on March 3rd
10
Measured sound speed profiles for March 3rd
0
7> ~
50 r
K
100 1-
E
a- 150 h
~ K
200 t
x
~
K
250
'A
1466
1468
1470
1472
1474
1476
1478
Sound speed, rn/sec
Figure 3.2: measured sound speed profiles on March 3rd
The thicker blue line is the mean sound speed at each depth, and is used for the TL calculations in
this work.
11
4. Data Processing
Basic Analysis
4.1.
Let the received pressure be I(r, t), where r is the receiver location, denoting the transmitter
location as the origin. In the frequency domain, the received pressure
is cD(r, f) =
fT '(r, t) exp(-2wTjft) dt, where T is the time window for which we perform the spectral
analysis.
The intensity of the signal is then defined by I(r, t) = I-(r, t) 2 1, and the average intensity is then
W(r)=
fT
I(r,t)dt, for a time window T. The Source Pressure Level (SPL) is defined as
1 Olog(W), for a time window that contains the whole received signal, and in our case T= Isec.
4.2.
Methodology
The first stage in the analysis was to find the received signals out of all the data collected. In order
to do that, for each frequency the total received signal was correlated with the source signal, and
local peaks were found. Most of the data that is used in this work was taken at times when two
sources transmitted simultaneously, with different Pulse Repetition Intervals (PRI), so in order to
discern between peaks that are received from the relevant source and peaks that are from the second
source or from noise, each peak was tested for: (a) time difference between the peak and other
peaks, and (b) peak correlated level, to be between maximum and minimum values.
After the peak times were collected, the received pressure at a time window around each peak was
obtained, as well as the timestamp of the peak and the positions and aspects of both ships. The
nominal time window starts at the peak time, and ends after 1 second, which is the waveform
duration, since the dispersion of the signal is very low, as will be shown later in this document.
Next, the received signal was filtered using a band-pass filter, around its central frequency, in order
to omit noise, residue from previous signals of different frequencies and signals from the undesired
transmitter. The filtering was done by performing an FFT, setting all frequencies outside of the
bandwidth window as zero, and returning to time domain by applying an IFFT.
12
The result of the IFFT is referred to from this point on as the received signal, and will be denoted
as z.
This procedure was done both for the data received on the Reson hydrophone, transmitted by the
MIT OAWRS source array (this will be referred to as "MIT source array" transmissions), and for
the data received on the FORA receiver array, transmitted by the Northeastern University Lubell
source (this will be referred to as "NU source" transmissions). Since the FORA array is consisted
of multiple hydrophones, taking all received data as independent measurements may not be correct.
In order to get a complete, unbiased results, the analysis was conducted for several sets of data: 1.
All the MF hydrophones, as if the received signals are independent (denoted as "All
Hydrophones"); 2. Only the desensitized hydrophone; 3. One random MF hydrophone.
4.3.
Signal Degradation
The propagation of the signal in the ocean causes it to disperse and deteriorate, due to spreading,
bottom attenuation, multipath arrivals and random scatterers. Figures 4.1-4.2 show examples of
the signal pressure, the matched filter energy and the signal spectrum at the source and at the
receiver, at a frequency of 1600Hz, both for the MIT source array and the NU source.
13
signal deterioration, f-1600, MIT source
at the source
at 12209 m
x 10
-
1
U)
U)
U)
U)
0~
04
20-
2
-
-1
0
0.2
0.4
0.6
0
1
0.8
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
-10
x 10
8U-
3.
LLw
.M
60.5
42
0
0
0
0.6
0.4
0.2
0.8
0
1
-5
x 10
0.2
E
1.5-
03
1
-
U) 0.1
0.5
0-
1570
1580
1590
1600
1610
1620
0
1570
1630
1580
1590
1600
1610
1620
16 30
Figure 4.1: (a) The normalized pressure, (b) the normalized matched filter energy and (c) the signal spectrum at the
transmitter and at the receiver for the 1600 center frequency, MIT source array.
14
sensitized hydrophone
signal deterioration, f-1600, 162 data points,
x 10
1
4r
U)
504
-
IL
-1
0
0.2
0.4
0.6
0
1
0.8
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
1
-10
x 10
1
-
1.5
LL
1-
-
-
0.5
LuJ
0
0
0
0.2
0.4
0.6
0
1
0.8
-6
x10
0.2
E
*.)
U)
C)
4-
0.1
2
0
1570
1580
1590
1600
1610
1620
1630
1570
1590
1580
1600
1610
1620
1630
Figure 4.2: (a) The normalized pressure, (b) the normalized matched filter energy and (c) the signal spectrum at the
transmitter and at the receiver for a random hydrophone for the 1600 center frequency, NU source.
We can see that the matched filter energy has several peaks, due to multipath arrivals, and that the
received pressure and its spectrum are deteriorated compared to the transmitted signal.
Received Energy as a Function of Time Window
The total energy of a received signal is calculated by
fT
IP(r, t) 2 Idt. In order to view the
dependence of the energy on the time window used, we show in figures 4.3-4.4 the total energy of
all received signals as a function of the time window, starting 0.5 seconds before the beginning of
the received signal and ending 0.5 seconds after the 1 second duration of the signal, both for the
MIT source array and the NU source.
15
Parseval Sum vs. Time, f-955, 106 data points, MIT source
1
0.9
-
0.8
0.7
-
E
-
C,) 0.6
b)
0.50
ZI
0.3-
V
-
0.2
-
0.1
06
-0.5
0
0.5
1.5
Time from beginning of signal (sec)
Figure 4.3: The normalized energy of all received signals at 955Hz, MIT source array. The mean energy is shown by
the thick black curve.
16
Parseval Sum vs. Time, f-955, all hydrophones
-
0.9
-
0.8
-
0.7
E
-
0.6
-
. 0.5
0
0.4
Z
0.3
0.2
0.1
0
-0.5
0
0.5
time from beginning of signal
1
1.5
Figure 4.4: The normalized energy of all received signals at 955Hz, NU source. The mean energy is shown by the
thick black curve.
We can see that about 95% of the energy for the MIT source array and about 80% of the energy
for the NU source are within the one second window. This percentage is smaller for the NU source
than for the MIT source array, but still amounts for almost all of the energy. We can see that the
slope is highest within the 1 second window, so it may be deducted that the signals' energies are
within the 1 second window, and the reason for the large energy outside of the window is high
noise, probably due to the proximity of the receiver to the main source and random scattering and
echoes.
17
5. Fully Saturated Field Analysis
5.1.
General
In order to conduct a meaningful analysis for the experiment, it is important to discern whether the
received pressure fields are fully saturated. A fully saturated field is a field that can be described
by a Circular Complex Gaussian Random, which means that both the real and the imaginary parts
of the received signal has a Gaussian distribution (3). This section reproduces the analyses
conducted in (3) (4) (7) (5), in order to show that the received signals of the 2014 Nordic Seas
experiment are indeed CCGR and that the field is fully saturated.
5.2.
The distribution of the received field
For a CCGR field, the received signal has a Gaussian distribution, which can be written as Pr(x) =
1 exp(-
27r(X2)
(X(2
) (3). Figure 5.1 shows the distribution of all the received pressure
measurements for the MIT source array, for the 955Hz central frequency band, along with the
analytical distribution.
18
I
0.07
Pressure distribution, f-,955, 848000 measurements
I
I
I
I
I I
I
I
-
0.06
I
-
0.05
(/3
ci) 0.040
ci)
0.03
-
0
0
0
I
-
0.02
-
0.01
O'
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
real pressure
0.6
0.8
1
X10
Figure 5.1: Measured (blue histogram) and calculated (red line) distribution of the real part of the received pressure,
for 955Hz center frequency, MIT source array.
We can see that the distribution indeed seems to be normally distributed. However, since the
distribution shown uses all measurements in all received signals, one may question whether taking
8000 not independent measurements from each received signal is correct. For that reason, we
performed the same analysis for several subsets of measurements, that use only a small number of
random measurements from each signal. Figure 5.2 shows the results for four sample sizes, for the
NU source for the 955Hz frequency band.
19
Histogram of random samples, f-955, 106 pings
15 measurements from each ping
CD
~I)
C-)
C
'I)
0.2
0.15
0.15
0.1
0.1
0.05
0.05
-
5 measurements from each ping
0.2
0
-
0
U
0 L
0
-6
6
4
2
0
-2
-4
..
0
-2
-4
2
4
7
x 10
x 10
50 measurements from each ping
25 measurements from each ping
0.1
0.2
0.08-
0.15
-
U)
-
0.06-
0.10.04
-
C
'I)
0.05
0.020
-1
'
0
-6
-4
-2
0
2
real pressure
4
6
X 10
0
-0.5
real pressure
7
0.5
x 10
Figure 5.2: measured (blue histogram) and analytical (red line) distribution of subsets of measurements, for 5, 15, 25
and 50 random measurements in each received signal
We can see that the distribution indeed resembles a Gaussian distribution for all numbers of
random measurements, with increasing fit for larger sample size, as was expected of a CCGR field.
The distribution of the average intensity
5.3.
As shown in (3), for a CCGR signal, the power W has a gamma distribution, such that Pr(W) =
(/ww
- p- -, ,where t is the number of coherence cells, calculated by P= (w2)(w) 2
and W is the mean value of W. The number of coherence cells is "the number of independent
intensity fluctuations averaged during the measurement time T" (3), and is dependent on the
inverse of the standard deviation of the averaged intensity. A further discussion about the
properties of the number of coherent cells appears later in this paper.
20
Figures 5.3-5.5 show the calculated and the measured distribution of W, for both the MIT and the
NU sources (a random hydrophone and all hydrophones), for the 955Hz frequency band.
Distribution of W, f-955, 106 data points, MIT source
0.35
I
I
I
0.3
3-N 0.15-m-.04
C,)
E
0
-. 1o
00
0
1
2
4
3
W (Pa2 )
Figure
5
6
7
x 1 1
5.3: measured (blue histogram) and calculated (red line) distribution of the received power for the 955Hz
frequency band, MIT source array.
21
distribution of W, f-955, 151 data points, sensitized hydrophone
0.35
-
0.3
C
0
0.25
-
mu-3.3626
N
0.2
F
E
0
0. 15 V-
0.1
I
-j-
K11-
/
0.05
0
0.5
1.5
1
x 10
2.5
11
)
W (Pa2
2
Figure 5.4: measured (blue histogram) and calculated (red line) distribution of the received power for a random
sensitized hydrophone for the 955Hz frequency band, NU source.
22
distribution of W, f-955, 9792 data points, all hydrophones
0.05 - ----0-045-
mu-3.5824
-
0.04
0
-
0.035
0.03-
E 0.025
0
0.02
S0.015
0.01
0.005
0
0
1
0.5
3.5
3
2.5
2
1.5
W (Pa2)
X10
Figure 5.5: measured (blue histogram) and calculated (red line) distribution of the received power for all hydrophones
for the 955Hz frequency band, NU source.
We can see a fairly good fit between the analytical distribution and the measured distribution.
Results for all frequency bands are shown in appendix A.
The distribution of the energy
5.4.
Next we will analyze the distributions of three representations of energy: (a) the total received
energy, which is equal to the Parseval's sum (PS) energy, (b) the matched filter (MF) energy, and
(c) the central frequency (CF) energy.
(a) As was shown above, the total received energy is Ep, =
the
fT
Parseval's
sum
energy
Eps = ff2 |
fT
Itp(r, t) 2 Idt, and it is equal to
p(r, f)2
df,
where
PD(r,f)
=
W(r, t) exp(-2wrjft) dt is the Fourier transform of the received pressure. In our case,
since the time window is I sec, Eps is also equal to the received power, W.
23
(b) The matched filter energy is the most important property for signal processing purposes
(8), as it uses the similarity of the received signal to the transmitted signal. The matched
f
energy
is
calculated
4(r, f)H (fItm)exp(j2rft)df
tm))df
=
by
Emf
(r) = Ih(tltm) * p(r, t) 12
(rf)KQ*(f)exp(j2wf(t
ff2
-
filter
(8) (4) (7), where h(tltm) = Kq(t - tm) is the filter, with the Fourier
transform H(fItm) = KQ*(f)exp(-j2wf tm), K = (ff2Q(f)2Idf)os and tm is the
delay time. The result of the integral is a function of time, which has a strong peak, as
shown in figure 5.6. This peak is the matched filter energy, and is given by Emf =
max Emi
T
tm
normalized matched filter output, fs955
1
0.9
0.8
0.7
0.6
I
i
I
i~
0.5
0.4
0.3
0.2
0.1
0'
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
time
Figure 5.6: Matched filter output for the 955Hz central frequency band, MIT source array.
We can see that other than the main peak, there are lower peaks before and after the main
peak, that result from early and multipath arrivals.
24
(c) The central frequency energy is the power at the central frequency, multiplied by the
bandwidth: ECf =
I
(r, fC) 12 -BW, where BW is the bandwidth, 50Hz in our case. This
energy has no special significance, but is important for comparison and for coherence cells
number analysis.
For a CCGR signal, the distributions of these energies follow the gamma distribution as well, but
the number of coherence cells is calculated differently. Let ac(L) = std(L(dB)), where L =
10log(E) all energy levels in dB, then F(L) = 101og(e)
k-O(
1 )2
(4) (7). For ft = 1, the case
for instantaneous signals (time-bandwidth product of 1), the standard deviation a(L) = 5.6dB,
which is the value received by Dyer (6).
exp(-pEn/En), where En is the
The distribution of each energy is given by Pr(E) = (P/5)PEA F(y)
energy of each type normalized by the energy of the same type of the transmitted signal, and En is
the mean energy (4) (7). Figures 5.7-5.9 show the calculated and measured distributions for the
three types of energy for the 955Hz frequency band, for both the MIT source array and the NU
source (one random hydrophone and all hydrophones).
25
Distribution of the energy, f-955, 106 data points, MiT source
0.25
0.35
mu-1.119
0.3
0.2
0.2U)
-
CL 0.25
mu-1.808
iL.
mu-3.3
e
0
0
-0 0.15
0
-
0.15
0.2
.0
0.15
-
(
0
I
0.1
-
0.1
0.1
0.05
0.05
0.05
o
0
4
2
Eps (Pa 2 *sec)
10
0
0
0.5
Emf (Pa2 *sec)1w
1
0
0.5
1
Ecf (Pa2*sec)x 10-
Figure 5.7: The measured (blue histogram) and calculated (red line) distributions of the (a) PS, (b) MF and (c) CF
energies for the 955Hz frequency band, MIT source array.
26
distribution of the energy, f-955, 151 data points, sensitized hydrophone
0.5
0.25
0.35
.0.45
0.3
mu-1.99
YI)
CL
L0.25
mu-0.97
0.4
0.2
.3
O
mu-3.64
0
0.35
0
0.3
-0 0.15
-
0.2
0.25
U)
0.15
C)
-
0.1
0.1
I-
0.2
0.15
i
0.1
U.)E
0.05
0
0
0.5
Eps (Pa2 *secc 10
1
0
EL
1
Emf (Pa2*sec 10
0.05
2
0
0.5
1
Ecf (Pa 2*sec)x lo
Figure 5.8: The measured (blue histogram) and calculated (red line) distributions of the (a) PS, (b) MF and (c) CF
energies for a random hydrophone for the 955Hz central frequency, NU source.
27
distribution of the ener', f-955, 9792 data points, all hydrophones
110
- mu-3.97
0.045
0.11
~
0.16
.0
I
0.04 h
UL-
U/)
0.035
C
0
.0
0.03
h
-
mu-O.97
-
0.05
0.14
mu-2.03
IL
0
C0.04
0
Ci
0.12
K
0.1
CO)
0.025
0.08
*0
u- 0,03
0.02
0
0.06
0.015
0.04
0.01
-
0.01
0.02
0.005
0
0.5
01
1
Eps (Pa2 *sec 10 -8
0
2
Emf (Pa *sec 10
3
II-
L
0
1
0
2
1
Ecf (Pa2sec)x
10
Figure 5.9: The measured (blue histogram) and calculated (red line) distributions of the (a) PS, (b) MF and (c) CF
energies for all hydrophones, for the 955Hz frequency band, NU source.
We can see that the analytical calculations fit the measurements well for all energy representations,
both for the MIT and the NU source.
Results for all frequency bands are shown in appendix A.
Since in our case the PS energy and the average intensity are in face the same (due to the 1 second
averaging), but the number of coherence cells is calculated differently, it is interesting to compare
the analytical distribution of both. Figures 5.10-5.12 show this comparison for the 955Hz
frequency band, for both the MIT source array and the NU source (one random hydrophone and
all hydrophones).
28
PS energy and W distributions, f-955, 106 data points, MIT source
0.35
-
-I
PS distribution
W distribution
0.3-
-
0.25
-
0
--
0.!
0.1
CO0.1
0
0.0
0
0
0.5
1
2.5
2
1.5
2
2
Eps (Pa *sec) /W (Pa )
3.5
3
x1
Figure 5.10: Comparison between the probability distributions of the mean intensity W and the PS energy for the
955Hz frequency band, MIT source array.
29
PS energy and W distributions, f-955, 151 data points, sensitized hydrophone
0.35
---
PS distribution
W distribution
-
0.3
-
U)
0.25
-
C
0
0.2 V-
I
-T
L..
-
0.15
0
-
0.1
I
0.05
0
2
5
4
3
Eps, Pa2 *sec / W, Pa
2
6
x 10-
Figure 5.11: Comparison between the probability distributions of the mean intensity W and the PS energy for a
random hydrophone for the 955Hz frequency band, NU source.
30
PS energy and W distributions, f-955, 9792 data points, all hydrophones
0.05
I
I
ii
PS distribution
W distribution
-
0.045
0.04
-
If
0
0.035-
-
0.03
-
0.025
0.02
-
0
C.)
-
0.015
II
II
I
0.01
M
0.005
0
0
0.1
0.2
0.3
0.5
0.4
2
0.7
0.6
Eps, Pa *sec / W, Pa
2
0.8
0.9
1
x 10
-8
Figure 5.12: Comparison between the probability distributions of the mean intensity W and the PS energy for all
hydrophones for the 955Hz frequency band, NU source.
This comparison shows us that the PS energy and the averaged intensity result are very similar,
such that both methods seem to be equal in merit.
31
6. NU source and FORA array Properties
SPL measurements
6.1.
Figure 6.1 shows the NU source Source Pressure Level (SPL) measurements as a function of range
for all hydrophones.
SPL vs range, all hydrophones
120
120
AL
110100.
901.2
110
100
90
1.25
1.3
1 .2
1.4
1.35
4
1.25
1.3
1.35
x 10
CO)
x 10
1. 4
4
120
120
110100
V
0-
(n)
80
1.2
1.25
1.3
100901.2
1.4
1.35
4
1.25
1.3
1.35
X 10
CO)
x 10
1.4
4
110
100
100
-
EL
(n
80
1. 2
90
80
1.25
1.3
range (m)
1.2
1.4
1.35
1.25
1.3
range (m)
X41
1.35
1.4
4
Figure 6.1: SPL for all hydrophones for all frequencies, NU source.
Figure 6.2 shows the measures SPL as a function of hydrophone number, for three random
transmissions for the 955Hz frequency band.
32
Received level vs. Sesnor number, f-955, 9792 data points, all hydrophones
111
11000
109 -
0
108-
00
0
00
0o00
0)0
C
0
0
000
100-
107
0 0
0b
o0
(o
00
0
0
0
0
0
0
0oO
%00
0
00
G
I
50
40
30
20
10
0
0
00
0
I
I
I
60
70
O
4)
01
0 0
110 -
o
3:
000 0009 ou oo~SC
0.)-.C
000
o000
00
0
o
0
0
a
0) 105
0
>
C
o 00
0
-
115
100
0
20
10
0
108
0*0
106- 00
30
40
I
I
70
0O
0~
0
60
000
~
Q
104-
102
50
10
20
0y
o0000
1
40
30
0
0
50
60
70
Sensor Number
Figure 6.2: SPL as a function of sensor number for for the 955Hz frequency band, NU source.
6.2.
OAWRS array desensitized hydrophone
As stated above, the OWARS receiver array consists of several sensitized hydrophones as well as
one desensitized hydrophone. Since the gains used for the sensitized and the desensitized
hydrophones are not equal, we checked if the SPL results for both types of hydrophones are the
same. Figure 6.3 shows the measured SPL for all hydrophones for the 955Hz frequency bands,
where the green markers are the sensitized hydrophones and the red markers are the desensitized
hydrophone.
33
SPL, f-955, 9792 data points, all hydrophones
120
0 desnsitzed snso
-
0
snsitized sensors
desensitized sensors
115 [-
110
0
-o
105 H-
YI)
0
100 I-
'
951-
1.22
1.24
1.26
1.28
1.3
Range (m)
1.32
1.34
1.36
1.38
x 104
Figure 6.3: Measured SPL for the sensitized (green) and the desensitized (red) hydrophones as a function of range.
We can see that the mean value of the sensitized hydrophones SPL is higher by more than 2dB
than the mean value of the desensitized hydrophone SPL. For that reason, we based our results and
conclusions on the sensitized hydrophones' data. Figure 6.4 shows the mean SPL as a function of
the central frequency band.
34
mean SPL vs. frequency, all hydrophones
109
0
desensitized
not desensitized
108 h-
107
F
7-
1061=3
CO
I/
I
105 F
'
104 F
800
900
1000
1100
1400
1300
1200
1500
1600
frequqncy (Hz)
Figure 6.4: mean SPL values as a function of central frequency band for the sensitized hydrophones (red) and the
desensitized hydrophone (blue).
We see that the sensitized hydrophones are as much as 2dB higher, but as the frequency increases,
the difference becomes smaller.
Further results for the desensitized hydrophones are shown in appendix A.
6.3.
Signal correlation by sensor
It may be interesting to see the correlation between the sensors, as a signal is received by all of
-
(x-y)
,f(X 2). (y 2
, the covariance between two signals
)
them. The correlation coefficient is defined by pxy
divided by the product of the standard deviation of each signal. We took the first sensor to be the
reference signal, and plotted the absolute correlation coefficient as a function of sensor number in
figure 6.5.
35
abs of correlation coeffecient vs sensor number, f-955, 9792 data points
1
0.9
0.8
0.7
00.6
0
~
-
0
0.04
0.3
0.2
0.1
0
10
20
30
40
50
60
70
sensor number
Figure 6.5: Correlation coefficient as a function of sensor number for all hydrophones for the 955Hz frequency band,
NU source. The red line marks the l/e value.
We can see that the correlation is very high for the closer sensor, but decreases rapidly as the
sensors grows farther from the referrence sensor.
36
7. Additional Analyses
Matched filter degradation
7.1.
As we've shown above, the matched filter energy is the correlation between the transmitted and
the received signals, whereas the Parseval's sum energy is simply the received signal energy. The
difference between these energies (normalized to the respectful source energies), then, gives us a
measure of the deterioration of the signal through propagation. We define this difference as the
Matched Filter Degradation, Dmf = Lps -
LMF
(4) (7). Figures 7.1-7.3 show the matched filter
degradation as a function of range for both the MIT and the NU sources (one random hydrophone
and all hydrophones), for the 955Hz frequency band, with two trend lines - one for linear
dependence of the degradation on the range and one for exponential dependence.
Matched Filter Degradation vs range, f-955, MIT source
o DMF measurements
---linear dependence, R -0.8262
8
exponential dependence,R -0.84583
7
-o.
0<6,0
-
000
OW
0~
6
00-
9
5
0
0 OCAGBO
G~
4
1.2
1.25
1.35
1.3
range (m)
1.4
1.45
X10
4
Figure 7.1: Matched filter degradation as a function of range, for the 955Hz frequency band, MIT source array.
37
MF degradation vs range, f-955, 151 data points, sensitized hydrophone
11
o
DMF measurements
linear dependence, R-0.91893
10 F-
exponential dependence, 2-0.92611
9
LL
8
0
O
Q0
7-
-
6
51.22
1.24
1.26
1.28
1.3
range (m)
1.32
1.34
1.36
1.38
x 10
Figure 7.2: Matched filter degradation as a function of range for a random hydrophone, for the 955Hz frequency band,
NU source
38
MF degradation vs range, f-955, 9792 data points, all hydrophones
13
12
o
DMF measurements
--
linear dependence, R-0.89473
exponential dependence,
-0.90205
11
10
9
LL
M-
Q
8
A>1
7
6
5
4
1.22
1.24
1.26
1.28
1.3
1.32
1.34
1.36
range (m)
1.38
x 10
4
Figure 7.3: Matched filter degradation as a function of range for all hydrophones, for the 955Hz frequency band, NU
source
The degradation of the MIT source array is lower than that of the NU source by about ldB,
probably due to the fact that the MIT source array is directional and the NU source transmitted
from closer to the sea surface, which probably caused the signal to degrade more.
There is seemingly a linear dependence of the matched filter degradation on the range. According
to (4), this dependence is given by DMF(r) = c + mr, where r is the range, c is the offset and m
is the dispersion per unit distance. Figures 7.4-7.6 show the values of c and m, as a function of the
central frequency for both the MIT and the NU (one random hydrophone and all hydrophones)
sources.
39
c and m vs frequency, linear dependence, MIT source
3
-
2 .5
E
5
1 0
800
900
1000
1100
1200
1300
1400
1500
1600
I
-15
-20
V
0
-
-25
800
900
1000
1100
1200
1300
1400
1500
1600
frequency (Hz)
Figure 7.4: The coefficients for the linear dependence DMF(r) = c + mr, MIT source array.
40
c and m vs frequency, linear dependence, sensitized hydrophone
4.5
4
E 3.5
-30
-
3
800
I
900
I
1000
1100
1200
1300
I
I
1200
1300
I
I
I
1400
1500
1600
I
-3560 -40
-45-501
800
900
1000
1100
1400
1500
1600
frequency (Hz)
Figure 7.5: The coefficients for the linear dependence DMF (r) = c + mr, one hydrophone, NU source.
41
c and m vs frequency, linear dependence, all hydrophones
E
/
4.2
3.8
E
7
3.
800
I
I
900
1000
1100
I
I
I
1200
1300
1400
1600
1500
-34-36-38
N'
-V -40
N
0
7-
-42-44
-46S00
900
1000
1100
1200
1300
1400
1500
1600
frequency (Hz)
Figure 7.6: The coefficients for the linear dependence
DMF (r)
= c + mr, all hydrophones, NU source.
We can see that the degradation in our case is much higher than the results shown in (4), of c=0.60.7dB and m=0.05-0.17 dB/km. There may be several reasons for that: a. the experiments were
conducted in very different environments, with different parameters c and m; b. the ranges in this
analysis are higher than the ranges shown in (4); c. the range window in this analysis is small and
as such is susceptible to inaccuracies; and d. the model described in (4) may not be correct in our
case.
If we assume that the model given in (4) is inaccurate, we can offer a different model, which is an
exponential dependence of DMF on the range, such that DMF(r) = c -exp(Mr/c). For small mr/c,
c - exp
(')
= c + mr, the first order of the Taylor series expansion, which fits the linear
dependence shown in (4), and it can explain the degradation difference between our results and
the ones in (4).
42
When comparing the R squared values of the two models for all frequencies and all data sets, we
see that both models explain the data quite well, at similar compliance. Figures 7.7-7.9 show the c
and m values for the MIT source array and the NU source (one hydrophone and all hydrophones)
for the linear and for the exponential dependence.
c and m vs frequency, exponential dependence,
MIT source
0.05
-
0.04
-
0.03
E
-
0.02
0.01
80 0
V
1
1000
1100
I
1200
1300
1400
1500
1600
1200
1300
1400
1500
1600
-
-
0.1
900
I
0. 5-
U
0.0
I
800
900
II-II~
1000
1100
frequency (Hz)
Figure 7.7: The coefficients for the exponential dependence DMF(r)
43
=
c - exp(mr/c), MIT source array.
c and m vs frequency, exponential dependence, sensitized hydrophone
I
I
1300
1400
1500
1600
1400
1500
1600
0.01 2
0.0 1 -0.00 8-
0.00 6
E 0.00 4
0.00'2_ _I
I _
_
1
0.03
-
800
900
I
1000
I
1100
1200
I
I
I
I
1100
1200
1300
I
-
0.025
-
0.02
-
m 0.015
-
0.01
0.0050800
I
I
900
1000
frequency (Hz)
Figure 7.8: The coefficients for the exponential dependence DMF(r)
source.
44
=
c ' exp(mr/c) for one hydrophone, NU
c and m vs frequency, exponential dependence, all hydrophones
0.012
0.01
-
0.008
0.006-
0
E
0.004-
-
0.002
800
900
1000
1100
900
1000
1100
1200
1300
1400
1500
1600
1200
1300
1400
1500
1600
0.02 5
0.0 2
0.01 5
V
U
0.0
0.00 '5
800
frequency (Hz)
Figure 7.9: The coefficients for the exponential dependence DMF (r) = c - exp(mr/c) for all hydrophones, NU
source.
We can see that the coefficients are much closer to the values received in (4). Table 7.1 shows the
coefficients values received by both models and the respective R squared values.
Linear
MIT
NU
-
one
m (dB/km)
c (dB)
Coefficient
Exponential
linear
Exponential
R squared
Linear
Exponential
-28-(-15)
0.02-0.15
1.5-2.7
0.01-0.04
0.81-0.96
0.81-0.91
-48-(-34)
0.002-0.026
3.2-4.2
0.002-0.011
0.84-0.93
0.84-0.93
-46-(-36)
0.003-0.025
3.3-4
0.002-0.011
0.81-0.93
0.8-0.94
hydrophone
NU
-
all
hydrophones
45
-60-(-35)
-
NU
0.05-0.34
0.001-0.015
3.4-5.4
0.85-0.94
0.85-0.93
desensitized
hydrophone
Table 7.1: c and m coefficients for the dependence of the matched filer degradation on the range.
We can see that the values of c and m are much closer to the values shown in (4), a fact that may
suggest that the exponential model has merit over the linear model.
Number of coherence cells
7.2.
As mentioned above, the number of coherence cells is an important property of the field, as it
signifies the number of independent statistical fluctuations of the signal. The number of coherence
cells as a function of frequency for the MIT and the NU (one random hydrophone and all
hydrophones) sources are shown in figures 7.10-7.12.
number of coherence cells for all frequencies, MIT source
6
5
o
muW
o
muPs
o
mu mf
mucf
S4
0
0
3
E
321
'-
VSoo
900
1000
1100
1200
1300
frequency (Hz)
46
1400
1500
1600
Figure 7.10: Number of coherence cells for the received power (blue), Parseval's sum energy (red), matched filter
energy (black) and central frequency energy (green), MIT source array.
number of coherence cells for all frequencies, sensitized hydrophone
4.5 [
4
o
muW
0
mu Ps
o
mu
mf
mu
mcf
3.5 F
0
0
E
3
2.5 F
2
1.51
1
'
0
800
900
1000
1100
1200
1300
1400
1500
1600
frequency (Hz)
Figure 7.11: Number of coherence cells for the received power (blue), Parseval's sum energy (red), matched filter
energy (black) and central frequency energy (green) for a random hydrophone, NU source.
47
number of coherence cells for all frequencies, all hydrophones
-
6
5
0
muW
o
mu
0
mu mnf
mu(
=4
0
E
2
1
U
8oo
900
1000
1100
1200
1300
1400
1500
1600
frequency (Hz)
Figure 7.12: Number of coherence cells for the received power (blue), Parseval's sum energy (red), matched filter
energy (black) and central frequency energy (green) for all hydrophones, NU source
We can see that the number of coherent cells for the averaged intensity and for the PS energy are
very similar, but in some occasions with a difference of up to 1.5dB. We can also see that the
number of coherence cells for the CF energy is very close to one, an expected result, as the central
frequency energy is an instantaneous measurement. These results comply with the results shown
in (4), but a little higher for PS energy.
As shown in (3), (4), (5), the number of coherence cells depends on the time-bandwidth product.
In order to view this dependence, we further processed the data by taking only some of the
measurements of each 1 second received signal, to form shortened signals of duration r. Since the
signals are LFM signals, the bandwidth of a subset of duration T is then T/T - 50Hz. Figures 7.137.15 show the number of coherence cells and the standard deviation for the PS energy as a function
of bandwidth for all central frequencies, for the MIT source array and the NU source (one random
hydrophone).
48
number of coherence cells vs. B/fc, MIT source
5.5
O 850 Hz
955 Hz
1125 Hz
1335 Hz
1465 Hz
+
5
K
A A
4A
4.5
A,-
1600Hz
4
U
'/
0
U
0
-.
In
A
3.51-
A
0
0
0 '
3
n'
0
0
-C
0
U
0
O
/
CD
F
-
--------
0
+
ID
.0
E
C
A
2.5 r
-
9
0
I
/
4
2
1.5
-tQ
I,//
1
0
0.01
0.02
0.03
Relative BW B/fe
49
0.04
0.05
0.06
std vs. B/fC MIT source
6
o
+
5
0
5 \1465
~\
850 Hz
955 Hz
1125 Hz
1335 Hz
Hz
1600 Hz
'
4-
0
00
2.50
2
0
0.01
0.02
0.03
0.04
0.05
0
0.06
Relative BW B/fe
Figure 7.13: Number of coherence cells and standard deviation as a function of BW for all frequency bands, MIT
source array.
50
number of coherence cells vs. B/fCsensitized hydrophone
I
10
-
I
V
V
o
+
0
D
9
/
a
850 Hz
955 Hz
1125 Hz
1335 Hz
1465 Hz
1600Hz
/
U)
/
-ii
U
a,
U
C
0
0
-----------------------------
0
U
C
0
0
0
0
0 0
0
0
-o
/,
'po
/
E
0
0
2A
C
-I
3
//
/
+~~-+
i''2'
WA,
-,
+
,7
+-~
,,-~
.-
/
Ii,
ii,,
2 - 11/
I/i
1/1/
II
I,,
0
0.01
0.02
0.03
Relative BW B/fe
51
0.04
0.05
0.06
std vs. B/fCsensitized hydrophone
6
0
850 Hz
5.5
+
5
0
955 Hz
1125 Hz
1335 Hz
1465 Hz
1600 Hz
4.5
4
-o0
\
3
2.5
2
-
1.5
0
0
0.01
0.02
0.03
0.04
0.05
0.06
Relative BW B/fC
Figure 7.14: Number of coherence cells and standard deviation as a function of BW for one hydrophone for all
frequency bands, NU source
52
number of coherence cells vs. B/fcall hydrophones
6
0
0
0---
5
0
0
+
0
0Q- ---
-
5.5 F
E
0'
Co
4.5 l-
850 Hz
955 Hz
1125 Hz
1335 Hz
1465 Hz
1600 Hz
0
(-I
4
0
0
0
3.5
- -+
-
C
-
U
U
0
0
3
E
C
2.5
2
+ y
//
1.5
1
II&
0
0.01
0.02
0.03
Relative BW B/fe
53
0.04
0.05
0.06
std vs. B/fCall hydrophones
6
0
+
5.5
0
0
i
850 Hz
955 Hz
1125 Hz
1335 Hz
1465 Hz
1600 Hz
4.5
32.5 -~
0.100
0
2
1.5
.500
.300
-
0-o~-,U
-.
1
-
0.01
0
0.02
0.03
0.04
0.05
0.06
Relative BW B/fC
Figure 7.15: Number of coherence cells and standard deviation as a function of BW for all hydrophones for all
frequency bands, NU source
-
We can see that the number of coherence cells fits the dependence presented in (5), of ti = A
(A - 1)exp(-k
-),
for A and k constants, B the bandwidth and f, the central frequency. The
values for A and k that optimize the least means squares cost function are shown in figures 7.167.18.
54
A vs. frequency, MIT source
5
-I -
I
900
1000
I
I
900
1000
I
I
1200
1300
4.5
4
3.5 h3
2.5
280 0
-----
150 1
1100
1400
1500
1600
1500
1600
k vs. frequency. MIT source
I
I
I
1200
1300
1400
-
100
50-
'
0
Soo
1100
freq
Figure 7.16: the constants k, A for the dependence of the number of coherence cells on the bandwidth, as a function of
frequency, MIT source array
55
A vs. frequency, sensitized hydrophone
---
10
8<
6
4
2
900
800
1100
1000
1200
1300
1400
1500
1600
1400
1500
1600
-
k vs. frequency, sensitized hydrophone
150 ---
100
50
0
Soo
900
1000
1100
1200
1300
freq
Figure 7.17: the constants k, A for the dependence of the number of coherence cells on the bandwidth, as a function of
frequency for one hydrophone, NU source
56
A vs. frequency, all hydrophones
6
5-
3
800
900
1000
1100
1200
1300
1400
1500
1600
1400
1500
1600
k vs. frequency, all hydrophones
120
-
110
-
100
9080-
7060
800
900
1000
1100
1200
1300
f req
Figure 7.18: the constants k, A for the dependence of the number of coherence cells on the bandwidth, as a function of
frequency for all hydrophones, NU source.
The results for A and k shown here are slightly different than the results shown in (5), and we
cannot specify a clear trend for the parmeters.
7.3.
Correlation between signals
Next in our analysis we show the correlation of the received signal as a function of distance, in
order to have a measure of the distance in which the signal becomes uncorrelated. Figures 7.197.20 show the correlation coefficient as a function of distance from the closest signal, both for the
MIT source array and for the NU source (one random hydrophone).
57
abs correlation coeffecient vs distance, f-955, 106 data points, MIT source
-
0.9
0.8
0
0.7
01
0
W 0.6
0.5
0.4
I
0
500
I
~
1000
2000
1500
2500
distance (m)
Figure 7.19: Abs correlation coefficient as a function of distance from the reference location, MIT source array. The
red line marks the 1/e value.
58
abs correlation coeffecient as a function of distance, f-955, 151 data points, sensitized hydrophone
0.9
0.8-
0.7
0
t-
0.6 Ii-
0
Q
Q
0DU.
0
LL
CZ)
0.30.2-
0.1
0
200
400
800
600
1000
1200
1400
distance (m)
Figure 7.20: Abs correlation coefficient as a function of distance from the reference location for one hydrophone, NU
source. The red line marks the 1/e value.
We can see that for the MIT source array, the correlation coefficient is relatively high and
decreases with distance, and for our relevant distances it is always above the folding value of l/e.
For the MIT source array, on the other hand, the correlation is much lower, around the folding
value, so it is difficult to deduct if they are indeed correlated.
59
8. Conclusions
The propagation of acoustic waves in an underwater medium has several effects on the signal,
mainly transmission loss and added randomness to the received signals. This randomness, called
scintillation, was thoroughly researched in the past for fully saturated fields, and it was shown that
it is statistical in nature and is dependent on the number of independent statistical fluctuations,
which in turn depends on the range, the central frequency and the bandwidth of the signal. A fully
saturated field can be described by a Circular Complex Gaussian Random variable, which means
that both the real and the imaginary parts have Gaussian distribution.
In February 2014, the 2014 Nordic Seas Experiment was conducted in Norway, in which LFM
signals at central frequencies of 850Hz, 955Hz, 1125Hz, 1335Hz, 1465Hz and 1600Hz with 50Hz
bandwidth were transmitted and received repeatedly, using the OAWRS system, and large sets of
measurements of the returned echoes as well as the one way propagation were collected. These
measurements allowed us to conduct an analysis of the scintillation in this experiment, and to
compare this analysis to previous ones (3) (4) (5).
First, we showed that the received field is fully randomized by showing several properties of a
CCGR field:
1. The distribution of the field is circular complex Gaussian.
2. The distribution of the averaged intensity is the gamma distribution with a parameter i,
such that p =
(W)
2
3. The distribution of energy representations, for three representations of the energy, is the
gamma distribution with a parameter p, such that c(L) = 10log(e) Ti%(
_k)2,
where
17(L is the standard deviation of the respective energy.
After showing that the field is indeed fully saturated, we analyzed the matched filter degradation,
a value that signifies the deterioration of the signal through propagation, and we showed that it
increases with range with a seemingly linear or exponential dependence on the range, and that the
results that we received comply with the results received in (4) better for the exponential model.
60
Lastly, we showed that the number of coherence cells is dependent on the frequency and on the
bandwidth, and that our results fit relatively well with the results received in (5).
Throughout our analysis we showed that the data from the MIT source array features slightly less
signal degradation than the data from the NU source, but other than that, both data sets show very
good fit to the theory.
61
9. Appendix A
This appendix shows the complete results for the averaged intensity and the energy distributions,
the matched filter degradation and the Parseval's sum energy for all frequencies and all datasets.
Averaged intensity distribution
9.1.
Distribution of the averaged intensity,
MIT
source
f.955
f.850
0.4
0.4
0.2
0.2
00
0
4
2
8
6
10
0
2
4
8
6
14
13
C
0
X 10
X 10
f-1125
-
0.4
f.1335
0.2
-
-
0.2
0
L
0
-
0
0
1
0
4
14
3
2
2
1
3
4
5
6
14
X 10
x 10
f-1600
f.1465
0.4
0.5
-
0.20-
0L
0.5
1
1.5
W (Pa
)
0
0
2.5
2
X 10
14
2
4
W (Pa2
62
6
8
1012
Distribution of the averaged intensity, Lubell source, sensitized hydrophone
f-850
0.4
0.4
0.2-
0.2;
f-955
0
5
0
0
15
10
x 10
Li
0.5
2.5
x 10
f-1335
f-1125
0.2
-
0.1 -A
0
0
0
8
6
4
2
12
10
10
0
2
6
4
8
x 10
x 10
U
0
fwl600
fW1465
0.4
0.4
0.2-
0.2
0
'
2
6
4
W (Pa2
10
8
0
3
2
5
4
2
10
x 10
(
63
a
)
01
0
10
10
-
U
2
11
"a 0.4
0.2
1.5
1
10
1
x 10
Distribution of the averaged intensity, Lubell source, all hydrophones
f.850
f-955
----
0.05
0.04
0.02
0
0
-K
0
0.5
2
1.5
0
x 10
.0
0
1
11
x 10
f-1335
f-1125
0.05
50.05
0
4
3
2
11
0
0
0
0
15
10
10
5
0
0.5
2
1.5
1
11
x 10
x 10
0
f-1600
f-1465
0
0.05
1
0.05
0
0
0
0.5
1
W (Pa2
2
1.5
0
6
2
W (Pa2)
x 10
64
8
10
x 10
10
Distribution of the averaged intensity, Lubell source, desensitized hydrophone
f-850
f-955
0.2
0.4
0.1
0.20
0
2
6
4
x 10
0
15
10
5
0
8
10
10
x 10
f-1335
f-1125
' 0.
0.4
g 0.2
0.2
0
0)
0
0
0
2
8
6
4
2
8
10
6
4
10
x 10
x 10
f-1465
.
1600
.2
-
0.4
0.1
0
0
0
2
6
4
W (Pa2
8
x 1010
02
22
W (Pa 2
Figure 9.1: Distribution of the averaged intensity.
9.2.
Distribution of the PS energy
65
3
4
x 10
5
10
Distribution of the PS energy, MTT source
f.850
fw955
0.4
0.4
0.2
0.2L
0
0
1
0
2
0
4
3
1
2
3
4
-
-B
x 10
x 10
f.1125
f.1335
0.4
0.4
0.2
5 0.2-
S0 0
0
1
2
)
4
3
2
4
6
8
-9
-8
U
0
x 10
x 10
f-1600
f-1465
0.4
0.5
0.2
-
-
1
0
0
0.2
0.4
0.6
Eps (Pa 2*sec)
0
0
1
0.8
x 10
66
0.5
1
1.5
Eps (Pa 2*sec)
2
2.5
-9
x 14
Distribution of the PS energy, Lubell source, sensitized hydrophone
f.850
f-955
0.4
0.4
0.2
0
0
4
3
2
1
0
0
8
6
4
2
.9
-9
x 10
x10
'IL
.n
0
f-1125
f. 1335
4A
0.2
0.2K
0.1
U
C
0
0
0
U
U
0.5
2
1.5
1
3
2.5
0
0.5
1.5
1
2
3
2.5
-9
0
x 10
x10
x9
f.1600
f.1465
0.47
0.4
0.2-
0.2
0
0
0
0.5
1
1.5
Eps (Pa 2sec)
2
0
2.5
0.5
Eps (Pa 2*sec)
x 10-9
67
1.5
1
x 10
Distribution of the PS energy, Lubell source, all hydrophones
f-955
f-850
0.05
-
0.04
0.2
0
0
1
0
6
5
4
3
2
0
0.4
0.2
0.8
0.6
x 10
x 10
a.
f-1335
f-1125
0.05
0 0.05
*
00
0A
0
0
3
2
1
0
5
4
Li,
5
4
3
2
1
-9
-9
0
x 10
x 10
f-1600
f-1465
0.05
0.1
0.05
0
0
1
2
4
3
2
Eps (Pa *sec)
6
5
.LI
0
0
0.5
1
1.5
2
3
2.5
2
x 10
Eps (Pa *sec)
-
9
1
-8
68
x 10
Distribution of the PS energy, Lubell source, desensitized hydrophone
f-955
f.850
0.4
0.1
0.2
-
-
0.2
0
0
0
1.5
1
0.5
2
1
0
2.5
2
4
3
.9
x 10
x10
C,,
f.1335
.1125
0.4
o 0.4
0.2
-5 0.2
0
0
0
0.5
1.5
1
x 10
-9
.9
x10
fa1600
f.1465
0.2
W.4"
0.2
0
--
0.1
0.20
0.5
1
Eps (Pa 2sec)
1.5
2
X9
0
0.5
Eps (Pa 2sec)
Figure 9.2: Distribution of the Parseval's sum energy.
9.3.
2
1.5
0.5
0
2.5
2
-
U
Distribution of the MF energy
69
1.5
x 10
x9
Distribution of the MF energy, MIT source
f-955
f.850
0.4
A4
0.2
0. 2
Jj
C
0
0.2
0.4
0
1.2
1
0.8
0.6
0.2
-8
x 10
f.1335
f-1125
04-
r3
0.2-
S0S0
0.2
-
O
0
0.2
0.6
0.4
1
0.8
X10
U-
U
0
0.6
0.4
-8
0.8
18
0
0.5
1.5
1
2. 5
2
-9
x 10
x 10
f-1600
f-1465
1
0.2
0.5
0
0
0
0.5
1.5
1
2
Emf (Pa *sec)
0
2.5
x9
2
0.2
0.6
0.4
0.8
1
2
Emf (Pa *sec)
X 10
70
X 10
x9
Distribution of the MF energy, Lubell source, sensitized hydrophone
f-955
0.4
0.2
0.2
-
f-850
nA
0
0&
0.5
0
0
0.5
0
2
1.5
1
2
-9
1.5
-9
x 10
x 10
LiL
f.1335
f-1125
S0.2
0.41
0.2
r 0.1
0
0
0
0.2
0.4
0.6
0
1
0.8
1
0.8
0.6
0.4
0.2
-9
x 10
x10
f=1600
f=1465
0.4
0.4 --
0.2
0.2
0
-%%
0
0.2
0.6
0.8
0.4
Emf (Pa 2*sec)
1
0
1.2
1
2
3
Emf (Pa2*s ec)
x 10-9
71
4
5
6
x 10
Distribution of the MF energy, Lubell source, all hydrophones
f-955
f.850
0.17
0.1
0.05
0.05
C
0
0
2
1.5
1
0.5
0
0.5
1.5
1
2.5
2
x 10
x10
LL
3
-9
1-1335
f.1125
0.1
I0.05
M
0.05
0
0
0
U
U
0
2
1.5
1
0.5
x10
0
x 10
f-1465
W. 1
0.1
0.05
0
-9
f-1600
0.2
0L
2
1.5
1
0.5
-9
0
0.5
1
1.5
Emf (Pa 2*sec)
2
0
2.5
0.5
1.5
1
2
9
Emf (Pa 'sec)
72
x 10
Distribution of the MF energy, Lubell source, desensitized hydrophone
f.850
0.4
0.2
0.2
f.955
-
0.4
00
0
0
8
-10
6
4
2
0.2
x 10
f.1335
f.1125
S0.4
0.2
r3 0.2
0.1
0
0
0
U
0
1
0.8
0.6
0.4
0.2
0
5
4
3
2
1
-9
x 10
x10
.1600
f. 1465
0.4
0.2
0.2
-
0.4
0
0
0
2
1.2
-S
x 10
LL
8
10
6
4
2
Emf (Pa ,Sec)
0
1
4
3
2
6
5
-10
2
Emf (Pa *sec)
x 10
Figure 9.3: Distribution of the matched filter energy.
9.4.
1
0.8
0.6
0.4
Distribution of the CF energy
73
x 10
Distribution of the CF energy, MIT source
f-850
f-955
A
n4
nlA
0.2
0.2
0
0
0
0
5
-8
4
3
2
1
4
6
8
-8
x 10
x 10
U-
f-1125
CE0.
00.4
f-1335
n
15 0. 2
U
2
0
0.2
0
2
4
6
0
8
1
0
2
3
4
-8
-8
0
x 10
x 10
f- 1465
f-1600
0 .5
0.2
0
0
0
1
2
2
Ed (Pa *sec)
3
4
x 10-8
74
0
0.2
0.6
0.4
0.8
Ed (Pa 2'sec)
1
1.2
x 10
Distribution of the CF energy, sensitized hydrophone
f.955, 151 data points
f.850, 167 data points
0.5 L_
0.4
0.2
"
0
4
3
2
0
0
0.6
0.4
0.2
0.8
1
-8
-9
x 10
x 10
U-
f-1335, 146 data points
f.112 5, 159 data points
o
0.4
ia
0.2
U
S0
0
0
0.5
0
0
4
-9
3
2
1
0
0.5
1
2
1.5
3
2.5
-9
x 10
x 10
f-1600, 162 data points
f.1465, 157 data points
0.4
0.2
01
0
U.
1
0.5
Ecf (Pa 2sec)
0
1.5
0.2
0.4
0.6
2
0.8
Ecf (Pa *sec)
x 10'9
75
1.2
1
x 10
Distribution of the CF energy, all hydrophones
f-955, 9792 data points
f-850, 10743 data points
0.2
0.05
0.1
0
-
0.1
0
4
2
0-
8
6
0
0.5
1
2
1.5
-6
-9
x 10
x 10
L-
f.1335, 9573 data points
f- 1125, 10255 data points
n
C)
0.2
2%
0.1
0.1
0
U
U
U
0
0
0
4
2
0
8
6
2
4
8
6
-9
x 10
x 10
-9
f-1600, 10594 data points
f-1465, 10253 data points
0.2
0
0.05
L
0.1
0
0
1
2
Ecf (Pa2*sec)
0
4
3
.9
x 10
76
0.5
1
1.5
Ecf (Pa 2*sec)
2
2.5
x 10
-9
Distribution of the CF energy, desensitized hydrophone
f.955, 150 data points
f-850, 165 data points
0.4
0.4
.--
0.2
0.2
0
0
1
0
2
4
3
4
3
2
1
0
-9
-9
x 10
x10
LL
U
f.1125, 154 data points
0.5
0.4
f-1335, 144 data points
F
.F
0.2
0
fa
0
0
L
1
2
0
4
3
0
0.5
1
-9
x 10
x10
f-1600, 164 data points
f.1465, 159 data points
A
n4
0.4
0.2
0.;
0
0
1
0.5
Ed (Pa 2*sec)
0
1.5
x 10 -9
0.5
1
Ed (Pa 2*sec)
Figure 9.4: Distribution of the central frequency energy.
9.5.
2.5
2
1.5
-9
Matched filter degradation
77
1.5
2
x 10
-9
Matched filter degradation vs range, MIT source
fw955
f-850
20
10
10
5-
0
1.2
01
1.25
1.35
1.3
1.4
x 10
1.25
1.2
1.45
AR
0
1.45
1.4
x 10
4
f-1335
1125
10
10
-U
1.35
1.3
4
5-
5-
0
1 .2
1.25
1.3
1.35
1.4
1.45
x 10
1.25
1.2
1.3
1.35
1.45
1.4
4
x 10
4
f-1600
f-1465
10
10r
-0
5-
0
1.2
5-
1.25
1.35
1.3
range (m)
1.4
0
1.2
1.45
x 104
78
0
1.25
1.35
1.3
range (m)
1.4
1.45
4
x 10
Matched filter degradation vs range, Lubell source, sensitized hydrophone
f-850
f-955
20
15
10-
10
0
1.2
1.25
1.3
1.35
51.2
1.4
x 10
1.25
20
10-
10
1.25
1.3
1.4
4
f-1335
f-1125
1.2
1.35
x 10
20
0
1.3
4
1.35
0
1.2
1.4
x 10
1.25
1.3
1.4
1.35
4
4
x 10
f-1600
f1465
20
20
10
10
1
0
-
0
1.2
1.25
1.3
range (m)
1.2
1.4
1.35
x 10
4
79
1.25
1.3
range (m)
1.35
1.4
x 104
Matched filter degradation vs range, Lubell source, all hydrophones
fw850
f-955
20
10
10
-
20
0
1.2
1.25
1.35
1.3
01
1.2
1.4
1.25
1.3
1.35
4
1.4
x 10
x10
4
f-1335
f- 1125
20
25n
0
10
10
0
0
1 .2
1.25
1.3
1.35
1.2
1. 4
x 10
1.25
4
f-600
f-1465
10
10
-
20
1.25
1.3
range
(m)
1.4
1.35
x 10
0
01.2
1.3
4
0
1.4
1.35
x 10
1.2
4
80
1.25
1.3
range (m)
1.35
1.4
104
Matched filter degradation vs range, Lubell source, desensitized hydrophone
f.850
157
f.955
15
0;
10-
10-
5 LI1
1.25
1.2
1.3
1.35
5
1. 2
1.4
1.25
1.3
4
x 10
x 10
f.1335
f-1125
-
15
20
1.4
1.35
4
0
10-
10
0
5
0
1.2
1.25
1.3
1.35
1.2
1.4
1.25
1.3
1.35
1.4
4
4
x 10
x 10
f.1600
fa1465
20
1
10-
10-
0
0
1. 2
1.25
1.3
range (m)
1.35
1.2
1.4
x 10
1.25
1.3
range (m)
4
1.35
1.4
x 10
Figure 9.5: Matched filter degradation.
9.6.
Pa rseva l's sum energy as a function of time
window
81
Parseval Sum vs. Time, MIT source
f-955Hz
f-850Hz
1
0.5
0.5
0
-0 .5
0.5
0
0
1
1.5
-0.5
1
1.5
-0.5
0
0.5
1
1.5
C
0.5
1
1.5
1
1.5
E
f-1 125Hz
q)
1
0
0.5
-0.5
N
E
0
z
0
-0..5
0
0.5
01
f-1600Hz
f-1465Hz
1
1
0.5
0.5-
0
0-0.5
1
1.5
0.5
Time from beginning of signal (sec)
-0.5
0
0.5
Time from beginning of signal (sec)
82
Parseval Sum vs. Time, Lubell source
f-955Hz
f-850Hz
1
0.5
0.5
0
-0.5
-0.5
0
0.5
1
1.5
0
1
1.5
1
1.5
f-1335Hz
f.1125Hz
E
0.5
1
1
'.
0.5
0.5
z0
U-0.5
0
0.5
1
-0. 5
1.5
f.1465Hz
0
0.5
f.1600Hz
1
0.15 F
0.5 1
-0.5
1
0.5
Time from beginning of signal (sec)
0
-0.5
1.5
1
0.5
0
Time from beginning of signal (sec)
Figure 9.6: Parseval's sum energy as a function of time window.
83
1.5
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