HIGH RESOLUTION ANALYSIS OF EIGENRAY GAIN
PERTURBATIONS IN ULTRA-SHALLOW WATER
S.M. SIMMONS, O.R. HINTON, A.E. ADAMS, B.S. SHARIF AND J.A. NEASHAM
Department of Electrical and Electronic Engineering Merz Court,
University of Newcastle upon Tyne, Newcastle upon Tyne, NE3 1DQ,, UK
E-mail: [email protected]
This paper presents results obtained from the acoustic analysis of an ultra-shallow
channel of around 40 m in the North Sea over ranges of 0.9 km and 3.0 km. It is shown
how the channel is characterised by severe multipath propagation and signal fading. A
low frequency phenomenon is described that was apparent in all of the arrival paths to
the receiver array over these distances. The article then demonstrates how these
frequencies could arise as a result of an oscillation of the transmitter, possibly related to
the swell of the channel.
1
Introduction
The results and analysis presented in this paper are taken from the data obtained during
the first LOTUS (Long range Telemetry in Ultra-Shallow channels) project sea trials held
in the summer of 1999 [1]. The purpose of this project was to develop a system of digital
communication between deployed underwater units. These units could either be mounted
on the sea floor, free floating or attached to an un-tethered underwater vehicle. It was
envisaged that the distance between the nodes would be far greater than the depth of the
water column. The sea trials in 1999 were carried out in the North Sea off the North-East
Coast of England over a period of five days. The average depth of the sea was around 40
metres for the chosen deployments, with transmission distances of 0.8–10 km. The
shallow depth of the water combined with the medium to long ranges produced hostile
multipath effects as well as variable direct paths due to the seasonal conditions.
On each day of the trials, two transmitter units were deployed at different locations.
The transmitter hydrophones were approximately 5 m above the sea floor and transmitted
autonomously throughout the day. The receiver structure consisted of an array of 8
hydrophones. The bottom element of the array was 1 m above the sea floor, with an equal
vertical spacing of 3 m between the remaining single hydrophones and a central
horizontal structure of four of the hydrophones. The data was recorded on one of the
support vessels that had a link to the receiver array, which was deployed at the beginning
of the experiment. A representation of the transmitter and receiver structures is shown in
Fig. 1.
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N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 303-310.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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Command Link (not used)
Receiver
Transmitters
Figure 1. Transmitter and receiver structures.
2
Chirp analysis
During each day of the trials the two transmitters generated a wide range of data formats
to assess the multi-user capability of the communications network. At the start of each
day a chirp signal was transmitted for around half an hour. This was to provide data from
which the statistical properties of the fading, multipath channel could be analysed. The
chirp signal was designed to enable a high-resolution analysis of the channel and also to
ensure that the current channel response is well separated from the echoes of the previous
transmissions. The frequency of the chirp was 8–12 kHz over a period of 12.5 ms
throughout the trials. The repetition rate of the chirp was 25 ms on the first two days (0.9
km and 3 km range) and 50 ms on the final three days (3 km, 5 km and 8 km range). The
signal was transmitted at a level of 186 dB (re 1 µPa at 1m) and sampled at 48 kHz.
Figure 2(a) shows the received signal at the bottom hydrophone element over a
period of 100ms on the first day of the trials transmitted over a range of 0.9 km and Fig.
1(b) shows the signal after cross-correlation with the chirp.
0.1
8
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6
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Correlation Amplitude
Signal Amplitude
0.04
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(b)
Figure 2. (a) Received signal and (b) cross-correlation with the chirp.
It was assumed that the peak of the cross-correlation in the periodicity of the chirp
represents the direct path gain at that instant. Hence by taking the values of the maximum
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peaks it is possible to infer the variation of the direct path gain with time. The sampling
period is the inverse of the chirp repetition rate; giving a high resolution of 40 Hz. Figure
3(a) shows the direct path correlation amplitude over a period of 25 s for the bottom
receiver element. Low frequency periodic behaviour at around 10 s can be observed in
the direct path gain. Also present is higher frequency periodic behaviour, which was
analysed using the Wigner-Ville transform with a Choi kernel.
The transformation is shown in Fig. 3(b) corresponding to the direct path gain
between 3 s and 15 s from Fig. 3(a) after filtering of the low frequency oscillations. The
periodicity varies approximately sinusoidally between 2 Hz and 10 Hz. The period of this
change in frequency correlates with the low frequency oscillation of the direct path gain
of around 10 s periodicity. During the dry tests prior to the sea trials, oscillations were
observed in the peak of the correlation due to the difference in the transmitter and
receiver clock crystals. It is this phenomenon that is responsible for the oscillations in the
frequency band 2–10 Hz shown in Fig. 3.
9.5
12
10
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8
8
Time (s)
Direct Path Correlation Amplitude
9
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15
Time (s)
(a)
20
25
1
2
3
4
5
6
Frequency (Hz)
7
8
9
10
(b)
Figure 3. (a) Direct path gain of the bottom element of the receiver array and (b) the Wigner-Ville
time-frequency transformation of the gain.
The impulse response estimates were filtered above 2 Hz and squared to separate the
effects induced the channel properties from the artefact effects of the difference in the
two crystal oscillator frequencies. Figure 4(a) shows a 100 ms series of the filtered chirps.
The impulse responses were then time aligned, assuming that the transmitter and receiver
crystals were operating at exactly 48 kHz. Figure 4(b) shows a contour plot of a section
of the aligned responses over a period of 12.5 s for the lower receiver element. It can be
seen from the plot that the responses are misaligned due to the differences in the sampling
frequencies. Further to the gradient of the peak values, an oscillation can be observed
with a period of around 10 s. The oscillation of the position of the peak values was
extracted and is shown in Fig. 5. This oscillation appears to be a variation in the time of
arrival of the direct path. As can be seen from Fig. 4(b) this oscillation also occurs in the
multipath arrivals. Although not shown here, the oscillations were also present in the
responses obtained from the other 7 elements of the array.
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0.8
Normalized Impulse Response
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0
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(a)
(b)
Figure 4. (a) Normalized impulse responses after squaring and filtering and (b) a contour plot of
the responses after time alignment for the bottom receiver element.
0.2
Variation in Time of Arrival (ms)
0.15
0.1
0.05
0
-0.05
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0
20
40
60
80
Time (s)
100
120
Figure 5. The apparent variation of the time of arrival of the lowest receiver element direct path.
The gradient of the time of arrival shown in Fig. 4(b) corresponds to a difference in
the transmitter and receiver crystal oscillators of just under 5 Hz. The combination of this
frequency with the variation in the time of arrival shown in Fig. 5 accounts for the
variation in the artefact frequency shown in Fig. 3(b).
The plots of Figs. 6(a) and 6(b) show the variation in the direct path for the bottom
receiver element for a period of over 2 minutes at a range of 0.9 km and 3.0 km
respectively. At the shorter range an oscillation in the amplitude can be observed with a
period of around 10 s. At the longer range there still appears to be low frequency
oscillations, although not as regular and pronounced as at the shorter range. Figures 7(a)
and 7(b) show the power spectra of the direct path gain at a range of 0.9 km and 3.0 km
respectively, estimated using the data shown in Fig. 6. The spectrum shows the presence
of the 0.1 Hz period as well as what appears to be a second harmonic at 0.2 Hz for the
shorter range. The power spectrum at the larger range displays similar behaviour in terms
of low frequency components, although at a slightly lower frequency and lower power
due to the greater attenuation.
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55
2.5
Direct Path Correlation Amplitude
Direct Path Correlation Amplitude
50
45
40
35
30
2
1.5
1
0.5
25
20
0
20
40
60
80
Time (s)
100
0
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120
20
40
60
80
Time (s)
(a)
100
120
(b)
300
0.06
250
0.05
Power Spectrum Amplitude
Power Spectrum Amplitude
Figure 6. Direct path amplitude variation over 130 s for the bottom receiver element at a range of
(a) 0.9 km and (b) 3.0 km.
200
150
100
50
0
-0.8
0.04
0.03
0.02
0.01
-0.6
-0.4
-0.2
0
0.2
Frequency (Hz)
0.4
0.6
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0
-0.8
-0.6
-0.4
-0.2
0
0.2
Frequency (Hz)
(a)
0.4
0.6
0.8
(b)
Figure 7. The power spectrum of the direct path for ranges of (a) 0.9 km and (b) 3.0 km.
200
100
180
90
160
Power Spectrum Amplitude
80
140
70
120
60
100
50
40
80
30
60
20
40
10
20
0
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Frequency (Hz)
(a)
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0.8
0
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-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
(b)
Figure 8. (a) The Fourier transform of the cross-covariance of (a) the direct path at the bottom and
top receivers and (b) the direct path and second dominant arrival at the bottom element.
Figure 8(a) shows the Fourier transforms of the cross-covariance of the direct path at
the bottom and top receivers at a range of 0.9 km. The plot is very similar to the power
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S.M. SIMMONS ET AL.
spectrum of Fig. 7(a). Hence there is a high degree of correlation between the received
signals at the different elements due to the large wavelength. The same correlation can be
seen in the Fourier transform of the cross-covariance of the direct path at the bottom
receiver with the second significant arrival. All of the direct paths and later arrivals were
found to be highly correlated for all of the arrays.
Figure 9 shows the evolution of the multipath signals over a period of 500 s for four
of the receiver elements. The contour plots were obtained by aligning the direct path at
each element. The direct path appears at around a 2 ms (aribitrary) delay from the
beginning of the sequence. This direct path is not visible on Fig. 9(b) as the amplitude is
too small to show up on the plot. Further to the direct paths there are two distinguishable
arrivals visible. The delay of the first of these arrivals decreases as the height above the
sea floor increases, indicating that it is a surface reflection. The delay of the second
dominant arrival after the direct path behaves in the opposite manner, indicating it has
been reflected off the sea floor. Closer inspection of Fig. 9(d) for the top element shows
the presence of an arrival between the direct path and the first dominant arrival from the
other plots. This arrival has been reflected from the sea floor and has been lost on the
other plots as it is too close to the direct path and the resolution is not fine enough. The
most noticeable feature of the plots shown in Fig. 9 is the large fading of the later arrivals
over long periods.
500
500
0.8
450
0.8
450
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400
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400
0.6
0.6
350
350
0.5
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200
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300
Time (s)
Time (s)
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2
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5
Delay (ms)
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8
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1
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Delay (ms)
(a)
(b)
(c)
(d)
6
7
8
Figure 9. Evolution of the multipath propagation paths over 500 s for receiver elements at (a) 1 m,
(b) 4 m, (c) 8 m and (d) 14 m above the sea floor.
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ANALYSIS OF EIGENRAY GAIN PERTURBATIONS
Figure 10 shows the direct path over 500 s for the bottom elements at a range of 0.9
km and 3.0 km. The amplitude of the direct path tended to remain fairly constant for each
element at the shorter range and varied substantially at the longer range. The amplitudes
at the different elements however tended to vary a great deal from one another. The large
degree of fading at the 3.0 km range suggests that the arrival is in fact a reflection, as it
exhibits similar fading behaviour to the reflected paths at 0.9 km. It is possible for no
direct path exists between the transmitter and the receiver at the time of year of the trials
due to the downward refraction caused by the sound speed profile. However, this is not
verifiable as no sound speed recordings were taken.
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3.5
3
Correlation Peak Amplitude
Correlation Peak Amplitude
50
40
30
20
10
0
0
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2
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1
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200
Time (s)
250
300
350
0
0
50
100
150
(a)
200
Time (s)
250
300
350
(b)
Figure 10. Variation of the direct path gain for the lowest receiver element over 375 s for (a) day 1
of the trials at 0.9 km range and (b) day 2 at 3.0 km range.
3
Discussion
Figure 11 shows the normalised power obtained from a simulation of the correlation of a
signal consisting of two chirps with different delays. It can be seen that for certain
differences in delays between the two chirps a considerable amount of signal fading
occurs. The maximum fading occurs when there is a lag of about 0.05 ms corresponding
to an underwater path difference of around 70 mm. Such a delay corresponds to the
geometry of the transmitter and receiver arrays used in the trials. Hence it is thought that
the fading seen in the direct path of Fig. 9(b) is attributable to this phenomenon.
1
0.9
0.8
Normalized Power
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
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0.6
Delay Difference (ms)
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1
Figure 11. The normalized peak correlation amplitude of the sum of two chirps with different
delays.
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Low frequency oscillations appear in the amplitude of all of the arrivals for both
ranges examined in this paper. The frequency of the oscillations remains virtually
constant at the range of 0.9 km and less so at the longer range of 3.0 km. The period of
the major component of the oscillations correlates with what appears to be a variation in
the travel time delay of all of the paths. Possible mechanisms for the generation of the
travel time delay perturbations include the crystal oscillator behaviour, a change in the
sound speed and travel path by mechanisms such as the swell and finally an oscillation of
either the transmitter and/or the receiver array.
The sea state at the time of the trials was Beaufort state 1 with a 1 to 1.5 m swell
having a 10 s to 15 s period. Hence the variation in the travel time could be associated
with the swell. One possible mechanism for the generation of the travel-time delays is an
oscillation of the transmitter. A peak-peak oscillation of around 0.3 m of the transmitter
would produce travel time delays equivalent to those observed. It is unlikely the receiver
is oscillating, as the frequency shift of the artefact frequency was the same for all of the
elements [2]. The effect of the increase of depth due to the swell is not enough to account
for a sufficient change in sound speed on its own. The most overriding piece of evidence
is the correlation between the travel-time delay and the amplitude oscillations in the
paths. As demonstrated in Fig. 11 a small change in the time delay between the arrivals of
two chirps can result in large fading. If all of the travel-time delays oscillated with exactly
the same amplitude then no amplitude oscillations would occur. Hence it is necessary for
at least one of the paths to have a travel-time oscillation that is different in magnitude to
the others. This difference in the time of arrival variation magnitude is possible from the
geometry of the system of the trials, especially if it was correlated with the swell
(resulting in a slightly greater oscillation amplitude for surface reflections). If the crystal
oscillators had frequency variations that create an impression of a variation in the traveltime delay then there would be no change in the amplitude of the paths as all the delays
would be equal.
4
Conclusions
It has been shown from experimental data that severe multipath and fading occur in the
channel used in the LOTUS sea trials for the chirp signals used to infer the channel
properties. It is postulated that the fading of the chirp combined with a low frequency
oscillation of the transmitter unit, possibly related to the swell, creates the low frequency
phenomena observed in the arrival paths.
References
1. Adams, A.E., Hinton, O.R., Sharif, B.S., Salles, G., Orr, N. and Tsiminedis, C., An
experiment in sub-sea networks – The LOTUS sea trials. In Proc. 5th European
Conference on Underwater Acoustics, Lyon, France, 10–13 July, 2000.
2. Salles, G., Adams, A.E., Hinton, O.R., Sharif, B.S., Orr, N. and Tsiminedis, C., High
resolution analysis of ultra-shallow water acoustic travel time and gain perturbations. In
Proc. Oceans'2000, Rhode Island, USA, 17–20 Sep., 2000.