Introduction to Acoustics

186 Part A Propagation of Sound
Part A 5.7
a) Source–
receive array
b)
20
dB
–20
Dispersed signal
–10 0
d
0
50
100
150
200
0
50
100
150
200
0
Depth (m)
Mode 1 Mode N
PS
40
60
80
c)
20
40
60
80
0
10 20 30 40
Focused signal
50
0 10 20 30 40 50
Depth (m) Time (ms)
Range = 8km, pulse length = 2ms,
original source depth = 43m
the transmitted signal. A simple description of the received
signal, r(t), is that it is an attenuated, delayed,
and Doppler-shifted version of the transmitted signal
st(t),
r(t) → Re � αe iθ∼ st(t − T)e 2πi fct � 2πi fdt
e + n(t) ,
(5.89)
where α is the attenuation transmission loss and target
cross section, θ is a random phase from the range uncer-
1 2 3 4 5 6
Range (km)
Correlation (dB)
–10
–8
–6
–4
–2
0
Fig. 5.41a–c Ocean acoustic time-reversal mirror (a) The
acoustic field from a probe source (PS) is received on
a source–receive array (SRA). (b) The signal received on
the SRA with the first mode arriving first. At the SRA the
signal is digitized, time-reversed and retransmitted. (c) The
time-reversed signal received on an array at the same range
as PS. The signal has been refocused at the probe source
position with a resolution determined by the highest-order
mode surviving the two-way process
tainty compared to a wavelength, T is the range delay
time, fc is the center frequency of the transmitted signal
and fd is the Doppler shift caused by the target. The
correlation process will have an output related to the
following process,
��
�
�
�2
C(a) = �
� ˜r(t)˜s(t; a)dt�
� , (5.90)
where ˜s(t; a) is a replica of the transmitted signal
modified by a parameter set a which include the
propagation–reflection process, e.g., range delay and
Doppler rate. For the detection problem, the correlation
receiver is used to generate a sufficient statistic which is
the basis for a threshold comparison in making a decision
if a target is present. The performance of the detector is
described by receiving operating characteristic (ROC)
curves which plot the detection of probability versus
false-alarm probability, as parameterized by a statistics
of the signal and noise levels. The parameters a set the
range and Doppler value in the particular resolution cell
of concern. To estimate these parameters, the correlation
is done as a function of a.
For a matched filter operating in a background of
white noise detecting a point target in a given range–
Doppler resolution cell, the detection signal-to-noise
ratio depends on the average energy-to-noise ratio and
not on the shape of the signal. The waveform becomes
Fig. 5.42a,b Matched field processing example for a vertical
array in a shallow-water environment. Specific
information regarding the experiment can be found on the
web at http://www.mpl.ucsd.edu/swellex96/. (a) Bartlett
result with significant side-lobes only 3 dB down.
(b) Adaptive processor results shows considerable side-lobe
suppression. The processor is actually a white-noise constrained
MVDP for which the diagonal of the CSDM is
deliberately loaded by a specific algorithm to stabilize the
processor to some uncertainty in the environment and/or array
configuration. The ambiguity surfaces in (a) and (b) are
an incoherent average over eight tones at 53, 85, 101, 117,
133, 149, 165, 181, and 197 Hz