Introduction to Acoustics

a factor when there is a reverberant environment and
when one is concerned with estimating target range
and Doppler. A waveform’s potential for range and
Doppler resolution can be ascertained from the ambiguity
function of the transmitted signal. This ambiguity
function is related to the correlation process of (5.90)
for a transmitted signal scanned as a function of range
and Doppler,
Θ( ˆT, Tt, fd, ˆ fdt )
��
�
∝ �
� ˜s(t − T)˜st(t − ˆT)e 2πi( fdt − �
fd)t ˆ �2
dt�
� , (5.91)
where Tt and fdt are the true target range (time) and
Doppler, and ˆT and fd ˆ are the scanning estimates of the
range and Doppler. Figure 5.43 are sketches of ambiguities
functions of some typical waveforms. The range
resolution is determined by the reciprocal of the bandwidth
and the Doppler resolution by the reciprocal of
the duration. A coded or pseudo-random (PR) sequence
can attain good resolution of both by appearing as
long-duration noise with a wide bandwidth. Ambiguity
functions can be used to design desirable waveforms for
particular situations. However, one must also consider
the randomizing effect of the real ocean. The scattering
function describes how a transmitted signal statistically
redistributes its energy in the reverberant ocean environment
which causes multipath and Doppler spread. In
particular, in a reverberation-limited environment, only
increasing the transmitted power does not change the
signal-to-reverberation level. Signal design should minimize
the overlap of the ambiguity function of the target
displaced to its range and Doppler and the scattering
function.
5.7.2 Underwater Acoustic Imaging
Imaging can be divided into categories concerned with
water column and bottom properties. Here we describe
several applications of active SONAR to imaging the
ocean.
Water Column Imaging. Backscatter from particulate
objects that move along with the water motion (such as
biological matter, bubbles sediments) contains velocity
information because of the Doppler shift. An acoustic
Doppler current profiler (ADCP) might typically consist
of three or four source–receivers pointed in slightly different
directions but generally up (from the bottom) or
down (from a ship). The multiple directions are for resolving
motion in different directions. The Doppler shift
a)
b)
c)
T Ù
T Ù
T Ù
Underwater Acoustics 5.7 Active SONAR Processing 187
Fig. 5.43a–c Ambiguity function for several SONAR signals:
(a) rectangular pulse; (b) coded pulses; (c) chirped FM
pulse
of the returning scattered field is simply −2 f (v/c) (as
opposed to the more-complicated long-range waveguide
Doppler shift discussed in Sect. 5.4.4), where f is the
acoustic frequency, v is the radial velocity of the scatterer
(water motion), and c is the sound speed. With three
or four narrow-beam transducers, the current vector can
be ascertained as a function of distance from an ADCP
by gating the received signal and associating a distance
with the time gated segment of the signal. Water-column
motion associated with internal waves can be determined
by this process also where essentially one uses a kind
of ADCP points in the horizontal direction. For elab-
f Ù
d
f Ù
d
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d
Part A 5.7