Acoustic Communication 15.4 Propagation Channel 369
Part B | 15.4
are needed. Channel modeling thus becomes an important aspect of signal processing, and sparsing has been
investigated for decision-feedback equalization [15.36,
37], turbo equalization [15.38, 39], and multicarrier detection [15.40–42]. It is also important to note that
although a greater bandwidth implies more ISI and
more frequency selectivity, it also implies a better resolution in delay (less smearing in the observable channel
response). Hence, although the attendant signal distortion is perceived as more severe, channel estimation will
be more efficient if a proper sparse model is used, which
may, in turn, lead to improved signal processing. In addition, signaling at a higher rate enables more frequent
channel observations and, consequently, easier channel
tracking [15.43].
15.4.3 Time Variability:
Motion-Induced Doppler Distortion
There are two sources of the channel’s time variability: inherent changes in the propagation medium, which
contribute to signal fading, and those that occur because of the transmitter/receiver motion and contribute
to the frequency shifting. The distinction between the
two types of distortions is that the first one appears as
random, while the motion-induced Doppler effects can
be modeled in a deterministic manner and, therefore,
compensated to some degree through synchronization.
Motion of the transmitter, receiver, or a reflection
point along the signal path causes the path distances to
vary with time. The resulting Doppler effect is evident
as time compression/dilation of the signal, which causes
frequency shifting and bandwidth spreading/shrinking.
The magnitude of the Doppler effect is proportional to
the ratio a D v =c of the relative transmitter-receiver velocity to the speed of sound. Because the speed of sound
is very low as compared to the speed of electromagnetic waves, motion-induced Doppler distortion of an
acoustic signal can be extreme. AUVs move at speeds
that are on the order of a few m=s, but even without
intentional motion, underwater instruments are subject
to drifting with waves, currents, and tides, which may
occur at comparable velocities. In other words, there is
always some motion present in the system, and a communication system has to be designed taking this fact
into account. The only comparable situation in radio
communications occurs in low Earth orbiting (LEO)
satellite systems, where the relative velocity of satellites
flying overhead is extremely high (the channel there,
however, is not nearly as dispersive in delay). The major implication of motion-induced distortion is on the
design of synchronization algorithms.
To model the Doppler distortion, let us focus on
a single propagation path, assuming that the relative
transmitter/receiver velocity v p along this path stays
constant over some interval of time. The path delay can
then be modeled as
p .t/ D p a p t ;
(15.8)
where a p D v p =c is the Doppler factor corresponding to
the p-th path. If there is a single dominant component
of velocity, these factors can be approximated as equal
for all paths, a p D a; 8p; however, this is not the case
in general [15.37]. To assess the effect of time-varying
delay on the signal, let us focus on a particular signal
component centered around frequency f k in a narrow
band f f k . The signal s k .t/ and its equivalent baseband u k .t/ are related by
s k .t/ D Refu k .t/e
i2fkt
g :
(15.9)
Since the signal occupies only a narrow band of frequencies, its replica received over the p-th propagation
path is given by
s k;p .t/ D h p N
H 0 .f k /s k .t p .t// :
(15.10)
Defining the equivalent baseband component of the received signal via
s k;p .t/ D Refv k;p .t/e
i2fkt
g ;
(15.11)
we have the baseband relationship
v k;p .t/ D c k;p e
i2apfkt u k .t C a p t p / ;
(15.12)
where
c k;p D h p H 0 .f k /e
i2fkp
:
(15.13)
The Doppler effect is evident in two factors: (i) frequency shifting by the amount a p f k and (ii) time scaling
by the factor .1 C a p /. The situation of putting together
all the signal components at frequencies f 0 ; f 1 ; etc., that
span a wide bandwidth B D Kf , and assuming only
a single propagation path with the Doppler factor a is
illustrated in Fig. 15.11. This figure offers an exaggerated view of the Doppler effect, but nonetheless one
that illustrates the point: each spectral component in
a wideband mobile acoustic system is shifted by a different amount, and the total bandwidth B is spread over
B.1 C a/, i. e., a signal of duration T is observed at the
receiver as having duration T=.1 C a/.
The way in which these distortions affect signal detection depends on the actual value of the factor a. For
comparison, let us look at a highly mobile radio system:
at 160 km=h (100 mph), a D 1:5 10
7 . This value is
low enough that compression/dilation can be neglected.
Part B | 15.4
are needed. Channel modeling thus becomes an important aspect of signal processing, and sparsing has been
investigated for decision-feedback equalization [15.36,
37], turbo equalization [15.38, 39], and multicarrier detection [15.40–42]. It is also important to note that
although a greater bandwidth implies more ISI and
more frequency selectivity, it also implies a better resolution in delay (less smearing in the observable channel
response). Hence, although the attendant signal distortion is perceived as more severe, channel estimation will
be more efficient if a proper sparse model is used, which
may, in turn, lead to improved signal processing. In addition, signaling at a higher rate enables more frequent
channel observations and, consequently, easier channel
tracking [15.43].
15.4.3 Time Variability:
Motion-Induced Doppler Distortion
There are two sources of the channel’s time variability: inherent changes in the propagation medium, which
contribute to signal fading, and those that occur because of the transmitter/receiver motion and contribute
to the frequency shifting. The distinction between the
two types of distortions is that the first one appears as
random, while the motion-induced Doppler effects can
be modeled in a deterministic manner and, therefore,
compensated to some degree through synchronization.
Motion of the transmitter, receiver, or a reflection
point along the signal path causes the path distances to
vary with time. The resulting Doppler effect is evident
as time compression/dilation of the signal, which causes
frequency shifting and bandwidth spreading/shrinking.
The magnitude of the Doppler effect is proportional to
the ratio a D v =c of the relative transmitter-receiver velocity to the speed of sound. Because the speed of sound
is very low as compared to the speed of electromagnetic waves, motion-induced Doppler distortion of an
acoustic signal can be extreme. AUVs move at speeds
that are on the order of a few m=s, but even without
intentional motion, underwater instruments are subject
to drifting with waves, currents, and tides, which may
occur at comparable velocities. In other words, there is
always some motion present in the system, and a communication system has to be designed taking this fact
into account. The only comparable situation in radio
communications occurs in low Earth orbiting (LEO)
satellite systems, where the relative velocity of satellites
flying overhead is extremely high (the channel there,
however, is not nearly as dispersive in delay). The major implication of motion-induced distortion is on the
design of synchronization algorithms.
To model the Doppler distortion, let us focus on
a single propagation path, assuming that the relative
transmitter/receiver velocity v p along this path stays
constant over some interval of time. The path delay can
then be modeled as
p .t/ D p a p t ;
(15.8)
where a p D v p =c is the Doppler factor corresponding to
the p-th path. If there is a single dominant component
of velocity, these factors can be approximated as equal
for all paths, a p D a; 8p; however, this is not the case
in general [15.37]. To assess the effect of time-varying
delay on the signal, let us focus on a particular signal
component centered around frequency f k in a narrow
band f f k . The signal s k .t/ and its equivalent baseband u k .t/ are related by
s k .t/ D Refu k .t/e
i2fkt
g :
(15.9)
Since the signal occupies only a narrow band of frequencies, its replica received over the p-th propagation
path is given by
s k;p .t/ D h p N
H 0 .f k /s k .t p .t// :
(15.10)
Defining the equivalent baseband component of the received signal via
s k;p .t/ D Refv k;p .t/e
i2fkt
g ;
(15.11)
we have the baseband relationship
v k;p .t/ D c k;p e
i2apfkt u k .t C a p t p / ;
(15.12)
where
c k;p D h p H 0 .f k /e
i2fkp
:
(15.13)
The Doppler effect is evident in two factors: (i) frequency shifting by the amount a p f k and (ii) time scaling
by the factor .1 C a p /. The situation of putting together
all the signal components at frequencies f 0 ; f 1 ; etc., that
span a wide bandwidth B D Kf , and assuming only
a single propagation path with the Doppler factor a is
illustrated in Fig. 15.11. This figure offers an exaggerated view of the Doppler effect, but nonetheless one
that illustrates the point: each spectral component in
a wideband mobile acoustic system is shifted by a different amount, and the total bandwidth B is spread over
B.1 C a/, i. e., a signal of duration T is observed at the
receiver as having duration T=.1 C a/.
The way in which these distortions affect signal detection depends on the actual value of the factor a. For
comparison, let us look at a highly mobile radio system:
at 160 km=h (100 mph), a D 1:5 10
7 . This value is
low enough that compression/dilation can be neglected.