Acoustic Communication 15.5 Point-to-Point Links:Signal Processing 375
Part B | 15.5
within each band centered at f m;n ,
Z m;n D max t
˚
R rm;cm;n ../I mT s Ä t < .m C 1/T s
« :
(15.23)
If we assume once more that s m .t/ uses only one of N
bands and N is a power of 2, we identify the frequency
band that contains the most energy by comparing the
coefficients Z m;n ,
n max .m/ D max n fZ m;n I n D 1; : : : ; Ng :
(15.24)
Note that n max is a function of the symbol index m.
Under the same assumption, g m;n D 1 if n D n max , otherwise g m;n D 0. For example, if n max D 1, then g m;1 D
1 and g m;2 D g m;3 D g m;4 D 0. Therefore, s m .t/ contains
the couple of bits b m D .0; 0/. If n max D 2, then g m;2 D
1 and g m;1 D g m;3 D g m;4 D 0, so that s m .t/ contains the
couple of bits b m D .0; 1/, and so on.
15.5.2 Coherent Modulation/Detection
Coherent modulation methods include phase shift
keying (PSK) and quadrature amplitude modulation
(QAM). These methods offer bandwidth efficiency, i. e.,
the possibility to transmit more than 1 bit per second
per Hertz of occupied bandwidth. However, because the
information is encoded into the phase of the signal, precise knowledge of the received signal’s frequency and
phase is required in order to perform coherent detection.
This fact presents a major challenge because an acoustic channel introduces a rather severe phase distortion
on each of its multiple paths. A coherent receiver thus
needs to perform phase synchronization together with
channel equalization.
Coherent systems fall into two types: single-carrier
and multicarrier systems. In single-carrier systems,
a broadband information-bearing signal is directly
modulated onto the carrier and transmitted over the
channel. A typical high-rate acoustic signal occupies
several kHz of bandwidth over which it experiences
uneven channel distortion (Fig. 15.10). This distortion
must be compensated at the receiver through the process of equalization. Multicarrier modulation bypasses
this problem by converting the high-rate information
stream into many parallel low-rate streams, which are
then modulated onto separate carriers. The carriers
are spaced closely enough such that the channel appears as frequency-flat in each narrow subband. After
demodulation, each carrier’s signal now only has to
be weighted and phase-synchronized, i. e., a singlecoefficient equalizer suffices per carrier. Each of these
methods has its advantages and disadvantages when it
comes to practical implementation: single-carrier systems are capable of faster channel tracking but they
need high-maintenance equalizers; multicarrier systems
are efficiently implemented using the fast Fourier transform (FFT), but they have high sensitivity to residual
frequency offsets. In what follows, we review the basics of both types of systems as they apply to phasedistorted frequency-selective acoustic channels, and we
outline the current research trends.
Single-Carrier Modulation/Detection
The problem of joint phase tracking and equalization in single-carrier broadband systems was addressed
in [15.10]. The basic receiver structure [15.10] was extended to multichannel (array) configuration [15.57,
58] to enable diversity combining, which is often
essential on acoustic channels. The resulting multichannel decision-feedback equalizer (DFE), integrated
with a second-order phase-locked loop (PLL), provided the benchmark design for the high-speed acoustic
modem [15.55]. It also became a de-facto standard
for the development and comparison of future techniques, which focused on replacing the basic DFE with
more sophisticated equalization and channel estimation
schemes (e.g., turbo equalization and sparse channel estimation [15.39]), or inclusion of multiple transmitters,
be it in the form of multiuser systems [15.59, 60] or
multi-input multi-output (MIMO) structures for spatial
multiplexing and/or diversity [15.38, 61].
The block diagram of a multichannel DFE is shown
in Fig. 15.15. The receiver includes several stages:
precombining (which may or may not be used, depending upon the array structure), phase correction, and
multichannel equalization. The receiver is designed to
process an incoming signal of the form
v .t/ D
X
n
d.n/g c .t nT/e
iÂ.t/
C w .t/ ;
(15.25)
where d.n/ are the data symbols transmitted at the
rate of one symbol per T; g c .t/ D g T .t/ c.t/ g R .t/
is the composite impulse response of the transmitter,
channel, and receiver (all in equivalent baseband with
respect to the carrier frequency f c ); Â.t/ is the carrier
phase, and w .t/ is the noise. The channel response c.t/
and the phase Â.t/ are unknown (and possibly different across the array elements), necessitating an adaptive
receiver. Adaptive equalization has been considered
in two forms: direct, which does not perform explicit
channel estimation, and indirect, in which the channel
is first estimated and then used to adjust the equalizer.
In either form, the data symbols are estimated as
O
d.n/ D
P
X
pD1
a
H
p .n/x p .n/e
i O
Âp.n/
X
i>0
b
i .n/d.n i/ ;
(15.26)
Part B | 15.5
within each band centered at f m;n ,
Z m;n D max t
˚
R rm;cm;n ../I mT s Ä t < .m C 1/T s
« :
(15.23)
If we assume once more that s m .t/ uses only one of N
bands and N is a power of 2, we identify the frequency
band that contains the most energy by comparing the
coefficients Z m;n ,
n max .m/ D max n fZ m;n I n D 1; : : : ; Ng :
(15.24)
Note that n max is a function of the symbol index m.
Under the same assumption, g m;n D 1 if n D n max , otherwise g m;n D 0. For example, if n max D 1, then g m;1 D
1 and g m;2 D g m;3 D g m;4 D 0. Therefore, s m .t/ contains
the couple of bits b m D .0; 0/. If n max D 2, then g m;2 D
1 and g m;1 D g m;3 D g m;4 D 0, so that s m .t/ contains the
couple of bits b m D .0; 1/, and so on.
15.5.2 Coherent Modulation/Detection
Coherent modulation methods include phase shift
keying (PSK) and quadrature amplitude modulation
(QAM). These methods offer bandwidth efficiency, i. e.,
the possibility to transmit more than 1 bit per second
per Hertz of occupied bandwidth. However, because the
information is encoded into the phase of the signal, precise knowledge of the received signal’s frequency and
phase is required in order to perform coherent detection.
This fact presents a major challenge because an acoustic channel introduces a rather severe phase distortion
on each of its multiple paths. A coherent receiver thus
needs to perform phase synchronization together with
channel equalization.
Coherent systems fall into two types: single-carrier
and multicarrier systems. In single-carrier systems,
a broadband information-bearing signal is directly
modulated onto the carrier and transmitted over the
channel. A typical high-rate acoustic signal occupies
several kHz of bandwidth over which it experiences
uneven channel distortion (Fig. 15.10). This distortion
must be compensated at the receiver through the process of equalization. Multicarrier modulation bypasses
this problem by converting the high-rate information
stream into many parallel low-rate streams, which are
then modulated onto separate carriers. The carriers
are spaced closely enough such that the channel appears as frequency-flat in each narrow subband. After
demodulation, each carrier’s signal now only has to
be weighted and phase-synchronized, i. e., a singlecoefficient equalizer suffices per carrier. Each of these
methods has its advantages and disadvantages when it
comes to practical implementation: single-carrier systems are capable of faster channel tracking but they
need high-maintenance equalizers; multicarrier systems
are efficiently implemented using the fast Fourier transform (FFT), but they have high sensitivity to residual
frequency offsets. In what follows, we review the basics of both types of systems as they apply to phasedistorted frequency-selective acoustic channels, and we
outline the current research trends.
Single-Carrier Modulation/Detection
The problem of joint phase tracking and equalization in single-carrier broadband systems was addressed
in [15.10]. The basic receiver structure [15.10] was extended to multichannel (array) configuration [15.57,
58] to enable diversity combining, which is often
essential on acoustic channels. The resulting multichannel decision-feedback equalizer (DFE), integrated
with a second-order phase-locked loop (PLL), provided the benchmark design for the high-speed acoustic
modem [15.55]. It also became a de-facto standard
for the development and comparison of future techniques, which focused on replacing the basic DFE with
more sophisticated equalization and channel estimation
schemes (e.g., turbo equalization and sparse channel estimation [15.39]), or inclusion of multiple transmitters,
be it in the form of multiuser systems [15.59, 60] or
multi-input multi-output (MIMO) structures for spatial
multiplexing and/or diversity [15.38, 61].
The block diagram of a multichannel DFE is shown
in Fig. 15.15. The receiver includes several stages:
precombining (which may or may not be used, depending upon the array structure), phase correction, and
multichannel equalization. The receiver is designed to
process an incoming signal of the form
v .t/ D
X
n
d.n/g c .t nT/e
iÂ.t/
C w .t/ ;
(15.25)
where d.n/ are the data symbols transmitted at the
rate of one symbol per T; g c .t/ D g T .t/ c.t/ g R .t/
is the composite impulse response of the transmitter,
channel, and receiver (all in equivalent baseband with
respect to the carrier frequency f c ); Â.t/ is the carrier
phase, and w .t/ is the noise. The channel response c.t/
and the phase Â.t/ are unknown (and possibly different across the array elements), necessitating an adaptive
receiver. Adaptive equalization has been considered
in two forms: direct, which does not perform explicit
channel estimation, and indirect, in which the channel
is first estimated and then used to adjust the equalizer.
In either form, the data symbols are estimated as
O
d.n/ D
P
X
pD1
a
H
p .n/x p .n/e
i O
Âp.n/
X
i>0
b
i .n/d.n i/ ;
(15.26)