Tài liệu Digital communication receivers P2 - P1 pptx

PART C
Baseband Communications
Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing
Heinrich Meyr, Marc Moeneclaey, Stefan A. Fechtel
Copyright
 1998 John Wiley & Sons, Inc.
Print ISBN 0-471-50275-8 Online ISBN 0-471-20057-3
Chapter 2 Baseband Communications
2.1 Introduction to Digital Baseband Communication
In baseband communication, digital information is conveyed by means of a
pulse train. Digital baseband communication is used in many applications, such as
.
Transmission at a few megabits per second (Mb/s) of multiplexed digitized
voice channels over repeatered twisted-pair cables
.
Transmission of basic rate ISDN (16Okb/s) over twisted-pair digital subscriber
lines
.
Local area networks (LANs) and metropolitan area networks (MANS) oper-
ating at 10-100 Mb/s using coaxial cable or optical fiber
.
Long-haul high-speed data transmission over repeatered optical fiber
.
Digital magnetic recording systems for data storage
This chapter serves as a short introduction to digital baseband communication.
We briefly consider important topics such as line coding and equalization, but
without striving for completeness. The reader who wants a more detailed treatment
of these subjects is referred to the abundant open literature, a selection of which
is presented in Section 2.1 S.
2.1.1 The Baseband PAM Communication System
Baseband communication refers to the case where the spectrum of the trans-

mitted signal extends from zero frequency direct current (DC) to some maximum
frequency. The transmitted signal is a pulse-amplitude-modulated (PAM) signal:
it consists of a sequence of time translates of a baseband pulse which is amplitude-
modulated by a sequence of data symbols conveying the digital information to be
transmitted.
A basic communication system for baseband PAM is shown in Figure 2-l.
TRANSMllTER
I
CHANNEL
I RECEIVER
1
I
I
I
I
I
I
Figure 2-l Basic Communication System for Baseband PAM
61
Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing
Heinrich Meyr, Marc Moeneclaey, Stefan A. Fechtel
Copyright
 1998 John Wiley & Sons, Inc.
Print ISBN 0-471-50275-8 Online ISBN 0-471-20057-3
62 Baseband Communications
At the transmitter, the sequence of information bits (bk) is applied to an encoder,
which converts {bk} into a sequence (uk} of data symbols. This conversion is
called
line coding,
and will be considered in more detail in Section 2.1.3. The

information bits assume the values binary zero (“0”) or binary one (“l”), whereas
the data symbols take values from an alphabet of a size
L
which can be larger than
2. When
L
is even, the alphabet is the set {fl, f3, . . . . =t(L - l)}, for an odd
L
the alphabet is the set (0, f2, f4, . . . . =t(L - 1)).
The data symbols enter the transmit filter with impulse response gT (t), whose
Fourier transform is denoted by GT(w). The resulting transmit signal is given by
s(t)=~u,gT(t-mT-ET)
(2-l)
m
where VT is the symbol rate, i.e., the rate at which the data symbols are applied
to the transmit filter. The impulse response g*(t) is called the baseband
pulse of
the transmit signal. The quantity ET is a fractional unknown time delay between
the transmitter and the receiver (1~1 5 3). The instants {H’} can be viewed as
produced by a hypothetical reference clock at the receiver. At the transmitter, the
lath channel symbol ak: is applied to the transmit filter at the instant Kf + ET,
which is unknown to the receiver, Figure 2-2 shows a baseband
pulse g*(t) and
a corresponding PAM signal s(t), assuming that I, = 2.
Figure
2-2 (a) Baseband PAM Pulse gT(t), (b) Binary PAM Signal s(t)
2.1 Introduction to Digital Baseband Communications
63
The channel is assumed to be linear. It introduces linear distortion and adds
noise. The linear distortion (amplitude distortion and delay distortion) is char-

acterized by the channel frequency response C(u). It causes a broadening of
the transmitted pulses. The “noise” is the sum of various disturbances, such as
thermal noise, electronics noise, cross talk, and interference from other commu-
nication systems.
The received noisy PAM signal is applied to a receive filter (which is also
called data filter) with frequency response GR(w). The role of this filter is to
reject the noise components outside the signal bandwidth, and, as we will explain
in Section 2.1.2, to shape the signal. The receive filter output signal y(t; E) is
sampled at symbol rate l/T. From the resulting samples, a decision (&) is made
about the data symbol sequence (ah}. The sequence (&k} is applied to a decoder,
which produces a decision
11
8, on the information bit sequence { bk ).
The signal at the output of the receive filter is given by
y(t; E) = c a,g(t - mT - ET) + n(t)
(2-2)
m
where g(t) and n(t)
are the baseband pulse and the noise at the receive filter
output. The Fourier transform G(w) of the baseband pulse g(t) is given by
G(w) = Gz+)C(+z+)
(z-3)
Let us denote by
{kT
+
ZT}
the sequence of instants at which the sampler at the
receive filter output is activated. These sampling instants are shifted by an amount
tT
with respect to the instants

(IcT}
produced by the hypothetical reference clock
of the receiver. Then the lath sample is given by
!/k(e) =
ak SO(e) + c
ak-na h(e) + nk
Q-4)
m#O
where yk(e), h(e),
and nk are short-hand notations for y(
IcT + 2T; E),
g(mT -
eT),
and
n( IcT
+
CT),
while e = E - i denotes the difference, nor-
malized by the symbol duration
T,
between the instant where the Kth symbol ak
is applied to the transmit filter and the Lth sampling instant at the receiver.
In order to keep the decision device simple, receivers in many applications
perform symbol-by-symbol decisions: the decision &k is based only on the sample
yk (e). Hence, only the first term of the right-hand side of (2-4) is a useful one,
because it is the only one that depends on ck. The second term is an
intersymbol
infelference
(ISI) term depending on ck
-m with

m
# 0, while the third term is
a noise term. When the noise
n(t)
at the receive filter output is stationary, the
statistics of the noise sample nk do not depend on the sampling instant. On the
other hand, the statistics of the useful term and the IS1 in (2-4) do depend on the
sampling instant, because the PAM signal is cyclostationary rather than stationary.
Let us consider given sampling instants
(IcT
+
gT}
at the receive filter output.
64
Baseband Communications
The symbol-by-symbol decision rule based on the samples YA! (e) from (2-4) is
m - 1 <
yk(e)/go(e) 5 m + 1
m # k(L -
1)
Cik = Y- 1
L - 2 < !/k(e)h’O(e)
-L+l
yk(e)/gO(e> 5 -L + 2
(2-5)
where the integer
m
takes on only even (odd) values when
L is odd (even), This
decision rule implies that the decision device is a slicer which determines the

symbol value &k which is closest to & (e)/go( e). In the absence of noise, the
baseband communication system should produce no decision errors. A necessary
and sufficient condition for this to be true is that the largest magnitude of the IS1
over all possible data sequences is smaller than 1 go(e) I, i.e., M(e) > 0 where
M(e) is given by
W4 = I
go(e)
1 - max
thn) m;to am g-m e
E ()I
(2-6)
When M(e) < 0, the data symbol sequence yielding maximum IS1 will surely give
rise to decision errors in the absence of noise, because the corresponding yk (e) is
outside the correct decision region. When M(e) > 0, a decision error can occur
only when the noise sample nk from (2-4) has a magnitude exceeding M(e) ; M(e)
is called the
noise margin
of the baseband PAM system. The noise margin can be
visualized by means of an
eye diagram,
which is obtained in the following way.
Let us denote by ~e(t ; E) the receive filter output signal in the absence of noise, i.e.,
yo(t;&) = Cam g(t - mT- 0)
m
(2-7)
The PAM signal ~o(t ; E) is sliced in segments yo,i (t ; E), having a duration equal
to the symbol interval 2’:
!Jo(t; d
iT 5
t

< (i + 1)T
PO,&; E) =
(2-Q
0
otherwise
The eye diagram is a display of the periodic extension of the segments
yo,i(t;
E).
An example corresponding to binary PAM
(L
= 2) is shown in Figure 2-3. As
g(t)
has a duration of three symbols, the eye diagram for binary PAM consists of
23 = 8 trajectories per symbol interval. Because of the rather large value of g(r),
much IS1 is present when sampling the eye at
t
= 0. The noise margin M(e)
for a specific sampling instant is positive (negative) when the eye is open (closed)
at the considered instant; when the eye is open, the corresponding noise margin
equals half the vertical eye opening,
The noise margin M(e) depends on the sampling instants IcT +
2T
and the
unknown time delay
ET
through the variable e =
e - i. The optimum sampling
instants, in the sense
of minimizing the decision error probability when the worst-
2.1 Introduction to Digital Baseband Communications

65
(a)
(b>
Figure 2-3
(a) Baseband PAM Pulse g(t), (b) Eye Diagram for Binary PAM
case IS1 is present, are those for which M(e) is maximum. Using the appropriate
time origin for defining the baseband pulse g(t) at the receive filter output, we can
assume without loss of generality that M(e) becomes maximum for e = 0. Hence,
the optimum sampling instants are IcT+ ET, and e = E - E^ denotes the timing error
normalized by the symbol interval. The sensitivity of the noise margin M(e) to
the normalized timing error e can be derived qualitatively from the eye diagram:
when the horizontal eye opening is much smaller than the symbol interval T, the
noise margin and the corresponding decision error probability are very sensitive
to timing errors.
Because of the unknown delay 0 between the receiver and the transmitter,
the optimum sampling instants { IcT + ET} are not known a priori to the receiver.
Therefore, the receiver must be equipped with a structure that estimates the value of
e from the received signal. A structure like this is called timing recovery
circuit
or
symbol synchronizer. The
resulting estimate 6 is then used to activate the sampler
at the instants (Kf + Z7’). The normalized timing error e = E - i should be kept
small, in order to avoid the increase of the decision error probability, associated
with a reduction of the noise margin M(e).
2.1.2 The Nyquist Criterion for Eliminating ISI
It is obvious that the shape of the baseband pulse g(t) and the statistics of
the noise n(t) at the output of the receive filter depend on the frequency response
66
Baseband Communications

GR(w) of the receive filter.
Hence, the selection of
GR(w)
affects the error
probability when making symbol-by-symbol decisions. The task of the receive
filter is to reduce the combined effect of noise and ISI.
Let us investigate the possibility of selecting the receive filter such that all
IS1 is eliminated when sampling at the instants {kT + ET}. It follows from (2-4)
that IS1 vanishes when the baseband pulse g(t) at the receive filter output satisfies
g(mT) =
0 for
m # 0.
As G( w is the Fourier transform of g(t),
g (mT)
is
)
for all
m
given by
+w
g(mT) =
J
dw
G(w) exP (Mq g
-W
+w (2n+l)*lT
= c / G(w) exp (jm&‘)g
“=-00(2n-1)x/T
(2-9)
Taking into account that exp(jmwT) is periodic in w with period

27r/T,
we obtain
AIT
h-m =
J
‘%d (w)
dw
exP (jw T) 217
-nJT
where Gad(w) is obtained by folding G(w):
&d(w) = E
G(w - F)
r&=-w
(2- 10)
(2-l 1)
Note that Gad(W) is periodic in w with period
27r/T.
It follows from (2-9) that
Tg (-mT)
can be viewed as the
mth
coefficient in the Fourier-series expansion
of Gfid(w):
Gad(w) = T c g(-mT)
exp
(jmwT)
m=-co
(2-12)
Using (2-12) and the fact that Gad(w) is periodic in w, we obtain
g(mT) =0

for
m#O
tj Gad(W) is constant for 10 1 <
x/T
(2-13)
This yields the well-known
Nyquist criterion for
zero ISI: a necessary and sufficient
condition for zero IS1 at the receive filter output is that the folded Fourier transform
Gfid(w) is a constant for Iw 1 <
?r/T.
The Nyquist criterion for zero IS1 is sometimes referred to as
the&st Nyquist
2.1 Introduction to Digital Baseband Communications
67
criterion. A pulse satisfying this criterion is called an interpolation pulse or a
Nyquist-I pulse. Let us consider the case where G(w) is band-limited to some
frequency B; i.e., G(w) = 0 for Iw( > 27rB.
l
When B < 1/(2T), G~,-J(w) = G(u) for 1~1 < n/T. As G(w) = 0 for
27rB < IwI < r/T, G
fld w cannot be constant for 1~1 < x/T. Taking (2-3)
( )
into account, it follows that when the bandwidth of the transmit filter, of the
channel or of the receive filter is smaller than
1/2T,
it is impossible to find
a receive filter that eliminates ISI.
.
When B

=
l/(273,
Gm(
w is constant only when, within an irrelevant
)
constant of proportionality, G(w) is given by
T
I4 < 4T
G(w)
=
(2- 14)
0
otherwise
The corresponding baseband pulse g(t) equals
sin (Irt/T)
dt) = &/T
(2- 15)
.
Using (a close approximation of) the pulse (sin (rt/T))/(nt/T) is not practi-
cal: not only would a complicated filter be required to approximate the abrupt
transition in G(w) from (2-14), but also the performance is very sensitive to
timing errors: as the tails of the pulse (sin (st/T))/(rt/T) decay as l/t, the
magnitude of the worst-case IS1 tends to infinity for any nonzero timing error
e, yielding a horizontal eye opening of zero width.
When B >
1/(2T),
the baseband pulse g(t) which eliminates IS1 is no longer
unique. Evidently, all pulses that satisfy g(t) = 0 for It I 2 T eliminate ISI.
Because of their time-limited nature, these pulses have a large (theoretically
infinite) bandwidth, so that they find application only on channels having a

bandwidth B which is considerably larger than
1/(2T);
an example is optical
fiber communication with on-off keying of the light source. When bandwidth
is scarce, one would like to operate at a symbol rate
l/T
which is only slightly
less than 2 B. This is referred to as narrowband communication.
When
1/(2T)
< B <
l/T,
the Nyquist criterion (2-13) is equivalent to
imposing that G(w) has a symmetry point at w = ?r/T:
G($+u)+G*(F-w)
=G(O) for (u(<?r/T (2- 16)
A widely used class of pulses with
1/(2T)
< B <
l/T
that satisfy (2- 16) are the
cosine rolloff pulses (also called raised cosine pulses), determined by
sin (?rt/T) cos (curt/T)
dt) = &/T
1-
4cx2t2/T2
(2- 17)
68
Baseband
Communications

withO<cu< 1. Fora=
0, (2-17) reduces to (2-15). The Fourier transform
G(w) of the pulse g(t) from (2-17) is given by
G(w) =
{
:,2 [l
- sin (w)]
0
~~~~\~~~~!r(l+ Q) (2-18)
W
-= a!
Hence, the bandwidth B equals (1 + a)/(2T), and a/(2T) denotes the excess
bandwidth [in excess of the minimum bandwidth 1/(2T)]. cy is called the rolloff
factor. Some examples of cosine rolloff pulses, their Fourier transform and the
corresponding eye diagram are shown in Figure 2-4. Note that IS1 is absent when
sampling at the instants
kT.
The horizontal eye opening decreases (and, hence,
the sensitivity to timing error increases) with a decreasing rolloff factor.
From the above discussion we conclude that a baseband PAM pulse g(t) that
(a)
09
Figure 2-4 Cosine Rolloff Pulses:
(a) Baseband Pulse gT(t) , (b) Fourier
Transform G(w) , (c) Eye Diagram for Binary PAM (25% Rolloff), (d) Eye
Diagram for Binary PAM (50% Rolloff), (e) Eye Diagram for Binary PAM (100%
Rolloff)
2.1 Introduction to Digital Baseband Communications
69
roll-off = 25%

1.
0.
-1.
(d
(4
roll-off = 50%
1.0
0.5
0.0
-0.5
-1.0
010
015
1.0
1.5
2.0
VT
roll-off = 100%
1
70
Baseband Communications
eliminates IS1 must satisfy the Nyquist criterion (2-13). In order that a receive
filter exist that eliminates ISI, it is necessary that the available bandwidth exceed
half the symbol rate.
As the receive filter which eliminates (or at least substantially reduces) IS1
yields a baseband pulse g(t) whose folded Fourier transform Gad(w) is essentially
flat, the receive filter is often referred to as a (linear)
equalizer.
The equalizer
must compensate for the linear distortion introduced by the channel and therefore

depends on the channel frequency response C(w). When there is sufficient a
priori knowledge about C(w), the equalizer can be implemented as a fixed filter.
However, when there is a rather large uncertainty about the channel characteristics,
the equalizer must be made adaptive.
Generally speaking, the equalizer compensates for the channel attenuation
by having a larger gain at those signal frequencies that are more attenuated by
the channel. However, the noise at those frequencies is also amplified, so that
equalization gives rise to a
noise enhancement.
The larger the variation of the
channel attenuation over the frequency interval occupied by the transmit signal,
the larger this noise enhancement.
2.1.3 Line Coding
In many baseband communication systems, there is some frequency value B
beyond which the linear distortion rapidly increases with frequency. For example,
the attenuation (in decibels) of a twisted-pair cable is proportional to the square-
root of the frequency (skin effect). This sets a limit on the bandwidth that can
be used for baseband transmission: if the transmit signal contained components at
too high frequencies, equalization of the severe linear distortion would give rise
to a large noise enhancement, yielding a considerable performance degradation.
In addition, in many applications the transmitted signal is severely distorted near
zero frequency, because of transformer coupling or capacitive coupling, which
reject DC. In these cases, the transmit signal should have low spectral content
near zero frequency, in order to avoid excessive linear distortion and a resulting
performance degradation.
It is clear from the above that we must control the transmit spectrum in order to
avoid both high frequencies and frequencies near DC. We recall from Section 1.1.4
that the power spectrum S,(w) of the transmit signal s(t) from (2-l) is given by
S&) = $s.(
ejwT) IGT (w) 1’

(2-19)
where Sa ( ejwT)
is the power spectrum of the data symbol sequence. Hence, the
control of the spectrum is achieved by acting on the transmit pulse g(t) and/or on
the spectrum of the data symbol sequence. The latter is achieved by means of line
coding: line coding involves the specification of the encoding rule that converts
the information bit sequence {bk} into the sequence {ak} of data symbols, and
therefore affects the spectrum of the data symbol sequence.
2.1 Introduction to Digital Baseband Communications
71
In addition to spectrum control, line coding should also provide timing
information. Most symbol synchronizers can extract a reliable timing estimate
from the received noisy PAM signal, only when there are sufficient data symbol
transitions. When there are no data symbol transitions (suppose uk = 1 for all E),
the receive filter output signal in the absence of noise is given by
YO(CE) =
E (
g t-kT-ET)
= ;-j-j q!) exp [j?z& -q]
(2-20)
00
Note that ya(t; 6) is periodic in t with period T, so that one could be tempted to
conclude that timing information can easily be extracted from yo(t; E). However,
when G(w) =
0 for Iwl >
27rB
with
B
< l/T (as is the case for narrowband
communication), the terms with

k
# 0 in (2-20) are zero, so that yo~(t; E) contains
only a DC component, from which obviously no timing information can be derived.
The same is true for wideband pulses with G(27rm/T) = 0 for m # 0 (as is the
case for rectangular pulses with duration T). Hence, in order to guarantee sufficient
timing information, the encoding rule should be such that irrespective of the bit
sequence (bk}, the number of successive identical data symbols in the sequence
{CQ} is limited to some small value.
As the spectrum SQ (eiWT)
is periodic in w with period
27r/T,
it follows
from (2-19) that the condition S,(w) = 0 for IwI >
27rB
implies GT(w) = 0 for
1~1 >
27rB.
Hence, frequency components above w =
2nB
can be avoided only
by using a band-limited transmit pulse. According to the Nyquist criterion for zero
ISI, this band-limitation on GT(w) restricts the symbol rate l/T to l/T < 2
B.
A low spectral content near DC is achieved when Ss(0) = 0. This condition
is fulfilled when either GT( 0) = 0 or So ( ej”) = 0.
.
When GT(O) = 0 and l/T is required to be only slightly less than
2B
(i.e., narrowband communication), the folded Fourier transform GH&) of
the baseband pulse at the receive filter output is zero at w = 0. This indicates

that equalization can be performed only at the expense of a rather large noise
enhancement.
The zero in the folded Fourier transform Gfid(U) and the
resulting noise enhancement can be avoided only by reducing the symbol
rate l/T below the bandwidth
B.
Hence, using a transmit pulse gT(t) with
GT(O) =
0 is advisable only when the available bandwidth is sufficiently
large, but not for narrowband applications.
.
In the case of narrowband communication, the recommended solution to
obtain S8 (0) =
0 is to take SQ (ej ‘) = 0. Noting that S, (ej”) can be
expressed as
72
Baseband Communications
it follows that Sa (ej”) = 0 when the encoding rule is such that the magnitude
of the
running digital sum,
RDS (n), given by
RDS(n) = 2 uk
k=-oo
(2-22)
is limited for all N, and for any binary sequence (bk} at the encoder input.
For some encoders, there exist binary input strings (such as all zeroes, all ones,
or alternating zeroes and ones) which cause long strings of identical data symbols
at the encoder output.
In order that the transmitted signal contains sufficient
timing information, the probability of occurrence of such binary strings at the

encoder input should be made very small. This can be accomplished by means
of a scrambler. Basically, a scrambler “randomizes” the binary input sequence
by modulo-2 addition of a pseudo-random binary sequence. At the receiver, the
original binary sequence is recovered by adding (modulo-2) the same pseudo-
random sequence to the detected bits.
Binary Antipodal Signaling
In the case of binary antipodal signaling, the channel symbol c&k equals +l
or -1 when the corresponding information bit bk is a binary one or binary zero,
respectively. Unless the Fourier transform G(w) of the baseband pulse at the
receive filter output satisfies G(27rm/T) # 0 for at least one nonzero integer
m,
this type of line coding does not provide sufficient timing information when
the binary information sequence contains long strings of zeroes or ones. The
occurrence of such strings can be made very improbable by using scrambling.
Also, in order to obtain a zero transmit spectrum at DC, one needs
GT(O)
= 0.
Consequently, the magnitude of the running digital sum is limited, so that the
codes yield no DC,
Quaternary Line Codes
In the case of quaternary line codes, the data symbol alphabet is the set
{f l,f3}. An example is 2BIQ, where the binary information sequence is
subdivided in blocks of 2 bits, and each block is translated into one of the four
levels fl or f3. The 2BlQ line code is used for the basic rate ISDN (data rate
of 160 kb/s) on digital subscriber lines.
2.1.4 Main Points
In a baseband communication system the digital information is conveyed by
means of a pulse train, which is amplitude-modulated by the data. The channel
2.1 Introduction to Digital Baseband Communications
73

is assumed to introduce linear distortion and to add noise. This linear distortion
broadens the transmitted pulses; the resulting unwanted pulse overlap gives rise
to ISI.
The receiver consists of a receive filter, which rejects out-of-band noise.
Data detection is based upon receive filter output samples, which are taken once
per symbol. These samples are fed to a slicer, which makes symbol-by-symbol
decisions. The decisions are impaired by IS1 and noise that occurs at the sampling
instants.
The receive filter output should be sampled at the instants of maximum noise
margin. These optimum sampling instants are not a priori known to the receiver. A
timing recovery circuit or symbol synchronizer is needed to estimate the optimum
sampling instants from the received noisy PAM signal.
The receive filter must combat both noise and ISI. According to the Nyquist
criterion, the receive filter should produce a pulse whose folded Fourier transform
is essentially flat, in order to substantially reduce the ISI. Such a filter is called
an equalizer. When the system bandwidth is smaller than half the symbol rate,
equalization cannot be accomplished.
In many applications, the channel attenuation is large near DC and above some
frequency B. In order to avoid large distortion, the transmit signal should have
negligible power in these regions. This is accomplished by selecting a transmit
pulse with a bandwidth not exceeding B, and by means of proper line coding to
create a spectral zero at DC. Besides spectrum control, the line coding must also
provide a sufficient number of data transitions in order that the receiver is able
to recover the timing.
2.1.5 Bibliographical Notes
Baseband communication is well covered in many textbooks, such as [ l]-[6].
These books treat equalization and line coding in much more detail than we have
done. Some interesting topics we did not consider are mentioned below.
Ternary Line Codes
In the case of ternary line codes, the data symbols take values from the set

I-2,0, $2). In the following, we will adopt the short-hand notation (- , 0, +}
for the ternary alphabet.
A simple ternary line code is the alternate mark inversion (AMI) code, which
is also called bipolar. The AM1 encoder translates a binary zero into a channel
symbol 0, and a binary one into a channel symbol + or - in such a way that
polarities alternate.
Because of these alternating polarities, it is easily verified
that the running digital sum is limited in magnitude, so that the transmit spectrum
is zero at DC. Long strings of identical data symbols at the encoder output can
occur only when a long string of binary zeroes is applied to the encoder. This
yields a long string of identical channel symbols 0. The occurrence of long strings
of binary zeroes can be avoided by using a scrambler. The AM1 decoder at the
74 Baseband Communications
Table 2-l 4B3T Line Code [l]
Binary input block
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110

1111
Ternary output block
Mode A
Mode B
+o-
+O-
-+o
-+o
o-+
o-+
+-0
+-0
++o
0
o++
0
+o+
-O-
+++

++-
+
-++
+
+-+
-+-
+00
-00
o+o
o-o

oo+
oo-
o+-
o+-
-o+
-o+
receiver converts the detected ternary symbols into binary symbols. 0 is interpreted
as binary zero, whereas + and -
are interpreted as binary one. The AM1 code uses
one ternary symbol to transmit one bit of information. Hence the efficiency of the
AM1 code, as compared to transmitting statistically independent ternary symbols,
equals l/ log, 3
z 0.63. AM1 is widely used for transmission of multiplexed
digitized voice channels over repeatered twisted pair cables at rates of a few
megabits per second.
A higher efficiency and more timing information than (unscrambled) AM1 are
obtained when using ternary block codes, which map blocks of
k
bits to blocks of
n
ternary symbols; such codes are denoted as
kBnT.
As an example, we consider
the
4B3Tcode,
which maps 4 bits to 3 ternary symbols according to Table 2-l.
Note that there are two “modes”: when the running digital sum is negative
(nonnegative), the entries from the first (second) column are used. In this way,
the magnitude of the running digital sum is limited, which guarantees a spectral
zero at DC. Also, it is not possible to have more than five successive identical

2.1 Introduction to Digital Baseband Communications 75
ternary symbols, so that timing information is always available. The efficiency of
the 4B3T code equals 4/(3 log2 3) N 0.84. 4B3T achieves a higher efficiency than
AMI, but shows a higher encoding/decoding complexity.
Binary Line Codes
In many applications involving optical fiber communication, the light source
is keyed on/off. In this case, the channel symbols are binary, and the symbol
alphabet is denoted {+, -}.
Binary block codes converting a block of m information bits into a block
of n binary channel symbols are denoted mBnB; their efficiency as compared to
uncoded binary transmission equals m/n.
In the case of zero-disparity codes, each block of n binary channel symbols
contains the same number (n/2) of +‘s and -‘s. The number of possible code
words equals N =
(n!)/((n/2)!)2, but the number of code words actually used
in a mBnB zero-disparity code equals 2m, which is the largest power of 2 not
exceeding N. As the running digital sum is limited to the interval (-n/2, n/2),
zero disparity codes yield a spectral null at w = 0. Also, there are sufficient
data transitions for providing timing information. The IB2B zero-disparity code
is called Manchester code (also called biphase) whose two code words are +-
and -+. The Manchester code is used in coaxial-cable-based Ethernet local area
networks in the token ring and in fiber optical communication systems, but its
efficiency is only 0.5. The efficiency of the mBnB zero-disparity code increases
with increasing n, but at the cost of increased encoding/decoding complexity.
A higher efficiency than for zero-disparity codes is obtained when using
bimode mBnB codes, where the code words do not have the same number of
symbols + and As for the 4B3T ternary code described earlier, each block of
m information bits can be represented by one of two code words; the code word
reducing the magnitude of the running digital sum is selected by the encoder.
Equalization

.
When only a single data symbol is transmitted, the receiver’s decision is
affected only by additive noise, because IS1 is absent. The signal-to-noise ratio
at the input of the slicer is maximized when the receive filter is the matched
j&r. The frequency response of the matched filter is G~(w)C*(W)/SN(W),
where GT(w) and C(
w ) are the Fourier transforms of the transmit pulse and
the channel impulse response and SN(W) is the spectrum of the noise at the
receiver input. When the additive noise is Gaussian and the values that can
be assumed by the data symbols are equiprobable, it can be shown that the
optimum receiver, in the sense of minimizing the decision error probability,
is the matched filter followed by the slicer. The corresponding decision error
probability is called the matched filter bound: it is a lower bound on the
76
Baseband Communications
decision error probability of a baseband PAM communication system that is
affected by Gaussian noise and ISI.
The optimum linear equalizer, in the sense of minimizing the mean-square
error between the sample at the input of the slicer and the corresponding
data symbol, turns out to be the cascade of a matched filter and a transversal
filter operating at a rate l/T. Because of the noise enhancement caused by
the equalizer, the decision error probability is larger than the matched filter
bound [7, 81.
When symbol-by-symbol decisions are made, but the receiver is allowed
to use decisions about previous data symbols, the IS1 caused by previous
data symbols (i.e., the postcursor ISI) can be subtracted from the samples at
the input of the slicer. This yields the decision-feedback equalizer (DFE),
consisting of a forward equalizer which combats noise and precursor IS1 (Le.,
IS1 caused by future data symbols) and a feedback filter which generates from
the receiver’s decisions the postcursor IS1 to be subtracted. The optimum

forward equalizer (in the sense of minimizing noise and precursor ISI) is
the cascade of the matched filter and a noise-whitening transversal filter
operating at a rate l/T. The DFE yields less noise enhancement than the
linear equalizer, assuming that the decisions that are fed back are correct,
However, because of the decision-feedback, the DFE can give rise to error
propagation [7][8].
The optimum receiver (in the sense of minimizing sequence error probability)
in the presence of IS1 is the Viterbi equalizer (VE). It does not make symbol-
by-symbol decisions, but exploits the correlation between successive receive
filter samples for making a decision about the entire sequence by using a
dynamic programming algorithm, operating on matched filter output samples
taken at the symbol rate [9-l 11. When the eye at the matched filter output is
open, the performance of the VE is very close to the matched filter bound [ 111.
Fractionally spaced equalizers (i.e.,
transversal filters operating at a rate
exceeding l/T) are able to compensate for timing errors [ 121.
Various algorithms exist for updating adaptive equalizers [13].
Line
Coding
.
Other ternary line codes than AM1 and 4B3T from Section 2.1.3 are bipolar n
zero substitution (Bnzs), high-density bipolar n (HDBn), pair-selected ternary
(PST), and MS43 [14].
l
Other binary line codes than those considered in Section 2.1.3 are the Miller
code (also called delay modulation), coded mark inversion (CMI), and bit
insertion codes such as mBIC and DmBlM [ 15, 161.
.
The fiber-distributed data interface (FDDI) is a standard for a 100 Mb/s fiber-
optic token ring. It uses a 4B5B line code with ample timing information,

but with nonzero DC content.
2.1 Introduction to Digital Baseband Communications
77
.
In the case of partial response coding (which is also called correlative level
encoding), a controlled amount of IS1 is introduced deliberately by passing
the data symbols to a transversal filter operating at the symbol rate, in order
to perform spectral shaping. This transversal filter and the transmit filter can
be combined into a single filter. Denoting the frequency response in the
z-domain of the transversal filter by T(z), typical frequency responses are
T(z)=
1 - z-l
(dicode)
T(z)=
1+ z-l
(duobinary class 1)
T(z)=
(1 + z-‘) (1 - z-l) = 1 - zB2
(modified duobinary class 4)
(2-23)
Frequency responses having a factor
1
- z-l yield a spectral null at w = 0,
whereas a factor 1 + z- ’
gives rise to a spectral null at the Nyquist frequency
W
=
r/T.
A spectral null at w
=

r/T
allows transmission with the minimum
bandwidth B = 1/(2T). The transmit signal is given by (2-l), where {ak}
denotes the sequence of filtered symbols at the output of the transversal filter
T(z).
A simple receiver detects the filtered data symbols by performing
symbol-by-symbol decisions (the optimum receiver would use the Viterbi
algorithm in order to exploit the correlation between filtered data symbols).
As the filtered symbols have more levels than the unfiltered symbols, a
degradation of the decision error probability occurs. Decisions about the
unfiltered data symbols could be obtained by applying the decisions {uk}
about the filtered data symbols to a filter with frequency response l/T(x), as
shown in Figure 2-5. As
T(z)
is a polynomial in z, l/T(z) is the frequency
response of an all-pole filter.
An all-pole filter can be realized only by
means of feedback, so that the performance of the system shown in Figure
2-5 is affected by error propagation. It can be shown that the problem of
error propagation is circumvented by preceding the unfiltered data symbols
at the transmitter, before entering the transversal filter
T(z).
Because of
the preceding, the unfiltered data symbols can be recovered by means
of
noise
kT+$T
received
signal
K-

unfiltered
data out
Figure 2-5 Partial Response System with Error Propagation
78
Baseband Communications
received
signal
kT+h
Figure
2-6 Partial Response System with Preceding to Avoid Error Propagation
memoryless symbol-by-symbol decisions (as indicated in Figure 2-6), so that
error propagation does not occur [17]-[21].
Bibliography
[l] E. A. Lee and D. G. Messerschmitt,
Digital Communications.
Boston: Kluwer
Academic, 1988.
[2] J. Bellamy,
Digital Telephony.
New York: Wiley, 2nd ed., 1991.
[3] S. Benedetto, E. Biglieri, and V. Castellani,
Digital Transmission Theory.
Englewood Cliffs, NJ: Prentice-Hall, 1987.
[4] R. D. Gitlin, J. F. Hayes, and S. B. Weinstein, “Data Communications
Principles,” New
York: Plenum,
1992.
[5] R. Lucky, J. Salz, and E. Weldon, “Principles of Data Communication,” New
York: McGraw Hill,
1968.

[6] J. G. Proakis,
Digital Communications.
Auckland: McGraw-Hill, 1989.
[7] D. G. Messerschmitt,
“A Geometric Theory of Intersymbol Interference.
Part I: Zero-Forcing and Decision Feedback Equalization,”
BSTJ,
vol. 52,
pp. 1483-1519, Nov. 1973.
[8] C. A. Belfiore and J. H. Park, Jr., “Decision Feedback Equalization,”
Proc.
IEEE,
vol. 67, pp. 1143-1156, Aug. 1979.
[9] G. D. Forney,
“Maximum-Likelihood Sequence Estimation of Digital Se-
quences in the Presence of Intersymbol Interference,”
IEEE Trans. Zn-
form.
Theory,
vol. IT-18, pp. 363-378, May 1972.
[lo] D. G. Messerschmitt, “A Geometric Theory of Intersymbol Interference.
Part II: Performance of the Maximum Likelihood Detector,”
BSTJ,
vol. 52,
pp. 1521-1539, Nov. 1973.
[ 1 l] G. Ungerboeck, “Adaptive ML Receiver for Carrier-Modulated Dat-
Transmission Systems,”
IEEE Trans. Commun. Technol.,
vol. COM-22,
pp. 624-636, May 1974.

2.2 Clock Synchronizers
79
[ 121 G. Ungerboeck,
“Fractional Tap-spacing Equalizer and Consequences for
Clock Recovery in Data Modems,”
IEEE Trans. Commun.,
vol. COM-24,
pp. 856-864, Aug. 1976.
[ 131 S. U.
H.
Qureshi, “Adaptive Equalization,”
Proc. IEEE,
vol.
73, pp. 1349-
1387, Sept. 1985.
[14] P. A. Franaszek,
“Sequence-State Coding for Digital Transmission,”
BSTJ,
vol.
47, pp. 134-157, Jan. 1968.
[ 151 S. Kawanishi, N. Yoshikai, J. Yamada, and K. Nakagawa, “DmB 1M Code and
Its Performance in a Very High-Speed Optical Transmission System,”
IEEE
Trans. Commun., vol.
COM-36, pp. 951-956, Aug. 1988.
[ 161 N. Yoshikai, S. Nishi, and J. Yamada, “Line Code and Terminal Configuration
for Very Large-Capacity Optical Transmission Systems,”
IEEE J. Std. Areas
Commun.,
vol. SAC-4, pp. 1432-1437, Dec. 1986.

[ 171 P. Kabal and S. Pasupathy, “Partial-Response Signaling,”
IEEE Trans. Com-
mun.,
vol. COM-23, pp. 921-934, Sept. 1975.
[ 181 H. Kobayashi, “Correlative Level Coding and maximum-Likelihood Decod-
ing,”
IEEE Trans. Inform. Theory,
vol. IT- 17, pp. 586-594, Sept. 1971.
[19] H. Kobayashi, “A Survey of Coding Schemes for Transmission or Recording
of Digital Data,”
IEEE Trans. Commun. Technol.,
vol. COM- 19, pp. 1087-
1100, Dec. 1971.
[20] E. R. Kretzmer, “Generalization of a Technique for Binary Data Communica-
tion,”
IEEE Trans. Commun. Technol.,
vol. COM-14, pp. 67-68, Feb. 1966.
[21] A. Lender, “The Duobinary Technique for High-Speed Data Transmission,”
IEEE Trans. Commun. Electon,,
vol. 82, pp. 214-218, May 1963.
2.2 Clock Synchronizers
2.2.1 Introduction
The digital information, embedded in the transmitted PAM signal, is recovered
at the receiver by means of a decision device. This decision device operates on
samples of the noisy PAM signal y(t; e), taken at symbol rate l/T at the receive
filter output, which is given by
y(t; E) = C am g(t - mT - ET) + n(t)
m
(2-24)
In (2-24) (am} is a sequence of zero-mean data symbols, g(t) is the baseband

PAM pulse at the receive filter output,
eT
is an unknown fractional time delay
(-l/2 5 c 5 l/2), and n(t) represents zero-mean additive noise. For maximum
noise immunity, the samples upon which the receiver’s decision is based should
be taken at the instants of maximum eye opening. As the decision instants are a
80
Baseband Communications
Y(t; d
Loop
Filter
- vco l
Figure 2-7 Ordinary PLL Operating on PAM Signal
priori unknown (because of the unknown delay ET) the receiver must contain a
device which makes an estimate of the normalized delay. Such a device is called
a
clock synchronizer
or
symbol synchronizer.
The timing estimate E^ is used to
bring the sampling clock, which activates the sampler at the receive filter output,
in close synchronism with the received PAM signal. This is achieved by adjusting
the phase of this sampling clock according to the value of the estimate E^.
The received noisy PAM signal contains no periodic components, because the
channel symbols (a,} have zero mean. Therefore, an ordinary PLL (see Chapter
2 of Volume I) operating on the filtered received signal y(t; E) cannot be used to
generate a clock signal which is in synchronism with the received PAM signal. Let
us illustrate this fact by considering a PLL with multiplying timing error detector:
the local reference signal r(t; i) given by
r(t; 6) = l&i Kr

sin ($ (t-eT))
(2-25)
and is multiplied with the noisy PAM signal y(t ; E), as shown in Figure 2-7. Taking
into account (2-24), the timing error detector output signal equals
z(t; E, i) = c a, g(t - mT - ET) + n(t)
fi Ii’
sin
77-h
]
r
($(t-gT))
(2-26)
For any values of E and 2, the statistical average of the timing error detector output
is identically zero, because the channel symbols {a,} and the additive noise
nit)
have zero mean. As the average timing error detector output is zero irrespective of
E and E^, there is no deterministic force that makes the PLL lock onto the received
PAM signal.
2.2.2 Categorization of Clock Synchronizers
From the operating principle point of view, two categories of synchronizers
are distinguished, i.e.,
error-trucking
(or feedback, or closed loop) synchronizers
and
feedforward
(or open loop) synchronizers.
A general error-tracking synchronizer is shown in Figure 2-8. The noisy PAM
signal y(t; e) and a locally generated reference signal r(t; i> are “compared” by
2.2 Clock Synchronizers
81

PAM
) Receive
Y(p)
l
Sampler
c Decision
Data
Signal
Filter
Device
out
4
I
I
Timing
Error
Detector
I
Reference
Signal
Generator
2
Loop
Adjustmert
Filter
of B
I
L
Figure 2-8 General Error-Tracking Synchronizer
means of a

timing
error
detector,
whose output gives an indication of the magnitude
and the sign of the
timing error e
= & - 2. The filtered timing error detector output
signal adjusts the timing estimate e in order to reduce the timing error e. The
timing estimate 2 is the normalized delay of the reference signal ~(t; e) which
activates the sampler operating on y(t ; E). Hence, error-tracking synchronizers use
the principle of the PLL to extract a sampling clock which is in close synchronism
with the received PAM signal. Properties of error-tracking synchronizers will be
studied in detail in Section 2.3.
Figure 2-9 shows a general feedforward synchronizer. The noisy PAM receive
signal y(t; e) enters a
timing detector,
which “measures” the instantaneous value
of c (or a function thereof). The noisy measurements at the timing detector output
are averaged to yield the timing estimate e (or a function thereof),
PAM
) Receive
Data
Signal
Filter
yW
l
Sampler
. Decision
Device
out

4
__) Timing
Detector
l
Averaging t
Reference
- Signal
I
Filter
Generator
Figure 2-9 General Feedforward Synchronizer
82 Baseband Communications
YW
) Nonlinearity
) Bandpass Filter
Sampling
or PLL
Clock
Figure 2-10 General Spectral Line Generating Synchronizer
An important subcategory of both error-tracking and feedforward synchroniz-
ers is formed by the
spectral line generating synchronizers.
A general spectral line
generating synchronizer is shown in Figure 2-10. The received PAM signal, which
does not contain any periodic components, passes through a suitable nonlinearity.
In most cases, the output of the nonlinearity is an even function of its input. In Sec-
tion 2.4, where spectral line generating synchronizers are treated in detail, we will
show that the output of the nonlinearity contains periodic components, the phase
of which is related to the normalized delay t. Viewed in the frequency domain,
the output of the nonlinearity contains spectral lines at multiples of the channel

symbol rate l/T. The periodic component with frequency l/T can be tracked by
means of an ordinary PLL, whose VCO output signal then controls the sampler
at the output of the receive filter. When the periodic component at frequency
l/T is extracted by means of a PLL, the spectral line generating synchronizer
belongs to the category of error-tracking synchronizers, because the VCO of the
PLL is driven by an error signal depending on the normalized delay difference
e
= &-
E^. Alternatively, the periodic component with frequency l/T can be
selected by means of a narrowband bandpass filter, tuned to the channel symbol
rate l/T, and serves as a clock signal which activates the sampler at the output
of the receive filter. When the periodic component at frequency l/T is extracted
by means of a bandpass filter, the spectral line generating synchronizer belongs to
the category of feedforward synchronizers. Note that the feedforward spectral line
generating synchronizer makes no explicit estimate of E (or a function thereof);
instead, the cascade of the nonlinearity and the narrowband bandpass filter gives
rise directly to the reference signal ~(t; e).
Besides the above categorization into error-tracking and feedforward synchro-
nizers, other categorizations can be made:
.
When a synchronizer makes use of the receiver’s decisions about the trans-
mitted data symbols for producing a timing estimate, the synchronizer is said
to be
decision-directed;
otherwise, it is
non-data-aided.
.
The synchronizer can operate in continuous time or in discrete time. Discrete-
time synchronizers use samples of the PAM signal y(t ; E), and are therefore
well-suited for digital implementation.

In Section 2.2.3 we will present examples of synchronizers belonging to various
categories.
2.2.3 Examples
In this section we give a few specific examples of synchronizers, belonging
to the various categories considered in Section 2.2.2. Their operation will be
2.2 Clock Synchronizers
83
Figure 2-11 Baseband PAM Pulse g(t) Used in Examples
explained mainly in a qualitative way. A detailed quantitative treatment of these
synchronizers will be presented in Section 2.5.
For all cases, it will be assumed that the synchronizers operate on a noiseless
PAM waveform y(t; &), with a baseband pulse g(t), given by
g(t) =
$ (1+ cos ($))
ItI < T
(2-27)
0
otherwise
The baseband PAM pulse g(t) is shown in Figure 2-l 1; note that its duration equals
two channel symbol intervals, so that successive pulses overlap. The channel
symbols (uk} independently take on the values -1 and 1 with a probability of
l/2 (binary antipodal signaling).
The Squaring Synchronizer
The squaring synchronizer is a spectral line generating synchronizer. The
block diagram of the squaring synchronizer is shown in Figure 2-12. The PAM
signal y(t ; &) enters a prefilter, which in our example is a differentiator. The
squared differentiated signal contains spectral lines at DC and at multiples of the
channel symbol rate
l/T;
the spectral line at the channel symbol rate is selected

by means of a bandpass filter (feedforward synchronizer), or is tracked by means
of a PLL (error-tracking synchronizer).
Y (f 2)
d
it&E)
i*(t;E) Bandpass Sampling
dt
e Squarer
) Filter
or PLL
Clock
Figure 2-12 Block Diagram of Squaring Synchronizer
84
Baseband Communications
Figure 2-13 shows the PAM signal y(t; e), its time derivative $(t; E) and
the squarer output i2 (t; 6).
The squarer output consists of a sequence of
identical pulses, with randomly missing elements; more precisely, the interval
(mT+&T,mT+ET+T)
contains a pulse if and only if a, # cs,,,+l, i.e., when
a channel symbol transition occurs. The squarer output*i2(t; E) can be decomposed
as the sum of two terms. The first term is the statistical expectation
E [i2(t; e)] ,
which is periodic in t with period T; this is the useful term, consisting of spectral
lines. The second term is a zero-mean disturbance jr2 (t ; e) -
E
[ g2 (t ; E)] , which
is caused by the random nature of the channel symbols. This term is a
self-noise
term, which does not contain spectral lines and, hence, disturbs the synchronizer

operation.
The Synchronizer with Zero-Crossing Timing Error Detector
The synchronizer with zero-crossing timing error detector (ZCTED) is an
error-tracking synchronizer. The block diagram of this synchronizer is shown in
Figure 2-14 and its operation is illustrated in Figure 2-15.
The VCO output signal r(t; e) is a square wave with a frequency equal to
$0: E)
A
(k+l )T+ET (k+P)T+eT
0
1 I
I
I
kT+eT
(k+3)T+tzT
1 kT+eT
(k+l)T+&T
(k+P)T+&T (k+3)T+eT
kT+eT (k+ 1 )T+ET
(k+P)T+eT (k+3)T+eT
i ‘(1; e)-E[jr2(t; E)]
Figure
2-13 Illustration of Squaring Synchronizer Operation