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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
[...]... using a scrambler The AM1 decoderat the 74 Baseband Communications Table 2-l 4B3T Line Code [l] Ternary output block Binary input block Mode A Mode B 0000 +o- +O- 0001 -+ o -+ o 0010 o-+ o-+ 0011 +-0 +-0 0100 0101 ++o o++ 0 0 0110 0111 +o+ +++ -O - 1000 1001 + +-+ + + + 1010 +-+ -+ - 1011 +00 -0 0 1100 o+o o-o 1101 oo+ oo- 1110 o +- o +- 1111 -o+ -o+ receiverconvertsthe detectedternary symbolsinto binary... single filter Denoting the frequency responsein the z-domain of the transversalfilter by T(z), typical frequencyresponses are T(z)= T(z)= T(z)= 1 - z-l 1+ z-l (1 + z-‘) (1 - z-l) = 1 - zB2 (dicode) (duobinary class 1) (modified duobinary class 4) ( 2-2 3) Frequencyresponses having a factor 1 - z-l yield a spectralnull at w = 0, whereasa factor 1+ z- ’ gives rise to a spectralnull at the Nyquist frequency... * Sampling Clock Figure 2-1 4 Block Diagram of Synchronizerwith ZCTED YOi El o\fip&y +-: I I I I I I r(t; 2 ) I I I I I I I I I I o I I I I I I 4 I \/ ’ kT +tT- I I I I I I I I I ’ w (k+3)T +i?T - (k+W+t?T y;:’ 1 et \I X(t; E,e ) +-+ L 1 a-t-E[x(t E,)I * t X(t; E, 8 A 0 I I 0 )-E[x(t; E, 8 I I I I I j @t )] - I Figure 2-1 5 Illustration of ZCTED Operation j @t 85 86 Baseband Communications the channel... received signal K- unfiltered data out Figure 2-5 Partial ResponseSystem with Error Propagation Baseband Communications 78 kT+h received signal Figure 2-6 Partial Response Systemwith Precedingto Avoid Error Propagation memorylesssymbol-by-symboldecisions(as indicated in Figure 2-6 ), so that error propagationdoes not occur [17 ]-[ 21] Bibliography [l] E A Lee and D G Messerschmitt, Digital Communications... Performancein a Very High-SpeedOptical TransmissionSystem,” IEEE Trans Commun., vol COM-36, pp 95 1-9 56, Aug 1988 [ 161 N Yoshikai, S Nishi, and J Yamada,“Line Code and TerminalConfiguration for Very Large-CapacityOptical TransmissionSystems,”IEEE J Std Areas Commun., vol SAC-4, pp 143 2-1 437, Dec 1986 [ 171 P Kabal and S Pasupathy,“Partial-Response Signaling,” IEEE Trans Commun., vol COM-23, pp 92 1-9 34, Sept 1975... error detector: the local referencesignal r(t; i) given by r(t; 6) = l&i Kr sin ($ (t-eT)) ( 2-2 5) and is multiplied with the noisy PAM signal y(t ; E), as shownin Figure 2-7 Taking into account ( 2-2 4), the timing error detectoroutput signal equals z(t; E, i) = c a, g(t - mT - ET) + n(t) ] fi 77-h Ii’ r sin ($(t-gT)) ( 2-2 6) For any valuesof E and 2, the statisticalaverageof the timing error detectoroutput... absenceof noise is given by YO(CE) = = g ( t-kT-ET) E ;-j-j q!) exp [j?z& -q] ( 2-2 0) -0 0 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 extractedfrom yo(t; E) However, when G(w) = 0 for Iwl > 27rB with B < l/T (as is the case for narrowband E) communication) ,the terms with k # 0 in ( 2-2 0) are zero, so that yo~(t; contains... Level Coding and maximum-Likelihood Decoding,” IEEE Trans Inform Theory, vol IT- 17, pp 58 6-5 94, Sept 1971 [19] H Kobayashi,“A Survey of Coding Schemes Transmissionor Recording for of Digital Data,” IEEE Trans Commun Technol., vol COM- 19, pp 10871100, Dec 1971 [20] E R Kretzmer, “Generalizationof a Techniquefor Binary Data Communication, ” IEEE Trans Commun Technol., vol COM-14, pp 6 7-6 8, Feb 1966 [21]... (Figure 2- 19, and in the M&M timing error detector output (Figure 2-1 7) Besides self-noise, also additive noise at the input of the receiver affects the operation of the clock synchronizer However, in the case of terrestrial baseband communication, self-noise is the dominating disturbance for the following reasons: Additive noise levels are small (signal-to-noise ratios for terrestrial baseband communication. .. 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) ( 2-2 4) m In ( 2-2 4) (am} is a sequenceof zero-meandata 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-meanadditive noise For maximum noise immunity, the samplesupon which the receiver’s decision .
+o-
+O-
-+ o
-+ o
o-+
o-+
+-0
+-0
++o
0
o++
0
+o+
-O-
+++
+ +-
+
-+ +
+
+-+
-+ -
+00
-0 0
o+o
o-o
oo+
oo-
o +-
o +-
-o+
-o+. ISBN 0-4 7 1-5 027 5-8 Online ISBN 0-4 7 1-2 005 7-3
Chapter 2 Baseband Communications
2.1 Introduction to Digital Baseband Communication
In baseband communication,