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,