`
`
`
`
`
`
`
`
`
`
`
`
`
`i\__
`
`
`
`,
`
`.
`
`’
`
`r
`
`\
`
`
`
`X
`
`\\
`
`\
`
`‘
`
`~
`
`\
`
`,
`
`
`
`,
`_
`\
`/
`
`77k
`,
`‘7,” "7-77'
`i,_
`7\
`*7
`
`\
`
`
`
`7/;
`
`7 "/7 '
`
`“
`
`
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 1
`
`

`

`Petitioner Sirius XM Radio Inc. - Ex. 1012, p.‘2
`
`Copyright © 1989, 1983 by B. P. Lathi
`All rights reserved. No part of this publication may be
`reproduced or transmitted in any form or by any means,
`electronic or mechanical, including photocopy, recording,
`or any information storage and retrieval system, without
`permission in writing from the publisher.
`
`Request for permission to make copies ofany part ofthe work
`should be mailed to: Copyrights and Permissions Department,
`Holt, Rinehart and Winston, Inc. , Orlando, Florida 32887.
`
`Library of Congress Cataloging-in-Publication Data
`Lathi, B. P. (Bhagwandas Pannalal)
`Modern digital and analog communication systems/RP. Lathi.—
`
`cm. — (HRW series in electrical engineering)
`p.
`Includes bibliographies and index.
`ISBN 0-03-027933-X
`l. Telecommunication systems.
`3. Statistical communication theory.
`621.38’0413—dc19
`
`2. Digital communications.
`I. Title.
`II. Series.
`88-25151
`CIP
`
`The Dryden Press
`Saunders College Publishing
`Printed in the United States of America
`0 l 2
`016
`9 8 7 6 5 4 3
`ISBN U-DB-DE‘?‘333-X
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 2
`
`

`

`a scheme would be difficult because of the requirement of generation and detection of
`pulses of precise amplitudes. Such practical difficulties would then set a limit on the
`rate of communication.
`
`In conclusion, we have demonstrated qualitatively the basic role played by B and
`SNR in limiting the performance of a communication system. These two parameters
`then represent the ultimate limitation on a rate of communication. We have also
`demonstrated the possibility of trade or exchange between these two basic parameters.
`Equation (1.1) can be derived from Eq. (1.2).
`It should be remembered that
`Shannon’s result represents the upper limit on the rate of communication over a
`channel and can be achieved only with a system of monstrous and impracticable
`complexity and a time delay in reception approaching infinity. Practical systems
`operate at rates below the Shannon rate. In Chapter 8, we shall derive Shannon’s result
`and compare the efficiencies of various communication systems.
`
`1.4 MODULATION
`
`Baseband signals produced by various information sources are not always suitable for
`direct transmission over a given channel. These signals are usually further modified
`to facilitate transmission. This conversion process is known as modulation. In this
`process, the baseband signal is used to modify some parameter of a high-frequency
`carrier signal.
`A carrier is a sinusoid of high frequency, and one of its parameters—such as
`amplitude, frequency, or phase—is varied in proportion to the baseband signal m(t).
`Accordingly, we have amplitude modulation (AM), frequency modulation (FM), or
`phase modulation (PM). Figure 1.7 shows a baseband signal m(t) and the correspond—
`ing AM and FM waveforms. In AM, the carrier amplitude varies in proportion to m (I),
`and in FM, the carrier frequency varies in proportion to m(r).
`At the receiver, the modulated signal must pass through a reverse process called
`demodulation in order to retrieve the baseband signal.
`As mentioned earlier, modulation is used to facilitate transmission. Some of the
`important reasons for modulation are given below.
`
`Ease of Radiation
`
`For efficient radiation of electromagnetic energy, the radiating antenna should be of
`the order of one-tenth or more of the wavelength of the signal radiated. For many
`baseband signals, the wavelengths are too large for reasonable antenna dimensions.
`For example, the power in a speech signal is concentrated at frequencies in the range
`of 100 Hz to 3000 Hz. The corresponding wavelength is 100 km to 3000 km. This
`long wavelength would necessitate an impracticably large antenna. Instead, We mod—
`ulate a high—frequency carrier, thus translating the signal spectrum to the region of
`
`
`
`
`
`Modulating (baseband) signal
`
`Amplitude-modulated wave
`
`
`
`Frequency-modulated wave
`
`Figure 1.7 Modulation.
`
`carrier frequencies that corresponds to a much smaller wavel
`1 MHz carrier has a wavelength of only 300 meters and requ1res
`is of the order of 30 meters. In this aspect, modulation is lil<
`signal hitchhike on a high—frequency sinusoid (carrier). The c:
`signal may be compared to a stone and a piece of paper. .If we
`of paper, it cannot go too far by itself. But by wrapplng 1t aro
`it can be thrown over a longer distance.
`
`Simultaneous Transmission of Several Signals
`
`Consider the case of several radio stations broadcasting audi
`rectly, without any modification. They would interfere with
`spectra of all the signals occupy more or less the same bandw
`possible to broadcast from only one radio or TV stat10n at a
`because the channel bandwidth may be much larger than that
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 3
`
`

`

`the contents of this book will be
`red to transmit this book, all that is needed is to transmit
`e an infinite number of levels are available, it is possible
`iceivable message. Cataloging of such a code may not
`de the point. The point is that if the noise is zero,
`problem, at least theoretically. Implementation of such
`:cause of the requirement of generation and detection of
`Such practical difficulties would then set a limit on the
`
`:monstrated qualitatively the basic role played by B and
`nce of a communication system. These two parameters
`imitation on a rate of communication. We have also
`f trade or exchange between these two basic parameters.
`erived from Eq. (1.2). It should be remembered that
`the upper limit on the rate of communication over a
`i only with a system of monstrous and impracticable
`y in reception approaching infinity. Practical systems
`nnon rate. In Chapter 8, we shall derive Shannon’s result
`of various communication systems.
`
`y various information sources are not always suitable for
`iven channel. These signals are usually further modified
`his conversion process is known as modulation. In this
`1 is used to modify some parameter of a high—frequency
`
`of high frequency, and one of its parameters—such as
`ase—is varied in proportion to the baseband signal m(t).
`itude modulation (AM), frequency modulation (FM), or
`ure 1.7 shows a baseband signal m (t) and the correspond-
`In AM, the carrier amplitude varies in proportion to m (I),
`iency varies in proportion to m(t).
`dulated signal must pass through a reverse process called
`'etrieve the baseband signal.
`nodulation is used to facilitate transmission. Some of the
`ilation are given below.
`
`
`
`-
`'
`'
`Petitioner S'
`Irlus XM Radio Inc. O[\IJEXM1012, p. 4
`1.4 MODULATl
`
`Carrier
`
`m(t)
`
`Modulating (baseband) signal
`
`
`
`Amplitude-modulated wave
`
`
`
`Frequency-modulated wave
`
`Figure 1.7 Modulation.
`
`to a much smaller wavelength. For example, a
`carrier frequencies that corresponds
`1 MHZ carrier has a wavelength of only 300 meters and requires an antenna whose size
`is of the order of 30 meters. In this aspect, modulation is like letting the baseband
`signal hitchhike on a high-frequency smusoid (carrier). The carrier and the baseband
`signal may be compared to a stone and a piece of paper. If we wrsh to throw a piece
`far by itself. But by wrapping it around a stone (a carrier),
`of paper, it cannot go too
`it can be thrown over a longer distance.
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 4
`
`

`

`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 5
`
`4.1 BASEBAND AND CARRIER COMMUNICATION 223
`
` In baseband communication, baseband signals are transmitted without modu-
`lation, that is, without any shift in the range of frequencies of the signal. Because the
`baseband signals have sizable power at low frequencies, they cannot be transmitted
`over a radio link but are suitable for transmission over a pair of wires or coaxial cables.
`Local telephone communication and short-haul PCM (between two exchanges) use
`baseband communication. Because baseband communication uses only baseband fre—
`quencies, its uses are rather restricted. Also, because the transmission of signals at
`lower frequencies is in general more difficult, it is desirable to shift the signal spectrum
`to a higher—frequency range by modulation. Moreover,
`the vast spectrum of fre-
`quencies available because of technological advances cannot be utilized by a baseband
`scheme. By modulating several baseband signals and shifting their spectra to non—
`overlapping bands, one can use all the available bandwidth more efficiently. Long-
`haul communication over a radio link also requires modulation to shift the signal
`spectrum to higher frequencies to enable efficient power radiation using antennas of
`reasonable dimensions. Yet another use of modulation is to exchange transmission
`bandwidth for the SNR.
`
`
`
`ulation
`
`
`
`mplitude
`dodulation
`
`
`that causes a shift of the range of frequencies in a signal. It
`idvantages, as mentioned in Chapter 1. Before discussing
`int to distinguish between communication that does not use
`mmunication) and communication that uses modulation (car-
`
`Communication that uses modulation to shift the frequency spectrum of a signal
`is known as carrier communication.
`In this mode, one of the basic parameters
`(amplitude, frequency, or phase) of a sinusoidal carrier of high frequency cu). is varied
`in proportion to the baseband signal m (t). This results in amplitude modulation (AM),
`frequency modulation (FM), or phase modulation (PM), respectively. The latter two
`types of modulation are similar, in essence, and are grouped under the name angle
`modulation. Modulation is used to transmit analog as well as digital baseband signals.
`A comment about pulse-modulated signals (PAM, PWM, PPM, PCM, and DM)
`is in order here. Despite the term modulation, these signals are baseband signals. The
`term modulation is used here in another sense. Pulse—modulation schemes are really
`baseband coding schemes, and they yield baseband signals. These signals must still
`modulate a carrier in order to shift their spectra.
`
`4.2 AMPLITUDE MODULATION: DOUBLE SIDEBAND (DSB)
`
`carrier
`unmodulated
`the
`amplitude A, of
`the
`amplitude modulation,
`In
`AC cos (wct + 06) is varied in proportion to the baseband signal (known as the modu-
`lating signal). The frequency wc and the phase 66 are constant. We can assume 6, = 0
`without a loss of generality. If the carrier amplitude A, is made directly proportional
`to the modulating signal m(t), the modulated carrier is m(t) cos wct (Fig. 4.1c). As
`seen earlier [Eq. (2.63a)], this type of modulation simply shifts the spectrum of m(I)
`to the carrier frequency (Fig. 4.1c); that is, if
`
`m(r) <—> M(w)
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 5
`
`

`

`m(t) cos wot
`
`
`
`m(t)
`
`
`
`cos wot
`
`(a)
`
`Figure 4.1 DSB-SC modulation.
`
`bands. For instance, if m(t) = cos wmt, then the modulated signal
`
`m(t) cos wct = cos wmt cos wrt
`_ l
`— §[cos (a). + com)! + cos (a), — wm)t]
`The component of frequency wt. + com is the upper sideband, and that of frequency
`(1).. - mm is the lower sideband, corresponding to the modulating signal of frequency
`tum. Thus, each component of frequency mm in the modulating signal gets translated
`into two components, of frequencies to, + (um and w, — com, in the modulated signal.
`Note that the modulated signal m(t) cos (0,1, as seen from the above equation, has
`
`
`
`demodulation, or detection. Observe that if the modulated carrier spectrur
`is shifted again by i cut, we get back the desired baseband spectrum plus
`spectrum at i2wc, which can be suppressed by a lowpass filter (Fig. 4.1e)
`that in order to demodulate, we should multiply the incoming modulati
`cos (act and pass the product through a lowpass filter (Fig. 4.161). This C(
`be directly verified from the identity
`(m(t) cos wct) (cos wot) = £[m(t) + m(t) cos 2am]
`
`and
`
`(m (t) cos wct) (cos on) <—> mm) + ,1.[M(w + 2w.) + M(w — 2(
`It can be seen from Fig. 4.1e that a lowpass filter allows the des
`M(w) to pass and suppresses the unwanted high-frequency spectrum cent
`A possible form of lowpass—filter characteristics is shown (dotted)
`The demodulator is shown in Fig. 4. id. It is interesting to observe that
`the receiver is similar to that required at the transmitter. This method
`the baseband signal is called synchronous detection, or coherent detect
`Thus, for demodulation, we need to generate a local carrier at the rt
`chronism with the carrier that was used at the modulator.
`The relationship of B to w,
`is of interest. From Fig. 4.1 it
`a)C Z 27rB in order
`to avoid the overlap of M(w + wc) and 1‘
`wC < 2718, the information of m(t) is lost in the process of modul
`impossible to retrieve m(t) from the modulated signal m(t) cos am.
`therefore, the only requirement is that w. Z 2773. The practical fat
`impose additional restrictions. A radiating antenna can radiate only
`without distortion. This means that to avoid distortion caused by the ran
`(06/27rB > 1. The broadcast band AM radio uses is the band 550 kl
`or a ratio of coy/2778 roughly in the range of 100 to 300.
`
`I EXAMPLE 4.1
`
`Assuming DSB—SC modulation, sketch the modulated waveforms.
`The DSB-SC waveform for the Signal in Fig. 4.20 is shown it
`signal in Fig. 4.2c is a digital signal (polar signaling). The modula
`shown in Fig. 4.2d. The modulated signal is also polar. This is a I
`Sec. 3.9). This example is given here to stress that modulation is
`analog as well as digital signals. I
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 6
`
`

`

`
`
`the Signal E (t) cos wct (provided* E (t) > 0 for all t)
`(4.9b) is A + m(t) (provided A + m(t) > 0 for all 0’. Th
`Fig. 4.10. If A is large enough to make A + m(t) positiv
`m(t) from (pAM(t) simply reduces to envelope detection.
`The condition for demodulation by an envelope deter
`
`A + m(t) > 0
`
`for allt
`
`This is the same as
`
`A Z —m(t)min
`
`m(t)
`
`(a)
`
`A+m(t)>0
`
`forallt
`
`
`
`A + m(t)
`
`
`Envelope
`
`(d)
`
`Figure 4.10 AM signal and its envelope.
`
`*E(t) must also be a slowly varying signal as compared to cos
`
`or coherent (also homodyne) demodulators.*
`
`I EXAMPLE 4.3
`
`Analyze the switch
`demodulator.
`The input signal is m (t) cos
`off of the input signal. The out
`
`is used as a synchronous
`ing modulator in Fig. 4.6a when it
`cart. The carrier causes the periodic switching on and
`put is m(t) cos (of! k(t).
`1
`2
`
`m(t) cos wctk(t) = m(t) cos wct[§ + Fr (cos wet - —15 cos 3am + -
`
`I
`
`~ >]
`
`17
`
`.
`.
`7mm + other terms centered at (of, 2a)” .
`When this signal is passed through a lowpass filter, the output is the desired signal
`
`(1/7r)m(t). I
`
`phase for synchronous
`
`bstantial complexity in
`
`4.3 AMPLITUDE MODULATION (AM)
`Generally speaking, suppressed-carrier systems need sophisticated circuitry at the
`receiver for the purpose of generating a local carrier of exactly the right frequency and
`'
`‘ ems are very efficient from the
`point of view of power require
`'
`. ln point—to—point commu—
`nications, where there is one transmit
`the receiver system can be justified, provided it results in a large enough saving in
`expensive high-power transmitting equipment. On the other hand, for a broadcast
`system with a multitude ofreceivers for each transmitter, it is more economical to have
`one expensive high-power transmitter and simpler, less expensive receivers.
`applications, a large carrier signal is transmitted along with the suppressed—carrier—
`modulated signal m(t) cos (aft, thus eliminating the need to generate a local carrier
`signal at the receiver. This is the so-called AM (amplitude modulation), in which the
`transmitted signal cpAMU) is given by
`) = m(t) cos wct + A cos wyt
`
`‘PAM (f
`
`(4.9a)
`
`(4.9b)
`
`= [A + m(t)] cos cop!
`
`I...
`
`same thing. The term homodyne is used
`t, and homodyne mean the is used for the purpose of translating the
`* The terms synchronous, coheren
`to contrast with heterodyne, where a different carrier frequency
`spectrum (see Example 4.2).
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 7
`
`

`

`
`
`3d through a lowpass filter. Therefore, all four types of
`ier can also be used as demodulators, provided the bandpass
`placed by lowpass filters of bandwidth B.
`e receiver must generate a carrier in phase and frequency
`3ming carrier. These demodulators are called synchronous,
`
`iodulator in Fig. 4.6a when it
`
`is used as a synchronous
`
`(t) cos (art. The carrier causes the periodic switching on and
`he output is m(t) cos (pct k(t).
`
`1
`1(1) cos wct — + — cos wot — — cos 3wct + -
`3
`
`-
`
`-
`
`m(t) + other terms centered at (of, 2mm .
`
`.
`
`.
`
`:d through a lowpass filter, the output is the desired signal
`
`aressed—carrier systems need sophisticated circuitry at the
`f generating a local carrier of exactly the right frequency and
`emodulation. But such systems are very efficient from the
`requirements at the transmitter. In point-to—point commu-
`one transmitter for each receiver, substantial complexity in
`)e justified, provided it results in a large enough saving in
`insmitting equipment. On the other hand, for a broadcast
`f receivers for each transmitter, it is more economical to have
`r transmitter and simpler, less expensive receivers. For such
`'ier signal is transmitted along with the suppressed-carrier-
`)s (0,1, thus eliminating the need to generate a local carrier
`is is the so-called AM (amplitude modulation), in which the
`
`(4.9a)
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 8
`4.3 AMPLITUDE MODULATION (AM)
`235
`
`The spectrum of (pm/1(1) is the same as that of m(t) cos cert plus two additional impulses
`at ta),
`(MN) (—> %[M(w + (06) + M(w — w..)] + wA[5(w + w.) + 15(0) - an]
`
`(4.9c)
`
`The modulated signal tpAM(t) is shown in Fig. 4.10d. Because E (t) is the envelope ‘of
`the signal E (t) cos (0,1 (provided* E(t) > 0 for all t), theenvelope of tpwtt) in hq.
`(4.9b) is A + m(t) (provided A + m(t) > 0 for all t). This fact is also evrdent from
`Fig. 4.10. If A is large enough to make A + m(t) positive for all t, the recovery of
`m(t) from (pAM(I) simply reduces to envelope detection.
`The condition for demodulation by an envelope detector is
`A + m(t) > 0
`for all t
`This is the same as
`A 2 we)...
`
`(4.103)
`
`<4-10b>
`
`m(t)
`
`l—>
`
`(a)
`
`A+m(t)>0
`
`for all!
`
`
`
`
`
`
`Envelope
`
`A + m(t)
`
`Envelope
`
`M + m(t)|
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 8
`
`

`

`
`
` Lowpass
`
`[A + mm] cos wct 0
`mm
`
`
`Figure 4.13 Rectifier detector for AM.
`
`It is interesting to note that rectifier detection is in effect synchronous detectiori
`performed without using a local carrier. The high carrier content In the received s1gna
`makes this possible.
`
`In an envelope detector, the output of the detector follows the
`Envelope Detector.
`envelope of the modulated signal. The circuit shown in Fig. 4.14 functions as an
`
`[A + m(t)] cos wc’
`
`
`
`
`e
`
`Figure 4.14 Envelope detector for AM.
`
`envelope detector. On the positive cycle of the input signal, the capacrtor Chcharge:
`up to the peak voltage of the input signal. As the Input Signal. falls below t 1113 peak
`value, the diode is cut off, because the capacitor voltagev(wh1ch IS very nearly t e pg:
`voltage) is greater than the input signal voltage, thus causmg the'diode to open. in]:
`capacitor now discharges through the resistor R at a slow rate. During the nexthpocsi‘ 1d
`cycle, when the input signal becomes greater than the capac1tor voltage, t
`ei
`1¥he
`conducts again. The capacitor again charges to the peak value of th1s (new) cyc e.
`
`
`
`positive peaks (RC > 1 / to.) Making RC too large, howe\
`sible for the capacitor voltage to follow the envelope (see Fi‘
`be large compared to 1 /w(. but should be small compared 1
`highest frequency in m(t) (see Example 4.6). This,
`a), > 2778, a condition that is necessary for a well-define
`The envelope—detector output is A + m(t) with a ripplt
`term A can be blocked out by a capacitor or a simple RC 1
`may be reduced further by another (lowpass) RC filter.
`
`I EXAMPLE 4.6
`
`For tone modulation (Example 4.4), determine the upper l
`the capacitor voltage follows the envelope.
`
`Cl Solution: Figure 4.15 shows the envelope and the vol
`
`
`
`Capacitor voltage
`(RC discharge)
`E(l — 1/ RC)
`
`
`
`
`Envelope
`
`I——>
`
`Figure 4.15
`
`The capacitor discharges from the peak value E at some art
`voltage of across the capacitor is given by
`
`115 = Ee"/RC
`
`Because the time constant is much larger than the interval be
`cycles of the carrier (RC > 1 / (up), the capacitor voltage DC
`for a short time compared to its time constant. Hence, the e)
`imated by a straight line obtained from the first two terms in T
`
`DC —E<1
`
`t
`
`RE)
`
`The slope of the discharge is —E /RC . In order for the capaci
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 9
`
`

`

`{/,p++mun
`%M+mm]
`
`
`im+mm
`7T
`
`
`
`
`
`that rectifier detection is in effect synchronous detection
`)cal carrier. The high carrier content in the received signal
`
`envelope detector, the output of the detector follows the '
`signal. The circuit shown in Fig. 4.14 functions as an
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 10
`
`4.3 AMPLITUDE MODULATION (AM)
`
`241
`
`thus changing the capacitor
`
`capacitor discharges slowly during the cutoff period,
`voltage very slightly.
`During each positive cycle, the capacitor charges up to the peak voltage of the
`input signal and then decays slowly until the next positive cycle. The output voltage
`thus follows the envelope of the input. A ripple signal of frequency (1),, however, is
`caused by capacitor discharge between positive peaks. This ripple is reduced by
`increasing the time constant RC so that the capacitor discharges very little between the
`positive peaks (RC > 1/ (0,). Making RC too large, however, would make it impos-
`sible for the capacitor voltage to follow the envelope (see Fig. 4.14). Thus, RC should
`be large compared to 1/ we but should be small compared to 1/27TB, where B is the
`highest frequency in m(t) (see Example 4.6). This, incidentally, also requires that
`(0,. > 2773, a condition that is necessary for a well-defined envelope.
`The envelope—detector output is A + m(t) with a ripple of frequency w... The dc
`term A can be blocked out by a capacitor or a simple RC highpass filter. The ripple
`may be reduced further by another (lowpass) RC filter.
`
`I EXAMPLE 4.6
`
`For tone modulation (Example 4.4), determine the upper limit on RC to ensure that
`the capacitor voltage follows the envelope.
`
`[:1 Solution: Figure 4.15 shows the envelope and the voltage across the capacitor.
`
`Capacitor voltage
`(RC discharge)
`
`E(l — NRC)
`
`
`
`
`Envelope
`/
`
`I—>
`
`Figure 4.15
`
`The capacitor discharges from the peak value E at some arbitrary instant I = 0. The
`voltage 05 across the capacitor is given by
`
`CC = E€_!/RC
`
`Because the time constant is much larger than the interval between the two successive
`cycles of the carrier (RC > l/ w), the capacitor voltage 0C discharges exponentially
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 10
`
`

`

`
`
`Figure 4.29
`
`Linearity of Amplitude Modulation
`
`In all the types of modulation discussed thus far, the modulated signal (excluding the
`carrier term) satisfies the principles of superposition. For example,
`if modulating
`signals m1(t) and m2(t) produce modulated signals* (pl(t) and (p20), respectively, then
`the modulating signal klm1(t) + k2m2(t) produces the modulated signal k1 (p10) +
`k2<p2(r). The reader can verify linearity for all types of amplitude modulation (DSB,
`SSB, AM, and VSB). This property is valuable in analysis. Because any signal can
`be expressed as a sum (discrete or in continuum) of sinusoids, the complete description
`of the modulation system can be expressed in terms of tone modulation. For example,
`if m(t) = cos wmt (tone modulation), the DSB—SC signal is
`
`cos wmt cos (0.! = %[COS (wi- — 60m)t + COS (w, + (”mm
`
`This shows that DSB—SC translates a frequency com to two frequencies, wt. — cum (LSB)
`and w(. + wm (USB). We can generalize this result to any nonsinusoidal modulating
`signal m(t). This is precisely the result obtained earlier by using a more general
`analysis.
`
`4.7 DIGITAL CARRIER SYSTEMS
`
`As seen earlier, digital signals can be modulated by several schemes such as ASK,
`PSK, FSK, etc. Demodulation of digital—modulated signals is similar to that of
`analog-modulated signals. For example, ASK (see Fig. 3.50) can be demodulated
`coherently (synchronous) or noncoherently (envelope detection). The noncoherent
`scheme performance is close to the performance of the coherent scheme when the
`noise is small. The difference in the two schemes is pronounced when the noise is
`large. This behavior is similar to that observed in analog signals.
`In PSK, a 1 is transmitted by a pulse A cos wrt and a 0 is transmitted by a pulse
`—A cos wft (see Fig. 4.2d). The information in PSK signals therefore resides in the
`carrier phase. These signals cannot be demodulated noncoherently (envelope de-
`tection) because the envelope is the same for both 1 and 0. The coherent detection is
`similar to that used for analog signals. Methods of carrier synchronization are also the
`same as those used for analog signals. A small pilot can be transmitted along with the
`
`*Note that we are excluding the carrier term from <p.(t) and (pm). In short, superposition applies to
`the suppressed—carrier portion only. For more discussion, see Van Trees.5
`
`
`
`In this case, a 1 is encoded by the same pulse used to
`.
`b1t (no trans1tlon) and a 0 is encoded by the negative of the
`prev10us data bit (transition). This is shown in Fig. 4.3061
`
`Datal.101100011
`Encoded
`baseband
`
`signal
`
`(a)
`
` Lowpass
`
`Figure 4.30
`
`(a) Differential coding. (b) Differential PSK receiver
`
`received pulse sequence indicates 0 and no transition indi
`absolute signs of the received pulses are not important for det
`IS the change in signs of successive pulses. These sign Chang
`even if the demodulating carrier has a sign ambiguity.
`Differential coding also facilitates noncoherent detectior
`known as difi‘erential PSK or DPSK (Fig. 4.301)), we avc
`carrier by observing that the received modulated signal itself
`w1th.a possible sign ambiguity. For demodulation, in place «
`received signal delayed by To (one bit interval). If the receive
`prev1ous pulse, the product y(t) = A2 cos2 cart, and the lov~
`A2/2. If the received pulse is of opposite sign, y(t) = —
`—A2/2. In differential coding,
`two pulses of the same pc
`trans1tion) indicates a 1 and two pulses of opposite polarity
`indicates a 0. Hence, the positive value of z(t) is immediate]
`negative z(t) is detected as a 0.
`
`*Precoding discussed in connection with duobinary is actually diff
`transmitted by no transition and a 1 is transmitted by a transition.
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 11
`
`

`

`
`
`
`
`Petition’é’r’s’i'rius' XMRadio Inc. - EX. 1012, p. 12
`
`4.7 DIGITAL CARRIER SYSTEMS
`
`267
`
`modulated signal. In the absence of a pilot, one of the self-synchronization methods
`such as the Costas loop or the signal squaring technique discussed in Sec. 4.5 can be
`used. Because these techniques yield a carrier with sign ambiguity (or phase ambiguity
`of 77),
`they cannot be used directly to demodulate PSK. This is because a sign
`ambiguity in the demodulating carrier can detect a negative pulse as a positive pulse
`(detect 0 as 1) and vice versa. This problem can be solved by encoding the data by
`difi‘erential code before modulation.
`In this case, a 1 is encoded by the same pulse used to encode the previous data
`bit (no transition) and a 0 is encoded by the negative of the pulse used to encode the
`previous data bit (transition). This is shown in Fig. 4.30:1. Thus a transition in the
`
`Datall01100011
`
`Encoded
`baseband
`
`signal
`
`(a)
`
`I»
`
` iA cos “’c’
`
`Lowpass
`filter
`
`Figure 4.30
`
`(a) Differential coding. (b) Differential PSK receiver.
`
`('3)
`
`the
`received pulse sequence indicates 0 and no transition indicates 1.* Therefore,
`absolute signs of the received pulses are not important for detection. What is important
`is the change in signs of successive pulses. These sign changes are correctly detected
`even if the demodulating carrier has a sign ambiguity.
`Differential coding also facilitates noncoherent detection of PSK. In this scheme,
`known as differential PSK or DPSK (Fig. 4.3019), we avoid generation of a local
`carrier by observing that the received modulated signal itself is a carrier (:A cos cart)
`with a possible sign ambiguity. For demodulation, in place of the carrier, we use the
`received signal delayed by T0 (one bit interval). If the received pulse is identical to the
`previous pulse, the product y(t) = A2 cos2 (opt, and the lowpass filter output 2(1‘) =
`A2/2. If the received pulse is of opposite sign, y(t) = —A2 cos2 wit and z(t) =
`
`1 discussed thus far, the modulated signal (excluding the
`'inciples of superposition. For example,
`if modulating
`ce modulated signals* cp.(t) and (p20), respectively, then
`:t) + k2m2(t) produces the modulated signal klrp1(t) +
`"y linearity for all types of amplitude modulation (DSB,
`property is valuable in analysis. Because any signal can
`te or in continuum) of sinusoids, the complete description
`I be expressed in terms of tone modulation. For example,
`iulation), the DSB—SC signal is
`
`5 (wt — wm)t + cos (coy + w,,,)t]
`
`tslates a frequency a)". to two frequencies, wt — (um (LSB)
`n generalize this result to any nonsinusoidal modulating
`:ly the result obtained earlier by using a more general
`
`als can be modulated by several schemes such as ASK,
`ition of digital-modulated signals is similar to that of
`For example, ASK (see Fig. 3.50) can be demodulated
`Ir noncoherently (envelope detection). The noncoherent
`ie to the performance of the coherent scheme when the
`ice in the two schemes is pronounced when the noise is
`Iar to that observed in analog signals.
`ed by a pulse A cos w(.t and a 0 is transmitted by a pulse
`. The information in PSK signals therefore resides in the
`
`Petitioner Sirius XM Radio Inc. - Ex. 1012, p. 12
`
`

`

`Convolutional (or recurrent) codes, first introduced by Elias in-1955,3 d1ffer frolm
`- block codes as follows. In a block code, the block of n code d1g1ts generated by t. e
`encoder in any particular time unit depends only on the block of k 1nput data 1g:jts
`within that time unit. In a convolutional code, on the other hand, the block of n (:0 1:
`digits generated by the encoder in a particular time unit depends not only. on the-111.00
`of k message digits within that time unit but also on the block of data d1g1ts vylit
`in a
`previous span of N — 1 time units (N > 1). For convolutional codes,.k an
`r}: are:
`usually small. Convolutional codes can be devised for correctmg random errors, urs
`errors, or both. Encoding is easily implemented by shift reglsters. As a class, con-
`volutional codes invariably outperform block codes of the same order of compleitity.
`A convolutional coder with constraint length N cons1sts of an N-stage sh1ft_reglster
`and v modulo-2 adders. Figure 9.5 shows such a coder for the case of N — 3 and
`
`
`
`Coded—sequence output
`
`way, when the third message digit 0 enters the register, we have s1 = 0, s2 — , an
`
`Figure 9.5 A convolutional coder.
`
`= 2. The message digits are applied at the input of the shift register. The coded dlgiyt
`stream is obtained at the commutator output. Thecommutator samples the v modu o—
`adders in sequence, once during each input—bit mterval. We shall explain thlS oper-
`ation with reference to the input digits 11010. In1t1ally, all the stages of the reglster
`are clear; that is, they are in a 0 state. When the first data d1g1t 1 enters the reglsltler,
`the stage sl shows 1 and all the other stages (s2 and 53) are unchanged, that 1s, t ey
`are in a 0 state. The two modulo-2 adders show vi = 1 and 02 = 1. The commugatoi
`samples this output. Hence the coder output is 11.'Whenl the second messagPeI
`it
`enters the register, it enters the stage 51, and the previous 1 in s] is shifted to s2. dellicez,
`s1 and s2 both show 1, and 53 is still unchanged; that 1s, 1t is in a 0 state. The mo u o-
`adders now show 01 = 0 and v; = 1. Hence, the decoder output is 01. In flielsamg
`
`register in order to influence the N groups of 0 digits. Hence
`are 11010, we actually apply 11010000 (the digits augmented
`of the shift register. It can be seen that when the last digit of ‘
`stream enters s], the last digit of the message stream has passed
`of the register, and the register is in clear state. The reader c
`output is given by 11
`01
`01
`00
`10
`(N + k)v digits in the coded output for every k data digits. Ir
`hence, there are approximately kv coded output digits for eve
`an efficiency'l' 77 = l /0.
`It can be seen that unlike the block coder, the convolutio
`continuous basis, and each data digit influences N groups of
`
`The Code Tree
`
`Coding and decoding is considerably facilitated by what is k]
`which shows the coded output for any possible sequence of da
`for the coder in Fig. 9.5 with k = 5 is shown in Fig. 9.6. W
`the coder output is 00, and when it