Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 1
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 1
`
`

`

`Copyright © 1989, 1983 by B. P. Lathi
`All rights reserved. No part of this publication may be
`Teproducedortransmitted in any form or by any means,
`electronic or mechanical, including photocopy, recording,
`or any information Storage andretrieval System, without
`permission in writing from the publisher.
`
`Request for permission to makecopiesofany 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/B.P. Lathi,—
`_ 2nd ed.
`p.
`cm. — (HRWseriesin electrical engineering)
`Includes bibliographies and index.
`ISBN 0-03-027933-X
`1. Telecommunication Systems.
`3. Statistical communication theory.
`621.38'0413—dce19
`
`2. Digital communications.
`I. Title.
`II. Series.
`88-25151
`CIP
`
`The Dryden Press
`Saunders College Publishing
`Printed in the United States of America
`012
`016
`9876543
`ISBN O-03-027933-x
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 2
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 2
`
`

`

`if the noise is zero,
`is that
`is beside the point. The point
`that
`be practical, but
`communication ceases to be a problem, at least theoretically. Implementation of such
`a scheme would be difficult because of the requirement ofgeneration 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
`SNRin 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 betweenthese 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 Shannonrate. In Chapter 8, we shall derive Shannon’s result
`and comparethe efficiencies of various communication systems.
`
`1.4 MODULATION
`
`Basebandsignals produced byvarious 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 basebandsignalis 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/().
`Accordingly, we have amplitude modulation (AM), frequency modulation (FM), or
`phase modulation (PM). Figure 1.7 shows a baseband signal m(r) and the correspond-
`ing AM and FM waveforms. In AM, the carrier amplitude varies in proportion to m(t),
`and in FM, the carrier frequency varies in proportion to m(f).
`At the receiver, the modulated signal must pass through a reverse process called
`demodulation in order to retrieve the basebandsignal.
`As mentioned earlier, modulation is used to facilitate transmission. Some of the
`important reasons for modulation are given below.
`
`Ease of Radiation
`
`Forefficient 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 wavelengthsare too large for reasonable antenna dimensions.
`For example, the powerin a speech signal is concentrated at frequenciesin 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
`
`
`
`Carrier
`
`m(t)
`
`
`
`Modulating (baseband) signal
`
`Amplitude-modulated wave
`
`
`
`Frequency-modulated wave
`
`Figure 1.7 Modulation.
`
`carrier frequencies that corresponds to a much smaller wavel
`1 MHzcarrier has a wavelength of only 300 meters and require:
`is of the order of 30 meters. In this aspect, modulation islik
`signal hitchhike on a high-frequency sinusoid (carrier). The cz
`signal may be comparedto a stone anda piece of paper. If we
`of paper, it cannot gotoo far by itself. But by wrapping it aro
`it can be thrown overa 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 ofall the signals occupy more orless the same bandw
`possible to broadcast from only one radio or TV station at a
`because the channel bandwidth may be muchlarger than that
`
`Petitioner Sirius XM RadioInc. - Ex. 1022, p. 3
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 3
`
`

`

`the contents of this book will be
`age. For example,
`-ed to transmit this book, all that is neededis to transmit
`e an infinite numberoflevels 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
`scause of the requirementof generation and detection of
`Suchpractical 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
`1 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 sourcesare not alwayssuitable for
`iven channel. These signals are usually further modified
`his conversion process is known as modulation. In this
`1 is used to modify some parameterof a high-frequency
`
`of high frequency, and oneofits parameters—such as
`ase—is varied in proportion to the baseband signal m(f).
`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(t),
`lency 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
`lation are given below.
`
`sctromagnetic energy, the radiating antenna should be of
`iore of the wavelength of the signal radiated. For many
`
`©
`
`1.4 MODULATION 13
`
`
`
`Carrier
`
`mt)
`
`Modulating (baseband) signal
`
`Amplitude-modulated wave
`
`
`
`Frequency-modulated wave
`Figure 1.7 Modulation.
`carrier frequencies that corresponds to a much smaller wavelength. For example, a
`1 MHzcarrier has a wavelength ofonly 300 meters and requires an antenna whosesize
`like letting the baseband
`is of the order of 30 meters. In this aspect, modulation is
`signal hitchhike on a high-frequency sinusoid (carrier). The carrier and the baseband
`signal may be comparedto a stone and a piece of paper. if we Wi
`i
`of paper,it cannot go too far by itself. But by wrapping it around a stone (a carrier),
`it can be thrown over a longer distance.
`
`ish to throw a piece
`
`Simultaneous Transmission of Several Signals
`Consider the case of several radio stations broadcasting audio baseband signals di-
`rectly, without any modification. They would interfere with each other because the
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 4
`
`

`

`ond, the baseband is 0 to f, Hz.
`
`mplitude
`Aodulation
`
`
`
`that causes a shift of the range of frequenciesin a signal. It
`idvantages, as mentioned in Chapter |. Before discussing
`int to distinguish between communication that does not use
`mmunication) and communication that uses modulation (car-
`
`CARRIER COMMUNICATION
`
`d to designate the bandoffrequencies ofthe signal delivered
`
`4.1 BASEBAND AND CARRIER COMMUNICATION=223
`
`
`
`—E_
`
`
`
`ulation
`
`In baseband communication, baseband signals are transmitted without modu-
`lation, that is, without any shift in the range of frequencies ofthe signal. Because the
`basebandsignals have sizable power at low frequencies, they cannot be transmitted
`over a radio link but are suitable for transmission overa pair of wires or coaxial cables.
`Local telephone communication and short-haul PCM (between two exchanges) use
`baseband communication. Because baseband communication uses only basebandfre-
`quencies, its uses are ratherrestricted. Also, because the transmission of signals at
`lower frequenciesis in general moredifficult, it is desirable to shift the signal spectrum
`to a higher-frequency range by modulation. Moreover,
`the vast spectrum of fre-
`quenciesavailable because of technological advances cannotbeutilized by a baseband
`scheme. By modulating several baseband signals and shifting their spectra to non-
`overlapping bands, one canuseall the available bandwidth moreefficiently. 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.
`Communication that uses modulation to shift the frequency spectrum ofa 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 «, is varied
`in proportion to the basebandsignal 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 schemesare really
`baseband coding schemes, and they yield baseband signals. These signals muststill
`modulate a carrier in order to shift their spectra.
`
`4.2 AMPLITUDE MODULATION: DOUBLE SIDEBAND (DSB)
`carrier
`In
`amplitude modulation,
`the
`amplitude A, of
`the
`unmodulated
`A, cos (w,t + 6.) is varied in proportion to the baseband signal (knownas the modu-
`lating signal). The frequency w, and the phase 6, are constant. We can assume 6, = 0
`without a loss of generality. If the carrier amplitude A, is madedirectly proportional
`to the modulating signal m/(r), the modulated carrier is m(t) cos wt (Fig. 4.1c). As
`seen earlier [Eq. (2.63a)], this type of modulation simply shifts the spectrum of m(t)
`to the carrier frequency (Fig. 4.1c); that is, if
`m(t) @ M(w)
`
`(4.1)
`m(t) cos wt 2 4[M(w + w) + M(w — @,)]
`The bandwidth of the modulated signal is 2B Hz, which is twice the bandwidth ofthe
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 5
`
`

`

`and —w,), as seen from Eq. (4.1). To recover the original signal m'
`modulated signals, it is necessary to retranslate the spectrum to its origi!
`The process of retranslating the spectrum to its original position is re
`demodulation, or detection. Observethatif the modulated carrier spectrur
`is shifted again by +a, we get back the desired basebandspectrum plus
`spectrum at +2, which can be suppressedby a lowpassfilter (Fig. 4. le)
`that in order to demodulate, we should multiply the incoming modulat
`cos wf and pass the product through a lowpassfilter (Fig. 4.1d). This cc
`be directly verified from the identity
`(m(f) COS Wel) (COs wt) = s[m(t) + m(t) cos 2w.t|
`
`and
`
`(m(t) Cos Wet) (COS Wet) 1M(w) + 4[M(@ + 20.) + M(@ — 2
`It can be seen from Fig. 4.le that a lowpass filter allows the des
`M(w) to pass and suppresses the unwanted high-frequency spectrum cen!
`A possible form of lowpass-filter characteristics is shown (dotted)
`The demodulator is shown in Fig. 4.1d. It is interesting to observe that
`the receiver is similar to that required at the transmitter. This method
`the basebandsignalis called synchronous detection, or coherent detect
`use a carrier of exactly the same frequency (and phase) as was used fe
`Thus, for demodulation, we need to generate a local carrier at the re
`chronism with the carrier that was used at the modulator.
`The relationship of B to is of interest. From Fig. 4.1 iti
`wo, 2 27B in order
`to avoid the overlap of M(w + w,) and |
`@,. < 27B, the information of m(t) is lost in the process of modul
`impossible to retrieve m(t) from the modulated signal m(f) cos at.
`therefore, the only requirement is that w, = 27B. The practical fac
`impose additional restrictions. A radiating antenna can radiate only
`without distortion. This means that to avoid distortion caused bythe rai
`w,/27B > i. The broadcast band AM radio uses is the band 550 kk
`or a ratio of w,/2mB roughly in the range of 100 to 300.
`
`@ EXAMPLE 4.1
`Baseband signals shown in Fig. 4.2a and c modulate a carrier ¢
`Assuming DSB-SC modulation, sketch the modulated waveforms.
`The DSB-SC waveform for the signal in Fig. 4.2a 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 RadioInc. - Ex. 1022,
`
`COs wt
`
`(d)
`
`
`
`Figure 4.1. DSB-SC modulation.
`
`bands. For instance, if m(t) = COS nf, then the modulated signal
`m(t) COS @.f = COS Wmt COS Wel
`= bfeos (@. + Wm)t + COS (W. — Wm)t|
`The component of frequency w, + @,is the upper sideband, and that of frequency
`W, — W,» is the lower sideband, corresponding to the modulating signal of frequency
`Wm Thus, each component of frequency mn in the modulating signal gets translated
`into two components, of frequencies @,. + mn and w, — @,, in the modulated signal.
`
`COS wl
`(a)
`
`|M(w)|
`
`m(t)
`
`m(t) COs wt
`
`Note that the modulated signal m(1) cos wt, as seen from the above equation, has
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 6
`
`

`

`filters at the output are replaced by lowpass filters of bandwidth B.
`For demodulation, the receiver must generate a carrier in phase and frequency
`synchronism with the incoming carrier. These demodulators are called synchronous,
`or coherent (also homodyne) demodulators.*
`
`@ EXAMPLE4.3
`
`is used as a synchronous
`Analyze the switching modulator in Fig. 4.6a when it
`The input signal is m(Z) cos a1. The carrier causes the periodic switching on and
`demodulator.
`off of the input signal. The output is m(Z) COS Wet k(t).
`m(t) cos w,tk(t) = m(t) cos of + 7 (cos wt — 50s 3w.t t-° |
`1
`2
`‘
`m(t) + other terms centered at @., 2@.
`-
`+
`+
`al-
`Whenthis signalis passed through a lowpass filter, the output is the desired signal
`
`(A/mm). a
`
`4.3. AMPLITUDE MODULATION(AM)
`Generally speaking, suppressed-carrier systems need sophisticated circuitry at the
`receiverforthe purpose of generating a local carrier ofexactly theright frequency and
`phase for synchronous demodulation. But such systems are very efficient from the
`point of view of power requirements at the transmitter. In point-to-point commu-
`nications, where there is one transmitter for each receiver, substantial complexity in
`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
`systemwithamultitudeofreceivers foreachtransmitter, itis more economicaltohave
`one expensive high-power transmitter and simpler, less expensive receivers. For such
`applications, a large carrier signal is transmitted along with the suppressed-carrier-
`modulated signal m(f) COS @el, 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 @am(t) 1S given by
`@am(t) = mt) cos w,t + A cos wt
`(4.9a)
`Ml [A + m(1)J cos wt
`(4.9b)
`
`—_————_—
`
`*The terms synchronous, coherent, and homodyne mean the same thing. The term homodyneis used
`to contrast with heterodyne, where a different carrier frequency is used for the purpose oftranslating the
`spectrum (see Example 4.2).
`
`
`
`The modulated signal gam(t) is shown in Fig. 4.10d. Beca
`the signal E(t) cos wt (provided* E(t) > 0 for all #),
`(4.9b) is A + m(f) (provided A + m(t) > 0 forall t). Th
`Fig. 4.10. If A is large enough to make A + m(t) positiv
`m(t) from @am(t) simply reduces to envelope detection.
`The condition for demodulation by an envelope detec
`At+m(t) >90
`for all ¢
`This is the same as
`A = —mM(Dmin
`
`m(t)
`
`(a)
`
`A+ m(t)>0
`
`At m(t) $0
`
` The spectrum of gam(t) is the same as that of m(1) cos w,t pl
`
`for all ¢
`A+ m(t)
`
`
`Envelope
`
`Figure 4.10
`
`(d)
`AMsignalandits envelope.
`
`* E(t) must also be a slowly varying signal as compared to cos
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022,
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 7
`
`

`

`2d through a lowpass filter. Therefore, all four types of
`ier can also be used as demodulators, provided the bandpass
`placed by lowpassfilters of bandwidth B.
`e receiver must generate a carrier in phase and frequency
`oming carrier. These demodulators are called synchronous,
`me) demodulators.*
`
`iodulator in Fig. 4.6a when it
`
`is used as a synchronous
`
`‘t) cos w,t. The carrier causesthe periodic switching on and
`he output is m(t) cos w,t k(t).
`
`1
`2
`1
`1(t) cos wt] = + — [cos wt — > cos 3w,.t ++: +
`2 3
`
`m() + other terms centered at w,, 20... ..
`:d through a lowpassfilter, the output is the desired signal
`
`(ULATION (Ai)
`
`here a different carrier frequencyis used for the purpose oftranslating the
`
`(4.9a)
`(4.9b)
`
`
`
`y
`
`q
`
`4.3 AMPLITUDE MODULATION(AM)
`
`235
`
`The spectrum of Pam(“)is the same asthat of m(r) cos wt plus two additional impulses
`at +o,
`galt) © H[M(o + @) + Mw ~ 0] + rALB(w + @) + Oo ~ 00]
`‘
`(4.9¢)
`The modulated signal gam(f)is shownin Fig. 4.10d. Because E(t) is the envelope of
`the signal E(t) cos wt (provided* E(t) > 0 for all t), the envelope of Pam(t) in Eq.
`(4.9b) is A + m(t) (provided A + m(t) > 0 for all t). This fact is also evident from
`Fig. 4.10. If A is large enough to make A + m(f) positive for all ft, the recovery of
`m(t) from gam() simply reduces to envelope detection.
`The condition for demodulation by an envelope detector is
`Atm(t)>0
`for all t
`This is the same as
`A = —M(Dmin
`
`(4.10a)
`
`(4.10b)
`
`m(t)
`
`(a)
`
`A+ m(t)>90
`
`for all 7
`
`A+ m(t) $0
`
`for all ¢
` Envelope
`|A + m(t)|
`
`A+ m(t)
`
`Envelope
`
`sressed-carrier systems need sophisticated circuitry at the
`f generatingalocalcarrier of exactly the right frequency and
`2modulation. 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
`de justified, provided it results in a large enough saving in
`ansmitting 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
`‘jer signal is transmitted along with the suppressed-carrier-
`9s wt, thus eliminating the need to generate a local carrier
`is is the so-called AM (amplitude modulation), in which the
`is given by
`»t + A COs wt
`| cos at
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 8
`
`

`

`[a + m(t)] cos w,t 4 m(t))44+ mo)
`
`thus follows the envelope of the input. A ripple signal of{
`caused by capacitor discharge between positive peaks.
`increasing the time constant RCso that the capacitor dischar
`positive peaks (RC > 1!/w,). Making RC too large, howev
`sible for the capacitor voltage to follow the envelope (see Fi
`be large compared to 1/«, but should be small compared|
`highest frequency in m/(r) (see Example 4.6). This, incid
`w, > 27B, a condition that is necessary for a well-define
`yt
`Tv
`The envelope-detector output is A + m/(t) with a rippk
`Lowpass
`” <<
`
`
`term A can be blocked out by a capacitor or a simple RC |
`filter
`[A + m(t)] cos wt()
`may be reduced further by another (lowpass) RCfilter.
`
`
`@ EXAMPLE 4.6
`
`For tone modulation (Example 4.4), determine the upper|
`the capacitor voltage follows the envelope.
` O Solution: Figure 4.15 shows the envelope and the vol
`
`Figure 4.13 Rectifier detector for AM.
`
`It is interesting to note that rectifier detection is in effect synchronous derection
`performed withoutusing a local carrier. The high carrier content in the received signal
`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 w,1
`
`Figure 4.14 Envelope detector for AM.
`
`envelope detector. On the positive cycle of the input signal, the capacitor Cohare’
`up to the peak voltage of the input signal. As the input signal falls below t is peat
`value, the diodeis cut off, because the capacitor voltage (which is very nearly the be
`voltage) is greater than the input signal voltage, thus causing thediode to open. a ©
`capacitor now discharges throughtheresistor R at a slow rate. During the nextPos ‘
`cycle, when the input signal becomes greater than the capacitor voltage, t . wore
`conducts again. The capacitor again charges to the peak value of this (new) cycle.
`
`
`
`The capacitor discharges slowly during the cutoff period,
`
`Capacitor voltage
`(RC discharge)
`E(1 — 1/ RC)
`
`
`
`
`Envelope
`
`Figure 4.15
`
`The capacitor discharges from the peak value E at some art
`voltage vc across the capacitor is given by
`ve = Ee /®C
`
`Becausethe time constantis muchlargerthantheinterval be
`cycles of the carrier (RC > 1/q,), the capacitor voltage v¢
`for a short time comparedto its time constant. Hence, the e»
`imated bya straight line obtained from thefirst two termsin ”
`
`te =E(1 4
`
`Theslope of the discharge is -E/RC. In orderfor the capaci
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 9
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 9
`
`

`

`Le + mio]
`
`4A + me]
`
`tor again chargesto the peakvalueof this (new) cycle. The
`
`Lowpass
`filter
`
`
`
`
`- for AM.
`
`that rectifier detection is in effect synchronous detection
`deal 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
`
`)
`
`R
`
`r(t
`Vol
`
`or for AM.
`
`dositive cycle of the input signal, the capacitor C charges
`he inputsignal. As the inputsignal falls below this peak
`recausethe capacitor voltage (which is very nearly the peak
`
`
`
`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 w,, however, is
`caused by capacitor discharge between positive peaks. This ripple is reduced by
`increasing the time constant RC so that the capacitor discharges verylittle between the
`positive peaks (RC > 1/w,). 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/«, but should be small compared to 1/27B, where B is the
`highest frequency in m(t) (see Example 4.6). This, incidentally, also requires that
`w,. > 27B, 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 de
`term A can be blocked out by a capacitor or a simple RC highpass filter. The ripple
`may be reduced further by another (lowpass) RCfilter.
`
`Mi EXAMPLE 4.6
`
`For tone modulation (Example 4.4), determine the upper limit on RC to ensure that
`the capacitor voltage follows the envelope.
`
`
`
` Solution:
`
`Figure 4.15 shows the envelope and the voltage across the capacitor.
`
`Capacitor voltage
`(RC discharge)
`
`E(1 — t/ RC)
`
`
`
`
`Envelope
`a“
`
`
`Figure 4.15
`
`The capacitor discharges from the peak value E at somearbitrary instant t = 0. The
`voltage vc across the capacitor is given by
`vo = Ee t/RC
`
`Becausethe time constant is much larger thanthe interval between the two successive
`cycles of the carrier (RC > 1/w,), the capacitor voltage uc discharges exponentially
`_for a short time comparedtoits time constant. Hence, the exponential can be approx-
`imatedbya straight line obtained from thefirst two terms in Taylor’s series of Ee~'/*°.
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 10
`
`

`

`
`
`@, ~ 2000
`
`w, + 2000
`
`Figure 4.29
`
`Linearity of Amplitude Modulation
`In all the types of modulation discussed thusfar, the modulated signal (excluding the
`carrier term) satisfies the principles of superposition. For example,
`if modulating
`signals m,(t) and m,(¢) produce modulated signals* 9(f) and ¢,(t), respectively, then
`the modulating signal k,m,(t) + k,m,(1) produces the modulated signal A; ¢,() +
`ko,(t). 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 Wpt (tone modulation), the DSB-SC signal is
`COS Wl COS Wet = {COS (We — Wm)t + COS (@, + @,,)t]
`This shows that DSB-SCtranslates a frequency ,, to two frequencies, @ — Wn (LSB)
`and w. + w, (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.
`
`ambiguity in the demodulating carrier can detect a negative
`(detect 0 as 1) and vice versa. This problem can be solvec
`differential code before modulation.
`In this case, a 1 is encoded by the same pulse usedto
`bit (no transition) and a 0 is encoded by the negative of the
`previous data bit (transition). This is shownin Fig. 4.30a
`
`Data 110110002842
`Encoded
`baseband
`signal
`
`t—
`
`(a)
`
`
`+A cos w,t
`L owpass
`filter
`
`
`
` modulated signal. In the absenceofa pilot, one ofthe self
`
`Figure 4.30
`
`(a) Differential coding. (b) Differential PSK receiver
`
`(b)
`
`received pulse sequence indicates 0 and no transition indi
`4.7. DIGITAL CARRIER SYSTEMS
`absolute signsof the receivedpulses are not importantfor det
`As seenearlier, digital signals can be modulated by several schemes such as ASK,
`is the change in signs of successive pulses. These sign chan;
`PSK, FSK, etc. Demodulation of digital-modulated signals is similar to that of
`even if the demodulating carrier has a sign ambiguity.
`analog-modulated signals. For example, ASK (see Fig. 3.50) can be demodulated
`Differential coding also facilitates noncoherent detectior
`coherently (synchronous) or noncoherently (envelope detection). The noncoherent
`known as differential PSK or DPSK (Fig. 4.30b), we avec
`scheme performance is close to the performance of the coherent scheme when the
`carrier by observing that the received modulated signalitself
`noise is small. The difference in the two schemesis pronounced whenthe noise is
`with a possible sign ambiguity. For demodulation, in place '
`received signal delayed by T,(onebit interval). If the receive
`large. This behavior is similar to that observed in analog signals.
`In PSK, a1is transmitted by a pulse A cos w,f and a 0 is transmitted by a pulse
`previous pulse, the product y(t) = A* cos* w,t, and the low
`—A cos w,t (see Fig. 4.2d). The information in PSK signals therefore resides in the
`A*/2. If the received pulse is of opposite sign, y(t) = -
`—A*/2. In differential coding, two pulses of the same pc
`carrier phase. These signals cannot be demodulated noncoherently (envelope de-
`tection) because the envelope is the same for both 1 and 0. The coherentdetection is
`transition) indicates a 1 and twopulses of opposite polarity
`similar to that used for analog signals. Methods ofcarrier synchronization are also the
`indicates a 0. Hence, the positive value of z(t) is immediatel
`sameas those used for analog signals. A small pilot can be transmitted along with the
`negative z(t) is detected as a 0.
`
`In short, superposition applies to
`*Note that we are excluding the carrier term from ¢,() and ¢2(1).
`the suppressed-carrier portion only. For more discussion, see Van Trees.”
`
`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. 1022, p. 11
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 11
`
`

`

`
`
`
`
`4.7 DIGITAL CARRIER SYSTEMS
`
`267
`
`
`
`w, + 2000
`
`dulation
`
`1 discussed thus far, the modulated signal (excluding the
`‘inciples of superposition. For example,
`if modulating
`ce modulated signals* g(t) and ¢)(t), respectively, then
`‘t) + k)m,(t) produces the modulated signal k, g(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
`1 be expressed in terms of tone modulation. For example,
`julation), the DSB-SC signal is
`
`3 (W. — Wnt + COS (@ + On)t]
`islates a frequency w,, to two frequencies, @ — Wn (LSB)
`n generalize this result to any nonsinusoidal modulating
`ly the result obtained earlier by using a more general
`
`YSTEMS
`
`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
`xe to the performance of the coherent scheme when the
`ice in the two schemesis pronounced when the noiseis
`lar to that observed in analog signals.
`ed by a pulse A cos @,f and a 0 is transmitted by a pulse
`. The information in PSK signals therefore resides in the
`ls cannot be demodulated noncoherently (envelope de-
`ye is the same for both 1 and 0. The coherent detection is
`1g signals. Methods ofcarrier synchronization are also the
`
`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 yielda carrier with sign ambiguity (or phase ambiguity
`of a),
`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
`differential 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. 4.30a. Thus a transition in the
`
`Data 11011000411
`Encoded
`baseband
`signal
`
`i
`
`(a)
`
`
`XA cos wf
`Lowpass
`filter
`
`
`
`(b)
`
`Figure 4.30
`
`(a) Differential coding. (b) Differential PSK receiver.
`
`the
`received pulse sequence indicates 0 and no transition indicates 1.* Therefore,
`absolute signs of the received pulses are not important for detection. Whatis 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. 4.306), we avoid generation of a local
`carrier by observing that the received modulated signalitself is a carrier (+A cos @,t)
`with a possible sign ambiguity. For demodulation, in place of the carrier, we use the
`received signal delayed by 7, (one bit interval). If the received pulse is identical to the
`previous pulse, the product y(t) = A? cos? w,t, and the lowpass filter output z() =
`A’/2. If the received pulse is of opposite sign, y(‘) = —A’ cos? wt and z(‘) =
`—A’/2. In differential coding,
`two pulses of the same polarity in succession (no
`transition) indicates a 1 and two pulses of opposite polarity in succession (transition)
`indicates a 0. Hence, the positive value ofz(t) is immediately detected as a 1 and the
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 12
`
`

`

`9.6 CONVOLUTIONAL CODES
`
`Convolutional (or recurrent) codes, first introduced by Elias in 1955,” differ trom
`- block codes as follows. In a block code, the block of n code digits generated °y tk e
`encoder in any particular time unit depends only on the block of & input data its
`within that time unit. In