`
`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 pan 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 of any 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.—
`2nd ed.
`
`cm. — (HRW series in electrical engineering)
`p.
`Includes bibliographies and index.
`ISBN 0-03—027933—X
`1. Telecommunication systems.
`3. Statistical communication theory.
`621.38’0413—dcl9
`
`2. Digital communications.
`I. Title.
`II. Series.
`88-25151
`UP
`
`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 0-03-027‘333-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 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
`
`
`
`Carrier
`
`177(1)
`
`
`
`Modulating (baseband) signal
`
`Amplitude-modulated wave
`
`
`
`Frequency-modulated wave
`
`Figure 1.7 Modulation.
`
`carrier frequencies that corresponds to a much smaller wayel
`1 MHZ carrier has a wavelength of only 300 meters and requ1res
`is of the order of 30 meters. In this aspect, modulation is 1il<
`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 wrapping it 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 statlon at a
`because the channel bandwidth may be much larger than that
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 3
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 3
`
`

`

`the contents of this book will be
`age. For example.
`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(r).
`itude modulation (AM), frequency modulation (FM). or
`ure 1 .7 shows a baseband signal mt!) and the correspond
`In AM, the carrier amplitude varies in proportion to m (r).
`tency 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.
`
`:ctromagnetic energy, the radiating antenna should be of
`tore of the wavelength of the signal radiated. For many
`
`
`
`1.4 MODULATlON 13
`
`
`
`Carrier
`
`117(1)
`
`Modulating (baseband) signal
`
`Amplitude—modulated wave
`
`
`
`Frequency-modulated w ave
`
`Figure 1.7 Mod ulation.
`
`carrier frequencies that corresponds to a much smaller wavelength. For example, a
`1 MHz carrier has a wavelengt
`.
`'
`' es an antenna whose size
`'
`is of the order of 30 meters. In this aspect,
`l hitchhike on a high—frequency sinusoid (carrier
`signa
`signal may be compared to a stone and a piece of paper. If we w
`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.
`
`Simultaneous Transmission of Several Signals
`Consider the case of several radio stations broadcasting audio baseband signals di—
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 4
`
`

`

`
`
`WWQWWW“
`
`
`
`mplitude
`dodulation
`
`
`that causes a shift of the range of frequencies in a signal. It
`idvantages, as mentioned in Chapter 1. Before discussing
`mt to distinguish between communication that does not use
`mmum‘cation) and communication that uses modulation (car-
`
`CARRIER COMMU NICATION
`
`d to designate the band of frequencies of the signal delivered
`
`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 none
`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.
`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 at. 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
`A, cos (an! + 6,.) is varied in proportion to the baseband signal (known as the modu—
`lating signal). The frequency we and the phase 6,. are constant. We can assume 0, = 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 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. 4.16); that is. if
`m(!) <—> M(a))
`
`m(t) cos an! (—> %[M(w + wt) + M(w — cud]
`
`(4.1)
`
`The bandwidth of the modulated signal is 28 HZ. which is twice the bandwidth of the
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 5
`
`

`

`COS wet
`
`Lowpass
`filter
`
`m(t)
`
`
`
`
`m(t) cos wet
`
`cos Luci
`
`(d)
`
`Figure 4.1
`
`DSB—SC modulation.
`
`bands. For instance, if m(t) = cos wmt, then the modulated signal
`
`m(t) cos wtt = cos cum! cos wvt
`= %[cos (on. + 0),")1 + cos (nu — what]
`The component of frequency our + w," is the upper sideband, and that of frequency
`w) — tom 18 the lower sideband, corresponding to the modulating signal of frequency
`rum. Thus, each component of frequency cum in the modulating signal gets translated
`into two components, of frequencies w). + a)", and cup — mm, in the modulated signal.
`Note that the modulated signal m(t) cos (out, as seen from the above equation, has
`
`
`
`
`
`
`
`
`
`
`
`
`and —w,.), as seen from Eq. (4.1). To recover the original signal mt
`modulated signals, it is necessary to retranslate the spectrum to its origii
`The process of retranslating the spectrum to its original position is re
`demodulation, or detection. Observe that if the modulated carrier spectrur
`is shifted again by :wc, we get back the desired baseband spectrum plus
`spectrum at :ch, which can be suppressed by a lowpass filter (Fig. 4.1a)
`that in order to demodulate. we should multiply the incoming modulati
`cos cart and pass the product through a lowpass filter (Fig. 4.1d). This C(
`be directly verified from the identity
`(m(t) cos (out) (cos root) = l3[m(t) + m(r) cos 2am]
`
`and
`
`(m(t) cos wrt) (cos wit) <—> %M(w) + %[M(co + 20%) + 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. ld. 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
`use a carrier of exactly the same frequency (and phase) as was used f1
`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 a),
`is of interest. From Fig. 4.1 it
`we 2 21TH in order
`to avoid the overlap of M(w + car) and 1‘
`wt < 2778, the information of m (t) is lost in the process of modul
`impossible to retrieve m(r) from the modulated signal m(t) cos wot.
`therefore, the only requirement is that a), Z 2778. The practical fat
`impose additional restrictions. A radiating antenna can radiate only
`without distortion, This means that to avoid distortion caused by the ra:
`wc/27rB > 1. The broadcast band AM radio uses is the band 550 kl
`or a ratio of cut/2778 roughly in the range of 100 to 300.
`
`I EXAMPLE 4.1
`Baseband signals shown in Fig. 4.20 and c modulate a carrier c
`Assuming DSB—SC modulation. sketch the modulated waveforms.
`The DSB—SC waveform for the signal in Fig. 4.20 is shown ir
`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 l
`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. 1022 p 6
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 6
`
`

`

`filters at the output are replaced by lowpass filters of bandwidth 8.
`For demodulation, the receiver must generate a carrier in phase and frequency
`'
`'
`arrier. These demodulators are called synchronous,
`
`I EXAMPLE 4.3
`
`in Fig. 4.6a when it
`is used as a synchronous
`Analyze the switching modulator
`demodulator.
`m (1) cos a), I. The carrier causes the periodic switching on and
`The input signal is
`off of the input signal. The output is mm cos am k(t).
`m(t) cos wczktt) = m(t) cos wct[§ + j}; (cos wct - %cos 3th + -
`l
`2
`
`l
`
`~ >]
`
`d for the purpose of translating the
`
`
`
`m(t) + other terms centered at my, 2w” .
`.
`.
`-l7T
`When this signal is passed through a lowpass filter. the output is the desired signal
`
`(1/1r)m(r).l
`
`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
`phase for synchronous demodulation. But such systems are very efficient from the
`point of view of power requirements at the transmitter.
`ln 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
`system with amultitude of receivers for each transmitter, it is more economical to have
`one expensive high—power transmitter and simpler, less expensive receivers. For such
`applications, a large carrier signal is transmitted along with the suppre
`modulated signal m(t) cos um, thus eliminating the need to generate a local carrier
`iver. This is the so-called AM (amplitude modulation), in which the
`signal at the rece
`transmitted signal rpAMtt) is given by
`(4.9a)
`(PAMU) = mt!) Cos w,.t + A cos wct
`= [A + m(t)] cos wt!
`
`ssedrcarrier—
`
`(4.9b)
`
`"—
`* The terms synchronous, coherent. and homodyne mean the same
`to contrast with heterodyne. where a different carrier frequency is use
`spectrum (see Example 4.2).
`
`thing. The term homodyne is used
`
`The modulated signal QDAMU) is shown in Fig. 4.10d. Beca
`the Signal EU) cos wft (provided* E(t) > 0 for all t)
`(4_.9b) is A + m(z‘) (provided A + mm > 0 for all 1),. Th
`F1g. 4.10. HA is large enough to make A + mm positiv
`m(t) from (pAMU) simply reduces to envelope detection.
`The condition for demodulation by an envelope deter
`
`A+m(z)>0
`This is the same as
`A Z —m(t)min
`
`forallr
`
`m(t)
`
`A+m(t)>0
`
`for all:
`
`I—>
`
`(a)
`
`A+m(l)}‘>0
`
`
`
`
`
`Envelope
`A + m(t)
`
`(d)
`
`Figure 4.10 AM signal and its envelope.
`
`*E(t) must also be a slowly varying signal as compared to cos
`
`Petitioner Sirius XM Radio Inc. - Ex. 16272 p 7
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 7
`
`

`

`:d 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,
`'ne) demodulators.*
`
`iodulator in Fig. 4.60 when it
`
`is used as a synchronous
`
`(t) cos wit. The carrier causes the periodic switching on and
`be output is m(z‘) cos wrt k(t).
`
`1
`2
`l
`1(1) cos (UPI 7 + — cos (act — — cos 3am + -
`2
`7T
`3
`
`-
`
`-
`
`rm(t) + other terms centered at a)” 2w...
`
`.
`
`.
`
`.
`
`:d through a lowpass filter, the output is the desired signal
`
`tULATION (AH)
`
`)ressed-carrier systems need sophisticated circuitry at the
`fgenerating a local carrier of exactly the right frequency and
`:modulation. 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 no.1. thus eliminating the need to generate a local carrier
`is is the so~called AM (amplitude modulation), in which the
`is given by
`
`)‘J + A cos wltt
`
`] cos air!
`
`(4.9a)
`
`(4.91))
`
`
`
`4.3 AMPLITUDE MODULATION (AM)
`
`235
`
`The spectrum of tpAMU) is the same as that of m (t) cos a). t plus two additional impulses
`at : wt
`We) <—> %[M(w + at.) + Mtw , up] + wAtétw + wt) + 5t“) ' will
`'
`
`(4.90)
`
`(I) is shown in Fig. 4.10d. Because E(r) is the envelope of
`The modulated signal (pAM
`E(t) > 0 for all t), the envelope of «pAM(t) in Eq,
`the signal E(t) cos an (provided*
`1 r). This fact is also evident from
`(4.9b) is A + m(t) (providedA + m(t) > 0 for al
`ositive for all r, the recovery of
`Fig 4.10. HA is large enough to make A + m(t) p
`.
`m(t) from tpAMU) 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 -m(t)min
`
`(4.10:1)
`
`(4'10b)
`
`m(t)
`
`(—>
`
`(a)
`
`A+m(t)>0
`
`foralll
`
`A + m(t)j>0
`
`for all!
`
`l' t
`
`
`
`
`
`
`
`
`
`Envelope
`A + "1(1)
`
`Envelope
`
`M + m(t)l
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 8
`
`

`

` itA + mm]
`
`
`
` Lowpass
`
`filter
`
`[A + m(t)] cos wct .
`
`
`Figure 4.13 Rectifier detector for AM.
`
`It is interesting to note that rectifier detection is in effect synchronous detectionl
`performed without using a local carrier. The high carrier content in the received signa
`makes this possible.
`
`In an envelope detector, the output of the detector follows the
`Envelope Detector.
`hown in Fig. 4.14 functions as an
`envelope of the modulated signal. The circuit s
`
`e
`
`thus follows the envelope of the input. A ripple signal of 1
`caused by capacitor discharge between positive peaks.
`increasing the time constant RC so that the capacitor dischar
`positive peaks (RC > l/w..). 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). > 2173, a condition that is necessary for a well~defme
`The envelopedetector output is A + m(t) with a ripplt
`term A can be blocked out by a capacitor or a simple RC I
`may be reduced further by another (lowpass) RC filter.
`
`I EXAMPLE 4.6
`
`For tone modulation (Example 4.4), determine the upper 1
`the capacitor voltage follows the envelope.
`
`l: Solution: Figure 4.15 shows the envelope and the vol
`
`Capacitor voltage
`(RC discharge)
`E(l — If RC)
`
`
`
`
`Envelope
`
`l—-—>
`
`Figure 4.15
`
`The capacitor discharges from the peak value E at some art
`voltage or across the capacitor is given by
`
`cc = Ee’W‘“
`
`Because the time constant is much larger than the interval be
`cycles of the carrier (RC > 1 / (up), the capacitor voltage 1;(-
`for a short time compared to its time constant. Hence, the e)
`imated by a straight line obtained from the first two terms in '.
`
`0C 213(1 ~55)
`
`The slope of the discharge is —E/RC. In order for the capaci
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 9
`
`
`
`Figure 4.14 Envelope detector for AM.
`
`envelope detector. On the positive cycle of the input signal, the capacttor Chchargel:
`up to the peak voltage of the input signal. As the mput Signal. falls below t as peak
`value, the diode is cut off, because the capacitor voltage (which IS very nearly t e pp:
`voltage) is greater than the input signal voltage, thus causmg thedtode to open. if c;
`capacitor now discharges through the resistor R at a slow rate. During the nexthpog 1:
`cycle, when the input signal becomes greater than the capacrtor 'voltage, t
`ei 1%:
`conducts again. The capacitor again charges to the peak value of this (new) cyc e.
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 9
`
`

`

`
`
`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 very little between the
`positive peaks (RC > l/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 l/w,. but should be small compared to 1/2778, where B is the
`highest frequency in m(t) (see Example 4.6). This, incidentally, also requires that
`w, > 2178, 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.
`
`
` Solution:
`
`Figure 4.15 shows the envelope and the voltage across the capacitor.
`
`Capacitor voltage
`(RC discharge)
`
`E(l 1* I“ RC)
`
`
`
`Envelope
`
`
`
`—>
`
`/ ]
`
`Figure 4.15
`
`The capacitor discharges from the peak value E at some arbitrary instant I = 0. The
`voltage vc across the capacitor is given by
`
`DC = E€_l/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 cc discharges exponentially
`. for a short time compared to its time constant. Hence, the exponential can be approx—
`imated by a straight line obtained from the first two terms in Taylor‘s series of Ee‘mc.
`
`ti
`
`/[A + mm]
`%[A + mm]
`
`
`
`Lowpass
`filter
`
`
`
`'forAM.
`
`that rectifier detection is in effect synchronous detection
`Jcal 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
`
`
`
`or for AM.
`
`)ositive cycle of the input signal, the capacitor C charges
`he input signal. As the input signal falls below this peak
`tecause the capacitor voltage (which is very nearly the peak
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 10
`
`

`

`
`
`my 7 2000
`
`w, + 2000
`
`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 mm and m2(t) produce modulated signals* <p.(t) and (pm), respectively, then
`the modulating signal klm1(t) + k:m;(t) produces the modulated signal k1 (N!) +
`k3<p2(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 wmt (tone modulation). the DSBVSC signal is
`
`cos wmt cos curt = %[C05 (in, — mm)! + cos (L0,. + w,,,)t]
`
`This shows that DSB—SC translates a frequency cum to two frequencies, cur — cum (LSB)
`and wt + a)", (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 digitalrmodulated 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 a“ and a 0 is transmitted by a pulse
`-A cos tuft (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
`
`In short. superposition applies to
`* Note that we are excluding the carrier term from ip.(r) and 902(1).
`the suppressed-carrier portion only. For more discussion, sec Van Trees.S
`
`
`
`ambiguity in the demodulating carrier can detect a negative
`(detect 0 as 1) and vice versa. This problem can be solvec
`difi‘eremial code before modulation.
`
`In this case. a 1 is encoded by the same pulse used to
`.
`bit (no transition) and a 0 is encoded by the negative of the
`preVious data bit (transition). This is shown in Fig. 4.30a
`
`Datallfllloool]
`Encoded
`baseband
`signal
`
`t—>
`
`iA cos (of:
`Lowpass
`filter
`
`
`
`(b)
`
`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 chani
`even if the demodulating carrier has a sign ambiguity.
`Differential coding also facilitates noncoherent detectior
`known as diflerentia/ PSK or DPSK (Fig. 4.30h), we ave
`carrier by observing that the received modulated signal itself
`With. a possible sign ambiguity. For demodulation, in place .
`received signal delayed by T, (one bit interval). If the receive
`preVious pulse, the product _y(t) = A2 cos2 (0,1, and the 10v
`A‘/3. If the received pulse is of opposite sign, v(t) = -
`—A‘/2. In differential coding, two pulses of the'same pc
`transition) 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. 1022, p. 11
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 11
`
`

`

`
`
`
`
`4.7 DIGITAL CARRIER SYSTEMS
`
`267
`
`
`
`wr + 2000
`
`dulation
`
`1 discussed thus far, the modulated signal (excluding the
`'inciples of superposition. For example.
`if modulating
`ce modulated signals" (p.(t) and 9920), respectively, then
`Lt) + k1m3(t) produces the modulated signal kltplU) +
`'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,
`lulation), the DSB—SC signal is
`
`((4),. — wm)t + cos (a), + wm)ll
`
`islates a frequency mm to two frequencies, wt — (um (LSB)
`n generalize this result to any nonsinusoidal modulating
`ly the result obtained earlier by using a more general
`
`{STEMS
`
`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
`lar to that observed in analog signals.
`ed by a pulse A cos (at and a 0 is transmitted by a pulse
`. The information in PSK signals therefore resides in the
`ls cannot be demodulated noncoherently (envelope de-
`>e is the same for both 1 and 0. The coherent detection is
`)g signals. Methods of carrier 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 yield a carrier with sign ambiguity (or phase ambiguity
`of 71'),
`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
`diflerential code before modulation.
`In this case, a l 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. 4.3011. Thus a transition in the
`
`Data1101100011
`Encoded
`baseband
`
`signal
`
`’_’
`
`(a)
`
`
`iA cos wot
`Lowpass
`filter
`
`
`
`('3)
`
`Figure 4.30
`
`(a) Differential coding. (b) Differential PSK receiver.
`
`the
`received pulse sequence indicates 0 and no transition indicates l.* 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 am)
`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 cosZ (opt, and the lowpass filter output 2(t) =
`A2/2. If the received pulse is of opposite sign. y(t) = ~A2 cos2 an and 2(t) =
`—A2/2. 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 of 2(1) is immediately detected as a l and the
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 12
`
`

`

`9.6 CONVOLUTIONAL CODES
`
`Convolutional (or recurrent) codes, first introduced by Elias in'l955,3 differ frokrn
`- block codes as follows. In a block code, the block of n code digits generated bcy t. e
`encoder in any particular time unit depends only on the block of k input data igijts
`within that time unit. In a convolutional code, on the other hand, the block of nbclo It:
`digits generated by the encoder in a particular time unit depends not only. on the. hoc
`of k message digits within that time unit but also on the block of data digits vz