`
`
`
`
`
`— gh oe Se ae — : = —_
`
`
`
`
`
`
`
`t
`
`
`
`ue
`
`ym
`
`\
`
`og
`
`
`
`
`
`
`
`4e
`
`
`
`pa
`Ns
`
`Pure
`
`‘
`
`aes
`
`2
`”
`me Ss
`
`=
`
`oe
`
`
`
`
`
`
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 1
`
`

`

`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 2
`
`Copyright © 1989, 1983 by B. P. Lathi
`All rights reserved. No part of this publication may be
`reproducedortransmitted 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 makecopies 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/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—dc19
`
`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
`
`

`

`
`
`Baseband signals produced by various information sources are not alwayssuitable 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 basebandsignal 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(s).
`Accordingly, we have amplitude modulation (AM), frequency modulation (FM), or
`phase modulation (PM). Figure 1.7 shows a basebandsignal m(r) and the correspond-
`ing AM and FM waveforms. In AM, the carrier amplitude varies in proportion to m(t),
`carrier frequencies that corresponds to a much smaller wavel
`and in FM, the carrier frequency varies in proportion to m(q).
`1 MHz carrier has a wavelength of only 300 meters and require:
`At the receiver, the modulated signal must pass through a reverse processcalled
`is of the order of 30 meters. In this aspect, modulation is lik
`demodulation in order to retrieve the baseband signal.
`signal hitchhike on a high-frequency sinusoid (carrier). The cé
`As mentioned earlier, modulation is used to facilitate transmission. Some of the
`signal may be comparedto a stone andapiece of paper. If we
`important reasons for modulation are given below.
`of paper, it cannot go too far by itself. But by wrapping It aro
`it can be thrown over a longer distance.
`
`
`
`Frequency-modulated wave
`
`Figure 1.7. Modulation.
`
`a scheme would bedifficult because of the requirementof generation and detection of
`pulses of precise amplitudes. Such practical difficulties would thenset 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 Chapter8, we shall derive Shannon’s result
`and comparethe efficiencies of various communication systems.
`
`1.4 MODULATION
`
`
`
`Modulating (baseband) signal
`
`Amplitude-modulated wave
`
`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
`basebandsignals, the wavelengths are too large for reasonable antenna dimensions.
`For example, the powerin a speechsignalis 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
`
`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 Radio Inc. - Ex. 1022, p. 3
`
`

`

`the contents of this book will be
`ed to transmit this book, all that is neededis to transmit
`e an infinite numberof levels are available, it is possible
`\ceivable message. Cataloging of such a code may not
`de the point. The point is that if the noise 1s zero,
`problem,at least theoretically. Implementation of such
`scause of the requirement of 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
`nnonrate. In Chapter 8, we shall derive Shannon’s result
`of various communication systems.
`
`y various information sources are not alwayssuitable for
`'ven channel. These signals are usually further modified
`his conversion process is known as modulation. In this
`| is used to modify some parameter of a high-frequency
`
`of high frequency, and one ofits parameters—such as
`ase—is varied in proportion to the baseband signal m(f).
`tude modulation (AM), frequency modulation (FM), or
`ire 1.7 shows a basebandsignal m/(t) and the correspond-
`In AM, the carrier amplitude varies in proportion to m (t),
`lency varies in proportion to m(f).
`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.
`
`a
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 4
`1.4 MODULATION
`
`Carrier
`
`m(t)
`
`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 whose size
`is of the order of 30 meters. In this aspect, modulation is like letting the baseband
`signal hitchhike on a high-frequency sinusoid (carrier). The carrier and the baseband
`signal may be comparedto a stone and a piece of paper. Ifwe wish to throw a piece
`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
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 4
`
`

`

`4.1 BASEBAND AND CARRIER COMMUNICATION=223
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 5
`
`
`
`ulation
`
` 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 cannotbe 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 baseband fre-
`quencies, its uses are rather restricted. 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 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 ,is varied
`in proportion to the basebandsignal m(1). 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. Modulationis used to transmit analog as well as digital basebandsignals.
`A commentabout pulse-modulated signals (PAM, PWM, PPM, PCM, and DM)
`is in order here. Despite the term modulation, these signals are basebandsignals. The
`term modulation is used here in another sense. Pulse-modulation schemesare really
`baseband coding schemes, andthey yield baseband signals. These signals muststill
`modulate a carrier in order to shift their spectra.
`
`ond, the basebandis 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-
`
`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 basebandsignal (knownas the modu-
`lating signal). The frequency w,and the phase 6, are constant. Wecan assume 6, = 0
`without a loss of generality. If the carrier amplitude A, is made directly proportional
`to the modulating signal m(r), the modulated carrier is m(t) cos wt (Fig. 4.1¢). 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(o)
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 5
`
`

`

`m(t)
`
`(b)
`
`~ On) m(t) COS w,t
`
`COS wet
`
`(d)
`
` 6,
`
`c
`
`a
`ON
`
`ON .
`
`Figure 4.1. DSB-SC modulation.
`
`bands. For instance, if m(t) = COS @nl, then the modulated signal
`m(t) COS Wt = COS Wnt COS Wet
`‘eos (We + Wmn)t + COS (@. — W,»)t|
`The component of frequency w, + W, is the upper sideband, and that of frequency
`W, — Wm is the lower sideband, corresponding to the modulating signal of frequency
`Wr. Thus, each component of frequency in the modulating signal gets translated
`into two components,of frequencies @ + Wm and w, — @,, in the modulated signal.
`Note that the modulated signal m(t) cos wf, as seen from the above equation, has
`
` componentetitia;nerctiiiws XKMrRRAURSIALOe ox. 4999pn.6 1
`
`demodulation,or detection. Observethatif the modulated carrier spectrut
`is shifted again by +@-, we get back the desired baseband spectrum 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 w,t and pass the product through a lowpassfilter (Fig. 4.1d). This ce
`be directly verified from the identity
`(m(t) CoS wet) (COs wt) = $[m(1) + m(f) cos 2u,t|
`and (m(t) cos at) (COS Wet) 1M(w) + G{M(@ + 2) + M(w — 2
`t a lowpassfilter allows the des
`It can be seen from Fig. 4. le tha
`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, ot coherent detect
`use a carrier of exactly the same frequency (and phase) as was used f
`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 it
`wo. 227B in order
`to avoid the overlap of M(w + w,) and /
`w, < 27B, the information of m(f) is lost in the process of modul
`impossible to retrieve m(f) from the modulated signal m(t) cos wt.
`therefore, the only requirement is that w. 2 27B. The practical fa
`impose additional restrictions. A radiating antenna can radiate only
`without distortion. This means that to avoid distortion caused by the ra’
`w,/27B > i. The broadcast band AM radio uses is the band 550 kt
`or a ratio of w,/27B roughly in the range of 100 to 300.
`
`EXAMPLE4.1
`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. 4.2¢ is a digital signal (polar signaling). The module
`shown in Fig. 4.2d. The modulated signal is also polar. This is a
`Sec. 3.9). This example is given here to stress that modulation is
`analog as well as digital signals. a
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 6
`
`

`

`synchronism with the incomingcarrier. These demodulators are called synchronous,
`or coherent (also homodyne) demodulators.*
`
`1
`
`2
`
`(/mm(t). a
`
`spectrum (see Example 4.2). Petiti
`
`4.3 AMPLITUDE MODULATION(AM)
`Generally speaking, suppressed-carrier systems need sophisticated circuitry at the
`receiverforthe purpose ofgenerating a local carrier ofexactly the rightfrequency 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, providedit results in a large enough saving in
`expensive high-power transmitting equipment. On the other hand, for a broadcast
`systemwithamultitudeofreceivers foreachtransmitter, itis more economical tohave
`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(t) cos @-f, thus eliminating the need to generate a local carrier
`signal at the receiver. Thisis the so-called AM (amplitude modulation), in which the
`transmitted signal @am(t) is given by
`a(t) = m(t) COs @t + A cos w,t
`(4.9a)
`={A+ m(t)] cos Wet
`(4.9b)
`
`Wi EXAMPLE 4.3
`
`demodulator.
`
`is used as a synchronous
`Analyze the switching modulator in Fig. 4.6a when it
`The input signal is m(t) cos wt. The carrier causes the periodic switching on and
`off of the input signal. The outputis m(t) COS @t k(t).
`m(t) cos w,tk(t) = m/(t) Cos wutl5 + 7 (cos wt — ,cos 3w.t + °° |
`m(t) + other terms centered at @,, 20, ---
`al-
`Whenthis signal is passed through a lowpassfilter, the output is the desired signal
`
`the signal E(t) cos wt (provided* E(t) > 0 for all #),
`(4.9b) is A + m(t) (provided A + m(t) > 0 for all t). Th
`Fig. 4.10. If A is large enough to make A + m(t) positis
`m(t) from gam(¢) simply reduces to envelope detection.
`The condition for demodulation by an envelope dete
`A+ m(t) >90
`for all ¢
`
`This is the same as
`
`A 2 —M(O)min
`
`m(t)
`
`(a)
`
`A+ m(t) > 0
`
`for allt
`
`\
`
`—_————
`
`*The terms synchronous, eoherent, 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
`
`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. 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
`yming carrier. These demodulators are called synchronous,
`
`odulator in Fig. 4.6a when it
`
`is used as a synchronous
`
`‘t) cos w,t. The carrier causes the periodic switching on and
`he output is m(t) cos at k(t).
`
`1
`1(t) cos wt] = + — [cos wt — > cos 3w,.t ++ °°
`3
`
`mn(t) + other terms centered at w,., 20,,...
`d through a lowpassfilter, the output is the desired signal
`
`yressed-carrier systems need sophisticated circuitry at the
`f generating a localcarrier 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
`ye 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 economicalto have
`r transmitter and simpler, less expensive receivers. For such
`ier signal is transmitted along with the suppressed-carrier-
`s w,t, thus eliminating the need to generatea local carrier
`is is the so-called AM (amplitude modulation), in which the
`
`(4.9a)
`
`Petitioner Sirius XM RadioInc. - Ex. 1022, p. 8 |i
`4.3 AMPLITUDE MODULATION (AM)
`235
`
`Ul
`
`at +a,
`
`The spectrum of am(t) is the same asthat of (1) cos @,t plus two additional impulses
`gam(t) @ E[M(o + @) + M(o — @)) + TALa(w + 0) + 5(w — w)]
`
`‘
`
`(4.9c)
`
`The modulated signal ¢gau(t) is shown in Fig. 4.10d. Because E (t) is the envelope of
`the signal E(f) cos wt (provided* E(t) > 0 for all 1), the envelope of gam(t) in Eq.
`(4.9b) is A + m(t) (provided A + m(t) > 0 for all ¢). This fact is also evident from
`Fig. 4.10. If A is large enough to make A + m(t) positive for all r, the recovery of
`m(t) from @am(t) simply reduces to envelope detection.
`The condition for demodulation by an envelope detectoris
`A+ m(t) > 0
`for all t
`
`(4.10a)
`
`This is the same as
`
`Az —m(f)min
`
`(4.10b)
`
`m(t)
`
`(a)
`
`A+ m(t) $0
`
`At m(t)>0
`
`for allt
`
`for all ¢
`|A + m(t)|
` Envelope
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 8
`
`

`

`
`
`positive peaks (RC > 1/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 |
`highest frequency in m(t) (see Example 4.6). This, incid
`w, > 27B, a condition that is necessary for a well-define
`The envelope-detector output is A + m(#) with a rippl
` Lowpass
`
`term A can be blocked out by a capacitor or a simple RC|
`
`[A + m(1)] cos wtC) filter
`may be reduced further by another (lowpass) RC filter.
`
`
`M@ EXAMPLE 4.6
`
`Figure 4.13 Rectifier detector for AM.
`
`It is interesting to note that rectifier detection is in effect synchronous ee
`performed without using a localcarrier. The high carrier contentin the received signa
`makesthis 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 ws
`
`
`
`
`Figure 4.14 Envelope detector for AM.
`
`
`
`Because the time constant is much larger than the interval be
`cycles of the carrier (RC > 1/w,), the capacitor voltage vc
`envelopedetector. On the positive cycle of the input signal, the capacitor Cohare.
`for a short time comparedto its time constant. Hence, the e)
`up to the peak voltage of the input signal. As the input signal falls below t Hs peat
`imatedbyastraight line obtained from thefirst two termsin”
`value, the diodeis cut off, because the capacitor voltage(which is very nearly the Peal
`voltage) is greater than the input signal voltage, thus causing thediode to open. wee
`capacitor now discharges through the resistor R at a slow rate. During the nex!Pos -
`cycle, when the input signal becomes greater than the capacitor voltage, t . one
`conducts again. The capacitor again charges to the peak value of this (new) cycle.
`
`The Peéiijaner SithsrgeMsRagiqnhtgs tHeXculQ?2Zero thi
`
`For tone modulation (Example 4.4), determine the upper|
`the capacitor voltage follows the envelope.
`Q) Solution: Figure 4.15 shows the envelope and the vol
`
`
`
`Capacitor voltage
`(RC discharge)
`E(1 — t/ RC)
`
`
`
`
`Envelope
`
`Figure 4.15
`
`The capacitor discharges from the peak value E at someart
`voltage vc across the capacitor is given by
`tc = EeWt/RC
`
`ve = e(1 a)
`
`t
`
`The slope of the discharge is -E/RC. In order for the capaci
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 9
`
`

`

`fi4[A+ mio)
`
`
`that mi]
`Tv
`
`
`
`or again chargesto the peak value of this (new) cycle. The
`
`
`
`
`
`that rectifier detection is in effect synchronous detection
`ycal 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
`
`v,(t)
`
`,0sitive cycle of the input signal, the capacitor C charges
`
`
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, 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 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 > 1/,). Making RC too large, however, would makeit impos-
`sible for the capacitor voltage to follow the envelope (see Fig. 4.14). Thus, RC should
`be large compared to 1/w, but should be small compared to 1/27B, where B is the
`highest frequency in m(r) (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 dc
`term A can be blocked out by a capacitor or a simple RC highpassfilter. 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.
`
`C Solution: Figure 4.15 shows the envelope and the voltage across the capacitor.
`
`
`
`Capacitor voltage
`(RC discharge)
`E(l — t/ RC)
`
`
`
`
`
`Envelope
`“
`
`Figure 4.15
`
`The capacitor discharges from the peak value E at some arbitrary instant r = 0. The
`voltage vc across the capacitor is given by
`te = Ee t/R€
`
`Because the time constant is muchlarger than the interval between the two successive
`cycles of the carrier (RC > 1/w,), the capacitor voltage uc discharges exponentially
`_for a short time comparedto its time constant. Hence, the exponential can be approx-
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, 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 m,(t) and m)(t) produce modulated signals* ¢(¢) and ¢,(#), respectively, then
`the modulating signal kym,(f) + k,m2(t) produces the modulated signal k, g(t) +
`k>p,(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 @,,¢ (tone modulation), the DSB-SCsignal is
`COS Wat COS Wt = $[COS (W. — Wm)t + COS (@ + Om)t]
`This shows that DSB-SCtranslates a frequency a,, to two frequencies, @ — Wm (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.
`
`Figure 4.30
`
`(a) Differential coding. (b) Differential PSK receiver
`
`received pulse sequence indicates 0 and notransition indi
`4.7. DIGITAL CARRIER SYSTEMS
`absolute signs of the receivedpulses are not importantfor det
`Asseen earlier, digital signals can be modulated by several schemes such as ASK,
`is the changein 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 noncoherentdetectior
`coherently (synchronous) or noncoherently (envelope detection). The noncoherent
`known as differential PSK or DPSK (Fig. 4.30b), we avc
`scheme performanceis close to the performance of the coherent scheme when the
`carrier by observing that the received modulatedsignalitself
`noise is small. The difference in the two schemes is pronounced whenthe noise 1s
`with a possible sign ambiguity. For demodulation, in place.
`received signal delayed by 7,(one bit interval). If the receive
`large. This behavioris similar to that observed in analog signals.
`In PSK, a1is transmitted by a pulse A cos wf and a 0 is transmitted by a pulse
`previous pulse, the product y(t) = A? cos? w,t, and the lov
`A*/2. If the received pulse is of opposite sign, y(t) = -
`—A cos w,t (see Fig. 4.2d). The information in PSKsignals therefore resides in the
`~A*/2. In differential coding,
`two pulses of the same px
`carrier phase. These signals cannot be demodulated noncoherently (envelope de-
`tection) because the envelopeis the same for both 1 and 0. The coherent detection is
`transition) indicates a 1 and twopulses of opposite polarity
`similar to that used for analog signals. Methodsof carrier synchronization are also the
`indicates a0. Hence, the positive value of z(t) is immediate]
`same as those used for analog signals. A small pilot can be transmitted along with the
`negative z(t) is detected as a 0.
`
`* Note that we are excluding the carrier term from y(t) and ¢2(¢). In short, superposition applies to
`the suppressed-carrier portion only. For more discussion, see Van Trees.”
`
`* Precoding discussed in connection with duobinary is actually dift
`transmitted by no transition and a 1 is transmitted by a transition.
`
`In this case, a 1 is encoded by the same pulse used to
`bit (no transition) and a 0 is encoded by the negative ofthe
`previous data bit (transition). This is shown in Fig. 4.30a
`
`Data 1101100042141
`Encoded
`baseband
`signal
`
`(a)
`
` Lowpass
`
` Petitiqnaneaiuaat Rede?of FOBA Ble self
`
`Petitioner Sirius XM Radio Inc. - Ex. 1022, p. 11
`
`

`

`
`
`
`
`Petitioner Sirius XM RadioInc. - Ex. 1022, 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 techniquesyield a 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. Thusa transition in the
`
`Data 1101 1 000i21«1
`
`Encoded
`baseband
`signal
`
`i
`
`(a)
`
`
`XA cos w,t
`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. What is important
`is the change in signs of successive pulses. These sign changesare 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. 4.30b), we avoid generation of a local
`carrier by observing that the received modulated signal itself 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 pulseis identical to the
`previous pulse, the product y(t) = A? cosw,t, and the lowpassfilter output z(7) =
`A*/2. If the received pulse is of opposite sign, y(t) = —A* cos? wt and z(f) =
`
`1 discussed thus far, the modulated signal (excluding the
`inciples of superposition. For example,
`if modulating
`ce modulated signals* ,(t) and @)(t), respectively, then
`t) + kym,(t) produces the modulated signal k,g,(1) +
`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
`. be expressed in terms of tone modulation. For example,
`julation), the DSB-SCsignal is
`
`(We. — Wy)t + COs (@. + @,)t]
`slates a frequency w,, to two frequencies, @ — @, (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,
`tion of digital-modulated signals is similar to that of
`For example, ASK (see Fig. 3.50) can be demodulated
`r noncoherently (envelope detection). The noncoherent
`e to the performance of the coherent scheme when the
`ce in the two schemesis pronounced whenthe noise is
`lar 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. 1022, p. 12
`
`

`

`way, when the third message digit 0 enters the register, we have s, = 0, s. = 1, an Petitioner Sirius XM RadioInc. - Ex. 1022, p. 13"
`
`Coding and decoding is considerably facilitated by whatis k
`which showsthe codedoutputfor any possible sequence of da
`for the coder in Fig. 9.5 with k = 5 is shownin Fig. 9.6. W
`the coder output is 00, and whenit is 1, the output is 11. Th
`tree branchesthatstart at the initial node. The upper branch rep!
`branch represents 1. This convention will be followed throu
`nodeofeachof the two branches, wefollow a similar procedur
`second data digit. Hence, two branchesinitiate from each nox
`and the lower one for 1. This continues until the kth data digit.
`input digits are 0 (augmented digit), and we have only one
`Hence, in all there are 32 (or 2") outputs corresponding to 2* pos
`coded output for input 11010 can be easily read fromthis tree
`in Fig. 9.6).
`Figure 9.6 showsthat the code tree becomesrepetitive afte
`can be seen from the fact that the two blocks enclosedinsic
`identical. This meansthat the output from the fourth input dig
`the first digit was 1 or 0. This is not surprising in view ofthe fa
`input digit enters the shift register, the first input digit is shif
`and it ceases to influence the output digits.
`1x)x2%3x4 .
`.
`. and the data vector Ox)x2x3x4 .
`third group of output digits. It is convenient to label the four
`nodes appearing at the beginningofthe third branch) as nodes a
`Therepetitive structure begins at the fourth level nodes and con
`
`
`register in order to influence the N groups of v digits. Hence
`are 11010, we actually apply 11010000 (the digits augmented
`of the shift register. It can be seen that whenthelast digit of
`stream enterss,, the last digit of the message stream haspassed
`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? 7 ~ I/v.
`It can be seen that unlike the block coder, the convolutio
`continuousbasis, and each data digit influences N groups of
`
`The Code Tree
`
`* For a systematic code, one of the output digits must be the data digitit
`tIn general, instead of shifting one digit at a time, b digits may be shi
`y = b/v.
`
`Convolutional (or recurrent) codes, first introduced by Elias in 1955,° differ from
`- block codes as follows. In a block code, the block of n code digits generated °y the
`encoderin any particular time unit depends only on the block of k input data ‘es
`within that time unit. In a convolutional code, on the other hand,the block of n “° .
`digits generated by the encoderin a parti