`
`CHAPTER
`
`5
`
`Modulation Techniques
`for Mobile Radio
`
`Moriuhm'on is the process oi'encoding infor-
`
`mation from a message source in a manner suitable for transmission. ll 80'1"“
`ally involves translating,r a baseband messatr0 signal (called “I" ”WW“ to a
`bandpass signal at f'requgncies that, are very high when compared tn the base-
`hand frequency. The bandpass signal
`is called the modulated signal and the
`hasehand message signal is called the modulating signal. Modulation may be
`done by varying the amplitude. phase. or frequency ol'a high frequency carrier m
`accordance with the amplitude of the message signal. DP’HUdNmeml
`l5 the pro-
`cess of extracting the baseband message from the carrier so that it may l)“ Pm'
`cessed and interpreted hy the intended receiver {also called the still?)-
`This chapter describes various modulation techniques that are used in
`mobile communication systems. Analog modulation schemes that are employed
`in first generation mobile radio systems. as well as digital modulation schemes
`proposed for use in present and future systems. are covered. Since digital modu-
`lation offers numerous benefits and is already being used to replace conventional
`analog systems. the primary emphasis of this chapter is on digital modulation
`schemes. However. since analog systems are in widespread use. and will con-
`tinue to exist. they are treated first.
`Modulation is a topic that is covered in great detail in various communica-
`tions textbooks. Here. the coverage focuses on modulation and demodulation as
`it applies to mobile radio systems. A large variety of modulation techniques have
`been studied for use in mobile radio communications systems. and research is
`ongoing. Given the hostile fading and multipath conditions in the mobile radio
`channel. designing a modulation scheme that
`is resistant to mobile channel
`impairments is a challenging task. Since the ultimate goal of'a modulation tech-
`nique is to transport the message signal through a radio channel with the best
`Qualcomm Incorporated
`Exhibit 1008
`
`197
`
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`Qualcomm Incorporated
`Exhibit 1008
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`193
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`Ch. 5 . Moduiallon Techniques for Mobile Radio
`
`possible quality while occupying the least amount of radio spectrum. new
`
`advances in digital signal processing continue to bring about new forms of modu-
`
`lation and demodulation. This chapter describes many practical modulation
`
`schemes. receiver architectures. demgn trade-oil's. and their performance under
`various types ofchannel impairments.
`
`5.1 Frequency Modulation vs. Amplitude Modulation
`
`Frequency modulation (PM) is the most popular analog modulation tech—
`nique used in mobile radio systems. In FM. the amplitude of the modulated car~
`rier signal
`[S kept constant while its frequency is varied by the modulating
`message signal. Thus. FM signals have all their information in the phase or fre-
`quency of the carrier. As shown subsequently. this provides a nonlinear and very
`rapid improvement in reception quality once a certain minimum received signal
`level. called the FM threshold.
`is achieved.
`In amplitude modulation (AM)
`schemes. there is a linear relationship between the quality of the received signal
`and the power of the received signal since AM signals superimpose the exact rel-
`ative amplitudes of the modulating signal onto the carrier. Thus. AM signals
`have all their information in the amplitude ofthe carrier. FM olTers many advan-
`tages over amplitude modulation (AM). Which makes it a better choice for many
`mobile radio applications.
`Frequency modulation has better noise immunity when compared to ampli-
`tude modulation. Since signals are represented as frequency variations rather
`than amplitude variations, FM signals are less susceptible to atmospheric and
`impulse noise. which tend to cause rapid fluctuations in the amplitude of the.
`received radio signal. Also. message amplitude variations do not carry informa-
`tion in FM. so burst noise does not affect FM system performance as much as AM
`systems. provided that the FM received signal is above the FM threshold. Chap-
`ter 4 illustrated bow small-scale fading can cause rapid fluctuations in the
`received signal, thus FM offers superior qualitative performance in fading when
`compared to AM. Also.
`in an FM system.
`it is possible to tradeofT bandwidth
`occupancy for improved noise performance. Unlike AM. in an FM system. the
`modulation index. and hence bandwidth occupancy. can be varied to obtain
`greater signal-to-noise performance. It can be shown that. under certain condi-
`
`tions. the FM signal-to-noise ratio improves 6 dB for each doubling of bandwidth
`occupancy. This ability of an FM system to trade bandwidth for SNR is perhaps
`the most important reason for its superiority over AM. However. AM signals are
`able to occupy less bandwidth as compared to FM signals. since the transmission
`system is linear. in modern AM systems. susceptibility to fading has been dra-
`matically improved through the use ofin-band pilot tones which are transmitted
`along with the standard AM signal. The modern AM receiver is able to monitor
`the pilot tone and rapidly adjust the receiver gain to compensate for the ampli-
`tude fluctuations.
`
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`
`
`Amplitude Modulation
`
`199
`
`An FM signal is a constant envelope signal, due to the fact that the envelope
`of the carrier does not change with changes in the modulating signal. Hence the
`transmitted power of an FM signal is constant regardless ofthe amplitude of the
`message signal. The constant envelope of the transmitted signal allows efficient
`Class C power amplifiers to be used for RF power amplification of FM. In AM,
`however. it is critical to maintain linearity between the applied message and the
`amplitude of the transmitted Signal, thus linear Class A or A8 amplifiers, which
`are not as power efficient. must he used.
`
`The issue of amplifier efficiency is extremely important when designing
`portable subscriber terminals since the battery life of the portable is tied to the
`power amplifier efficiency. Typical efficiencies for Class C amplifiers are 70%,
`meaning that 70% of the applied DC power to the final amplifier circuit is con-
`verted into radiated RF power. Class A or AB amplifiers have efficiencies on the
`order of 30-40%. This implies that for the same battery, constant envelope FM
`modulation may provide twice as much talk time as AM.
`Frequency modulation exhibits a so-called capture efi‘ect characteristic. The
`capture olTect is a direct result of the rapid nonlinear improvement in received
`quality for an increase in received power. If two signals in the same frequency
`band are available at. an FM receiver, the one. appearing at the higher received
`signal level is accepted and demodulated. while the weaker one is rejected. This
`inherent ability to pick up the strongest signal and reject the rest makes FM sys—
`tems very resistant to co-channel interference and prowdes excellent subjective
`received quality. In AM systems. on the other hand. all of the interferers are
`received at once and must be discriminated after the demodulation process.
`While FM systems have many advantages over AM systems, they also have.
`certain disadvantages. FM systems require a wider frequency band in the trans-
`mitting media (generally several times as large as that needed for AM) in order
`to obtain the advantages of reduced noise and capture effect. FM transmitter
`and receiver equipment is also more complex than that used by amplitude modu-
`lation systems. Although frequency modulation systems are tolerant to certain
`types of signal and circuit nonlinearities. special attention must be given to
`phase characteristics. Both AM and FM may be demodulated using inexpensive
`noncoherent detectors. AM is easily demodulated using an envelope detector
`whereas FM is demodulated using a discriminator or slope detector. AM may be
`detected coherently with a product detector. and in such cases AM can outper-
`form FM in weak signal conditions since FM must. be received above threshold.
`
`5.2 Amplitude Modulation
`
`In amplitude modulation. the amplitude of a high frequency carrier signal
`is varied in accordance to the instantaneous amplitude of the modulating mes-
`sage signal. If Avcosizrcfrr.)
`is the carrier signal and m (t)
`is the modulating
`message signal. the AM signal can be represented as
`
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`

`____________.___——-——-—
`Ch. 5 . Modulaiion Techniques for Mobile Hadio
`200
`
`(5.1)
`SAM”) =Ac[l+m(t}]cos (Zfifcl)
`The modulation index k of an AM signal is defined as the ratio of the peak
`message signal amplitude to the peak carrier amplitude. For a sinusoidal modu-
`lating signal m (t) = (Am/AP) cos (27rfmt) , the modulation index is given by
`A
`k = —'"
`
`(5.2)
`
`The modulation index is often expressed as a percentage, and is called percent-
`age modulation. Figure 5.1 shows a sinusoidal modulating signal and the corre-
`sponding AM signal. For the case shown in Figure 5.1, Am = 0.5Ar, and the
`signal is said to be 50% modulated. A percentage of modulation greater than
`100% will distort the message signal if detected by an envelope detector. Equa-
`tion (5.1) may be equivalently expressed as
`
`
`
`Sm“)
`
`time —o
`
`(bl
`
`Figure 5.1
`(a) A sinusoidal modulating signal.
`(b) Corresponding AM signal with modulation index 0.5
`
`where git) is the complex enveIOpe of the AM signal given by
`
`3mm = Re {gmexp UZTrfctH
`
`gU) =Acll+m(t)]
`
`(5.3)
`
`(5.4)
`
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`

`
`
`Amplitude Modulation
`
`The spectrum of an AM signal can be shown to be
`
`,
`I
`Swtf‘) = iAcle-fc) +M(f—fr) +é(f+fc) +M(f+fc)l
`
`201
`
`(5-5)
`
`is the message signal spec-
`where 6(-) is the unit impulse function, and M (f)
`trum. Figure 5.2 shows an AM spectrum for a message signal whose magnitude
`spectrum is a triangular function. As seen from Figure 5.2, the AM spectrum
`consists of an impulse at the carrier frequency, and two sidebands which repli-
`cate the message spectrum. The sidebands above and below the carrier fre-
`
`quency are called the upper and lower sidebands, respectively. The bandwidth of
`an AM signal is equal to
`
`where fm is the maximum frequency contained in the modulating message sig-
`nal. The total power in an AM signal can be. shown to be
`
`BAM = arm
`
`(5.6]
`
`Pa. = iAEH +2<mm>+<m2tti>|
`
`(5‘7)
`
`the modulating signal
`If
`the average value.
`represents
`(-)
`where
`"1”} = kcos (2nfmt) . equation (5.7} may be simplified as
`2
`
`is
`
`(5.8)
`P;\M=%A:ll+Pml =Pc[1+3']
`where PC = fig/2 is the power in the carrier signal. Pm = (mz{t)) is the power
`in the modulating signal mm. and k is the modulation index.
`
`k
`
`
`
`Example 5.1
`A zero mean sinusoidal message is applied to a transmitter that radiates an
`AM signal with 10 kW poww, Compute the carrier power if the modulation
`index is 0.6. What percentage of the total power is in the carrier? Calculate the
`power in each sideband.
`
`Solution to Example 5.1
`Using equation (5.8] we have
`
`[+0.6 /2
`1+k2/2
`Percentage power in the carrier is
`P
`
`P ‘
`«M
`
`3-: me = EL :00 = 34.7%
`IO
`
`Power in each sidehand is given by
`_
`l
`ENDAM—Pc) = 0.51(10F8.47) — 0.765 kW
`
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`202
`
`Ch. 5 - Modulation Techniques for Mobile Radio
`
`IMUJI
`
`
`
`Upper
`
`upper
`sideband
`
` lowcr
`
`suit-hand
`
`
`
`
`'chfm
`'fr
`'fi' +fm
`fe’fm
`fc
`ft +fm
`I
`
`Figure 5.2
`(a) Spectrum ofa message signal.
`(b) Spectrlim of the corresponding AM signal.
`
`5.2.1 Single Sideband AM
`
`Since both the sidebands of an AM signal carry the same information. it is
`possible to remOVe one of them without losing any information. Single sideband
`(SSB) AM systems transmit only one of the sidebands (either upper or lower)
`about the carrier. and hence occupy only half the bandwidth of conventional AM
`systems. An SSB signal can be mathematically expressed as
`
`3933(1) = A: [mltlcosumn we (t) sin (zit/Ln]
`
`(5.9)
`
`where the negative sign in equation (5.9) is used for upper sideband SSH and the
`positive sign is used for lower sideband 888. The term wit (t) denotes the Hilbert
`transform of m (t) which is given by
`
`(5.10)
`mm = mm ®hHT(t) = mu) 83%
`and HHTU) . the Fourier transform of hHTU) , corresponds to a —90° phase shift
`netwark
`
`H(
`
`I)
`
`=
`
`*j
`{ .
`J
`
`f>0
`f<0
`
`5.
`
`(
`
`11)
`
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`
`Amplitude Modulation
`
`203
`
`The two common techniques used for generating an 858 signal are the fil-
`ter method and the balanced modulator method. In the filter method. 888 Sig-
`nals are generated by passing a double sideband AM signal through a bandpass
`filter which removes one of the sidehands. A block diagram of such a modulator
`
`is shown in Figure 5.3a. Excellent sideband suppression can be obtained using
`crystal filters at an intermediate frequency (IF).
`
`mlt}
`
` Bandpass Filler
`
`(filters out one
`ofthe sidebands)
`
`
`8353”)
`
`Acc0s(2nf,tl
`
`(a)
`
`m“)
`
`Carrier
`
`
`Osci I later
`
`fr
`
`
`
`
`90°
`
`
`Phase Shift
`
`
`835””)
`
`Figure 5.3
`Generation ofh‘SB using (a) a sideband filter. and (b) balanced modulator.
`
`lb)
`
`Figure 5.3b shows a block diagram of a balanced modulator which is a
`direct implementation of equation (5.9). The modulating signal is split into two
`identical signals. one which modulates the in-phase carrier and the other which
`is passed through a —90" phase shifter before modulating a quadrature carrier.
`The sign used for the quadrature component determines whether USSB or LSSB
`is transmitted.
`
`5.2.2 Pilot Tone 358
`
`While 8813 systems have the advantage of being very bandwidth efficient.
`their performance in fading channels is very poor. For proper detection of $88
`
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`204
`
`Ch. 5 - Modulation Techniques for Mobile Radio
`
`the frequency of the oscillator at the product detector mixer in the.
`signals,
`receiver must be the same as that of the incoming carrier frequency. Ifthese tWo
`frequencies are not identical. product detection will lead to shifting the demodu-
`lated spectrum by an amount equal to the difference in the frequencies between
`the incoming carrier and local oscillator. This leads to an increase or decrease in
`the pitch of the received audio signal. In conventional SSB receivers. it is diffi-
`cult to electronically tune the local osctllator frequency to the identical frequency
`ofthe incoming carrier. Doppler spreading and Rayleigh fading can shift the sig-
`nal spectrum causmg pitch and amplitude variations in the received signal.
`The-“9 Problems may be overcome by transmitting a low level pilot tone along
`with the SSH signal. A phase locked loop at the receiver can detect this pilot tone
`and use it to lock the frequency and amplitude of the local oscillator. Ifthe pilot
`tone and the information bearing signal undergo correlated finding. it is possible
`at the receiver to counteract the effects of fading through signal processing based
`on tracking the pilot tone. This process is called feedf'orword signal regeneration
`(FFSR). By tracking the pilot tone, the phase and amplitude of the transmitted
`signal can be reestablished. Keeping the phase and amplitude of the received
`Pilot tone as a reference. the phase and amplitude distortions in the received
`sidebands caused by Rayleigh fading can be corrected.
`Three different
`types of pilot.
`tone SSB systems have been developed
`[Gos78].lLus78|,[Wel78l. All three systems transmit a low level pilot tone, usu-
`ally -7.5 dB to -15 dB below the peak envelope power of the single sideband sig-
`nal. rl‘hey essentially differ in the spectral positioning ofthe low level pilot tone.
`One system transmits a low level carrier along with the sideband signal (tone—in-
`band). while the other two place a pilot tone above or within the 888 band.
`The tone-in-band SSH system offers many advantages which make it par-
`ticularly suited to the mobile radio environment. In this technique. a small por-
`tion of the audio spectrum is removed from the central region ofthe audio ha nd
`using a notch filter. and a low level pilot tone is inserted in its place. This has the
`advantage of maintaining the low bandwidth property of the SSH signal, while
`at the same time providing good adjacent channel protection. Due to very high
`correlation between the fades experienced by the. pilot tone and the audio sig-
`nals. a tone-in—band system makes it possible to employ some form of feedfor-
`ward automatic gain and frequency control to mitigate the effects of multipath
`induced fad ng.
`
`For proper operation of tone-in-band SSB. the tone must be transparent to
`data and be spaced across the band to avoid spectral overlap with audio frequen-
`cies. McGeehan and Batt-man lMcGRdl proposed a Transparent TbneJn-Band
`
`(TTIB) system which satisfies these requirements. Figure 5.4 illustrates the pro—
`posed technique. The baseband signal spectrum is split into two approximately
`equal width segments. The upper frequency hand is filtered out separately and
`upconverted by an amount equal to the required notch width. The low level pilot
`
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`
`Ampluude Modulation
`
`205
`
`tone is added to the center of the resultant notch. and the composite signal is
`then transmitted. At the receiver. the pilot tone is removed for automatic gain
`and frequency control purposes, and complementary frequency translation oper-
`ations are performed to regenerate the audio spectrum. The TTIB system
`directly trades system bandwidth for notch width. The selection of notch width
`
`depends on the maximum Doppler spread induced by the channel, as well as
`practical filter rollofT factors.
`
`
`
`Transmitter
`
`Receiver
`
`aLm__.
`
`jlm 2
`
`r
`
`W
`
`Bandwidth =1er}
`——~> Frequency
`
`.
`
`_
`
`m
`
`—+ frequency
`
`Figure 5.4
`Illustration of transparent tone-in-band system [From [MCG34] (Q IEEEJ‘ Only positive frequencies
`are shown, and the two different cross-hatchings denote different spectral bands.
`
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`
`Ch. 5 - Modulation Techniques for Mobile Radio
`
`5.2.3 Demodulation of AM signals
`
`AM demodulation techniques may be broadly divided into two categories:
`coherent and noncoherent demodulation. Coherent demodulation requires knowl—
`
`edge of the transmitted carrier frequency and phase at the receiver. whereas
`noncoherent detection requires no phase information. In practical AM receivers.
`the received signal is filtered and amplified at the carrier frequency and then
`converted to an intermediate frequency (IF) using a superhetrodyne receiver.
`The IF signal retains the exact spectral shape as the RF signal.
`Figure 5.5 shows a block diagram ofa product detector which forms a coher-
`ent demodulator for AM signals. A product detector (also called a phase detector)
`is a down converter circuit which converts the input bandpass signal to a base-
`hand signal. If the input to the product detector is an AM signal of the form
`R (H cos (Enfrt + 8,) . the output of the multiplier can be expressed as
`
`01(1) = Rm cos (Znfiuoriancos (2m: + B")
`
`(5.12)
`
`is the oscillator carrier frequency, and B, and (in are the received signal
`where f.-
`phase and oscillator phases.
`respectively. Using trigonometric identities in
`Appendix D, equation (5.12) may he rewritten as
`
`(5.13)
`u, (t) = éAnRumoswr—Oui +;ADR(t)cos [n2fct +9300]
`Since the low pass filter following the product detector removes the douhle
`carrier frequency term. the output is
`
`{5.14)
`so] = mm
`umm = %A0R(1)COS[Br
`where K is a gain constant. Equation (5.14) shows that the. output. of the low
`pass filter is the demodulated AM signal.
`AM signals are often demodulated using noncoherent envelope detectors
`which are easy and cheap to build. An ideal envelope detector is a circuit that
`has an output proportional to the real envelope of the input. signal. If the input to
`the envelope detector is represented as R (t) cos (7-an + 8,), then the output is
`given by
`
`umm = KJRHJI
`
`(5.15)
`
`where K is a gain constant. As a rule, envelope detectors are useful when the
`input signal power is at least 10 dB greater than the noise power. whereas prod-
`uct detectors are able to process AM signals with input signal-to—noise ratios well
`below 0 dB.
`
`5.3 Angle Modulation
`
`FM is part of a more general class of modulation known as angle modula-
`tion. Angle modulation varies a sinusoidal carrier signal in such a way that the
`
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`
`
`Angle Modulation
`
`207
`
`1
`Haul”) = 3:101“st (Gr—30)
`
`RH) cos (2an+ 0,)
`
`
`
`Aucos (2nfct + (in)
`
`Figure 5.5
`Block diagram ofa product detector.
`
`angle of the carrier is varied according to the amplitude of the modulating base-
`band signal. In this method. the amplitude of the carrier wave is kept constant
`(this is why FM is called constant envelope). There are a number of ways in
`which the phase B (t) of a carrier signal may be varied in accordance with the
`
`baseband signal; the two most important classes of angle modulation being fre-
`quency modulation and phase modulation.
`Frequency modulation (FM) is a form of angle modulation in which the
`instantaneous frequency of the carrier signal is varied linearly with the base-
`
`band message signal mil}. as shown in equation (5.16).
`
`f
`
`SW“) = Arena [211le + 0(1)] = Accos[lnfrt + 2nkfImmldn]
`
`(5.16)
`
`where AF is the amplitude ofthe carrier, ft is the carrier frequency, and kf is the
`Frequency deviation constant (measured in units of Hz/volt). If the modulating
`signal is a sinusoid of amplitude Am , and frequency f"I , then the FM signal may
`be expressed as
`
`SW”) = Accos[21tfrl+ ff ”'sin(2nfmt)]
`
`
`kA
`
`(5.17)
`
`Phase modulation (PM) is a form of angle modulation in which the angle
`(Ht) of the carrier signal is varied linearly with the baseband message signal
`mm, as shown in equation (5.18).
`
`SW“) = A‘,cos[2nf;.t+kum(t)]
`
`{5.18)
`
`In equation (5.18) k0 is the phase deviation constant (measured in units of radi-
`ans/volt).
`
`From the above equations, it is clear that an FM signal can be regarded as
`a PM signal in which the modulating wave is integrated before modulation. This
`means that an FM signal can be generated by first integrating m (t) and then
`using the result as an input to a phase modulator. Conversely, a PM wave can be
`generated by first differentiating m. (t) and then using the result as the input to
`a frequency modulator.
`
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`203
`
`Ch 5 - Modulation Techniques for Mobile Radio
`
`The frequency modulation index {if defines the relationship between the
`message amplitude and the bandwidth of the transmitted signal. and is given by
`
`k A,
`Bf : .LJ ‘
`W
`
`.3
`I
`W
`
`{5.19)
`
`where Am is the peak value ofthe modulating signal. of is the peak frequency
`deviation ofthe transmitter and W is the maxmium bandwidth ofthe niodulab
`
`ing signal. If the modulating signal is a low pass signal. as is usually the case,
`then W is equal to the highest frequency component fmtu present in the modu-
`lating signal.
`The phase modulation index [JP is given by
`
`where Al) is the peak phase deviation of the transmitter.
`
`
`
`tip = tun,“ : an
`
`(5.20)
`
`Example 5.2
`A sinusoidal modulating signal, m it) = 4cosln4 x [0%. is applied to an FM
`modulator that has a frequency deviation constant gain of It] kHz/V. Compute
`(a) the peak frequency deviation. and (bl the modulation index.
`
`Solution to Example 5.2
`Given:
`
`Frequency deviation constant Ila,r = [0 kHz/V
`Modulating frequency, fm = 4 kHz
`a) The maximum frequency deviation will occur when the instantaneous value
`of the input signal is at its maximum. For the given mm, the maximum
`value is 4 V. and hence the peak deviation is equal to
`of = 4Vx in kll/‘V = Jo kHz
`
`h} The modulation index is given by
`
`5.3.1 Spectra and Bandwidth of FM Signals
`
`tone is used such that m (ti = Amcosilnfmt. the
`When a sinusoidal test
`spectrum of Stan”) contains a carrier component and an infinite number of
`sidebands located on either side ofthe carrier frequency, spaced at integer multi-
`ples of the modulating frequency fm . Since Sm”) is a nonlinear function of
`mm, the spectrum of an FM signal must be evaluated on a case-by-case basis for
`a particular modulating wave shape ofinterest. It can be shown that for a sinu-
`soidal message, amplitudes of the spectral components are given by Bessel func-
`tions of the modulation index Hf.
`
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`

`
`
`Angle Modulalion
`
`209
`
`An FM signal has 98% of the total transmitted power in a RF bandwidth
`
`31‘ , given by
`
`Br = 2(Bf+ llfm
`
`(Upper bound)
`
`Br = 2Af
`
`(Lower hound}
`
`(5.21)
`
`(5.22)
`
`The ab0ve approximation of FM bandwidth is called Carson's rule. Carson‘s rule
`states that for small values of modulation index “3!" I ), the spectrum of an FM
`wave is effectively limited to the carrier frequency fc , and one pair of side hand
`frequencies at fc if . and that for large values of modulation index, the band-
`width approaches, and is only slightly greater than. 20f.
`As a practical example of quantifying the spectrum of an FM signal. the
`US. AMPS cellular system uses a modulation index Bf = 3, and fm = 4 kHz.
`Using Carson's rule, the AMPS channel bandwidth has an upper bound of 32
`kHz and a lower hound of 24 kHz. However, in practice. the AMPS standard only
`specifies that the modulation products outside 20 kHz from the carrier shall not
`exceed 26 dB below the. unmodulated carrier. It is further specified that the mod-
`
`ulation products outside 145 kHz from the carrier shall not exceed 45 dB below
`the unmodulated carrier lEIAQDl.
`
`
`
`Example 5.3
`An 880 MHZ carrier signal is frequency modulated using a 100 kHz sinusoidal
`modulating waveform. The peak devration of the FM signal is soo kHz. Ifthis
`FM signal is received by a superheterodyne receiver havmg an ll“ frequency of
`5 MHZ. determine the IF handwidth necessary to pass the signal.
`
`Solution to Example 5.3
`Given:
`
`Modulating frequency, fm = It)” kHz
`Frequency dewation. Af = 500 it”!
`
`Therefore modulation index. [5,. = Afz'fm = 500 mu = 5
`Using Carson‘s rule, the bandwidth occupied by the FM signal is given by
`RT = 2(pf+ nfm = 2(5+ I) lllllkllz = IZOUkHz
`The IF filter at the receiver needs to pass all the components in this band-
`width, hence the IF filter should be designed for a bandwidth of 1200 kHz.
`
`5.3.2 FM Modulation Methods
`
`There are basically two methods of generating an FM signal: the direct
`
`method and the indirect method. In the direct method, the carrier frequency is
`directly varied in accordance with the input modulating signal. In the indirect
`
`method, a narrowband FM signal is generated using a balanced modulator. and
`
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`on 5 - Moduiaiion Techniques for Mobile Radio
`
`frequency multiplication is used to increase both the frequency deviation and the
`carrier frequency to the required level.
`Direct Method
`
`In this method, voltage-controlled oscillators (VCO) are used to vary the
`frequency of the carrier signal in accordance with the haseband signal amplitude
`variations. These oscillators use devices with reactance that can he varied by the
`
`application ofa voltage. where the reactance causes the instantaneous frequency
`of the VCO to change proportionally. The most commonly USEd variable reacn
`tance device is the voltagebvariable capacitor called a usractor. ’I‘he voltage-vari-
`able capacitor may be obtained, for example. by using a reverse biased p-n
`junction diode. The larger the reverse voltage applied to With a diode,
`the
`smaller the transition capacitance will be of the diode. By incorporating such a
`device into a standard Hartley or Colpitts oscillator. FM signals can be gener-
`ated. Figure 5.6 shows a simple reactance modulator. While VCOs offer a simple
`way to generate narrowhand FM signals, the stability of the center frequency
`(carrier) of the VCO becomes a major issue when it is used for wideband FM gen-
`eration. The stability of the VCO can be improved by incorporating a phase
`locked loop (PLL) which locks the center frequency to a stable crystal reference
`frequency.
`
`+ v
`
`araclor
`d lode
`
`modul
`Signa
`
`ting
`
`Figure 5.5
`A simple reactance modulator in which the capacitance ni'a varactor diode is changed to vary the fre-
`quency ofa simple oscillator. This circuit serves as a VCO.
`
`Indirect Method
`
`The indirect method of generating FM was first proposed by its inventor,
`Major Edwin Armstrong, in 1936. It is based on approximating a narrowband
`FM signal as the sum of a carrier signal and a single sideband (SSB) signal
`where the sidehand is 90° out of phase with the carrier. Usinga Taylor series for
`small values of 6(1). equation (5.16) can be expressed as
`
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`

`Angie Modulation
`
`Sm”) 5Acc052nfrt—Acett}sin2nfct
`
`211
`
`{5.23}
`
`where the first term represents the carrier and the second term represents the
`sideband.
`
`A simple block diagram of the indirect FM transmitter is shown in Figure
`5.7. A narrow band FM signal is generated using a balanced modulator which
`
`modulates a crystal controlled oscillator. Figure 5.7 is a direct implementation of
`equation (5.23}. The maximum frequency deviation is kept constant and small in
`order to maintain the validity of equation (5.23). and hence the output is a nar-
`rowband FM signal. A widehand FM signal is then produced by multiplying in
`
`frequency the narrowband FM signal using frequency multipliers. A disadvan—
`tage ofusing the indirect method for wideband FM generation is that the phase
`
`noise in the system increases with the Frequency multiplying factor N.
`
`modulating
`signal mm
`
`
`
`Frequency
`
`
`MUIUPU‘H' wideband
`FM
`
` + narrowhand
`
`l“ M
`
`Carrier
`
`Oscillator
`
`Figure 5.7
`Indirect method for generating a widehand FM Signal. A narrowband FM signal is generated using a
`balanced modulator and then frequency multiplied to generate a wideband FM Signal.
`
`5.3.3 FM Detection Techniques
`
`There are many ways to recover the original information from an FM sig-
`nal. The objective of all FM demodulators is to produce a transfer characteristic
`that is the inverse of that of the frequency modulator. That is, a frequency
`
`demodulator should produce an output voltage with an instantaneous amplitude
`that is directly proportional to the instantaneous frequency of the input FM sig-
`nal. Thus, a frequency-to-amplitude converter circuit is a frequency demodula-
`tor. Various techniques such as slope detection, zero-crossing detection, phase
`locked discrimination and quadrature detection are used to demodulate FM.
`Devices which perform FM demodulation are often called frequency discrimina-
`tors. In practical receivers, the RF signal is received, amplified. and filtered at
`the carrier and then converted to an intermediate frequency (IF) which contains
`the same spectrum as the original received signal.
`
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`.
`Slope Detector
`It can be easily shown that FM demodulation can be performed by taklng
`the time derivative (often called slope detection) of the FM signal. fOllflwed by
`envelope detection. A block diagram ofsuch an FM demodulator is shown in Fig-
`urc 5.8. The PM signal
`is first passed through an amplitude limiter which
`removes any amplitude perturbations which the signal might have. undergone
`due to fading in the channel. and produces a constant envelope signal. Using
`equation (5.16) the signal at the output of the limiter can be represented as
`r
`
`U1“) = Vicos [211:th +0{t)] = Vlcos anrt +2nkfIm lnldll
`
`{5.24)
`
`
` Envelope
`vi" (1‘)
`Limiter
`Dichrentiator
`
`Detector
`
`
`you: it)
`
`Figure 5.8
`Block diagram ofa slope detector type PM demodulator.
`
`Equation (5.24) can be differentiated in practice by passing the Sit-{1131
`through a filter with a transfer function that has gain that increases linearly
`with frequency. Such a filter is called a slope filter (Which is where the term slope
`detector derives its name). The output of the differentiator then becomes
`
`Uzi!) = +V.[2T[f‘.t+3?:|Sinf2flfrt+0{tl}
`and the output of the envelope detector becomes
`
`(5.25)
`
`(5.26)
`
`ll
`vomit) Vl[2nfc+%8(t)]
`= V|2nf; + V12rtk/m (t)
`The above equation shows that the output of the envelope detector contains
`a dc term proportional to the carrier frequency and a time-varying term propor-
`tional to the original message signal ma). The dc term can be filtered out using a
`capacitor to obtain the desired demodulated signal.
`Zero-crossing Detector
`When linearity is required over a broad range of frequencieS, such as for
`data communications, 3 zero-crossing detector is used to perform frequency-to-
`amplitude conversion by directly counting the number of zero crossings in the
`input FM signal. The rationale behind this technique is to use the output of the
`zero—crossing detector to generate a pulse train with an average value that is
`
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`

`Angle Modulation
`
`213
`
`proportional to the frequency ofthe input signal. This demodulator is sometimes
`referred to as a pulse-averaging discriminator. A block diagram of a pulse-aver-
`
`aging discriminator is shown in Figure 5.9. The input FM signal is