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**AM,FM, and digital modulation systems**

Chapter 5 AM,FM, and digital modulation systems

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**5.0 Introduction (Chapter objectives)**

Amplitude modulation and single sideband Frequency and phase modulation Digitally modulated signals(OOK, BPSK, FSK, MSK MPSK, QAM, QPSK, π/4QPSK, and OFDM) Spread sprectrum and CDMA system

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**5.0 Introduction (the goal of this chapter)**

Study g(t) and s(t) for various types of analog and digital modulations Evaluate the spectrum for various types of analog and digital modulations Examine some transmitter and receiver structures Learn about spread spectrum systems

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**5.0 Introduction (the key of this chapter)**

Grasping phase modulation and frequency modulation Grasping Binary modulation and Bandpass signaling Grasping Multilevel Modulated bandpass signaling Grasping Minimum-shift keying (MSK)and GMSK Knowing the principle of FDM, OFDM and Spread Spectrum Systems

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**5.0 Introduction (band-pass signal and its spectra)**

Communication system constructure input signal processing carrier circuits Transmission Medium (channel) transmitter g(t) s(t) r(t) output Modulation is the process of imparting the source information onto a Band-pass signal with a carrier frequency fc by the introduction of amplitude or phase perturbations or both.

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**5.0 Introduction (band-pass signal and its spectra)**

Theorem:Any physical band-pass waveform can be representative by g(t) is called the complex envelope of s(t),and fc is carrier frequency (in hertz), ωc=2πfc Notice: The desired type of modulated signal,s(t),is obtained by selecting the appropriate modulation mapping function g[m(t)],where m(t) is the analog or digital base-band signal. The voltage (or current)spectrum of the band-pass signal is and the PSD is

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5.1 Amplitude Modulation The complex envelope of an AM signal is given by Fig.5-1 Where Ac specifies the power level and m(t) is the modulating signal. The representation for AM signal is given by:

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**5.1 Amplitude Modulation (modulation percentage for AM signal )**

Definition %positive modulation= (Amax-Ac)/ Ac ×100=max[m(t)] ×100 %negative modulation= (Ac-Amin) / Ac×100=-min[m(t)] ×100 %overall modulation= (Amax- Amin)/ (2Ac)×100 ={max[m(t)]-min[m(t)]}/2 ×100 where Amax is the maximum value of Ac [1+m(t)], and Ac is the level of the AM envelope in the absence of modulation. notice:The percentage of modulation can be over100 %(Amin will have a negative value).If the transmitter uses a two-quadrant multiplier that produces a zero output when Ac[1+m(t)] is negative,the output signal will be:

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5.1 Amplitude Modulation Which is a distorted AM signal which is call as over modulated signal . Its bandwidth is much wider than that of the undistorted AM signal. if the percentage of negative modulation is less than 100%,an envelope detector may be used to recover the modulation without distortion;if the percentage of negative modulation is over 100%,undistorted modulation can still be recovered provided the product detector is used. A product detector is superior to an envelope detector when the input signal-to-noise ratio is small.

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5.1 Amplitude Modulation because the total average normalized power of a band-pass waveform v(t) is given by Where “normalized” implies that the load is equivalent to 1 ohm. The normalized average power of the AM signal is: If the modulation contains no dc level,then 〈m(t) 〉=0,and the normalized power of the AM signal is

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5.1 Amplitude Modulation modulation efficiency:the percent of the total power of the modulated signal that conveys information. The highest efficiency that can be attained for a 100% AM signal would be 50%.(For the case when square-wave modulation is used). The normalized peak envelope power (PEP)of the AM signal:

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5.1 Amplitude Modulation The voltage spectrum of the AM signal is given by The AM spectrum is just a translated version of the modulation spectral component.The bandwidth is twice that of the modulation Example 5-1 Suppose that a 5000w AM transmitter is connected to a 50Ω load; If the transmitter is 100% modulated by a 1000Hz test tone. Then compute (1)the total actually average power, (2)actually PEP, (3) The modulation efficiency . Solution: the constant Ac is given by (1/2)Ac2/50=5000, thus peak voltage across the load will be Ac=707V during the times when there is no modulation.

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**5.1 Amplitude Modulation (1)the actual average power**

(2)then across the 50 Ω load, the PEP is: (3)The modulation efficiency would be:

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5.1 Amplitude Modulation

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5.1 Amplitude Modulation Fig. 4-2 Spectrum of AM signal

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**5.3 Double-sideband Suppressed Carrier**

A double-sideband suppressed carrier(DSB-SC) signal is an AM signal that has a suppressed discrete carrier. The voltage spectrum of the DSB-SC signal is The percent of modulation of a DSB-SC is :infinite The modulation efficiency of a DSB-SC is 100% A product detector (which is more expensive than an Envelope detector) is required for demodulation of the DSB-SC signal The sideband power of a DSB-SC signal is four times that of a comparable AM signal with the some peak level,that is to say,the DSB-SC signal has a four_fold power advantage over that of an AM signal

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**5.3 Double-sideband Suppressed Carrier**

Spectrum of DSB-CS signal

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**5.5Asymmetric sideband signals (Signal sideband)**

An upper single sideband (USSB) signal has a zero-valued spectrum for|f|<fc,where fc is the carrier frequency. A lower signal sideband (LSSB) signal has a zero-valued spectrum for |f|>fc, where fc is the carrier frequency. SSB-AM:The bandwidth is the same as that of the modulating signal (which is half the bandwidth of an AM or DSB-SC signal). The term SSB refers to the SSB-AM type of signal , unless otherwise denoted.

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**5.5Asymmetric sideband signals**

Theorem:The complex envelope of an SSB signal is given by Which results in the SSB signal waveform: Where the upper(-) sign is used for USSB and the lower (+) sign is used for LSSB Denotes the Hilbert transform of m(t), which is given by: Where h(t)=1/(πt), and H(f)=F[h(t)] corresponds to a -900 phase-shift network：

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**5.5Asymmetric sideband signals**

Proof: Taking the Fourier transform of the complex envelope of an SSB signal, we get: Because of Hilbert transform, we can find that the equation becomes: For USSB case, choose the upper sign, then: Substituting it into eq.(4-15), we have: Fig.5-4 Spectrum for a USSB signal

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**5.5Asymmetric sideband signals**

The normalized average power of the USSB signal is The SSB signal power is the power of the modulating signal〈m2(t)〉multiplied by the power gain factor Ac. The normalized peak envelope power (PEP) is :

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**5.5Asymmetric sideband signals**

Fig. 5-5 Generation of SSB

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**5.5Asymmetric sideband signals**

SSB signals have both AM and PM. The AM component (real envelope) is: The PM component is SSB signals may be received by using a super- heterodyne receiver that incorporates a product detector with θ0=0, thus the receiver output is: Where K depends on the gain of the receiver and the loss in the channel. In detecting SSB signals with audio modulation, the reference phase θ0 does not have to be zero, because the same intelligence is heard regardless of the value of the phase used, For digital modulation, the phase has to be exactly correct so that the digital waveshape is preserved

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**5.5Asymmetric sideband signals (Vestigial sideband)**

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**5.5Asymmetric sideband signals (Vestigial sideband)**

In certain application, a DSB modulation technique takes too much bandwidth for the channel, and an SSB technique is too expensive to implement, although it takes only half the bandwidth. In this case, a compromise between DSB and SSB, called vestigial sideband(VSB), is often chosen. VSB is obtained by partial suppression of one of the sidebands of a DSB signal. sideband of the DSB signal is attenuated by using a band-pass filter,called a vestigial sideband filter. The VSB signal is given by: Where s(t) is a DSB signal,and hv(t) is the impulse response of the VSB filter.The spectrum of the VSB signal is :

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**5.5Asymmetric sideband signals (Vestigial sideband)**

The modulation on the VSB signal can be recovered by a receiver that uses product detection or , if a large carrier is present, by the use of envelope detection. For recovery of undistorted modulation, the transfer function for VSB filter must satify the constraint: Proof: the product detector output is Thus only when the constraint satisfy, Vout(f)=KM(f) hold true.

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Summary AM DSB-SC SSB-AM VSB

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**Summary Example 5-2 if linear modulated signal is as following:**

s1(t)=cos(ω0t)cos (ωct) s2(t)(1+0.5sin (ω0t)) cos (ωct) Where ωc=6ω0, please giving their spectrum. Solution : (1) the spectrum is: -7ω0 -5ω ω ω0

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Summary (2) the spectrum is -7ω ω ω ω0 j ω ω S2(f)

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**5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal)**

PM and FM are special cases of angle-modulated signaling. In this kind signaling the complex envelope is: Here the real envelope R(t)=|g(t)|=Ac, is a constant, and the phase θ(t) is a linear function of the modulating signal m(t). However, g(t) is a nonlinear function of the modulation. The resulting angle-modulated signal is: For PM,the phase is directly proportional to the modulating signal Where the proportionality constant Dp is the phase sensitivity of the phase modulator, its units is radians per volt. For FM, the phase is proportional to the integral of m(t), so that:

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**5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal)**

Where the frequency deviation constant Df has units of radians/volt-sencond. From the last two equations, we can see that if we have a PM signal modulated by mp(t), there is also FM on the signal, corresponding to a different modulation waveshape that is given by: Where the subscripts f and p denote frequency and phase. Similarity, if we have an FM signal modulated by mf(t), the corresponding phase modulation on this signal is:

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**5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal)**

Fig. 5-7 Generation of FM from PM , and vice versa Direct PM circuit are realized sinusoidal signal through a time-varying circuit which introduces a phase shift that varies with the applied modulation voltage. Similarly, a direct FM circuit is obtained by varying the tuning of an oscillator tank circuit according to the Modulation voltage.

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**5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal)**

Definition: If a band-pass signal is represented by : Where Ψ(t)=ωct+θ(t), then the instantaneous frequency (hertz) of s(t) is: For the case of FM, the instantaneous frequency is: The instantaneous frequency varies about the assigned carrier frequency fc in a manner that is directly proportional to the modulated signal m(t).

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**5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal)**

The frequency deviation from the carrier frequency is: And the peak frequency deviation is : The peak-to-peak deviation is For FM signaling,the peak frequency deviation is related to the peak modulation voltage by: Where Vp=max[m(t)]

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**5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal)**

Fig.5-9 An increase in the amplitude of the modulation signal Vp will increase ΔF and the bandwidth of the FM signal. But will not affect the average power level of the FM signal which is Ac2/2 As Vp is increased,spectral components will appear farther and farther away from the carrier frequency,and the spectral components near the carrier frequency will decrease in magnitude,since the total power in the signal remains constant.This situation is distinctly different form AM signaling,where the level of the modulation affects the power in the AM signal,but does not affect it bandwidth.

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**5.6 Phase Modulation and Frequency Modulation (Representation of PM and FM signal)**

The peak phase deviation is defined by: the peak modulation voltage is Where Vp=max[m(t)]. Definition: The phase modulation index is given by: Where Δθ is the peak phase deviation Definition: The frequency modulation index is given by: Where ΔF is the peak frequency deviation and B is the bandwidth of the modulating signal, which, for the case of sinusoidal modulation, is fm, the frequency of the sinusoid.

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**5.6 Phase Modulation and Frequency Modulation (Spectra of Angle-Modulated Signals)**

As the spectrum of the band-pass waveform is Where G(f)=F[g(t)]=F[Acejθ(t)] is the spectra of complex envelope signal. For the type of AM modulation signaling, we able to obtain relatively simple formulas relating S(f) to M(f). For angle modulation signaling, this is not the case, because g(t) is a nonlinear function of m(t), thus, a general formula relating G(f) to M(f) cannot be obtained, because G(f)=F[g(t)]=F[Acejθ(t)] must be evaluated on a case-by-case basic for the particular modulating waveshape of interest. Since g(t) is nonlinear function of m(t), superposition does not hold, and FM spectra for the sum of two modulating waveshape is not the same as summing the FM spectra that were obtained when the individual waveshape were used

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**5.6 Phase Modulation and Frequency Modulation (Spectra of Angle-Modulated Signals)**

Example 5-2 spectrum of a PM or FM signal with sinusoidal modulation If the modulation on PM signal is : Then: Where the phase modulation index is βp =DpAm= β. When mf(t)=Amcosωmt in FM modulation, we can get the same phase function. Where β = βf =DfAm/ωm. The peak frequency deviation would be ΔF=DfAm/2π. The complex envelope is Which is periodic with period Tm=1/fm. Its Fourier series can be represented by:

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**5.6 Phase Modulation and Frequency Modulation (Spectra of Angle-Modulated Signals)**

Where Here Jn(β) is the Bessel function of the first kind of the nth, and J-n(β) =(-1)n Jn(β) hold true. Taking the Fourier transform of Eq.(5-55)， we get: Fig.5-10

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**In fact, 98%of the total power is constrained in that bandwidth**

5.6 Phase Modulation and Frequency Modulation (Spectra of Angle-Modulated Signals) Carson’s rule:the bandwidth of the angle-modulated signal depends on the phase modulation index or the frequency modulation index β, and bandwidth of the modulating signal. That is : In fact, 98%of the total power is constrained in that bandwidth Fig. 5.11

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**5.6 Phase Modulation and Frequency Modulation (Narrowband Angle Modulation)**

When θ(t) is restricted to a small value,say θ(t)<0.2rad, the complex envelope may be approximated by: Then a narrowband angle-modulated signal is: This signal is similar to an AM-type signal, except that the sideband term is 900 out of phase with the discrete carrier term. The spectrum of the narrowband angle-modulation signal is: where

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**5.6 Phase Modulation and Frequency Modulation (Narrowband Angle Modulation)**

Generation of NBFM Fig.5-12

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**5.6 Phase Modulation and Frequency Modulation (Widthband Angle Modulation)**

Theorem:For WBFM signaling ,where and B is the bandwidth of m(t),the normalized PSD of the WBFM signal is approximated by where fm(.) is the PDF of the modulating signal.

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**5.6 Phase Modulation and Frequency Modulation (Widthband Angle Modulation)**

Generation of WBFM fig.5-13

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**5.6 Phase Modulation and Frequency Modulation (Widthband Angle Modulation)**

Example 5-3 spectrum for WBFM with Triangular modulation. Fig.5-14 The PDF for triangular modulation is:

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**5.6 Phase Modulation and Frequency Modulation (Widthband Angle Modulation**

Where Vpis the peak voltage of the triangular waveform The PSD of the WBFM signal becomes Where the peak frequency deviation is:

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**5.6 Phase Modulation and Frequency Modulation (Widthband Angle Modulation**

Other example Fig. 5-15

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**5.6 Phase Modulation and Frequency Modulation**

some important properties of angle-modulated signals are: An angle-modulated is a nonlinear function of the Modulation and the bandwidth of the signal increases as the modulation index increases; The discrete carrier level changes depending on the modulating signal; The bandwidth of a narrowband angle-modulated signal is twice the modulating signal bandwidth The real envelope of an angle-modulated signal is constant, and does not depend on the level of the modulating signal

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**5.6 Phase Modulation and Frequency Modulation (Preemphasis and Deemphasis in Angle-Modulated system)**

preemphasis:If the level of the modulation is boosted at the top end of the spectrum,the SNR at the output of the receiver can be improved. Deemphasis:The level of the the modulated is attenuated at high frequencies on the receiver output. Preemphasized FM is actually a combination of FM and PM and combines the advantages of both with respect to noise performance

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**5.6 Phase Modulation and Frequency Modulation (Preemphasis and Deemphasis in Angle-Modulated system)**

Fig.5-16 Angle-modulated system with preemphasis and dedmphasis

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**5.7 Frequency-Division multiplexing and FM stereo**

Frequency-division multiplexing (FDM)is a technique for transmitting multiple message simultaneously over a wideband channel by first modulating the message signals onto several sub-carriers and forming a composite base-band signal that consists of the sum of these modulated sub-carriers.This composite signal may then be modulated onto the main carrier.

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**5.7 Frequency-Division multiplexing and FM stereo**

Fig.5-17 FDM system

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**5.7 Frequency-Division multiplexing and FM stereo**

The composite signal spectrum must consist of modulated signals that do not have overlapping spectra,the composite base-band signal then modulates a main transmitter to produce the PDM signal that is transmitted over the wide-band channel. The received FDM signal is first demodulated to reproduce the composite base-band signal that is passed through filters to separate the individual modulated sub-carriers.Then the sub-carriers are demodulated to reproduce the message signals m1(t),m2(t), and so on.

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**5.7 Frequency-Division multiplexing and FM stereo**

To obtain the compatibility feature,the left-and right -channel audios are combined to produce the monaural signal,and the difference audio is used to modulate a 38-KHz DSB-SC signal.A 19-KHz pilot tone is added to the composite base-band signal mb(t) to provide a reference signal for coherent sub-carrier demodulation in the receiver Fig. 5-18

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**5.9 Binary Modulated Bandpass Signaling**

Digitally modulated bandpass signals are generated by using the complex envelopes for AM, PM,FM, or QM signaling. But the modulating signal m(t) is a digital signal given by the binary or multilevel line codes

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**5.9 Binary Modulated Bandpass Signaling**

binary bandpass signaling techniques : on-off keying (OOK) or Amplitude shift keying(ASK), Binary phase-shift keying (BPSK) and Frequency-shift keying(FSK). Fig.5-19 Bandpass digitally modulated signals

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**5.9 Binary Modulated Bandpass Signaling (OOK signal)**

where is the unipolar baseband data signal. It is shown that OOK is identical to unipolar binary modulation on a DSB-SC signal. PSD is ： comparison with(3.39b) complex envelope PSD

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**5.9 Binary Modulated Bandpass Signaling**

When m(t) has a peak value of A=2(1/2)，s(t) has an average normalized power of ; It shows that there is a frequency line in the PSD of complex envelope for OOK, and the OOK is AM-type signaling. The null-to-null bandwidth is2R, and the transmission bandwidth is∞ ,while the absolute bandwidth is . Bit rate is R=1/Tb. If raised cosine-rolloff filtering is used(to conserve bandwidth), the absolute baseband bandwidth is B=(1/2)(1+r)R,where D=R=2B/(1+r) and r is the rolloff factor of the filter. The absolute transmission bandwidth is BT=(1+r)R

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**5.9 Binary Modulated Bandpass Signaling (demodulation for OOK)**

Fig.5-21

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**5.9 Binary Modulated Bandpass Signaling (demodulation for OOK)**

1)Envelope detector(noncoherent detection) 2)product detector(coherent detection) with Low-pass Filter Processing 3) product detector(coherent detection) with Matched Filter Processing.This is an optimum detection of OOK—that is ,to obtain the lowest BER when the input OOK signal is corrupted by additive white Gaussian noise(AWGN)

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**5.9 Binary Modulated Bandpass Signaling**

Note: the optimum coherent OOK detector is more costly to implement than the noncoherent OOK detector. If the input noise is small, the noncoherent receiver may be the best solution, considering both cost and noise performance. The trade-off in BER performance between optimum coherent detection and nonoptimum noncoherent detection.

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**5.9 Binary Modulated Bandpass Signaling （BPSK）**

Bandpass signal for BPSK： Where m(t) is a polar baseband data signal. For convenience, let m(t) have peak values of ±1 and a rectangular pulse shape complex envelope representation Expanding equation above we get:

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**5.9 Binary Modulated Bandpass Signaling**

it can be shown that BPSK is also a form of AM-type signaling like OOK signaling. But when digital modulation index: Conclusion: For this optimum BPSK signal of h=1, the complex envelope is and it equivalent to DSB-SC signaling with a polar baseband data waveform

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**5.9 Binary Modulated Bandpass Signaling**

PSD of complex envelope for optimum BPSK Because m(t) is polar signaling, the PSD for the complex envelope as where s(t) has an average normalized power of Ac2/2 the null-to-null bandwidth is 2R , like OOK Detection for BPSK: 1) coherent detection 2) A optimum detection (the low-pass filter in fig.5.22a is replaced by an integrate-and-dump matched filter processing. )

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**5.9 Binary Modulated Bandpass Signaling**

Fig.5-21

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**5.9 Binary Modulated Bandpass Signaling**

Notice:unlike OOK signaling, synchronous detection must be used to detect BPSK ,the main reason is that there is no discrete carrier term in the BPSK signal;if a low-level pilot carrier is transmitted together with the BPSK signal, a PLL may be used to extract the carrier reference. Otherwise, a Costas loop or squaring loop may be used to synthesize the carrier reference because BPSK is DSB-SC signal if Costas loop and square loop are used, the phase ambiguity must be resolved. This can be accomplished by using differential coding at the transmitter input and differential decoding at the receiver output.

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**5.9 Binary Modulated Bandpass Signaling(DPSK )**

Although phase-shift-keyed signals cannot be detected incoherently, a partially coherent technique can be used whereby the phase reference for the present signaling interval is provided by a delayed version of the signal that occurred during the previous signaling interval if， the symbol phase relationship between binary sequence and 2DPSK signal is represented as：

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**5.9 Binary Modulated Bandpass Signaling**

detection partially coherent detection

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**5.9 Binary Modulated Bandpass Signaling (Frequency-shift keying (FSK))**

According to the method used to generate it, FSK signal can be classified as two different types: Discontinuous-phase FSK and Continuous-pahse FSK Discontinuous-phase FSK signal is represented by when m(t) is polar binary pulse waveform, we can get: The discontinuous phase function is

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**5.9 Binary Modulated Bandpass Signaling (Frequency-shift keying (FSK))**

Continuous-phase FSK In order to generate the continuous-phase FSK signal, the data signal are feed into a frequency modulator, This FSK signal is: thus its complex envelope can be represented by： where

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**5.9 Binary Modulated Bandpass Signaling (Frequency-shift keying (FSK))**

It can be shown that although m(t) is discontinuous at the switching time, the phase function θ(t) is proportional to the integral of m(t). If the serial data input waveform is binary, such as a polar baseband signal, the resulting FSK signal is called a binary FSK signal. Of course, a multilevel input signal would produce a multilevel FSK signal

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**5.9 Binary Modulated Bandpass Signaling (Frequency-shift keying (FSK))**

Bandwidth of FSK signaling:For the FSK signal the approximate transmission bandwidth is give by Carson’s rule: where B is the bandwidth of the digital modulation waveform. When modulating waveform is square-wave, the bandwidth is B=R. we can find that the this FSK transmission bandwidth becomes: if a raised cosine-rolloff premodulation filter is used, the transmission bandwidth of the FSK signal becomes:

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**5.9 Binary Modulated Bandpass Signaling (Frequency-shift keying (FSK))**

Generation of FSK(Fig 5-23)

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**5.9 Binary Modulated Bandpass Signaling (Detection of FSK Fig. 5-28)**

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**5.9 Binary Modulated Bandpass Signaling**

Example 1 Example 2 Example 3 Example 4

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**5.10 Multilevel Modulated Bandpass Signaling**

If a level stands for a k bits binary digits, the number of levels in the multilevel signal is : M=2k, The symbol rate(baud) of the multilevel signal is D=R/k，for example, if k=2, M=4 and baud D=R/2, where the bit rate is R=1/Tb。 Multilevel Modulated bandpass signaling used often have: QPSK; MPSK;QAM; OQPSK and π/4QPSK

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**5.10 Multilevel Modulated Bandpass Signaling (MPSK)**

In general, MPSK can also generated by using two quadrature carriers modulated by in-phase and quadrature components of the complex envelope except using a phase modulator, in that case: where the permitted values of x and y are is the permitted phase angles of the MPSK signal.

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**5.10 Multilevel Modulated Bandpass Signaling (QPSK)**

Fig 5-31

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**5.10 Multilevel Modulated Bandpass Signaling**

M-ary phase-shift keying(MPSK) with M=4 is called QPSK, its permitted values of complex envelope contains four points A plot of two possible sets of g(t) is shown as following

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**5.10 Multilevel Modulated Bandpass Signaling (QAM)**

in general, the QAM signal constellations are not restricted to have permitted signaling points only on a circle. The general QAM signal is: its complex envelope is where

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**5.10 Multilevel Modulated Bandpass Signaling (QAM)**

The waveforms of I and Q components are represented by: where h(t) is the pulse shape that is used for each symbol, and baud rate D=R/k Fig symbol QAM constellaltion

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**5.10 Multilevel Modulated Bandpass Signaling**

In some applications, the timing between the x(t) and y(t) components is offset by Ts/2=1/(2D), that is: this signal is called offset QAM(OQAM) Offset quadrature phase-shift keying(OQPSK) One popular type of offset signaling is offset QPSK(OQPSK) which is identical to offset QAM when M=4. The AM is reduced because a maximum phase transition of only π/2 occurs (as opposed to for QPSK) since the I and Q data cannot change simultaneously, because the data are offset.

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**5.10 Multilevel Modulated Bandpass Signaling (π/4 QPSK modulation)**

A π/4 QPSK signal is generated by alternating between two QPSK constellations that are rotated by π/4 with respect to each other, the two signal constellations are used alternately as follows: Given a point on one of the signal constellations that corresponds to two bits of input data, two new bits are read to determine the next point that is selected from the other constellation. For example an input data is “00,11,10,10,01” , if “00”correspond to a phase shift of Δθ=450, a “11” to Δθ=1350 , a “10” to Δθ=1350 ,a “10” to Δθ=-450 and so on.

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**5.10 Multilevel Modulated Bandpass Signaling (relationship between QPSK π/4 QPSKand OQPSK )**

comparison between QPSK, QPSK and OQPSK for non-rectangle pulse waveform Type of modulation Maximum phase shift AM big small smallest

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**5.10 Multilevel Modulated Bandpass Signaling**

PSD for MPSK,QAM,QPSK,OQPSK and π/4 QPSK the complex envelope for MPSK and QAM is represented by: where cn is a complex-valued random variable representing the multilevel value during the nth symbol pulse. And f(t)=Π(t/Ts) is the rectangular symbol pulse with symbol duration Ts, and its Fourier transform is thus the PSD for the complex envelope of MPSK or QAM signal with data modulation of rectangular bit shape is

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

background In practice, the communication system need to conserve efficiently bandwidth and improve the efficiency of power supply, for example Class C amplifiers without distortion can be used. Minimum-shift keying is another bandwidth conservation technique that has been developed. Its advantage of producing a constant-amplitude signal and , consequently, can be amplified with Class C amplifiers without distortion

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

Definition MSK is continuous 2FSK with minimum modulation index h=0.5 Properties of MSK 1)continuous binary FSK； 2)modulation index being minimum 3)two signals are orthogonal over the bit interval； 4)being identical with OQPSK when the pulse shape is sinusoidal type

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

Obtaining modulation index h For FSK According to property 1), we get: And according to 3), we have:

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

That is:

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

And obtain: when θ1≠ θ2 when θ1= θ2 Thus, the modulation index for MSK

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

complex envelope for MSK For the FSK signal over the signaling interval(0,Tb), the complex envelope is: or where The MSK signaling is:

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

Because : and

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

Type I MSK: Basic pulse waveform alternates between a positive and a negative half-cosinusoid Type II MSK:Basic pulse waveform always a positive half cosinusoid The instantaneous frequency is: where

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

PSD for MSK Because x(t) and y(t) have independent data and their dc value is zero, and since g(t)=x(t)+jy(t), the PSD for the complex envelope is: Since the pulse width is 2Tb, this PSD becomes: where ,is the pulse shape. For the MSK half-cosinusoidal pulse shape, we have:

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

and its Fourier transform is: Thus, the PSD for the complex envelope for an MSK signal is:

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

Generation of Fast MSK signals Parallel Generation of Type I MSK signals Serial Generation of MSK

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**Minimum-Shift Keying (MSK) and GMSK**

Gaussian-filtered MSK (GMSK) Before the data are frequency modulated onto the carrier, the data are filtered by a filter having a Gaussian-shaped frequency response characteristic. The transfer function of the Gaussian low-pass filter is Properties of GMSK 1) Low spectral sidelobes on the transmitted MSK signal 2) constant envelope

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

Comparison of the spectral efficiencies of various types of digital signal Table 5-7 spectral efficiency of digital signals

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**5.11 Minimum-Shift Keying (MSK) and GMSK**

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**5.12 Orthogonal Frequency Division Multiplexing (OFDM)**

comparion between FDM and OFDM a. FDM b. OFDM

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**5.12 Orthogonal Frequency Division Multiplexing (OFDM)**

principle of OFDM

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**5.12 Orthogonal Frequency Division Multiplexing (OFDM)**

OFDM modulator

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**5.12 Orthogonal Frequency Division Multiplexing (OFDM)**

complex envelope of OFDM Where is a constant， PSD for OFDM Because the PSD of each carrier is of the form |Sa(π(ƒ-ƒn))|2, the overall PSD for the complex envelope of the OFDM signal is

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**5.12 Orthogonal Frequency Division Multiplexing (OFDM)**

Application of OFDM Wireless LAN Digital Audio broadcasting in the European Digital Video broadcasting in European Broad wireless communication DMT in ADSL

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**5.13 Spread Spectrum System**

In communication systems mentioned above, we have concerned primarily with the performance of communication systems in terms of bandwidth efficiency and energy efficiency with respect to natural noise. However, in some application, we also need to consider multiple-access capability, antijam capability, interference rejection and covert operation, or low-probability of intercept(LPI) capability. These performance objectives can be optimized by using spread spectrum techniques. Advantage of spread spectrum techniques. 1 Low-probability of intercept; 2 Anti-jamming; 3 Multi-access

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**5.13 Spread Spectrum System**

An system which can be considered an SS system must satisfy two criteria: 1 The bandwidth of the transmitted signal s(t) needs to be much greater than that of the message m(t). 2 The relatively wide bandwidth of s(t) must be caused by an independent modulating waveform c(t) called the spreading signal, and this signal must be known by the receiver in order for the message signal m(t) to be detected. The SS signal is: its complex envelope is a function of both m(t) and c(t). In most cases, a product function is used， so that, g(t)=gc(t)gm(t)

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**5.13 Spread Spectrum System**

SS signals can be classified by the type of mapping functions that are used for gc(t). The mose common types of SS signals have: 1) Direct Sequence(DS) A DSB-SC type of spreading modulation is used, and gc(t)=c(t) is a polar NRZ waveform. 2) Frequency Hopping(FH) gc(t) is of FM type where there are M=2k hop frequencies determined by the k-bit words obtained from the spreading code waveform c(t). 3) Hybrid techniques A system include both DS and FH

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**5.13 Spread Spectrum System (Direct Sequence-DC )**

if information waveform m(t)=±1, gm(t)=Acm(t). for DC gc(t)=c(t). the complex envelope for the SS singal becomes: the DS signal is called a direct sequence spreading, spread spectrum signal(DS-SS)Fig.5-39a, c(t) is a polar spreading signal, which is generated by using a pseudonoise(PN) code generator, as shown in Fig.5-39b

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**5.13 Spread Spectrum System**

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**5.13 Spread Spectrum System**

maximum-length sequence, called m-sequence is a PN code which is generated by r shift register stages and has a maximum period of N=2r-1 chips. A m-sequence has some properties as following: P1. In one period, the number of 1’s is always one more than the number of 0’s; P2. the modulo-2 sum of any m-sequence, when summed chip by chip with a shifted version of the same sequence, produces another shifted version of the same sequence. P3. if a window of width r is slid along the sequence for N shifts, then all possible r-bit words will appear exactly once, except for the all 0 r-bit word. P4. if the 0’s and 1’s are represented by –1 and +1V, the autocorrelation of the sequence is :

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**5.13 Spread Spectrum System**

P4. if the 0’s and 1’s are represented by –1 and +1V, the autocorrelation of the sequence is : where

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**5.13 Spread Spectrum System**

The PSD for the complex envelope of BPSK-DS-SS signal is: Fig. 5-41 Without spreading, the level of the in-band PSD would be proportional to Ac2/(2Rb), but with spreading, the in-band spectral level drops to Ac2/(2Rc)

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**5.13 Spread Spectrum System (Receiver )**

If the input to the receiver consists of the SS signal plus a narrowband(sine wave) jammer signal, then: where the jamming signal is The output of despreader is After LPF, then the jammer power at the receiver output is

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**5.13 Spread Spectrum System (Receiver )**

The principle of LPI and anti-jamming

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**5.13 Spread Spectrum System (Frequency hopping )**

In a frequency-hopping(FH) SS system, there are M=2k hop frequencies controlled by the spreading code, in which k chip words are taken to determine each hop frequency. FH is accomplished by using a mixer circuit wherein the LO signal is provided by the output of a frequency synthesizer that is hopped by the PN spreading code. The serial-to-parallel converter programmable dividers in the frequency synthesizer. The k-chip word speifies one of the possible M =2k hop frequencies.

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**5.13 Spread Spectrum System (Frequency hopping )**

The FH signal receiver has the knowledge of the transmitter, c(t), so that the frequency synthesizer in the receiver can be hopped in synchronism with that at the transmitter. This despreads the FH signal, and the source information is recovered from the dehopped signal with the use of a conventional FSK or BPSK demodulator, as appropriate.

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**5.13 Spread Spectrum System (Frequency hopping )**

Fig.5-42

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5.14 Summary AM, SSB, PM, and FM signaling techniques were considered in detail Digital signaling techniques such as OOK, BPSK, FSK, MSK and OFDM were developed. The spectra for these digital signals were evaluated in terms of the bit rate of the digital information source Multilevel digital signaling techniques such as QPSK, MPSK and QAM, were also studied, and their spectra were evaluated. The key parts is 5.6, 5.9, 5.10, 5.11

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5.14 Homework Problem:

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Chapter 2 Continuous-Wave Modulation

Chapter 2 Continuous-Wave Modulation

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