Principles of Communications Lecture 7: Analog Modulation Techniques (5) Chih-Wei Liu 劉志尉 National Chiao Tung University [email protected]
Principles of CommunicationsLecture 7: Analog Modulation Techniques (5)
Chih-Wei Liu National Chiao Tung [email protected]
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Outlines
Linear Modulation
Angle Modulation
Interference
Feedback Demodulators
Analog Pulse Modulation
Delta Modulation and PCM
Multiplexing
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Analog Pulse Modulation
Message waveform is represented by regularly spaced sample values (sample signals) discrete in time.
Historically, these methods are the early attempts to achieve modern communications. They are in the twilight zone between analog and digital modulations.
Today, their basic forms can still be found in some electronic components such as ADC.
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Analog/Digital Pulse-coded
Analog pulse modulation: A pulse train is used as the carrier wave. Some characteristic feature of each pulse (e.g., amplitude, duration, or position) is used to represent message samples.PAM pulse amplitudePDM pulse durationPPM pulse position
Digital Pulse Modulation: Messages are discrete-amplitude (finite levels) samples.DM delta modulationPCM pulse-code modulation
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Pulse-Amplitude Modulation (PAM)
The amplitude of each pulse corresponds to the value of the message signal m(t) (at the leading edge of the pulse).
The pulse generator can be considered as a filter.
( 0.5 )( ) ( )
1, 2where 0, otherwise
Sc S
n
t nTm t m nT
WttW
=
+ =
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PAM Signals
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Demodulation
Recover M(f) m(t) samples
Recover M(f) m(t) message
Equalizer: Recover distorted signals particularly when the distortion method is known or estimated.
1/H(f) LPF
equalizer
mc(t) m(t) m(t)
)()()(
fHfMfM c=
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Pulse-Width Modulation (PWM)
Pulse width the values of messageSpectrum: complicated (Fourier-Bessel spectra)
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PWM/PPM Generation
Mod:
Demod: area of pulse.
Low-pass filtering (integration)
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Pulse-Position Modulation (PPM)
Pulse position the values of message
Spectrum: complicated
Demodulation: (1) LPF & integration
(2) convert PPM to PWM LPFConversion of PPM or PWM to PAM: a ramp generator (re)starts at kTs and stops at tk. (next page)
( ) ( )nn
x t g t t
=
=
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Conversion Between PWM & PPM
(integration)
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Delta Modulation
m(t) samples (analog amplitude) difference binary
or m(t) difference binary samplesOperations:
(1)
(2)
(3)
(4)
)()()( tmtmtd s=
0
0
, 0( ) ( ( )) =
, ( ) 0d(t)
t threshold d td t
=
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DM Signal Generation
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Slope Overload
The message signal m(t) has a slope greater than can be followed by the stair-step approximation ms(t).
Assume step-size = 0 slope (max) = 0/Ts
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Solution to Overload
Adaptive delta modulation -- adjust the step-size 0based on xc(t).
Idea: If m(t) constant, xc(t) alternates in sign
make 0 .
If m(t) ( or ) rapidly, xc(t) has the same polarity
make 0.Method: Detect the trend of signal
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Adaptive DM
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ADM Receiver
Transmit step-size or regenerate the step-size at the receiver according to pre-decided rules.
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Pulse-Code Modulation (PCM)
m(t) samples (analog amplitude) quantized samples binary representation binary modulated waveform (ASK (AM), PSK (PM), FSK (FM) to be discussed in Commun.II )
Main advantages of digital communication
more reliable communication
Main disadvantages of digital communication
wide BW ( reduced by compression)
complicated circuits ( cost reduced by VLSI)
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PCM Signal Generation
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BW of PCM
Assume the number of quantization levels=q=2n
Message BW = W
Sampling rate = 2W
2nW binary pulses/secondAssume maximum width of pulse,
transmission BW knW, k=constant
Hence, B k2Wlog2qRecovered message error is due to mainly quantization error. Thus, q error B
12nW
=
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Multiplexing
A number of data sources share the same communication channel.
Frequency-Division Multiplexing (FDM)
Quadrature Multiplexing (QM)
Time-Division Multiplexing (TDM)
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FDMSeveral message signals are translated, using modulation, to different spectral locations and added to form a baseband signal.
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Example: Stereophonic FM
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Quadrature Multiplexing (QM)
Quadrature-carrier multiplexing: transmit two signals on the same carrier frequency. (not exactly FDM)
Note that cos and sin are orthogonal.QM Quadrature Amplitude Modulation (QAM)
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1 2
1 2
1
( ) [ ( )cos ( )sin ].
If the receiver has a carrier phase error, i.e.,
( ) 2cos( ).( ) 2cos( )
[ ( )cos ( )sin ] + [ ( )cos(2 )
c C c c
c
r c
C
C c
x t A m t t m t t
LO t tx t t
A m t m tA m t t
= +
= + +
= + 2
1 2
( )sin(2 )].( ) [ ( )cos ( )sin ]. (ideal : 0 )
c
DD C
m t ty t A m t m t
+ +
=
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Time-Division Multiplexing (TDM)
Each message signal occupies a small time slot in every Ts second.
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BW of TDM
A rough estimate of BW
1
1
Baseband message BW = . There are channels.Samples per second = 2 .
Total samples per second: 2 . Or,
Total samples per second = 2 .
Total baseband BW to accommodate all sources
i
iN
s ii
N
ii
W NT WT
T n WT
W
=
=
=
1
= .N
ii
B W=
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Example: Digital telephony system
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Comparison of MUX
FDM: simple to implement,inter-modulation distortion (crosstalk) due to nonlinear channels
TDM: less crosstalk (in memoryless channels),difficult to keep synchronization (frame structure, header), digital (sampled) signals
QM: efficient use of channel, crosstalk between I & Q channels (needs coherent demodulation)