Modulation in Communication System Note

1. Analog Modulation
Digital Modulation
Error Probabilities for Binary Modulation
M-ary Digital Modulation
Modulation Techniques
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2. Modulation in Communication System
By modulating a higher frequency carrier wave, it is usually much more effective to transmit
data (although conceptually possible to transmit baseband signals directly).
Allows precise control of the radiated frequency spectrum, more efficient use of the allocated
RF bandwidth, and flexibility in accommodating different baseband signal formats.
In older analog modulation carrier, amplitude, frequency, and phase may vary continuously.
In modern digital-modulation wireless systems make more efficient use of the radio spectrum,
and usually requires less prime power.
performs better over a fading communications channel.
more compatible with the use of error-correcting codes.
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3. Analog Modulation
Transmitter is to modulate an RF carrier signal with the baseband data.
Receiver is to recover the baseband data from the received modulated carrier wave.
Modulator/demodulator provides the interface between the baseband information and the
IF signals.
IF signal in a receiver contains noise from the antenna and receiver circuitry with the
desired signal.
Demodulator play a critical role in the overall communication performance.
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4. SSB modulator and demodulator
SSB (single-side band)
SSB input signal to demodulator: ( )( ) cos ( )i IF mv t A t n tω ω= + +
ωIF - ωm ωIF + ωm ωIF + ωm
m(t): baseband signal, n(t): Gaussian white noise signal
1
( ) cos ( )
2 2
o m
A
v t t x tω= +SSB output signal:
Synchronous (Coherent) demodulator:
Modulator and demodulator LO are identical in freq. and phase.
LO LO
( ) cos mm t tω=
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5. DSB-SC modulator and demodulator
DSB-SC (double side-band suppressed carrier)
ωIF - ωm ωIF + ωm
DSB-SC input signal to demodulator:
DSB-SC output signal:
If mixer were ideal, the carrier freq. (fIF) would not be present in the output
so call suppressed carrier.
( ) ( )( ) cos cos ( )
2 2
i IF m IF m
A A
v t t t n tω ω ω ω= − + + +
1
( ) cos ( )
22
o m
A
v t t x tω= +
( ) cos mm t tω=
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6. DSB-LC modulator and demodulator
DSB-LC (double side-band large carrier)
ωIF - ωm ωIF + ωm
DSB-LC input signal to demodulator:
DSB-LC output signal:
The carrier freq. (fIF) would be present in the output.
DSB-LC: advantage Even if fIF much lower in amplitude than the sidebands, can
be used as a reference signal to phase-lock the local oscillator to synchronization
with the incoming signal.
( ) ( )( ) [1 ( )]cos ( ) cos cos cos ( )
2
i IF IF IF m IF m
mA
v t A m t t n t A t t t n tω ω ω ω ω ω= + + = + − + + +  
1
( ) cos ( )
2 2
o m
mA
v t t x tω= +
( ) cos mm t m tω=
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7. DSB-LC for Envelop Detection
Fig. Envelope detection of an AM signal
An advantage DSB-LC is that detection can be done without a
local oscillator and mixer, by using an envelope detector (non-
coherent demodulator).
The RC time constant should
be large enough so that the
capacitor voltage does not
decay too quickly before the
next carrier peak arrives.
But small enough so the
output can track the envelope
when it is decreasing.
DSB-LC detection can be done by using an envelope detector (without a LO & mixer)
It does not require the phase information of the incoming signal.
Much simpler receiver & inexpensive circuit for broadcast AM radio.
( ) cos mm t m tω=
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8. Block Diagram of Digital Modulation
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9. Binary Digital Modulation
Digital mod. v.s. Analog mod.
Improved performance in the presence of noise and fading
lower transmit power requirements
better suitability for transmission of digital data with error
correction and encryption.
Amplitude Shift Keying (ASK)
Frequency Shift Keying (FSK)
Phase Shift Keying (PSK)
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10. Binary Signals: RZ, NRZ
Binary signaling methods
(a) On-off return-to-zero (RZ) coding.
(b) Non-return-to-zero (NRZ) coding.
(c) Polar NRZ coding.
Binary modulation methods:
a sinusoida1 carrier wave is switched
between the binary symbols "0" and "1."
A carrier A cos(ωt + φ) with three degrees of freedom
corresponds to three fundamental binary modulation methods:
(a)
(b)
(c)
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11. ASK
ASK modulator Synchronous demodulation of ASK Envelope detection of ASK
m(t) = 0 or 1 ( )v t
1( )v t
( )ov t
This requires the LO to have precisely the same phase and
frequency as the incoming signal.
ASK can be demodulated coherently using a synchronous LO
and mixer, but it is also possible to demodulate ASK with an
envelope detector.
Although envelope detection cannot be used to demodulate a
DSB-SC signal, it can be used with an ASK DSB-SC waveform
because the modulating signal m(t) is never negative.
Another non-coherent demodulator is the rectifier,
or square-law, detector
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12. FSK
FSK modulator Synchronous demodulation of FSK
1
2
for ( ) 1
for ( ) 0
m t
m t
ω
ω
ω
=
= 
=
( ) 0 or 1m t =
After LPF only the DC term remains, resulting in a positive pulse at the output of the summer,
indicating that a "1" has been received.
FSK can also be demodulated using an envelope detector, thereby avoiding the requirement for
two coherent LO.
The outputs of the envelope detectors are combined with a summer to form a polar NRZ output.
LO
LO
1( )v t
2 ( )v t
Mixer
"1"
"0"
FSK
Env. det. FSK polar NRZ
( )v t =
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13. PSK
PSK modulator Synchronous demodulation of PSK
( ) 1 or -1m t =
1( )v t 0 ( )v t
( )v t
( )v t =
The spectrum of the PSK waveform is relatively wide in BW due to the sharp
transitions caused by phase reversal.
These are usually smoothed by filtering, but the resulting BW is usually still wide
enough that PSK is impractical for multichannel wireless systems.
Since the PSK waveform has a constant envelope, it cannot be demodulated with
an envelope detector.
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14. Carrier Synchronization
Synchronism implies that both frequency and phase are identical difficult to achieve.
A phase error ∆φ causes the output signal reduced in amplitude by cos ∆φ, a frequency error ∆ω
while an error introduces a factor of cos∆ω.
Ex: if set a criteria of requiring less than 45o phase error at a 1 GHz carrier frequency,
synchronization of the LO to the carrier must be better than T/8.
T/8 = f -1/8 = 109 Hz-1/8=1 ns/8 = 0.125 ns.
A free-running local oscillator will virtually never exhibit such synchronism due to frequency drift,
Doppler effects, and the arbitrary distance between Tx and Rx.
ASK and FSK Advantage: Demodulate without a synchronous LO by using envelope detection.
Disadvantage: bit error rates (BER) are bad.
LO be synchronized by two ways with an incoming carrier wave:
(1) transmit a pilot carrier (2) use a carrier-recovery circuit.
Transmitting a low-level carrier is probably the easiest way, as this signal can be used to phase-
lock the LO.
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15. Carrier recovery circuits use phase or frequency information from the received signal
to synchronize the local oscillator. (a phase-locked loop).
Carrier Recovery Circuits for Sync. PSK Demodulation
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16. Error Probability for Binary Modulation
PCM (pulse code modulation) signals and detections
PCM codes a binary "1" as a signal voltage s1(t), and a binary "0" as a signal voltage s2(t), each of bit duration T.
In Tx, PCM signals are used to modulate a carrier by amplitude, frequency, or phase modulation.
In Rx, synchronous demodulation or envelope detection (for ASK or FSK) can be used to recover s(t) = s1(t) or
s2(t).
The demodulated signal is then used to make the decision as to whether a binary "1" or "0" has been received. In
the absence of noise this can simply be done by setting a detection threshold, where "1" or "0" is decided using a
comparator circuit.
optimum correlation receiver for PCM detection
a single bit is received incorrectly is called the
probability of error, or the bit error rate (BER).
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17. BER (I)
Bit energy as the energy of the (non-zero) signal voltage over one bit period:
The noise power output from an integrator with a bandlimited white noise input:
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18. BER (II)
Synchronous ASK
Synchronous PSK
ASK v.s. PSK
Energy-to-noise ratio in PSK case differs by a factor of four (6 dB) compared to ASK.
This implies for the same BER, PSK requires only one-fourth the power of an ASK system.
Since an ASK signal is off half the time, so the average transmit power of an ASK is half that of
a PSK, for the same peak power (same signal voltage, V).
Thus, in terms of average transmit power, the PSK result is better by a factor of two (3 dB),
compared with ASK.
1
2
( ) "1"
( ) "0" 0
s t V
s t
= ⇒

= ⇒
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19. BER (III)
Synchronous FSK
In the synchronous FSK demodulator output noise consists of the difference between noise
that has passed through both the ω1, ω2 channels.
The variance of n(t) can be computed as (n1 and n2 are uncorrelated)
Above shows that the total noise power of the FSK demodulator is doubled relative to the
synchronous ASK or PSK demodulator.
Synchronous FSK requires 3 dB more signal power than PSK for the same BER, and 3 dB
less power than ASK on a peak power basis.
FSK and ASK, however, have equal BER when compared in terms of average transmit
power, since an ASK system transmits power only half the time.
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20. Bit rate and bandwidth efficiency (I)
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21. Bit rate and bandwidth efficiency (II)
spectrum density
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22. M-ary Digital Modulation
Binary mod. transmit one bit per signal interval with BW efficiency = 1 bps/Hz.
M-ray mod. more than one bit be transmitted per signaling interval.
Allows greater bit rates for the same bandwidth (but need more complex system).
Transmit M = 2n symbols for each signaling interval BW efficiency = n bps/Hz.
M-ray mod. can be done by using multiple discrete amplitude levels, or multiple phase states,
or with a combination of these.
Ex: Symbol rate: Rs, Effective bit rate: Rb = nRs.
Ex:
M-ary modulation methods
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23. QPSK (I)
QPSK
If we use four states, where n = 2 and M = 4, then we can transmit two bits, or four symbols, for
each signaling interval. This is called quadrature phase shift keying (QPSK).
The horizontal axis represents the in-phase (I) component, while the vertical axis represents the
quadrature (Q) component that is shifted 90o in phase.
Constellation diagramPhase representation
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24. The In-phase and Quadrature components of the QPSK signal
I and Q components of a QPSK signals
QPSK (II)
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25. QPSK Modulator
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26. QPSK Demodulator
Demodulation of QPSK requires coherent detection.
The demodulator uses two mixers with quadrature LO components to recover the I and Q signals.
PCM detectors, each consisting of an integrator and a sampler, are used to detect the I and Q NRZ data,
which is then decoded with a parallel-to-serial converter to provide serial binary output.
Since QPSK is a constant envelope modulation, the detectors can use a zero threshold.
Coherent QPSK demodulator
2
The const. C is defined as / 2 2A T
0( ) cos( ),
(2 1)
4
for 0, 1, 2, 3.
i i
i
s t A t
i
i
ω φ
π
φ
= +
= +
=
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27. Since the overall probability that a symbol is received
correctly is the product of the probabilities that each
correlator operates correctly, the overall probability of
error for a symbol is:
Twice data rate at same bandwidth and error rate as BPSK.
Probability of error of QPSK
Use QPSK with Gray coding, then we can assume that a symbol error is most likely to cause
only a single bit error. Then since each symbol contains two bits, the bit error rate for QPSK
will be one-half the symbol error rate:
Symbol period T is twice the bit period, Es = 2Eb, where Eb is the bit energy.
2
symbol period , bit period / .
n
b s
M
R nR
T T n
=
⇒ =
⇒ = =
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28. M-ary Phase Shift Keying
2
symbol period , bit period / ,
each of M-PSK symbols corresponds to bits of binary data.
efficiency of M-PSK is bps/Hz.
n
b s
M
R nR
T T n
M n
BW n
=
⇒ =
⇒ = =
⇒
⇒
The probability of a symbol error for M-PSK is
approximately given by:
If Gray coding is used:
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29. Quadrature Amplitude Modulation (QAM)
We can further generalize M-ary modulation by allowing the amplitudes of the I and Q
components of the carrier to vary arbitrarily.
4-QAM is identical to QPSK, if the signal amplitudes are constant.
An approximate expression for the symbol error rate of 16-QAM is given by
Because of the high BW efficiency that can be obtained with QAM, it is increasingly
being used in modem wireless systems, including point-to-point microwave radios,
LMDS systems, and the DVB-C digital video cable broadcasting system.
P.S.
M = 2n symbols BW efficiency = n bps/Hz.
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30. Channel capacity
It is possible to achieve as low error rate as is desired once Eb/no is above a critical value.
Since Eb = S/Rb, this also implies that, for a fixed signal power S, there is a critical value of the data
rate Rb for which the error rate can be made as small as desired.
This particular value is called the channel capacity, and is given by a formula derived by Shannon:
C : maximum data rate in bps
B : bandwidth in Hz
S : signal power in W
n0/2 : two-sided noise power spectral density.
Shannon channel capacity formula gives the upper bound on the maximum data rate that can be
achieved for a given channel in the presence of additive Gaussian noise.
Error correcting codes can provide performance close to the Shannon limit.
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