Digital Modulation IFolio
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1
DIGITAL MODULATION
DEPARTMENT OF ELECTRICAL, ELECTRONIC & SYSTEM ENGINEERING
UNIVERSITI KEBANGSAAN MALAYSIA
Prof. Dr. Mohammad Tariqul Islam
Jabatan Kejuruteraan Elektrik, Elektronik & Sistem
Universiti Kebangsaaan Malaysia
43600 UKM, Bangi, Selangor, Malaysia
Email: [email protected]
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Lecture Frame
Introduction
ASK- Amplitude Shift Keying
FSK- Frequency Shift Keying
PSK- Phase Shift Keying
QAM- Quadrature Amplitude Modulation
CPM- Continous Phase Modulation
MSK- Minimum Shift Keying
Application of Digital Modulation
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Introduction
The analog signal transmission which modulated
digitally between two communication systems, or
can be called digital radio system.
The trend today: The analog modulation system
(e.g AM, FM) is replaced by modern digital
modulation system that has many advantages as
compared to analog modulation.
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Introduction
Basic Digital Modulation:
ASK- Amplitude Shift Keying
FSK- Frequency Shift Keying
PSK- Phase Shift Keying
The Important parameter for digital modulation:
Capacity
Bits
Bit rate/ Baud rate
Bandwidth
Bit rate : number of data bits transmitted in one second in a
communication system.
Baud rate: number of times a signal in a communications
channel changes state or varies.
Bps = baud per second x number of bit per baud
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1. ASK- Amplitude Shift Keying
The easiest digital modulation system compare to other modulation scheme.
Also can be called as DAM.
ASK signal can be represent as:
vask(t) = [ 1 + vm(t) ] [ (A/2)*cos(ωct) ]
Where
vask(t) = ASK wave
vm(t) = Digital modulating signal (Voltage)
A/2 = Unmodulation carrier/Amplitude (Voltage)
ωc = Analog carrier (radians per sec, 2fct)
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1. ASK- Amplitude Shift Keying
ASK binary baseband represent signal
Modulating Signal
Modulated Signal
amplitude change
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2. FSK- Frequency Shift Keying
Digital modulation with low performance level. Similar with FM concept.
Can also be called as BFSK (Binary FSK)
Representing by
vfsk(t) = vc cos { 2 [ fc + vm(t)f ]*t) }
Where
vfsk(t) = FSK wave
vc = Analog peak carrier amplitude (Voltage)
fc = Analog carrier frequenc (Hertz)
vm(t) = Binary input signal (Voltage)
f = Analog carrier peak frequency range (Voltage)
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Teknik Pemodulasi Digit
2. FSK- Frequency Shift Keying
(continue)...
f = | fm – fs | / 2
fm = mark frequency
fs = space freuency.
Bandwidth FSK, B = 2 ( f + fb )
where
fb = Input bit rate
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2. FSK- Frequency Shift Keying
FSK wave represent in time domain, where
fc= 4 kHz
fs fm fs fs fs fs fs fm fm fm
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FSK- Frequency Shift Keying
Binary Input Output
Frequency
‘0’ Space ( fs )
‘1’ Mark ( fm )
Truth table for FSK
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Gaussian Minimum-Shift Keying A special case of FSK called Gaussian Minimum-Shift Keying (GMSK) is used in the GSM cellular radio and PCS systems to be described later. In a minimum shift system, the mark and space frequencies are separated by half the bit rate, that is,
0.5m s bf f f Here,
Frequency transmitted for mark (binary 1)
Frequency transmitted for space (binary 0)
Bit rate
mf
sf
bf
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If we use the conventional FM terminology (refer to FM slides),
we see that GMSK has a deviation each way from the center
(carrier) frequency of,
0.25 bf Which corresponds to modulation index of
f
m
mf
0.25 b
b
f
f
0.25
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Example: The GSM cellular radio system uses GMSK in a 100 kHz
channel, with a channel data rate of 170 kb/s. Calculate:
(a) The frequency shift between mark and space
(b) The transmitted frequencies if the carrier (center) frequency is
exactly 880 MHz
(c) The bandwidth efficiency of the scheme in b/s/Hz.
Answer:
(a) The frequency shift is
0.5 0.5 170 85m s bf f f kHz kHz
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(b) The shift each way from the carrier frequency is half that found in (a), so the maximum frequency is
And the minimum frequency is
(c) The GSM system has a bandwidth efficiency of
170/100=1.7 b/s/Hz, comfortably under the theoretical maximum of 2 b/s/Hz for a two-level code.
max 0.25 880 0.25 170 922.5c bf f f MHz kHz MHz
min 0.25 880 0.25 170 837.5c bf f f MHz kHz MHz
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Shannon-Hartley Theorem There is a theoretical limit to the maximum data rate that
can be transmitted in a channel with a given bandwidth.
The Shannon-Hartley theorem states:
22 logC B M
Here,
C=information capacity in bits per second
B=bandwidth n hertz
M=number of possible states per symbol
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Shannon Limit The information capacity of a channel cannot be increased
without limit by increasing the number of states because
noise makes it difficult to distinguish between signal
states. The ultimate limit is called the Shannon limit:
2log (1 / )C B S N
Here,
C=information capacity in bits per second
B=bandwidth n hertz
S/N=signal to noise ratio (as a power ratio, not in decibels)
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Example: A radio channel has a bandwidth of 12 kHz and a signal to
noise ratio of 20 dB. What is the maximum data rate that can be
transmitted:
(a) Using any system?
(b) Using a code with four possible states?
Answer:
(a) We need the signal to noise ratio as a power ratio.
We can convert the given decibel value as follows:
1 20
log10
S
N
100
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Using equation for shannon limit:
2log (1 / )C B S N
3
212 10 log 1 100 312 10 6.658211
79.89 /kb s
(b) We can use the equation derived for Shannon-Hartley theorem, to
find the maximum possible bit rate given the specified code and
bandwidth. (a). From the Shannon-Hartley equation:
22 logC B M3
22 12 10 log 4 32 12 10 2
48 /kb s
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Since this is less than the maximum possible for this channel, it should be possible to transmit over this channel, with a four-level scheme, at 48 kb/s. A more elaborate modulation scheme would be required to attain the maximum data rate of 79.89 kb/s for the channel.
We will then have to compare this answer with that of part
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Example: A typical dial-up telephone connection has a bandwidth of 2 kHz
and a signal to noise ratio of 20 dB. Calculate the Shannon limit.
Answer:
We need the signal to noise ratio as a power ratio. We
can convert the given decibel value as follows:
1 20
log10
S
N
100
2log (1 / )C B S N
3
22 10 log 101
13.316 /kb s
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3. PSK- Phase Shift Keying
One of the angle modulation form, the amplitude is fixed but in term of binary representation.
Is used when the FSK modulation cannot be accommodate for high data rate in limited band channel.
Is one of M-ary digital modulation scheme, similar to phase modulation. The different at input PSK, which is binary digital signal and limited output phase.
M-ary encoding: N = log2 M,
where
N = required number of bit
M = possible number of level, condition or combination with bit N.
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3. PSK- Phase Shift Keying
BPSK is the easiest form of PSK, where N = 1 and M =
2.
Therefore, BPSK only has 2 phase at carrier, which are
logic ‘1’ phase and logic ‘0’ phase.
Can be called as Phase Reversal Keying (PRK) and
Biphase Modulation
Advantages: Improvement of the BER performance
Disadvantages: Spectral is not efficient due to rapid
phase with the presence of bit 1
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3. PSK- Phase Shift Keying
BPSK wave representation in time domain
Rising point and every 1
Phase different
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3. PSK- Phase Shift Keying
The others PSK types:
Delta-Phase Shift Keying, DPSK
Quadrature-Phase Shift Keying, QPSK or
DQPSK
Offset QPSK
/4 Delta-Phase Shift Keying
8-Phase Shift Keying
16-Phase Shift Keying
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M-ary Modulation/BPSK • Signals of this type are called quaternary/quadrature PSK
(QPSK) signals. They are a special case of multi-PSK (MPSK)
signals. Binary PSK signals are often labeled as BPSK.
BPSK (M=2)
ψ (t)
2
“0” “1”
s s
8PSK (M=8)
ψ2(t)
1
− E E
2 ψ(t) “010”
s
3 “011” 001”
b b 1
QPSK (M=4)
s
4
E
s
“
2
“000”
ψ 2
(t
)
s
“110”
1
“01”
“00”
ψ
(t
)
s
s
s 1
2
E
1 5
“111” “100”
s
s
ψ(t
1
s
s )
s
6 8
“101”s
7
3
“11”
“10”
4
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4. QAM- Quadrature Amplitude
Modulation
Similar to PSK, additional on carrier amplitude.
The technique is used to obtain high data rate
in a band limited channel.
The elements position in constellation diagram
is optimized so that:
The distance between element is maximized
(dynamic range increased)
Low error possibility
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4. QAM- Quadrature Amplitude
Modulation
Advantage: High data rate and more bandwidth efficient as compared to FSK or QPSK
Disadvantage: Easier to be influenced by noise and the amplitude is always changing.
Types of QAM: 4-QAM
8-QAM
16-QAM
....
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Quadrature Amplitude Modulation (QAM) • More general types of multi-symbol signaling schemes may be
generated by letting ai and bi take on multiple values themselves.
• The resultant signals are QAM signals. Therefore QAM is a
combined multi-phase/multi-amplitude signaling scheme.
16-QAM
“0000”
s
ψ
“0001” s
2
(t)
“0011” s
“0010”
s
1 2
3
3 4
“1000”
s
“1001” “1011” “1010”
s s s 5 6
1
-3 -1
s s
7 8
1 3
ψ s s
1
(t)
9
10
-1
11
12 “1100” “1101”
s s
“1111” “1110”
s s
13 14
-3
15 16 “0100”
“0101”
“0111”
“0110”
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QAM- Quadrature Amplitude
Modulation
Constellation diagram of QAM symbol,
for M= 4,16 dan 64
16-QAM
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QPSK: Without Pulse Shaping
Data
0
0
1
1
Data
0
1
0
1
Data
00
01
180o
10
11
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M-ary Modulation/ Error
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M-ary Modulation: Error Performance
M=2
M=4
M=8
M=16
PE
Note!
“The same average symbol
energy for different sizes of
signal space”
Eb
/N
0
dB
Probability of symbol error for M-PSK
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Quadrature Amplitude Modulation (QAM)
• As the number of constellation size increases, the phase spacing
between signals reduces correspondingly.
• The channel noise and phase jitter makes it more difficult to
distinguish individual points in a constellation as the number of
point increases. This will produce more errors at the receiver.
• There is a limit on the number of QAM states that may be used.
• Shannon channel capacity theorem:
⎛
S
⎞
C
=
B
log
2
1+ ⎝ N
⎠
C = channel capacity (bits/s)
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5. CPM- Continuous Phase
Modulation
The phase of carrier signal is continously
modulated.
The signal power is mostly homogeneous;
advantages of CPM as compared to other
digital modulation schemes.
Memory phase; phase for every signal is
determined by total of cumulative phase of the
prior signal.
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5. CPM- Continuous Phase
Modulation
Transmitted CPM signal-memory types transmission
No Phase Change for Continuous bit
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Minimum-Shift-Keying (MSK) MSK: wider mainlobe, but
better energy compaction,
hence more bandwidth
efficient
QPSK: energy spreading out,
hence not bandwidth efficient
MSK: lower sidelobes
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6. MSK- Minimum Shift Keying
MSK encoding bit is implemented with
bits alternating between quadrature
components & every bit is coded to half
sinuisoidal wave– reduce the distortion.
Represented by
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MSK- Minimum Shift Keying
continue...
Where
Therefore, s(t) can be coded as
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MSK- Minimum Shift Keying
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Application of Digital Modulation
Modem in telephone line system use 3 technique of modulation: FSK, PSK and QAM
The good features of Modem:
High immunity to noise
low bandwidth consumption
Low power consumption
Low cost
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Application of Digital Modulation
Dual tone multi frequency (DTMF) use
the MFSK technique
16/64-Q digital terrestrial television
modulation in AM is used for UK and
64/256-QAM in US for digital cable
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Application of Digital Modulation
Standard Wireless LAN, IEEE 802.11x use
various of PSK method depends to the
required data rate.
Example, QPSK technique is used to obtain
data rate 11 Mbit/s for IEEE 802.11b.
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Application of Digital Modulation
Bluetooth uses /4-DQPSK at low data
rate 2 Mbits/s, and 8-DPSK at high data
rate 3 Mbits/s.
BPSK is used for RFID which utilized for
biometric passport & credit card
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Application of Digital Modulation