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Digital Modulation Techniques
Contents System Review The Fundamentals Digital Modulation Waveforms Bandwidth and Power Efficient
Waveforms
3
System Review
Source Encode
Source Encode
EncryptionEncryption
ChannelEncoderChannelEncoder
ModulatorModulator
ChannelChannel
D/A Conversion
D/A Conversion
DecryptionDecryption
Source Decoder
Source Decoder
ChannelDecoderChannelDecoder
DemodulatorDemodulator
AnalogInputsignal
AnalogOutputsignal
DigitalOutput
DirectDigitalInput
DSP/RFFront-End
DSP/RFFront-End
A/D Conversion
A/D Conversion
Multiple Access
Multiplex
Waveform Processing
4
The Fundamentals
Why Modulate? Antenna Length Multiple Access Shannon’s Capacity Theorem Bandwidth and Power
5
The Fundamentals- Modulation Principles Almost all communication systems transmit
data using a sinusoidal carrier waveform. Electromagnetic signals propagate well. Choice of carrier frequency allows placement of
signal in arbitrary part of spectrum. Modulation is implemented in practice by:
Processing digital information at baseband. Pulse shaping and filtering of digital waveform. Baseband signal is mixed with signal from oscillator
to bring up to RF. Radio frequency (RF) signal is filtered amplified and
coupled with antenna.
6
What is Modulation? Modulation shifts the spectrum of a baseband
signal to that it becomes a bandpass signal. A bandpass signal has non-negligible
spectrum only about some carrier frequency fc >> 0
Note: the bandwidth of a bandpass signal is the range of positive frequencies for which the spectrum is non-negligible.
Unless otherwise specified, the bandwidth of a bandpass signal is twice the bandwidth of the baseband signal used to create it.
BW=B BW=2B
7
Digital Modulation Techniques The Definition
Bits into Symbols and waveform Basic Types
Amplitude Modulation (ASK) Frequency Modulation (FSK) Phase Modulation (PSK)
)cos( tA c
Amplitude Frequency Phase
9
Waveform Processing
Generic Modulation Waveform Generator
I/Q-Comp. Mapping
SymbolConverter
Differential/Grey Encoder
PulseShaping
SamplingConverter
Input Bits
ModulatedSignal
Bit Rate Symbol Rate Sampling Rate
Minimum Rate ?
)(
sc Fnfje /2
10
Digital Modulation
Classification
Linear Modulation Techniques
Non-Linear Modulation Techniques
-Digital Phase Modulations (PSK)-Digital Amplitude and Phase Modulations (QAM)
-Continuous Phase Modulations (CPM)
- FSK- GMSK
Other Classifications:-Constant/Non-Constant Envelope-Bandwidth/Power Efficient Types
11
Linear Modulation
I/Q Complex Mapping Two independent real baseband signals (I and
Q, Inphase and quadrature) are transmitted by modulating them into cosine and sine waveforms of the carrier frequency- Increased bandwidth Efficiency.
For I- and Q-components, Nyquist pulse shaping principle (Overlapping pulses with zero-intersymbol interference, 0-ISI) is utilized in order to achieve high spectral efficiency.
12
Linear Modulation
Signal Representation
11,0,)()( 2
MkemTtgeAts tfj
m
jk
ck
Digital ModulationNyquist PulsesCarrier FrequencyM-ary Symbol Alphabet
1
0
)(2,2 M
j
jmmk nabb
M
M-ary Symbols Binary Bit Stream
13
Digital Modulation
Complex I/Q ModulationTaking Real Part of s(t)
)2sin()()2cos()(
)2cos()()(
tftQtftI
tfmTtgAts
cc
mkck
Where
mkk
mkk
mTtgAtQ
mTtgAtI
)(sin)(
)(cos)(
In-phase Channel
Quadrature-Phase Channel
14
Digital I/Q Modulation
Simplified Traditional Diagram
NyquistFilter
NyquistFilter
I(t)Re[]
Im[] Q(t)
)sin(
)cos(
kk
kk
jA
A
a(n)
)2cos( tfc
)2sin( tfc
s(t)
Constellation Mapping
15
Digital Modulation Complex Symbol Constellation Diagram
BPSK
,02
0)(
1,0,)(cos)(
kM
tQ
kmTtgtI
k
mk
BPSK, M=2
Re
Im
Mapping Rule
bit phase0 -> 01 ->
16
Complex Constellation
QPSK M=4
4/,4/3,4/3,4/44
2
)(sin)(
3,2,1,0,)(cos)(
k
mTtgtQ
kmTtgtI
k
mk
mk
QPSK, M=4
Bandwidth Efficiency = log2M = 2 bits/s/Hz
17
Complex Constellation
16-QAM M=16
1.0
3.0
-1.0
-3.0
k
k
mkk
mkk
A
mTtgAtQ
kmTtgAtI
)(sin)(
15,2,1,0,)(cos)(
Bandwidth Efficiency = log2M = 4 bits/s/Hz
18
QPSK Modulation
Phase Maping in QPSK Grey Encoding Differential Encoding
Bits Phase (Grey)
00011011
-3/43/4-/4/4
Phase(Diff. Change)
0/2/2
11
10
01
00
00
01
1011
19
QPSK Digital Modulator Architecture
SymbolConverter
Differential/Grey Encoder
Digital
Modulator
PulseShaping
SamplingConverter
Input Bits
ModulatedSignal
Baseband Processor
00 001 110 211 3
Binary-M-ary
0 123
-3/43/4-/4/4
b(n) nkcos
ksin
21
Pulse Shaping
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10-4
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
T (n+1)TnT
22
Digital Modulation Techniques
Role of Pulse Shaping Issues with QPSK Design Example
Input Bit Rate = 1MbpsPulse Shaping = 0.3B = ?
23
Digital Modulations
OQPSK Same Signal Constellation as QPSK Phase Variations Restricted to Only
90o Less Co-Channel Interference
24
Digital Modulations
OQPSK)2sin()()2cos()()( tftQtftIts cc
1
0
1
0
( ) cos ( )
( ) sin ( )2
K
kk
K
kk
I t A g t kT
TQ t A g t kT
SymbolConverter
Grey Encoder
QPSK
Modulator
SamplingConvert
Input Bits
ModulatedSignal
Insert T/2 Delay
25
Digital Modulations
MSK Continuous Phase Frequency Modulation Technique
1,4
2cos)(
kk
kc bxt
T
bfts
Carrier SymbolPeriod
InputSymbols
Continuous Phase
2)(
2 11
kkkk bb
kxx
26
Digital Modulation
MSK Phase Modulation
tftQtftIts cc 2sin)(2cos)()(
T
txbtQ
T
txtI
kk
k
2sincos)(
2coscos)(
Where
27
Digital Modulations
Comparison 1 0 0 1 0 0 001 1
I(t) forQPSK/OQPSK
Q(t) forQPSK
Q(t) forOQPSK
I(t) forMSK
Q(t) forMSK
29
Digital Modulations
GMSK Gaussian Filtered MSK Used in GSM and DECT More Compact Spectrum than MSK Some ISI Member of CPM Schemes
30
Digital Modulations
GMSK ),(2cos(
2)( ttf
T
Ets c
i
ii iTtqht )(2),( Where
,...2,1,0),1(,...,2,1 iMi
For GMSK2/1
2
h
M
t
dgtq )()(
)2/(
2ln
2erf)2/(
2ln
2erf
2
1)( Tt
BTt
B
Ttg bb
31
Digital Modulations
GMSK
222
2ln
2
2ln
2)(
tB
b
b
eBth
Filter Impulse Response
GaussianLPF
FM Modulatorh=0.5
(t) s(t)
32
Digital Modulations
/4-QPSK Better Bandwidth Efficiency than
GMSK Better Spectral Efficiency than
QPSK/OQPSK Both Absolute and Differential Phase
Encoding Used in IS-54 and PHS
33
Digital Modulations
/4-QPSK Gray Encoding
0 123
-3/4 3/4-/4/4
b(n) nncos
nsin/4
Gray Encoder
t=2nT
t=(2n+1) T
/4-QPSK Modulator
In Bits Modulated Signal
34
/4-QPSK
Differential Encoding
0 123
/43/4-/4-3/4
b(n) nncos
nsin/4
Differential Encoder
t=2nT
t=(2n+1)T
/4-QPSK Modulator
T
nnn 1
0
1 2
3
35
Digital Modulations
M-PSK
1,...,1,0,2
MaaM kkk
M=8
M=16
)2sin()()2cos()()( tftQtftIts cc
1
0
1
0
)(sin)(
)(cos)(
K
kk
K
kk
kTtAtQ
kTtAtI
36
Digital Modulation Techniques
Issues with MPSK Less Amplitude fluctuations Allows Differential Encoding Frequency/Phase Sync Problems with
Higher Order MPSK Degraded BER Performance for higher
Order as Non-Optimal Euclidean Distance Between Constellation Points.
37
Digital Modulation Techniques
M-QAM Better BER Performance for higher M
than equivalent M-PSK Bandwidth Efficient - Allows Power-
Bandwidth Tradeoffs Requires Linear/Linearised PAs Generally not Suitable for Wireless
Applications Used in DVB ETSI Standard
38
Digital Modulation Techniques
M-QAM
)2sin()()2cos()()( tftQtftIts cc
1
0
1
0
)(sin)(
)(cos)(
K
kkk
K
kkk
kTtAtQ
kTtAtI
M=16
Square Constellation Requires Absolute GrayEncoding