DSP for Software Radio
Waveform Processing – Single Carrier
Systems
Dr. Jamil Ahmad
Digital Modulation Techniques

Contents




System Review
The Fundamentals
Digital Modulation Waveforms
Bandwidth and Power Efficient Waveforms
2
System Review
Analog
Input
signal
Direct
Digital
Input
Analog
Output
signal
A/D
Conversion
D/A
Conversion
Source
Encode
Source
Decoder
Encryption
Digital
Output
Decryption
Multiplex
Channel
Encoder
Channel
Decoder
Modulator
Multiple
Access
Demodulator
DSP/RF
Front-End
Channel
DSP/RF
Front-End
Waveform Processing
3
The Fundamentals

Why Modulate?




Antenna Length
Multiple Access
Shannon’s Capacity Theorem
Bandwidth and Power
4
The FundamentalsModulation 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.
5
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 nonnegligible.
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
6
Digital Modulation Techniques


The Definition
 Bits into Symbols and waveform
Basic Types



Amplitude Modulation (ASK)
Frequency Modulation (FSK)
Phase Modulation (PSK)
A cos(  c t   )
Amplitude
Frequency
Phase
7
Digital Modulation
8
Waveform Processing

Generic Modulation Waveform
Generator
Modulated
Signal
Input
Bits
Symbol
Converter
Differential
/Grey
Encoder
I/Q-Comp.
Mapping
Pulse
Shaping
Sampling
Converter
 ()
e
Bit Rate
Symbol Rate
j 2  nf c / F s
Sampling Rate
Minimum Rate ?
9
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
10
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 zerointersymbol interference, 0-ISI) is utilized in order
to achieve high spectral efficiency.
11
Linear Modulation

Signal Representation
 
 j 2 fct 
j k
s ( t )      A k e g ( t  mT )  e
,

  m  

k  0 ,1  M  1
Digital Modulation Nyquist Pulses Carrier Frequency M-ary Symbol Alphabet
k 
2
M
M 1
 bm   ,
M-ary Symbols
bm 
2
j
a (n)
j0
Binary Bit Stream
12
Digital Modulation

Complex I/Q Modulation
Taking Real Part of s(t)

s (t ) 
A
k
g ( t  mT ) cos( 2  f c t   k )
m  
 I ( t ) cos( 2  f c t )  Q ( t ) sin( 2  f c t )
Where

I (t ) 

A k cos  k g ( t  mT )
In-phase Channel
A k sin  k g ( t  mT )
Quadrature-Phase Channel
m  

Q (t ) 

m  
13
Digital I/Q Modulation

Simplified Traditional Diagram
cos( 2 f c t )
Re[]
A k cos(  k )
a(n)
Nyquist
Filter
I(t)
s(t)
S

jA k sin(  k )
Im[]
Constellation Mapping
Nyquist
Filter Q(t)

sin( 2 f c t )
14
Digital Modulation

Complex Symbol Constellation Diagram

BPSK

I (t ) 

cos  k g ( t  mT ) ,
k  0 ,1
Im
m  
Q (t )  0
k 
2
M
Re
k  0 ,  
Mapping Rule
bit phase
0 -> 0
1 -> 
BPSK, M=2
15
Complex Constellation

QPSK

M=4

 cos 
I (t ) 
k
g ( t  mT ) ,
k
g ( t  mT )
k  0 ,1, 2 ,3
m  

Q (t ) 
 sin 
m  
k 
2
4
k

4
QPSK, M=4
  / 4 ,3 / 4 ,  3 / 4 ,   / 4 
Bandwidth Efficiency = log2M
= 2 bits/s/Hz
16
Complex Constellation

16-QAM

3.0
M=16

I (t ) 

A k cos  k g ( t  mT ) ,
k  0 ,1, 2 ,  15
1.0
m  

Q (t ) 

m  
A k sin  k g ( t  mT )
-1.0
k 
Ak 
-3.0
Bandwidth Efficiency = log2M
= 4 bits/s/Hz
17
QPSK Modulation

Phase Maping in QPSK


Bits
00
01
10
11
Grey Encoding
Differential Encoding
Phase
(Grey)
-3/4
3/4
-/4
/4
Phase
(Diff. Change)
0
/2
/2

01
11
00
10
00
01
11
10
18
QPSK Digital Modulator
Architecture
Baseband Processor
Input
Bits
Symbol
Converter
Binary- 00
M-ary 01
10
11
0
1
2
3
Differential
/Grey
Encoder
Pulse
Shaping
Digital
Modulator
b(n)  n
0
1
2
3
-3/4
3/4
-/4
/4
Sampling
Converter
Modulated
Signal
cos  k
sin  k
19
QPSK Modulator

Differential Encoder
 n   n 1    n
b(n)   n
0
1
2
3
0
/2
/2

cos  k
T
sin  k
20
Pulse Shaping
0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
-4
x 10
nT
T
(n+1)T
21
Digital Modulation Techniques



Role of Pulse Shaping
Issues with QPSK
Design Example
Input Bit Rate = 1Mbps
Pulse Shaping a = 0.3
B=?
22
Digital Modulations

OQPSK



Same Signal Constellation as QPSK
Phase Variations Restricted to Only 90o
Less Co-Channel Interference
23
Digital Modulations

OQPSK
s ( t )  I ( t ) cos( 2 f c t )  Q ( t ) sin( 2 f c t )
K 1
I ( t )  A  cos  k g ( t  kT )
k 0
K 1
Q ( t )  A  sin  k g ( t  kT 
k 0
Input
Bits
Symbol
Converter
Grey
Encoder
QPSK
Modulator
T
)
2
Sampling
Convert
Insert T/2
Delay
Modulated
Signal
24
Digital Modulations

MSK


Continuous Phase
Frequency Modulation Technique
 

bk 
s ( t )  cos  2  f c 
t  x k  ,
4
T

 

Carrier
bk   1
Symbol Continuous
Period Phase
Input
Symbols
k


x k   x k 1 
( b k 1  b k )   2
2


25
Digital Modulation

MSK

Phase Modulation
s ( t )  I ( t ) cos 2 f c t  Q ( t ) sin 2 f c t
Where
I ( t )  cos x k cos
t
2T
Q ( t )  b k cos x k sin
t
2T
26
Digital Modulations

Comparison
1 0 0 1 0 0 1 0 0 1
I(t) for
QPSK/OQPSK
Q(t) for
QPSK
Q(t) for
OQPSK
I(t) for
MSK
Q(t) for
MSK
27
Digital Modulation

Spectrum Comparison
QPSK/OQPSK
BPSK
MSK
28
Digital Modulations

GMSK





Gaussian Filtered MSK
Used in GSM and DECT
More Compact Spectrum than MSK
Some ISI
Member of CPM Schemes
29
Digital Modulations

GMSK
2E
s (t ) 
Where
T
cos( 2 f c t   ( t , a )
 ( t , a )  2  a i hi q ( t  iT )
i
a i   1,  2 ,...,  ( M  1),
i  0 ,  1,  2 ,...
t
q (t ) 
 g ( ) d 

For GMSK
M 2
h  1/ 2
g (t ) 
1 
 2 B b

 2 B b

erf
(
t

T
/
2
)

erf
(
t

T
/
2
)





2T 
 ln 2

 ln 2

30
Digital Modulations

GMSK
Filter Impulse Response
h (t ) 
2
ln 2
a(t)
Gaussian
LPF

Bb e
2
2
ln 2
2 2
Bb t
FM Modulator
h=0.5
s(t)
31
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
32
Digital Modulations

/4-QPSK

Gray Encoding
Gray Encoder
b(n)  n
In Bits
0
1
2
3
-3/4
3/4
-/4
/4
/4-QPSK Modulator
t=2nT
/4
cos  n
sin  n
Modulated Signal
t=(2n+1) T
33
/4-QPSK

Differential Encoding
0
1
Differential Encoder
b(n)   n
0
1
2
3
/4
3/4
-/4
-3/4
3
/4-QPSK Modulator
t=2nT
/4
t=(2n+1)T
2
cos  n
T
sin  n
 n   n 1    n
34
Digital Modulations

M-PSK
M=8
s ( t )  I ( t ) cos( 2 f c t )  Q ( t ) sin( 2 f c t )
K 1
I ( t )  A  cos  k  ( t  kT )
k 0
K 1
Q ( t )  A  sin  k  ( t  kT )
k 0
k 
2
M
ak ,
M=16
a k  0 ,1,..., M  1
35
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.
36
Digital Modulation Techniques

M-QAM





Better BER Performance for higher M than
equivalent M-PSK
Bandwidth Efficient - Allows PowerBandwidth Tradeoffs
Requires Linear/Linearised PAs
Generally not Suitable for Wireless
Applications
Used in DVB ETSI Standard
37
Digital Modulation Techniques

M-QAM
M=16
s ( t )  I ( t ) cos( 2 f c t )  Q ( t ) sin( 2 f c t )
K 1
I (t ) 

A k cos  k  ( t  kT )
k 0
K 1
Q (t ) 

A k sin  k  ( t  kT )
k 0
Square Constellation Requires Absolute GrayEncoding
38
Digital Modulation Techniques

M-QAM for Wireless
Application




Star Constellation
Non-Optimal ED
Allows Differential
Encoding
Viewed as 2 8-PSK
Signals
39