Post on 22-Apr-2018
transcript
Digital Modulation
On-Off keying (OOK), or amplitude shift keying (ASK)
Phase shift keying (PSK), particularly binary PSK (BPSK)
Frequency shift keying
Typical spectra
Modulation/demodulation principles
Main difference between digital and analog systems: goal of
transmission.
Advantages of digital modulation:
More flexibility through DSP (processing, services, etc.)
Noise/interference immunity; security
Fits to computer/data communications
Lecture 10
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 1(20)
Baseband Binary Modulation• Binary data representation: 0 or 1.
• Unipolar modulation: high level (e.g., 5V) / zero, or 1/0
• Bipolar modulation: +high level / -high level, or +1/-1
1
b
RT
= bit (data) rate, bit/s
L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.
NRZ
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 2(20)
Amplitude Shift Keying (ASK)• Switch on-off the carrier:
• Signal representation:
• Is it similar to something?
• Signal spectrum?
( ) ( ) ( )cos 2c c
x t A m t f t= π
( ) 1 or 0m t =
L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.
binary ASK:
general case: a fixed number of levels
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 3(20)
L.W
. C
ouch II,
Dig
ital and A
nalo
g C
om
munic
ation S
yste
ms, P
rentice H
all, 2001.
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 4(20)
Amplitude Shift Keying (ASK)
• Signal spectrum (FT):
• Square-wave message:
• Random message PSD:
• How to detect?
( ) ( ) ( )2
c
x m c m c
AS f S f f S f f= − + +
0
20
( ) ( ),
1 1sinc ,
2 2 2 2
m n
n
j n
nb
S f c f nf
n Rc e f
T
+∞
=−∞
π
= δ −
= = =
∑
L.W
. C
ouch II,
Dig
ital and A
nalo
g C
om
munic
ation S
yste
ms, P
rentice H
all, 2001.
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 5(20)
Binary Phase Shift Keying
• BPSK signal representation:
where is bipolar message.
• Another form of the BPSK signal ->
( ) ( )cos ( )c c
x t A t m t= ω + ∆ϕ⋅
( ) 1m t = ±
( ) cos cos
sin ( )sin
c c
c c
x t A t
A m t t
= ∆ϕ ω −
− ∆ϕ⋅ ω
L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 6(20)
Binary Phase Shift Keying
• Digital modulation index:
• Important special case (random message)
• Compare with ASK!
• How to detect?
2
d
∆ϕβ =
π
1d
β =
L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.
PSD
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 7(20)
Detection of BPSK
• Same as analog PM
• Add a quantizer (sign(*) function) to improve performance
(noise immunity)
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka
sign(.)out (+/-1)
8(20)
Frequency Shift Keying
• Discontinuous FSK: ( )( )
( )1 1
2 2
cos , mark (1)
cos , space (0)
c
c
A tx t
A t
ω + θ=
ω + θ
Not popular (spectral noise + PLL problems)
L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 9(20)
Frequency Shift Keying
• Continuous FSK:
L.W. Couch II, Digital and Analog Communication Systems, Prentice Hall, 2001.
( ) ( )0
cos
t
c cx t A t m d
= ω + ∆Ω τ τ
∫
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 10(20)
Pulse-Amplitude Modulation (PAM)
• Baseband modulation (no carrier yet)
• Baseband signal represents digital data (e.g. binary)
• PAM: a conversion of an analog signal to a pulse-type signal in
which the pulse amplitude carriers the analog information.
• This is the 1st step in converting an analog signal (waveform) to a
digital signal.
1 1
1
... ... ( ) ( )
n
n n k
k
b b A A x t A s t kT
=
→ → = −∑
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 11(20)
Pulse-Amplitude Modulation
• Based on the sampling theorem: analog band-limited (to Fmax
)
signal can be represented by its samples taken at
• PAM provides pulse-like waveform that contains the same
information as the original analog signal. Pulse rate [pulses/s] is
the same as fs .
• Pulse shape can be any. Discuss rectangular pulse waveform
first.
• Two types of sampling: natural sampling (gating) and
instantaneous sampling (flat-top or sample-and-hold).
max2
sf F≥
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 12(20)
Natural Sampling (Gating)
• The sampled (PAM) signal is
where
( ) ( ) ( ),
( )
s
s
k
x t s t x t
t kTs t
∞
=−∞
=
− = Π τ ∑
max1/ 2
s sf T F= ≥
( )sx t
( )x t
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 13(20)
Natural Sampling (Gating): Spectrum
• Spectrum (FT) of the sampled (PAM) signal is
where is the duty cycle of s(t).
[ ] ( )( ) ( ) sinc( ) ,sx s x s
k
S f FT x t d kd S f kf
∞
=−∞
= = −∑
/s
d T= τ
original signal spectrum sampled signal spectrum
( )x
S f
( )sx
S f
sinc( )d kd⋅
( )xd S f⋅
similar to ideal (delta-function) sampling?
Example:
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 14(20)
Natural Sampling: Proof
• Start with
• Find Fourier series of s(t):
• FT of s(t) is
• Finally,
• This concludes the proof.
• How to recover (demodulate) the original signal?
( ) ( ) ( ) ( ) ( )* ( )s
s x x sx t s t x t S f S f S f= ↔ =
( ) , sinc( )sjn t
n n
n
s t c e c d nd
∞
ω
=−∞
= = ⋅∑
( ) ( )s n s
n
S f c f nf
∞
=−∞
= δ −∑
( ) ( )* ( ) ( )sx x s n x s
n
S f S f S f c S f nf
∞
=−∞
= = −∑
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 15(20)
Instantaneous Sampling
• Also known as flat-top PAM or sample-and-hold.
• The sampled signal is
( ) ( )
* ( ) ( )
ss s
k
s s
k
t kTx t x kT
tx kT t kT
∞
=−∞
∞
=−∞
− = Π τ
= Π δ − τ
∑
∑
( )x t
( )sx t
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 16(20)
Instantaneous Sampling: Spectrum
• The sampled signal spectrum (FT) is
( )1
( ) ( ) , ( ) sinc( )sx x s
s k
S f H f S f kf H f fT
∞
=−∞
= − = τ ⋅ τ∑
Proof – homework. How to recover (demodulate) x(t) ?
original signal spectrum sampled signal spectrum
( )x
S f
( )sx
S f
sinc( )d f⋅ τ
( )sinc( )x
d f S f⋅ τ ⋅
Example:
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 17(20)
Baseband PAM: Generic Case
• Basic pulse shape is not necessarily rectangular. The
information is represented by the pulse amplitude Am
.
• M-ary PAM signal waveform:
• s(t) – signal waveform, T – symbol interval, M – the number of
symbols.
( ) ( ), 1,2,... , 0m mx t A s t m M t T= = ≤ ≤
2log [bits]bn M=
• The information transmitted by
one symbol:
• Transmitted signal sequence
T
( )s t
t
0
generic signal waveform
( ) ( )T k
k
x t A s t kT= −∑
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 18(20)
PAM: Energy, Spectrum
• Baseband signal energy:
• Depends on m.
• Bandpass PAM signal:
• Its spectrum (FT):
• It is DSB-SC signal! The bandwidth is twice of that of baseband
signal.
• Bandpass signal energy:
• Similar modulation formats: PPM, PWM.
2 2 2
0 0
( ) , ( )
T T
m m m s sE x t dt A E E s t dt= = =∫ ∫
( ) ( ) cos , 1, 2,... , 0m m cx t A s t t m M t T= ω = ≤ ≤
( )( ) ( ) ( )2m
m
x s c s c
AS f S f f S f f= − + +
22
0
( )2
T
mm m s
AE x t dt E= =∫
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 19(20)
Summary
Basic digital modulation formats. Unipolar and bipolar NRZ
baseband signals. ASK (OOK), PSK and FSK. Spectra and
bandwidth.
PAM. Instantaneous and flat-top sampling. Spectra of
sampled signals. Recovery (demodulation) of the original
signal. Generic form of a PAM signal.
Homework: Reading: Couch, 3.1, 3.2, 5.9. Study carefully all
the examples, make sure you understand and can solve them
with the book closed.
22-Mar-17 Lecture 10, ELG3175 : Introduction to Communication Systems © S. Loyka 20(20)