lecture3.ppt

27/4/00
p. 1
Postacademic Course on
Telecommunications
Module-3 Transmission Marc Moonen
Lecture-3 Transmitter Design K.U.Leuven/ESAT-SISTA
Module-3 : Transmission
Lecture-3 (27/4/00)
Marc Moonen
Dept. E.E./ESAT, K.U.Leuven
marc.moonen@esat.kuleuven.ac.be
www.esat.kuleuven.ac.be/sista/~moonen/

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Lecture-3 Transmitter Design K.U.Leuven-ESAT/SISTA
Lecture-3: Transmitter Design
Overview
• Transmitter : Constellation + Transmit filter
• Preliminaries : Passband vs. baseband transmission
• Constellations for linear modulation
->M-PAM / M-PSK / M-QAM
->BER performance in AWGN channel for transmission of
1 symbol (Gray coding, Matched filter reception)
• Transmission pulses :
->Zero-ISI-forcing design procedure for transmit pulse
(and receiver front-end filter), Nyquist pulses, RRC pulses

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Lecture-3: Transmitter Design
Lecture partly adopted from
Module T2
`Digital Communication Principles’
M.Engels, M. Moeneclaey, G. Van Der Plas
1998 Postgraduate Course on Telecommunications
Special thanks to Prof. Marc Moeneclaey

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Transmitter: Constellation + Transmit Filter
PS: channel coding (!) not considered here
s
k E
a .
r(t)
k
â
transmit
pulse
s(t)
n(t)
p(t) +
AWGN
transmitter receiver (to be defined)
h(t)
channel
...
constellation
transmit filter (linear modulation)
 

k
s
k
s kT
t
p
a
E
t
s )
(
.
.
)
(

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Transmitter: Constellation + Transmit Filter
-> s(t) with infinite bandwidth, not the greatest choice for p(t)..
-> implementation: upsampling/digital filtering/D-to-A/S&H/...
s
k E
a .
transmit
pulse
s(t)
p(t)
transmitter
discrete-time
symbol sequence
continuous-time
transmit signal
t
p(t)
Example:
t

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Preliminaries: Passband vs. baseband transmission (I)
Baseband transmission
• transmitted signal is
(linear modulation)
• transmitted signals have to be real,
hence = real, p(t)=real
• baseband means for
f
B
-B
0
)
( 
f
SLP
B
f 
|
|
)
( f
SLP
 

k
s
k
s
LP kT
t
p
a
E
t
s )
(
.
.
)
(
k
a

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Preliminaries : Passband vs. baseband transmission (II)
Baseband transmission model/definitions
g(t)=p(t)*h(t)*f(t) (convolution)
everything is real here!
s
k E
a .
r(t)
k
â
transmit
pulse
s(t)
n(t)
p(t) + f(t)
front-end
filter
AWGN
1/Ts
transmitter
receiver
(first version, see also Lecture4)
h(t)
channel

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Preliminaries : Passband vs. baseband transmission (III)
Bandpass transmission
transmitted signal is modulated baseband signal
)
(t
sLP
)
.
2
cos( 0t
f

f
B
-B
)
( f
SLP
)
(t
sBP
-fo
f
)
( f
SBP
fo fo+B

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Preliminaries : Passband vs. baseband transmission (IV)
Bandpass transmission:
• note that modulated
signal has 2x larger
bandwidth, hence
inefficient scheme !
• solution = accommodate
2 baseband signals in 1
bandpass signal :
I =`in-phase signal’
Q=`quadrature signal’
such that energy in BP is
energy in LP
2

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Preliminaries : Passband vs. baseband transmission (V)
• Convenient notation for `two-signals-in-one’ is
complex notation :
• re-construct `complex envelope’ from BP-signal
(mathematics omitted)
)
(
.
)
(
)
( t
s
j
t
s
t
s Q
I
LP 

low-pass filter

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Assignment 2.1
• Prove for yourself that this is indeed a correct
complex-envelope reconstruction procedure!
low-pass filter

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Preliminaries : Passband vs. baseband transmission (VI)
Passband transmission model/definitions
(mathematics omitted):
a convenient and consistent (baseband) model can be
obtained, based on complex envelope signals, that
does not have the modulation/demodulation steps:
k
â
f(t)
front-end
filter
1/Ts
receiver (first version)
r(t)
n’(t)
+
AWGN
s
k E
a .
transmit
pulse
s(t)
p(t)
transmitter
h’(t)
channel

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Preliminaries : Passband vs. baseband transmission (V)
k
â
f(t)
front-end
filter
1/Ts
receiver (first version)
r(t)
n’(t)
+
AWGN
s
k E
a .
transmit
pulse
s(t)
p(t)
transmitter
h’(t)
channel
=complex symbols
=usually a complex filter
)
(
)
(
' 0
2
t
h
e
t
h t
f
j 


=complex AWGN
=complex
=real-valued transmit pulse
Q
k
I
k
k a
j
a
a ,
, .



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Preliminaries : Passband vs. baseband transmission (VI)
• In the sequel, we will always use this baseband-
equivalent model, with minor notational changes
(h(t) and n(t), i.o. h’(t) and n’(t)).
Hence no major difference between baseband and
passband transmission/models (except that many
things (e.g. symbols) can become complex-valued).
• PS: modulation/demodulation steps are transparent
(hence may be omitted in baseband model) only if
receiver achieves perfect carrier synchronization
(frequency fo & phase).
Synchronization not addressed here
(see e.g. Lee & Messerschmitt, Chapter 16).

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Constellations for linear modulation (I)
Transmitted signal (envelope) is:
Constellations:
PAM PSK QAM
pulse amplitude modulation phase-shift keying quadrature amplitude modulation
4-PAM (2bits) 8-PSK (3bits) 16-QAM (4bits)
ps: complex constellations for passband transmission
I
R
I
R
I
R
 

k
s
k
s kT
t
p
a
E
t
s )
(
.
.
)
(

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Constellations for linear modulation (II)
M-PAM pulse amplitude modulation
• energy-normalized iff
• then distance between nearest neighbors is
larger d -> noise immunity (see below)
I
R
 
PAM
PAM
PAM
k A
M
A
A
a )
1
(
,.....,
3
, 




k
a
1
3
)
( 2


M
M
APAM
1
12
)
( 2


M
M
dPAM
d

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Constellations for linear modulation (III)
M-PSK phase-shift keying
• energy-normalized iff ….
• Then distance between nearest neighbors is








 1
,...,
1
,
0
|
)
2
.
exp( M
m
M
m
j
ak 
k
a
)
sin(
.
2
)
(
M
M
dPSK


d
I
R

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p. 18
Constellations for linear modulation (IV)
M-QAM quadrature amplitude modulation
• distance between nearest neighbors is
1
6
)
(


M
M
dQAM
d
I
R
 
QAM
QAM
QAM
k
Q
k
I A
M
A
A
a
a )
1
(
,.....,
3
,
, ,
, 




k
Q
k
I
k a
j
a
a ,
, .


)
(
)
(
)
( M
d
M
d
M
d QAM
PSK
PAM 


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BER Performance for AWGN Channel
BER=(# bit errors)/(# transmitted bits)
g(t)=p(t)*f(t) (convolution)
n’(t)=n(t)*f(t)
BER for different constellations?
r(t)
k
â
transmit
pulse
s(t)
n(t)
p(t) +
s
k E
a .
f(t)
front-end
filter
AWGN
channel
1/Ts
transmitter receiver
r’(t)

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p. 20
definitions:
- transmitted signal
- received signal (at front-end filter)
- received signal (at sampler)
g(t) =p(t)*f(t) = transmitted pulse p(t) filtered by front-end filter
n’(t) =n(t)*f(t) = AWGN filtered by front-end filter
)
(
'
)
(
.
.
)
(
' t
n
kT
t
g
a
E
t
r
k
s
k
s 

 
 

k
s
k
s kT
t
p
a
E
t
s )
(
.
.
)
(
)
(
)
(
.
.
)
( t
n
kT
t
p
a
E
t
r
k
s
k
s 

 

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Received signal sampled @ time t=k.Ts is...
1 = useful term
2= `ISI’, intersymbol interference (from symbols other than )
3= noise term
Strategy :
a) analyze BER in absence of ISI (=`transmission of 1 symbol’)
b) analyze pulses for which ISI-term = 0 (such that analysis
under a. applies)
c) for non-zero ISI, see Lecture 4-5






 

 




3
2
0
1
)
.
(
'
)
.
(
.
)
0
(
.
.
)
.
(
' s
m
s
m
k
k
s
s T
k
n
T
m
g
a
g
a
E
T
k
r 

 


k
a

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Transmission of 1 symbol over AWGN channel (I)
BER for different constellations?
k
â
transmit
pulse
n(t)
p(t) +
s
E
a .
0
f(t)
front-end
filter
AWGN
channel
1/Ts
...take 1 sample at time 0.Ts
transmit 1 symbol at time 0.Ts ...

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Transmission of 1 symbol over AWGN channel (II)
Received signal sampled @ time t=0.Ts is..
• `Minimum distance’ decision rule/device :
 







3
2
1
0 )
.
0
(
'
0
)
0
(
.
.
)
.
0
(
' s
s
s T
n
g
a
E
T
r 


n
s
s
M
n
i
s
s
i
g
E
T
r
g
E
T
r
a 

 






 )
0
(
.
)
.
0
(
'
min
)
0
(
.
)
.
0
(
'
ˆ
1
0
0

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p. 24
Transmission of 1 symbol over AWGN channel (III)
`Minimum distance’ decision rule :
Example : decision regions for 16-QAM
I
R

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p. 25
Transmission of 1 symbol over AWGN channel (IV)
Preliminaries :BER versus SER (symbol-error-rate)
• aim: each symbol error (1 symbol = n bits)
introduces only 1 bit error
• how? : GRAY CODING
make nearest neighbor symbols correspond to
groups of n bits that differ only in 1 bit position…
• …hence `nearest neighbor symbol errors’
(=most symbol errors) correspond to 1 bit error

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p. 26
Transmission of 1 symbol over AWGN channel (V)
Gray Coding for 8-PSK

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p. 27
Transmission of 1 symbol over AWGN channel (VI)
Gray Coding for 16-QAM

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p. 28
Transmission of 1 symbol over AWGN channel (VII)
• Computations : skipped
(compute probability that additive noise pushes received
sample in wrong decision region)
• Results:
neighbors
of
number
average
)
(
)
2
exp(
.
2
1
)
(
)
(
)
0
(
)
(
log
).
(
.
2
.
(
.
log
)
(
2
2
2
2
2
0
2













M
N
du
u
x
Q
df
f
F
g
M
M
d
N
E
Q
M
M
N
BER
x
b




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p. 29
Transmission of 1 symbol over AWGN channel (VIII)
Interpretation (I) : Eb/No
• Eb= energy-per-bit=Es/n=(signal power)/(bitrate)
• No=noise power per Hz bandwidth
lower BER for higher Eb/No

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p. 30
Transmission of 1 symbol over AWGN channel (IX)
Interpretation (II) : Constellation
for given Eb/No, it is found that…
BER(M-QAM) =< BER(M-PSK) =< BER(M-PAM)
BER(2-PAM) = BER(2-PSK) = BER(4-PSK) = BER(4-QAM)
higher BER for larger M (in each constellation family)

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p. 31
Transmission of 1 symbol over AWGN channel (X)
Interpretation (III): front-end filter f(t)
It is proven that
and that is obtained only when
this is known as the `matched filter receiver’
(see also Lecture-4)






df
f
F
g
2
2
)
(
)
0
(

1
0 

1


)
(
)
(
and
)
(
)
(
i.e.
,
)
(
)
(
2
*
*
f
P
f
G
t
p
t
f
f
P
f
F 




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p. 32
Transmission of 1 symbol over AWGN channel (XI)
Interpretation (IV)
with a matched filter receiver, obtained BER is
independent of pulse p(t)

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p. 33
Transmission of 1 symbol over AWGN channel (XII)
BER for M-PAM (matched filter reception)

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p. 34
Transmission of 1 symbol over AWGN channel (XIII)
BER for M-PSK (matched filter reception)

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p. 35
Transmission of 1 symbol over AWGN channel (XIV)
BER for M-QAM (matched filter reception)

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p. 36
Symbol sequence over AWGN channel (I)
• ISI (intersymbol interference) results if
• ISI results in increased BER
0
)
.
(
such that
0 

 s
T
m
g
m
g(t)=p(t)*f(t)

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p. 37
Symbol sequence over AWGN channel (II)
• No ISI (intersymbol interference) if
• zero ISI -> 1-symbol BER analysis still valid
• design zero-ISI pulses ?
0
)
.
(
:
0 

 s
T
m
g
m

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p. 38
Zero-ISI-forcing pulse design (I)
• No ISI (intersymbol interference) if
• Equivalent frequency-domain criterion:
This is called the `Nyquist criterion for zero-ISI’
Pulses that satisfy this criterion are called `Nyquist pulses’
0
)
.
(
:
0 

 s
T
m
g
m
)
0
(
constant
)
(
1
g
T
k
f
G
T k s
s








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p. 39
Zero-ISI-forcing pulse design (II)
• Nyquist Criterion for Bandwidth = 1/2Ts
Nyquist criterion can be fulfilled only when G(f)
is constant for |f|<B, hence ideal lowpass filter.

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p. 40
Zero-ISI-forcing pulse design (III)
• Nyquist Criterion for Bandwidth < 1/2Ts
Nyquist criterion can never be fulfilled

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p. 41
Zero-ISI-forcing pulse design (IV)
• Nyquist Criterion for Bandwidth > 1/2Ts
Infinitely many pulses satisfy Nyquist criterion

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p. 42
Zero-ISI-forcing pulse design (V)
• Nyquist Criterion for Bandwidth > 1/2Ts
practical choices have 1/T>Bandwidth>1/2Ts
Example:
Raised Cosine (RC) Pulses
1
0
factor'
off
-
`roll
:



(%)
100
.
Bandwidth
Excess
2T
1
Bandwidth





s

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p. 43
Zero-ISI-forcing pulse design (VI)
Example:
Raised Cosine Pulses
(time-domain)

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p. 44
Zero-ISI-forcing pulse design (VII)
Procedure:
1. Construct Nyquist pulse G(f) (*)
e.g. G(f) = raised cosine pulse
(formulas, see Lee & Messerschmitt p.190)
2. Construct F(f) and P(f), such that (**)
F(f)=P*(f) and P(f).F(f)=G(f) -> P(f).P*(f)=G(f)
e.g. square-root raised cosine (RRC) pulse
(formulas, see Lee & Messerschmitt p.228)
(*) zero-ISI, hence 1-symbol BER performance
(**) matched filter reception = optimal performance

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p. 45
Zero-ISI-forcing pulse design (VIII)
• PS: Excess BW simplifies implementation
-`shorter’ pulses (see time-domain plot)
- sampling instant less critical (see eye diagrams)
`eye diagram’ is `oscilloscope view’ of signal before
sampler, when symbol timing serves as a trigger
20%
excess-BW
100%
excess-BW

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p. 46
Zero-ISI-forcing pulse design (IX)
• PPS: From the eye diagrams, it is seen that
selecting a proper sampling instant is crucial
(for having zero-ISI)
->requires accurate clock synchronization,
a.k.a. `timing recovery’, at the receiver
(clock rate & phase)
->`timing recovery’ not addressed here
see e.g. Lee & Messerschmitt, Chapter 17

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p. 47
Questions….
1. What if channel is frequency-selective, cfr. h(t) ?
- Matched filter reception requires that F(f)=P*(f).H*(f)
- Zero-ISI requires that P(f).H(f).F(f)=Nyquist pulse
Is this an optimal design procedure ?
k
â
f(t)
front-end
filter
1/Ts
receiver (see lecture-4)
n(t)
+
AWGN
s
k E
a .
transmit
pulse
p(t)
transmitter
h(t)
channel

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p. 48
Assignment 2.2
Analyze this design procedure for the case where the
channel is given as
H(f) = Ho for |f|<B/2
H(f) = 0.1 Ho for B/2<|f|<B
discover a phenomenon known as `noise enhancement’
(=zero-ISI-forcing approach ignores the additive noise, hence may
lead to an excessively noise-amplifying receiver)
k
â
f(t)
front-end
filter
1/Ts
n(t)
+
AWGN
s
k E
a .
transmit
pulse
p(t)
transmitter
h(t)
channel

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p. 49
Questions….
2. Is the receiver structure (matched filter front-end +
symbol-rate sampler + slicer) optimal at all ?
Sampler works at symbol rate. With non-zero excess
bandwidth this is below the Nyquist rate.
Didn’t your signal processing teacher tell you never to do
sample below the Nyquist rate? Could this be o.k. ????
k
â
f(t)
front-end
filter
1/Ts
n(t)
+
AWGN
s
k E
a .
transmit
pulse
p(t)
transmitter
h(t)
channel

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p. 50
Conclusion
• Transmitter structure:
symbol constellation + transmit pulse p(t)
• Symbol constellation: PAM/PSK/QAM
BER-analysis for transmission of 1 symbol over AWGN-channel
-> Performance of matched filter receiver is independent of transmit pulse
• Transmit pulse p(t):
-> Zero-ISI-forcing design procedure for transmit pulse p(t)
and front-end filter f(t), for AWGN channels (-> RRC pulses)
-> Even though for more general channels this is not an optimal
procedure (see Lecture 4), transmit pulses are usually designed as
RRC’s.

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