modulation, demodulation and coding course 7 3 today, we are going to talk about: some bandpass...
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Digital Communications I:Modulation and Coding Course
Term 3 - 2008Catharina Logothetis
Lecture 7
Lecture 7 2
Last time we talked about:
Another source of error due to filtering effect of the system: Inter-symbol interference (ISI)
The techniques to reduce ISI Pulse shaping to achieve zero ISI at the
sampling time Equalization to combat the filtering effect of
the channel
Lecture 7 3
Today, we are going to talk about:
Some bandpass modulation schemes used in DCS for transmitting information over channel M-PAM, M-PSK, M-FSK, M-QAM
How to detect the transmitted information at the receiver Coherent detection Non-coherent detection
Lecture 7 4
Block diagram of a DCS
FormatSourceencode
FormatSourcedecode
Channelencode
Pulsemodulate
Bandpassmodulate
Channeldecode
Demod. SampleDetect
Channel
Digital modulation
Digital demodulation
Lecture 7 5
Bandpass modulation
Bandpass modulation: The process of converting a data signal to a sinusoidal waveform where its amplitude, phase or frequency, or a combination of them, are varied in accordance with the transmitting data.
Bandpass signal:
where is the baseband pulse shape with energy . We assume here (otherwise will be stated):
is a rectangular pulse shape with unit energy. Gray coding is used for mapping bits to symbols. denotes average symbol energy given by
( ) TtttitTEtgts ici
Ti ≤≤+∆−+= 0 )()1(cos2)()( φωω
)(tgT
)(tgT gE
sE ∑ == M
i is EM
E1
1
Lecture 7 6
Demodulation and detection
Demodulation: The receiver signal is converted to baseband, filtered and sampled.
Detection: Sampled values are used for detection using a decision rule such as the ML detection rule.
Nz
z1
z=∫T
0
)(1 tψ
∫T
0
)(tNψ)(tr
1z
Nz
z Decision circuits
(ML detector)m̂
Lecture 7 7
Coherent detection
Coherent detection requires carrier phase recovery at the
receiver and hence, circuits to perform phase estimation.
Sources of carrier-phase mismatch at the receiver: Propagation delay causes carrier-phase offset in
the received signal. The oscillators at the receiver which generate
the carrier signal, are not usually phased locked to the transmitted carrier.
Lecture 7 8
Coherent detection ..
Circuits such as Phase-Locked-Loop (PLL) are implemented at the receiver for carrier phase estimation ( ).
PLL
Oscillator 90 deg.
( ) )()(cos2)()( tnttTEtgtr iii
T +++= αφω ( )αω ˆcos2 +tT c
( )αω ˆsin2 +tT c
Used by correlators
αα ˆ≈
I branch
Q branch
Lecture 7 9
Bandpass Modulation Schemes
One dimensional waveforms Amplitude Shift Keying (ASK) M-ary Pulse Amplitude Modulation (M-PAM)
Two dimensional waveforms M-ary Phase Shift Keying (M-PSK) M-ary Quadrature Amplitude Modulation
(M-QAM) Multidimensional waveforms
M-ary Frequency Shift Keying (M-FSK)
Lecture 7 10
One dimensional modulation, demodulation and detection
Amplitude Shift Keying (ASK) modulation:
( )φω += tTEts ci
i cos2)(
( )
cos2)(
,,1 )()(
1
1
ii
c
ii
Ea
tT
t
Mitats
=
+=
==
φωψ
ψ
)(1 tψ1s2s0 1E
“0” “1”On-off keying (M=2):
Lecture 7 11
One dimensional mod.,…
M-ary Pulse Amplitude modulation (M-PAM)
( )tT
ats cii ωcos2)( =
( )
( )
gs
gii
gi
c
ii
EME
MiEE
EMia
tT
t
Mitats
3)1(
12
)12(
cos2)(
,,1 )()(
2
22
1
1
−=
−−==
−−=
=
==
s
ωψ
ψ 4-PAM:
)(1 tψ2s1s0gE3−
“00” “01”4s3s
“11” “10”
gE− gE gE3
Lecture 7 12
Example of bandpass modulation:Binary PAM
Lecture 7 13
Coherent detection of M-PAM
∫T
0
)(1 tψ
ML detector(Compare with M-1 thresholds))(tr 1z m̂
One dimensional mod.,...–cont’d
Lecture 7 14
Two dimensional modulation, demodulation and detection (M-PSK)
M-ary Phase Shift Keying (M-PSK)
+=
Mit
TEts cs
iπω 2cos2)(
( ) ( )
2
21
21
2211
2sin 2cos
sin2)( cos2)(
,,1 )( )()(
iis
sisi
cc
iii
EE
MiEa
MiEa
tT
ttT
t
Mitatats
s==
=
=
−==
=+=
ππ
ωψωψ
ψψ
Lecture 7 15
Two dimensional mod.,… (MPSK)
)(1 tψ
2s1sbE
“0” “1”
bE−
)(2 tψ
3s
7s
“110”)(1 tψ
4s 2ssE
“000”
)(2 tψ
6s 8s
1s5s
“001”“011”
“010”
“101”
“111” “100”
)(1 tψ
2s 1s
sE
“00”
“11”
)(2 tψ
3s 4s“10”
“01”
QPSK (M=4)
BPSK (M=2)
8PSK (M=8)
Lecture 7 16
Two dimensional mod.,…(MPSK) Coherent detection of MPSK
Compute Choose smallest2
1arctanzz φˆ
|ˆ| φφ −i
∫T
0
)(1 tψ
∫T
0
)(2 tψ)(tr
1z
2z
m̂
Lecture 7 17
Two dimensional mod.,… (M-QAM)
M-ary Quadrature Amplitude Mod. (M-QAM)
( )ici
i tTEts ϕω += cos2)(
( ) ( )
3)1(2 and symbols PAM are and where
sin2)( cos2)(
,,1 )( )()(
21
21
2211
−=
==
=+=
MEaa
tT
ttT
t
Mitatats
sii
cc
iii
ωψωψ
ψψ
( )
+−−+−+−+−+−
−−−+−−+−−−−+−−+−
=
)1,1()1,3()1,1(
)3,1()3,3()3,1()1,1()1,3()1,1(
, 21
MMMMMM
MMMMMMMMMMMM
aa ii
Lecture 7 18
Two dimensional mod.,… (M-QAM)
)(1 tψ
)(2 tψ
2s1s 3s 4s“0000” “0001” “0011” “0010”
6s5s 7s 8s
10s9s 11s 12s
14s13s 15s 16s
1 3-1-3
“1000” “1001” “1011” “1010”
“1100” “1101” “1111” “1110”
“0100” “0101” “0111” “0110”
1
3
-1
-3
16-QAM
Lecture 7 19
Two dimensional mod.,… (M-QAM)
Coherent detection of M-QAM
∫T
0
)(1 tψ
ML detector1z
∫T
0
)(2 tψ
ML detector
)(tr
2z
m̂Parallel-to-serialconverter
s) threshold1 with (Compare −M
s) threshold1 with (Compare −M
Lecture 7 20
Multi-dimensional modulation, demodulation & detection
M-ary Frequency Shift keying (M-FSK)
( ) ( )
Tf
titTEt
TEts c
si
si
21
2
)1(cos2cos2)(
=∆=∆
∆−+==
πω
ωωω
( )2
1
0
cos2)(
,,1 )()(
iis
sijii
M
jjiji
EE
jijiEat
Tt
Mitats
s==
≠===
== ∑=
ωψ
ψ
)(1 tψ
2s
1s
3s
)(3 tψ
)(2 tψsE
sE
sE
Lecture 7 21
Multi-dimensional mod.,…(M-FSK)
Mz
z1
z=∫T
0
)(1 tψ
∫T
0
)(tMψ)(tr
1z
Mz
zML detector:
Choose the largest element
in the observed vector
m̂
Lecture 7 22
Non-coherent detection
Non-coherent detection: No need for a reference in phase with the
received carrier Less complexity compared to coherent
detection at the price of higher error rate.
Lecture 7 23
Non-coherent detection …
Differential coherent detection Differential encoding of the message
The symbol phase changes if the current bit is different from the previous bit.
( ) ,...,MiTtttTEts ii 1 ,0 ,)(cos2)( 0 =≤≤+= θω
)())1(()( nTTnnT ikk φθθ +−=
)(1 tψ
iφ
1s2s 0
0 1 2 3 4 5 6 7 1 1 0 1 0 1 11 1 1 0 0 1 1 1π π π π π π0 0
Symbol index: Data bits:Diff. encoded bitsSymbol phase: kθ
kmk
Lecture 7 24
Non-coherent detection … Coherent detection for diff encoded mod.
assumes slow variation in carrier-phase mismatch during two symbol intervals.
correlates the received signal with basis functions uses the phase difference between the current received
vector and previously estimated symbol
( ) TttnttTEtr i ≤≤+++= 0 ),()(cos2)( 0 αθω
)(1 tψ
)(2 tψ
),( 11 ba),( 22 ba
iφ
( ) ( ) )())1(()())1(()( nTTnnTTnnT ijiji φθθαθαθ =−−=+−−+
Lecture 7 25
Non-coherent detection … Optimum differentially coherent detector
Sub-optimum differentially coherent detector
Performance degradation about 3 dB by using sub-optimal detector
∫T
0
)(1 tψ
)(tr m̂Decision
DelayT
∫T
0)(tr m̂Decision
DelayT
Lecture 7 26
Non-coherent detection … Energy detection
Non-coherent detection for orthogonal signals (e.g. M-FSK)
Carrier-phase offset causes partial correlation between I and Q branches for each candidate signal.
The received energy corresponding to each candidate signal is used for detection.
Lecture 7 27
Non-coherent detection …
Non-coherent detection of BFSK
∫T
0
)cos(/2 1tT ω
∫T
0)(tr
11z
12z
∫T
0
∫T
0
21z
22z
Decision stage:
)cos(/2 2tT ω
)sin(/2 2tT ω
)sin(/2 1tT ω
( ) 2
( ) 2
( ) 2
( ) 2 +
-
)(Tz
0ˆ ,0)( if1ˆ ,0)( if
=<=>
mTzmTz
m̂
212
211 zz +
222
221 zz +