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Modul #06
TE3223 TE3223 SISTEM KOMUNIKASISISTEM KOMUNIKASI 22SISTEM KOMUNIKASI SISTEM KOMUNIKASI 22
QAM & FSKModulasi,Demodulasi,Kinerja
Program Studi S1 Teknik TelekomunikasiDepartemen Teknik Elektro - Sekolah Tinggi Teknologi Telkomp gg g
Bandung – 2008
QAM (Quadrature Amplitude Modulation)
Gabungan Modulasi ASK dan QPSKAmplitude Shift Keying (ASK) modulation:p y g ( )
( )φω += tEts i cos2)( O ff k i (M 2)( )φω += tT
ts ci cos)(
1)()( Mitats == ψ )(1 tψ1s2s“0” “1”
On-off keying (M=2):
( )cos2)(
,,1 )()(
1
1
c
ii
tT
t
Mitats
+=
==
φωψ
ψ K )(1ψ0 1E
ii EaT
=
Modul 6 - Siskom 2 - QAM dan FSK 2
M-ary ASK
M-ary ASK sering disebut M-ary Pulse Amplitude modulation (M-PAM)p ( )
( )tT
ats cii ωcos2)( =T
ii Mitats ,,1 )()( 1 == ψ K
4-ASK = 4-PAM:
“00” “01” “11” “10”
( )c
EMia
tT
t
)12(
cos2)(1
−−=
= ωψ )(1 tψ2s1s0
gE3−
4s3s
gE− gE gE3
( )gii
gi
M
MiEE
EMia
)1(
12
)12(
2
22
−
−−==
=
s
Modul 6 - Siskom 2 - QAM dan FSK 3
gs EME3
)1(=
Error probability ….
Coherent detection of M-PAM (M-aryASK )ASK )
Decision variable: 1rz =
)(1 tψ2s1s0
“00” “01”4s3s
“11” “10”
4-PAM
1
)(1 tψ
0gE3− gE− gE gE3
∫T
0
ML detector(Compare with M-1 thresholds))(tr
1rm̂
4Modul 6 - Siskom 2 - QAM dan FSK
Error probability ….C h d i f M PAMCoherent detection of M-PAM ….Error happens if the noise, , exceeds in amplitude one-half of the distance between adjacent symbols. For symbols
mrn s−= 11
one half of the distance between adjacent symbols. For symbols on the border, error can happen only in one direction. Hence:
( )( ) ( )
gmme MmErnP <<>−== ss 11 ;1for ||||Pr)(
( ) ( )gMMege ErnPErnP −<−==>−== ssss 111111 Pr)( and Pr)(
( ) ( ) ( )−<+>+>−
== ∑ 1111
PrM1 Pr
M1||Pr2)(1)( EnEnEn
MMP
MMP ggg
M
meE s
M )1( 2 −
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛−=
−=>
−= ∫
∞
=
01
1
2)1(2)()1(2Pr)1(2
MM
1 NE
QM
MdnnpM
MEnM
M
MM
g
E ng
m
g
⎟⎟⎠
⎞⎜⎜⎝
⎛
−−
=0
22
1log6)1(2)(
NE
MMQ
MMMP b
E
gbs EMEME3
)1()(log2 ==Gaussian pdf with
zero mean and variance 2/0N
⎠⎝ 0
5Modul 6 - Siskom 2 - QAM dan FSK
Modulation: representation
• Any modulated signal can be represented as (include QPSK, QAM)s(t) = A(t) cos [ωct + φ(t)]
amplitude phase or frequency
s(t) = A(t) cos φ(t) cos ωct - A(t) sin φ(t) sin ωct
in-phase quadrature
• Linear versus nonlinear modulation ⇒ impact on spectral efficiency Linear: Amplitude or phase modulationN li f d l ti t l b d i
• Constant envelope versus non-constant envelope⇒ hardware implications with impact on power efficiency
Non-linear: frequency modulation: spectral broadening
p p p y(=> reliability: i.e. target BER at lower SNRs)
6Modul 6 - Siskom 2 - QAM dan FSK
Teknik Modulasi M-ary Kuadratur( diagram blok konseptual )
)( fA
)(tsI )(txI
)(tyI)2cos( tfA cπ
)(tb )(ty
)2sin( tfA cπ
)(tdI
)(tdQ
)(tsQ )(txQ
)(tyQ
)(Q
)2cos( tfA cπ
)(~ tb)(ˆ ty
)(~ tdI
)(tb)(ty
)2sin( tfA cπ
2÷
)(~ tdQ
7Modul 6 - Siskom 2 - QAM dan FSK
Bentuk gelombang 16 QAM
00.51
1.5
05)(tb )(ˆ ty
0 5 10 15 20 25 30 35 40-0.5
0
00.51
1.5 0 5 10 15 20 25 30 35 40
-5
-2024
)(tdI )(~ txI
0 5 10 15 20 25 30 35 40-0.5
0
-2024 0 5 10 15 20 25 30 35 40
-4
-202
)()(tX
ts
I
I )(~ tsI
0 5 10 15 20 25 30 35 40-4
4-2024
0 5 10 15 20 25 30 35 40
050
0.51
1.5
)(tyI)(~ tdI
0 5 10 15 20 25 30 35 40-4
-5
0
50 5 10 15 20 25 30 35 40
-0.5
-0.50
0.51
1.5
)(ty )(~ tb
0 5 10 15 20 25 30 35 405
0 5 10 15 20 25 30 35 400.5
8Modul 6 - Siskom 2 - QAM dan FSK
M-PSK and M-QAMComplex Vector Spaces: Constellations
M-PSK (Circular Constellations) M-QAM (Square Constellations)
Complex Vector Spaces: Constellations
16-PSK
bn 4-PSK16-QAM
4-PSK
bn
an an
Tradeoffs – Higher-order modulations (M large) are more spectrally
efficient but less power efficient (i.e. BER higher). – M-QAM is more spectrally efficient than M-PSK but
also more sensitive to system nonlinearities.
9Modul 6 - Siskom 2 - QAM dan FSK
Two dimensional mod.… (M-QAM)M ary Quadrature Amplitude Mod (M QAM)M-ary Quadrature Amplitude Mod. (M-QAM)
( )i tEts ϕω += cos2)( ( )ici tT
ts ϕω += cos)(
,,1 )( )()( 2211 =+= Mitatats iii ψψ K
( ) ( )
)1(2db lPAMdh
sin2)( cos2)(
)()()(
21
2211
−
==
ME
tT
ttT
t cc
iii
ωψωψ
ψψ
3)1(2andsymbolsPAM are and where 21 =
MEaa sii
( ) ⎥⎥⎤
⎢⎢⎡
−−−+−−+−−−−+−−+−
)3,1()3,3()3,1()1,1()1,3()1,1(
MMMMMMMMMMMM
L
L
( )
⎥⎥⎥⎥
⎦⎢⎢⎢⎢
⎣ +−−+−+−+−+−
++=
)1,1()1,3()1,1(
)3,1()3,3()3,1(, 21
MMMMMM
MMMMMMaa ii
L
MMMM
10Modul 6 - Siskom 2 - QAM dan FSK
Two dimensional mod.… (M-QAM)
16-QAM)(2 tψ
2s1s 3s 4s“0000” “0001” “0011” “0010”
3
6s5s 7s 8s1 313
“1000” “1001” “1011” “1010”
1
)(1 tψ
10s9s 11s 12s1 3-1-3
“1100” “1101” “1111” “1110”-1
14s13s 15s 16s“0100” “0101” “0111” “0110”
-3
11Modul 6 - Siskom 2 - QAM dan FSK
Two dimensional mod.… (M-QAM)
Coherent detection of M-QAM
)(1 tψz
∫T
0
ML detector1z
)(t m̂s) threshold1 with (Compare −M
T
)(2 tψ
)(tr
2z
mParallel-to-serialconverter
∫T
0
ML detector2zs) threshold1 with (Compare −M
12Modul 6 - Siskom 2 - QAM dan FSK
Error probability …
Coherent detection of M QAM
)(2 tψ
ss s s“0000” “0001” “0011” “0010”of M-QAM 2s1s 3s 4s
6s5s 7s 8s“1000” “1001” “1011” “1010”
)(1 tψ10s9s 11s 12s
“1100” “1101” “1111” “1110”
16-QAM
∫T
0
)(1 tψML detector1r
ˆs) threshold1 with (Compare −M
14s13s 15s 16s“0100” “0101” “0111” “0110”
∫T
)(2 tψML detector
)(tr
2r
m̂Parallel-to-serialconverter
∫0 s) threshold1 with (Compare −M
13Modul 6 - Siskom 2 - QAM dan FSK
Error probability …Coherent detection of M-QAM …M-QAM can be viewed as the combination of twomodulations on I and Q branches respectively
PAM−Mmodulations on I and Q branches, respectively. No error occurs if no error is detected on either I and Q branches. Hence:C id i th t f th i l d th litConsidering the symmetry of the signal space and orthogonality of I and Q branches:
branches) Q and Ion detectederror noPr(1)(1)( −=−= MPMP CE
( )( )Q) onerror I).Pr(no onerror Pr(nobranches) Q and I on detectederror noPr( =
( )( )22 1I) onerror Pr(no MPE−==
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛ −= 2
1log3114)(
NE
MMQ
MMP b
E Average probability of ⎟⎠
⎜⎝ −⎠⎝ 01 NMM symbol error for PAM−M
14Modul 6 - Siskom 2 - QAM dan FSK
Probability of symbol error for M-PAM
Note!• M = 2k
• “The same average symbol energy for different sizes of
EP
e e gy o d e e t s es osignal space”
Modul 6 - Siskom 2 - QAM dan FSK 15dB / 0NEb
Probability of symbol error for M-QAM
Note!• M = 2k
• “The same average symbol energy for different sizes of
EP
e e gy o d e e t s es osignal space”
Modul 6 - Siskom 2 - QAM dan FSK 16dB / 0NEb
Binary FSK
( ) ( ) bb Tttf
TEts ≤≤= 0 2cos2
01 π f0 and f1 are chosen such that
( ) ( ) bb
b
b
TttfTEts
T
≤≤= 0 2cos212 π ( ) ( ) orthogonal02cos2cos 1
00 →=∫ dttftf
bT
ππ
Modul 6 - Siskom 2 - QAM dan FSK 18
Coherent Detectionby Integrate and Dump / Matched Filter Receiverby teg ate a d u p / atc ed te ece e
Coherent detection utilizes carrier phase information and requires in-phase replica of the carrier at the receiver (explicitly or implicitly) It is easy to show that these two techniques have the sameIt is easy to show that these two techniques have the same performance:
( ) ( )h t s tτ= −
( ) ( ) ( )v t s t y tτ= − ⊗
( )y t ( )v T
0
( ) ( ) ( )( ) ( )
ys t y dτ
ττ τ τ∫
⊗
= −
( )t
( )s tτ −( )s t τ−
( )y t ( )v T
0( ) ( ) ( )v t s t y dτ τ τ τ∫= −19Modul 6 - Siskom 2 - QAM dan FSK
Coherent Detection
y0(Tb)
x(t) ( )tfT b
02cos2 π
( )tfT 12cos2 π
y1(Tb)
Tb
When s1(t) is transmitted: When s2(t) is transmitted:
( )( ) ⎥
⎦
⎤⎢⎣
⎡ +=⎥
⎦
⎤⎢⎣
⎡
nnE
TyTy b
b
b
1
0( )( ) ⎥
⎦
⎤⎢⎣
⎡+
=⎥⎦
⎤⎢⎣
⎡nE
nTyTy
bb
b
1
0
20
Let’s compare Error probability: BPSK vs BFSKBPSK vs BFSK
BPSK and BFSK with coherent detection:2/ ⎞⎛ ss
)(2 tψ )(tψ
2/
2/
0
21
⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
NQPB
ss
)(tψ
2s1sE
“0” “1”)(2ψ )(1 tψ
1s bE bE221 =− ss“0”BPSK BFSK
)(1 tψbEbE−
bE221 =− ss2s
)(2 tψ
bE
“1”
2⎟⎟⎠
⎞⎜⎜⎝
⎛=
NEQP b
B
0⎟⎟⎠
⎞⎜⎜⎝
⎛=
NEQP b
B
0 ⎠⎝ N 0 ⎠⎝
21Modul 6 - Siskom 2 - QAM dan FSK
Non-coherent DetectionBase on filtering signal energy on allocated spectra and usingBase on filtering signal energy on allocated spectra and using envelope detectorsHas performance degradation of about 1-3 dB when compared to coherent detection (depending on Eb/N0)to coherent detection (depending on Eb/N0) Examples:
2-ASK
2-FSK
22Modul 6 - Siskom 2 - QAM dan FSK
Error probability BFSK…
Non-coherent detection of BFSK)cos(/2 1 tT ω Decision variable:
Diff f l
∫T
0
)( 1
11r ( )2 2
122
111 rrz +=
21 zzz −=Difference of envelopes
∫T
0)(tr12r
Decision rule:
)sin(/2 1tT ω
( )2 + z m̂)(
∫T
0
21r)cos(/2 2 tT ω
( )2 - 0ˆ ,0)( if1ˆ ,0)(if
=<=>
mTzmTz
∫T
0
22r)sin(/2 2 tT ω
( )2
222
2212 rrz +=
∫0
23Modul 6 - Siskom 2 - QAM dan FSK
Error probability BFSK – cont’dNon-coherent detection of BFSK …
>+>= 112221 )|Pr(21)|Pr(
21 zzzzPB ss
[ ]
∫ ∫∫∞ ∞∞
⎥⎤
⎢⎡=>=
>=>= 2221221
112221
)|()|()|()|Pr(
),|Pr()|Pr(
)|(2
)|(2
dzzpdzzpdzzpzzz
zzzEzz
B
ssss
ss
∫ ∫∫ ⎥⎦⎤
⎢⎣⎡=>=
0 2221210 2222221 )|()|()|(),|Pr(2
dzzpdzzpdzzpzzzz
ssss
⎟⎟⎞
⎜⎜⎛
−= exp1 EP b Rayleigh pdf Rician pdf⎟⎟⎠
⎜⎜⎝
=02
exp2 N
PBy g p p
Similarly, non-coherent detection of DBPSK
⎟⎟⎞
⎜⎜⎛−= exp1 EP b
B ⎟⎟⎠
⎜⎜⎝ 0
exp2 N
PB
24Modul 6 - Siskom 2 - QAM dan FSK
Demodulation & Detection M-FSK
M-ary Frequency Shift Keying (M-FSK)
EE 22 ( ) ( )
f
titTEt
TEts c
si
si
1
)1(cos2cos2)(
ΔΔ
Δ−+==
ω
ωωω
Tf
22==Δ
π
M
∑)(3 tψ
( )
1
cos2)(
,,1 )()(
sijii
jjiji
jiEatt
Mitats
⎨⎧ =
==
== ∑=
ωψ
ψ K
s
3ssE
( )
2
0 cos)(
iis
ijii
EE
jiat
Tt
s==
⎩⎨
≠ωψ
2s
1s)(2 tψ
sE
E
)(1 tψ
sE
25Modul 6 - Siskom 2 - QAM dan FSK
Demodulation & Detection M-FSK
Coherent detection of M-FSK
)(tψ
⎥⎤
⎢⎡ z1∫
T
0
)(1 tψ
)(tr
1zML detector:
Choose m̂
⎥⎥⎥
⎦⎢⎢⎢
⎣ MzM z=
∫T
)(tMψ)(tr z Choose
the largest element in the observed vector
m
⎥⎦⎢⎣ Mz∫0 Mz
26Modul 6 - Siskom 2 - QAM dan FSK
Error probability …
Coherent detection of M-FSK …The dimensionality of signal space is M An upperThe dimensionality of signal space is M. An upper
bound for average symbol error probability can be obtained by using union bound. Hence
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛−≤
0
1)(NEQMMP s
E
or, equivalently
( ) ( )⎟⎟⎠
⎞⎜⎜⎝
⎛−≤
0
2log1)(N
EMQMMP bE
27Modul 6 - Siskom 2 - QAM dan FSK
Bit error probability versus symbol error probabilityerror probability
Number of bits per symbol For orthogonal M ary signaling (M FSK)
Mk 2log=
For orthogonal M-ary signaling (M-FSK)
12/
122 1
==−
k
kB
MM
PP
21lim
112
=
−−
∞→E
B
k
E
PP
MP
For M-PSK, M-PAM and M-QAM
2EP
1for <<≈ EE
B PkPP
28Modul 6 - Siskom 2 - QAM dan FSK
Probability of symbol error for M-FSK
Note!• M = 2k
• “The same average symbol energy for different sizes of
EP
e e gy o d e e t s es osignal space”
dB / 0NEb29Modul 6 - Siskom 2 - QAM dan FSK
Power Spectral FSKThe FSK wave can be written asThe FSK wave can be written as
( ) TtT
ttfTEts b
bc
b
b ππ 0 2cos2≤≤⎟⎟
⎠
⎞⎜⎜⎝
⎛±=
Th i h t i l t l i d d t f th
( ) ( ) ( )tfT
tTEtf
Tt
TEts c
bb
bc
bb
b ππππ 2sinsin22coscos2⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛= m
The in-phase component is completely independent of the input binary wave. The power spectral density of this component consists of two delta functions at f=+- 1/2TbTh d t t i l t d t th i t biThe quadrature component is related to the input binary wave and is given by
( ) 0 2⎪⎨
⎧≤≤= Tt
TE
tg bb
( )
( ) ( )2cos8
otherwise 0
=Ψ
⎪⎩
⎨
fTTEf
Ttg
bbb
b
π
Modul 6 - Siskom 2 - QAM dan FSK 30
( ) ( )2222 14 −=Ψ
fTf
b
gπ
Power Spectral FSK
( )2811 ⎤⎡ ⎞⎛⎞⎛ fTTEE ( )( )2222
2
14cos8
21
21
2 −+⎥
⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛++⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
fTfTTE
Tf
Tf
TEPSD
b
bbb
bbb
b
ππδδ
Modul 6 - Siskom 2 - QAM dan FSK 31
Power Spectral M-FSK
bTM 5.0hfor FSK ary-M •≈⇒= 2logBW deviation) (freq 0.5
Modul 6 - Siskom 2 - QAM dan FSK 32
Bandwidth vs. Power Efficiency(contoh M’ary PSK FSK dan M-ary QAM pada BER = 10-6 )
M-ary PSK 2 4 8 16 32
Rb / BW null 0 5 1 1 5 2 2 5
(contoh M ary PSK, FSK dan M-ary QAM pada BER = 10 6 )
Rb / BW null 0,5 1 1,5 2 2,5
Eb / ηo 10,5 10,5 14 18,5 23,4
M-ary FSK 2 4 8 16 32
Rb / BW null 0,4 0,57 0,55 0,42 0,29
Eb / ηo 13 5 10 8 9 3 8 2 7 5Eb / ηo 13,5 10,8 9,3 8,2 7,5
M-ary QAM 4 16 64 256 1024
Rb / BW ll 1 2 3 4 5Rb / BW null 1 2 3 4 5
Eb / ηo 10,5 15 18,5 24 28
33Modul 6 - Siskom 2 - QAM dan FSK
GMSK, varian of Frequency Shift Keying (FSK)Keying (FSK)
• Continuous Phase FSK (CPFSK) – digital data encoded in the frequency shift – typically implemented with frequency
modulator to maintain continuous phase
s(t) = A cos [ωct + 2 πkf ∫ d(τ) dτ]t
– nonlinear modulation but constant-envelope • Minimum Shift Keying (MSK)
s(t) A cos [ωct + 2 πkf ∫ d(τ) dτ]−∞
y g ( )– minimum bandwidth, sidelobes large – can be implemented using I-Q receiver
• Gaussian Minimum Shift Keying (GMSK) – reduces sidelobes of MSK using a premodulation filter
– used by RAM Mobile Data CDPD and HIPERLANused by RAM Mobile Data, CDPD, and HIPERLAN
34Modul 6 - Siskom 2 - QAM dan FSK