Modul_06 Siskom2_QAM & FSK

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


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


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)


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


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


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.


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


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


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


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


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


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


EP


Modul 6 - Siskom 2 - QAM dan FSK 16dB / 0NEb

Signal Space of several modulation


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


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 ⎠⎝


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


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


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


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


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


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


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


Probability of symbol error for M-FSK

Note!• M = 2k


EP


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


( ) ( )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


Power Spectral M-FSK

bTM 5.0hfor FSK ary-M •≈⇒= 2logBW deviation) (freq 0.5


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


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


Selamat Idul Fitri 1428 HMOHON MAAF LAHIR DAN BATINMOHON MAAF LAHIR DAN BATIN

Modul_06 Siskom2_QAM & FSK

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