MODULASI FSK Yuyun Siti Rohmah,ST.,MT

Binary FSK

2

b

b

b

b

b

b

TttfT

Ets

TttfT

Ets

0 2cos2

0 2cos2

12

01

f0 and f1 are chosen such that

orthogonal02cos2cos 1

0

0 dttftfbT

Demodulation & Detection M-FSK

• M-ary Frequency Shift Keying (M-FSK)

3

Tf

titT

Et

T

Ets c

si

si

2

1

2

)1(cos2

cos2

)(

2

1

0

cos

2)(

,,1 )()(

iis

sijii

M

j

jiji

EE

ji

jiEat

Tt

Mitats

s

)(1 t

2s

1s

3s

)(3 t

)(2 t

sE

sE

sE

Demodulation & Detection M-FSK

• Coherent detection of M-FSK

4

Mz

z

1

z

T

0

)(1 t

T

0

)(tM

)(tr

1z

Mz

z

ML detector: Choose

the largest element in the observed vector

m̂

Error probability …

• Coherent detection of M-FSK … • The dimensionality of signal space is M. An

upper bound for average symbol error probability can be obtained by using union bound. Hence

or, equivalently

5

0

1)(N

EQMMP s

E

0

2log1)(

N

EMQMMP b

E

Bit error probability versus symbol error probability

• Number of bits per symbol

• For orthogonal M-ary signaling (M-FSK)

• For M-PSK, M-PAM and M-QAM

6

2

1lim

1

2/

12

2 1

E

B

k

k

k

E

B

P

P

M

M

P

P

Mk 2log

1for EE

B Pk

PP

Probability of symbol error for M-FSK

7

EP

dB / 0NEb

Note! • M = 2k

• “The same average symbol energy for different sizes of signal space”

Power Spectral FSK • The FSK wave can be written as

• 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=+- 1/2Tb

• The quadrature component is related to the input binary wave and is given by

8

tfT

t

T

Etf

T

t

T

Ets

TtT

ttf

T

Ets

c

bb

bc

bb

b

b

b

c

b

b

2sinsin2

2coscos2

0 2cos2

2222

2

14

cos8

otherwise 0

0 2

fT

fTTEf

TtT

E

tg

b

bbbg

b

b

b

Power Spectral FSK

9

2222

2

14

cos8

2

1

2

1

2

fT

fTTE

Tf

Tf

T

EPSD

b

bbb

bbb

b

Power Spectral M-FSK

10

bTM

5.0hfor FSK ary-M 2logBW deviation) (freq 0.5

Let’s compare Error probability: BPSK vs BFSK

• BPSK and BFSK with coherent detection:

11

)(1 t

2s1s

bE

“0” “1”

bE

)(2 t

bE221 ss

)(1 t

2s

1s

)(2 t

bE

bE bE221 ss“0”

“1”

BPSK BFSK

2

0

N

EQP b

B

2/

2/

0

21

NQPB

ss

0

N

EQP b

B

Contoh Soal

• Suatu sinyal 2-FSK mempunyai amplituda ± 100 m volt, frekuensi pembawa (center) = 100 MHz, deviasi frekuensi = Rb/2, Bit Rate Informasi = Rb = 1 Mbps. • Gambarkan gelombang FSK tsb dan Gambarkan

konstellasi sinyalnya!

• Gambarkan spektrum frekuensinya !

• Berapakah Bandwidth sinyal FSK tsb jika roll of factor = 0.3 !

• Berapakah Pe (BER) jika sinyal FSK tsb bercampur dengan noise AWGN No= 10-10 W/Hz

12

THANK U

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