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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
13
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