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COMM702: Modulation II
Lecture 5
- Coherent and non-coherent binary pass-band data
transmission
Binary Frequency Shift Keying (BFSK) - FSK is treated as non-linear modulation since information is put into the
frequency.
Time domain representation:
The transmitted signal can be represented as:
• S1(t) represents symbol “1”.
• S2(t) represents symbol “0”.
Where:
- The minimum frequency spacing between two adjacent frequency slots to
ensure orthogonality for the continuous phase BFSK is
elsewhere ,0
0,2cos2
bib
b
i
TttfT
E
ts
b
cT
ff4
11
b
cT
ff4
12
bT2
1
2,1i
Phase Discontinuous Frequency Shift Keying
Phase Continuous Frequency Shift Keying
Generation of BFSK
Coherent Detection of BFSK
, and y2, x1H.W: derive the expressions for x
S(t)
Probability of error of Coherent BFSK
• There are two basis functions written as
• Since:
• As a result, the signal vectors are
elsewhere ,0
0,2cos2
bibi
TttfTt
elsewhere ,0
0,2cos2
bib
b
i
TttfT
E
ts
Probability of Error of Coherent BFSK (Cont.)
• From the figure, we have
• In case of Pr(0)=Pr(1), the probability of error is given by
• We observe that at a given value of Pe, the BFSK system requires twice as much power as the BPSK system.
bEd 212
0N
EQP b
e
Coherent Detection of BFSK -Non
Coherent Detection of BFSK (Cont.)-Non
Coherent Detection of BFSK (Cont.)-Non
coherent BFSK-Probability of Error of non
• Probability of Error:
The null to null bandwidth of FSK is
02exp
2
1
N
EP b
e
Bandwidth of FSK:
bRWB 2.
coherent FSK-Comparison of probability of error of coherent and non
02exp
2
1
N
EP b
cohnon
0N
EQP b
coherent
Comparison of probability of error of coherent BFSK and coherent PSK
• The probability of error of coherent FSK:
• The probability of error of coherent PSK:
• Case1: For the same energy per bit :
• Case2: For the same , the FSK needs to double to achieve the
same
0N
EQP b
FSKCoh
o
bPSKcoh
N
EQP
2
PSKcohFSKcoh PP
Thus the coherent BFSK is poorer by 3 dB than coherent PSK
bE
bE
ePeP
Power Spectral density of BFSK • Consider continuous phase FSK where f1 and f2 are different by 1/Tb. We
can write
Power Spectral density of BFSK
Power Spectral density of BFSK (cont.)
Power Spectral density of BFSK (cont.)
Comparison of BER of Different Binary Digital Modulations