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