Modulation of Digital Data: FSK

FSK – frequency of the carrier signal is varied to represent binary 1 or 0• both peak amplitude and phase remain constant during each bit interval

• demodulation: demodulator must be able to determine which of two possible frequencies is present at a given time

• advantage: FSK is less susceptible to errors than ASK – receiver islooking for specific frequency changes over a number ofintervals, so voltage (noise) spikes can be ignored

• disadvantage: FSK spectrum is 2 x ASK spectrum

• application: over voice lines, in high-frequency radio transmission, etc.

=1binary t),fAcos(20binary t),fAcos(2

s(t)2

1

ππ

f1<f2+A

-A

1

Modulation of Digital Data: FSK (cont.)

Example [ FSK ]

vd(t)

vc1(t)

vc2(t)

vFSK(t)

ω1 ωωd_max ω2ω1 ωω1-ωd_max

ω2 ω2+ωd_max

2

Modulation of Digital Data: FSK (cont.)

FSK-Modulated Signal: Frequency Spectrum

(t)vdDigital signal: - modulated with ω1 , and

- modulated with ω2

Modulated signal:

( ) ( )[ ]

( ) ( )[ ]

( ) ( )[ ]

( ) ( )[ ] ++++−+

++−−

++++−−

++−+=

=

=

−−+−⋅+

+

−+−+⋅=

=−⋅+⋅=

...t3ωωcost3ωωcos3π1

-tωωcostωωcosπ1tcosω

21

...t3ωωcost3ωωcos3π1

-tωωcostωωcosπ1tcosω

21

...tcos5ω5π2tcos3ω

3π2tcosω

π2

21tcosω

...tcos5ω5π2tcos3ω

3π2tcosω

π2

21tcosω

(t))vtcosω(t)vtcosω(t)v

0202

02022

0101

01011

0002

0001

d2d1FSK

...

1(

(t)v1-(t)'v dd =

3

PSK – phase of the carrier signal is varied to represent binary 1 or 0• peak amplitude and frequency remain constant during each bit interval

• example: binary 1 is represented with a phase of 0º, while binary 0is represented with a phase of 180º=πrad ⇒ PSK is equivalent to multiplying the carrier signal by +1 when the information is 1, and by-1 when the information is 0

• demodulation: demodulator must be able to determine the phase ofreceived sinusoid with respect to some reference phase

• advantage: PSK is less susceptible to errors than ASK, while itrequires/occupies the same bandwidth as ASK

more efficient use of bandwidth (higher data-rate) are possible, compared to FSK !!!

• disadvantage: more complex signal detection / recovery process, thanin ASK and FSK

+=

0binary ),tfAcos(21binary t),fAcos(2

s(t)c

c

πππ

Modulation of Digital Data: PSK

2-PSK, or Binary PSK,

since only 2 different phases

are used.

+A

-A

=0binary t),fAcos(2-1binary t),fAcos(2

s(t)c

c

ππ

4

Modulation of Digital Data: PSK (cont.)

Example [ PSK ]

vd(t)

vc(t)

vPSK(t)

ωc ωωd_max ωc ωωc+ωd_maxωc-ωd_max

5

Modulation of Digital Data: PSK (cont.)

PSK Detection / Recovery – multiply the received / modulated signalby 2*cos(2πfct)

• resulting signal

• by removing the oscillatory part with alow-pass filter, the original baseband signal(i.e. the original binary sequence) can beeasily determined

[ ] 1binary , t)fcos(41At)f(22Acos cc2 ππ +=

[ ] 0binary , t)fcos(41At)f(22Acos- cc2 ππ +−=

t)fAcos(2 cπ±( )2A cos1

21Acos2 +=

Ak = A, for binary 1Ak = -A, for binary 0

6

Modulation of Digital Data: PSK (cont.)

1 1 1 10 01 1 1 10 0Information

BasebandSignal

+A

-A0 T 2T 3T 4T 5T 6T

+A

-A0 T 2T 3T 4T 5T 6T

+A

-A0 T 2T 3T 4T 5T 6T

+A

-A0 T 2T 3T 4T 5T 6T

ModulatedSignal

x(t)

A cos(2πft) -A cos(2πft)

After multiplicationat receiver

x(t) cos(2πfct)

+A

-A0 T 2T 3T 4T 5T 6T

+A

-A0 T 2T 3T 4T 5T 6T

A {1 + cos(4πft)} -A {1 + cos(4πft)}

Basebandsignal discernable

after smoothing

+A

-A0 T 2T 3T 4T 5T 6T

sender

receiver

Signal shifted above / below zero level.

7

Modulation of Digital Data: PSK (cont.)

B

fc+B

f

ffc-B fc

• If bandpass channel has bandwidth Wc [Hz],

then baseband channel has Wc/2 [Hz] available, so

modulation system supports C = 2*(Wc/2) = Wc [pulses/second] recall Nyqyist Law: baseband transmission system of bandwidth Wc [Hz] can

theoretically support 2 Wc pulses/sec

Facts from Modulation Theory

Wc

Wc/2Baseband signal x(t)occupies bandwidth Wc/2

If

then

Modulated signal x(t)cos(2πfct) occupies

bandwidth Wc Hz

How can we recover the factor 2 in supported data-rate !?

Data rate = 2*Wc/2 = B [bps]

8

Modulation of Digital Data: PSK (cont.)

Example [ data rate of ASK signal ]

We have an available bandwidth of 100 kHz which spans from 200 – 300 kHz.What are the carrier frequency and the bit rate if we modulated our databy using ASK?

200 kHz 300 kHz

carrier signal = middle of the bandwidth = 250 kHzbandwidth of digital signal B = 50 kHzdigital data rate = 2* B = 100 kbps

B=50kHz

9

Example [ data rate of ASK signal ]

Assumptions are the same as in the previous example (200-300 kHzAvailable, for ASK modulated signal), but the line is full-duplex.

Modulation of Digital Data: PSK (cont.)

200 kHz 300 kHz

uplink downlink

bandwidth for uplink = bandwidth for downlink = 50 kHz

carrier for uplink = 225 kHz carrier for downlink = 275 kHz

bandwidth of digital signal = 25 kHz

digital data rate = 2* B = 50 kbps

10

Modulation of Digital Data: PSK (cont.)

Example [ data rate of FSK signal ]

Find the minimum bandwidth for FSK signal transmitting at 2000 bps using half-duplex mode, and the carriers are separated by 3000 Hz?

??? Hz

3000 Hz

overall bandwidth = band. dig. sig. + 3000 + band dig. sig. band. dig. sig. = C / 2 = 1000 Hzoverall bandwidth = 5000 Hz

11

Modulation of Digital Data: PSK (cont.)

QPSK = 4-PSK – PSK that uses phase shifts of 90º=π/2 rad ⇒ 4 differentsignals are generated, each representing 2 bits

• advantage: higher data rate than in PSK (2 bits per bitinterval), while bandwidth occupancy remains the same

• 4-PSK can easily be extended to 8-PSK, i.e. n-PSK

• however, higher rate PSK schemes are limited by the abilityof equipment to distinguish small differences in phase

+

+

+=

11binary ),2

3tfAcos(2

10binary ),tfAcos(2

01binary ),2

tfAcos(2

00binary t),fAcos(2

s(t)

c

c

c

c

ππ

ππ

ππ

π

12

Signal Constellation

Constellation Diagram – used to represents possible symbols that maybe selected by a given modulation scheme aspoints in 2-D plane

• X-axis is related to in-phase carrier: cos(ωct) the projection of the point on the X-axis defines

the peak amplitude of the in-phase component

• Y-axis is related to the quadrature carrier: sin(ωct) the projection of the point on the Y-axis defines

the peak amplitude of the quadrature component

• the length of the line that connects the point to theorigin is the peak amplitude of the signal element(combination of X and Y components)

• the angle the line makes with the X-axis is the phase of the signal element

13

+

+

+=

11binary ),2

3tfAcos(2

10binary ),tfAcos(2

01binary ),2

tfAcos(2

00binary t),fAcos(2

s(t)

c

c

c

c

ππ

ππ

ππ

π

Signal Constellation (cont.)

Example [ signal constellation of QPSK ]

t)fAsin(2- cπ

t)fAcos(2- cπ

t)fAsin(2 cπ

00A-A

A

-A

01

10

11

14

Signal Constellation (cont.)

Example [ other types of modulations ]

15