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ENSC327

Communication Systems

27: Digital Bandpass Modulation

(Ch. 7)

1

Jie Liang

School of Engineering Science

Simon Fraser University

Outline

7.1 Preliminaries

7.2 Binary Amplitude-Shift Keying (BASK)

7.3 Phase-Shift Keying (PSK)

7.4 Frequency-shifting Keying (FSK)

2

7.4 Frequency-shifting Keying (FSK)

7.7 M-ary Digital Modulation

7.8 Mapping of digitally modulated waveforms onto

constellations of signal points

7.1 Preliminaries

If the channel is low-pass (e.g., coaxial cable), we can transmit

the pulses corresponding to digital data directly.

If the channel is band-pass (e.g. wireless, satellite), we need to

use the digital data to modulate a high-freq sinusoidal carrier:

)2cos()( tfAtc pi +=

3

)2cos()(ccc

tfAtc pi +=

1. and 0represent to and 0 use : pic

Amplitude-Shift Keying (ASK):

Use two Acs to represent 0 and 1.

Phase-Shift Keying (PSK):

Frequency-Shift Keying (ASK):

use two fcs to represent 0 and 1.

7.1 Preliminaries

The amplitude of the carrier is usually chosen as

such that the carrier has unit energy measured over

.2

b

c

TA =

4

such that the carrier has unit energy measured over

one bit duration.

7.2 Binary Amplitude-Shift Keying

(BASK)

In BASK, the modulated wave is

==

0. symbolfor ,0

1, symbolfor ),2cos(2

)2cos(2

)()(tf

T

E

tfT

tbts cb

b

c

b

pipi

5

This is a special case of Amplitude Modulation (AM):

( ) ,)2cos()(1)( tftmkAtscacpi+=

Therefore the BASK spectrum has a carrier component.

Envelope detector can be used to demodulate the digital signal.

b(t) is the on-off signalling coding of the input binary data.

7.2 Binary Amplitude-Shift Keying

(BASK)

The average transmitted signal energy is

6


We first consider binary PSK (BPSK):

=+

=

0. symbolfor ),2cos(2

)2cos(2

1, symbolfor ),2cos(2

)(

tfT

Etf

T

E

tfT

E

ts

c

b

c

b

c

b

b

pipipi

pi

7

=+ 0. symbolfor ),2cos()2cos( tfT

tfT

c

b

c

b

pipipi

The two possible values are called antipodal signals.

A special case of DSB-SC:

No carrier component in the freq domain.

BPSK has constant envelope constant transmitted power. Desired in

many systems.

But cannot use envelope detector in the receiver, need coherent

detection.


Detection of BPSK signals:

Coherent DSB-SC receiver

Sample & decision-making: new to digital communication

Can reduce error rate. Advantage over analog comm.

8

Quadriphase-Shift Keying (QPSK)

Recall Chap 3.5: Quadrature-amplitude modulation (QAM):

Transmit two DSB-SC signals in the same spectrum region.

Use two modulators with orthogonal carriers.

9

)2sin()()2cos()()( :signal dTransmitte21

tftmAtftmAtsccccpipi +=

The two signals do not affect each other.


QAM can be generalized to digital modulation

In QPSK, the transmitted signal has four possible phases:

pi/4, 3pi/4, 5pi/4, 7pi/4.

+= ,0 ),4

)12(2cos(2

)(Ttitf

T

Ets c

i

pi

pi

i=1i=2

10

=

elsewhere. ,04)( Ttsi

Index i: 1, 2, 3, 4.

Each signal can represent two bits of binary data, called dibits.

Tb: bit duration.

T: Symbol duration.

Its easy to see that the energy of si(t) is E. This is the Symbol Energy.

Since each symbol represents 2 bits, the average transmitted energy per bit

is

i=3 i=4


To see the link with QAM:

+=

elsewhere. ,0

,0 ),4

)12(2cos(2

)(Ttitf

T

Ets c

i

pi

pi

22 EEpi

pi

pi

pi

=

11

)2sin(2

)()2cos(2

)(

)2sin()4

)12sin((2

)2cos()4

)12cos((2

)(

21tf

Ttatf

Tta

tfiT

Etfi

T

Ets

cc

cci

pipi

pi

pi

pi

pi

+=

=


Detection of QPSK:

Similar to QAM

Two coherent BPSK detectors.

)2sin(2

)()2cos(2

)()(21

tfT

tatfT

tatsccipipi +=

12

Two coherent BPSK detectors.

7.4 Frequency-Shift Keying (FSK)

=

=

=

2. i toscorrespond 0 symbolfor ),2cos(2

1, i toscorrespond 1 symbolfor ),2cos(2

)(

1

tfE

tfT

E

tsb

b

b

i

pi

pi

Binary FSK (BFSK): symbol 0 and 1 are represented

by two sinusoidal waves with different frequencies

13

f1 and f2 can be chosen such that neighboring signals

have continuous phases. This can reduce the bandwidth of

the transmitted waveforms.

This is called the Sunde BFSK.

= 2. i toscorrespond 0 symbolfor ),2cos(

22tf

T

E

b

bpi

Frequency-Shift Keying (FSK)

Example:

14

Continuous phase

can reduce bandwidth


M-ary PSK

M-ary QAM

M-ary FSK

Mapping waveforms to signal points

15

Mapping waveforms to signal points


During each symbol interval of duration T, the

transmitter sends one of M possible signal s1(t), ,

sM(t). M is usually a power of 2: M = 2^m.

M-ary modulation is necessary if we want to conserve

16

M-ary modulation is necessary if we want to conserve

the bandwidth.

But M-ary system needs more power and more

complicated implementation to achieve the same

error rate as binary system.

M-ary Phase-Shift Keying

Generalization of the QPSK

.0 1,-M0,...,i ),2

2cos(2

)( TtiM

tfT

Ets

ci=+=

pi

pi

This can be expressed as

17

Signal Space Diagram

As the increase of M, the receiver of the M-ary

modulation can become more complicated, because

for each input symbol, a naive receiver needs to

compare with M references.

18

It is thus necessary to simplify the signal

representation and therefore reduce the complexity of

the receiver.

The concept of signal space is useful here.

Signal Space Diagram

The signals si(t) can be written as

19

We can visualize the transmitted signals as points in a

K-dimensional space, with axes { })(tj

M-ary Phase-Shift Keying

In M-ary PSK: ( ) ( ).2sin22

sin2cos22

cos)( tfT

iM

EtfT

iM

Etsccipi

pi

pi

pi

=

We can define two orthonormal basis functions:

20

{si(t)} can be represented by

points on a signal space diagram.

The coordinate of each point:

8-PSK

In MPSK, the distance from the origin to

each point is equal to the signal energy E.

M-ary QAM

Recall Chap 3.5: QAM

)2sin()()2cos()()(21

tftmAtftmAtsccccpipi +=

If m1(t) and m2(t) are discrete, we get digital QAM:

22 EEpipi =

21

).2sin(2

)2cos(2

)( 00 tfbT

Etfa

T

Ets

cicipipi =

Example of signal space

diagram: 16-QAM

Possible values for ai, bi:

-3, -1, 1, 3.

Envelope is not constant.

Mapping of Modulated Waveforms

to Constellations of Signal Points

The correlator method is used in receiver in many systems:

Calculate the correlation of input with a pulse template,

Sample the output of the correlator,

Compare the sample with some thresholds to decode the bits.

For example, in BPSK, the template is simply the basis function:

22

function:

).2cos(2

)(1

tfT

tc

b

pi =

If the transmitter sends s1(t):

its correlation with the basis function is:



If the transmitter sends s2(t):

its correlation with the basis function is:

This can be represented by a one-dimensional diagram:

23

This can be represented by a one-dimensional diagram:



This diagram is useful in studying the effect of the noise.

When noise is considered, the received signal will be

noise. is )( ),()()( tntntstriiii

+=

The output of the correlator will be

24

( ) .)()()()()('0

10

1 ii

T

ii

T

iiivsdtttnsdtttntss

bb

+=+=+=

The output of the correlator will be

The noise ni(t) introduces some disturbs to the position of the desired point on the signal space diagram.

Decoding could be wrong if the noise is too large.

BPSK:



BFSK:

).2cos(/2)(

),2cos(/2)(11

tfTEts

tfTEtsbb

pi

pi

=

=

The transmitted signals can be written as:

25

).2cos(/2)(

),2cos(/2)(

22

11

tfTt

tfTt

b

b

pi

pi

=

=

).2cos(/2)(22tfTEts

bbpi=

The receiver takes correlation of the received signal with two basis functions:



If s1(t) is sent, the outputs of the two correlators are:

26

If s2(t) is sent, the outputs are:



So each signal can be represented by a point on a 2-D diagram:

27

1

2

The noise introduces some disturbs to the position of the desired point on the signal space diagram.

Decoding could be wrong if the noise is too large.



Compare the diagrams of BPSK and BFSK, we can see that the distance of the two points are

Since noise changes the position of the signal in the signal

28

Since noise changes the position of the signal in the signal space diagram at the receiver, we can see from these figures that BPSK is more robust to noise than the BFSK.

This will be studied in details in Chapter 10.

2bE

2bE

BPSK:BFSK:

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