Bandpass Modulation

Telecommunication Engineering

www.ee.ui.ac.id/wasp

Introduction

Digital modulation: the process by which digital symbols are transformed into

waveforms that are compatible with the characteristics of the channel

In baseband modulation the waveforms take the form of shaped pulses; In bandpass

modulation the shaped pulses modulate a sinusoid called carrier wave

The transmission of EM fields through space is accomplished with the use of

antennas. The size of antennas depends on the wavelength and the application

For cellular, the antenna are typically λ/4 in size while λ=c/f

Considering sending a baseband signal f = 3000 Hz by coupling it to an antenna

directly without a carrier wave. How large would the antenna have to be?

For the 3000 Hz baseband signal, λ/4 = 25000 m, so, to transmit a 3000 Hz

baseband signal without carrier-wave modulation, an antenna that spans 25000 m

would be required

Bandpass Modulation Techniques

Bandpass modulation (either analog or digital) is the process by which an information signal is converted to a sinusoidal waveform

The sinusoid has three parameters: amplitude, frequency, and phase

Bandpass modulation can be defined as the process whereby the amplitude, frequency, or phase of an RF carrier (or combination of them) is varied in accordance with the information to be transmitted

Digital modulation:

converting the binary PAM signal to sinusoidal signal

the sinusiod of duration T is referred to as a digital symbol

Bandpass Modulation Techniques

The general form of sinusoidal (carrier) wave is

where is the time-varying amplitude and is the

time-varying angle and given by

where is the radian frequency of the carrier and is

the phase

Remember that radian and linear frequency are related by

coss t A t t

t A t

0t t t

0 t

2 f

Bandpass Modulation Techniques

There are two types of digital modulation:

Coherent detection: the receiver exploits knowledge of the

carrier’s phase to detect the signals

Noncoherent detection: the receiver does not use phase

reference

SimplicityError

probability

Phase Shift Keying (PSK)

The general equation for PSK is

The phase have M discrete values

0

2cos , 0 , 1, ,s

i i

Es t t t t T i M

T

i t

2

, 1, ,i

it M M

M

Frequency Shift Keying (FSK)

The general expression for FSK:

where has M discrete values

2

cos , 0 , 1, ,si i

Es t t t T i M

T

i

Amplitude Shift Keying (ASK)

The general formula for ASK

where the amplitude have M discrete values

0

2cos , 0 , 1, ,

si

i

E ts t t t T i M

T

2 siE t T

Quadrature Amplitude Modulation (QAM)

It is combination of ASK and PSK

It has rectangular constellation

The general equation for M-QAM is

where

0 0

2cos sinsE

s t I t t Q t tT

0

I

n

n

I t C a Tv t nT

0

Q

n

n

Q t C a Tv t nT

, 1 , 3 , , 1I Q

n na a M M

Quadrature Amplitude Modulation (QAM)

So, the constellation points take place at

; , 1, 3, 1a jb a b M

Quadrature Amplitude Modulation (QAM)

Decision Regions

Error Probability

BPSK

QPSK

Note that BPSK and QPSK have the same bit error probability

but not symbol error probability

BFSK

0

2 bb

EP Q

N

0

2 bb

EP Q

N

0

bb

EP Q

N

Error Probability

M-PSK

M-QAM

2

2 0

22log sin

log

bb

EP Q M

M N M

2

02

4 1 2 log

1log

bb

M E MP Q

N MM M

Error Probability