Digital Modulation IFolio

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DIGITAL MODULATION

DEPARTMENT OF ELECTRICAL, ELECTRONIC & SYSTEM ENGINEERING

UNIVERSITI KEBANGSAAN MALAYSIA

Prof. Dr. Mohammad Tariqul Islam

Jabatan Kejuruteraan Elektrik, Elektronik & Sistem

Universiti Kebangsaaan Malaysia

43600 UKM, Bangi, Selangor, Malaysia

Email: [email protected]

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Lecture Frame

Introduction

ASK- Amplitude Shift Keying

FSK- Frequency Shift Keying

PSK- Phase Shift Keying

QAM- Quadrature Amplitude Modulation

CPM- Continous Phase Modulation

MSK- Minimum Shift Keying

Application of Digital Modulation

Introduction

The analog signal transmission which modulated

digitally between two communication systems, or

can be called digital radio system.

The trend today: The analog modulation system

(e.g AM, FM) is replaced by modern digital

modulation system that has many advantages as

compared to analog modulation.

Introduction

Basic Digital Modulation:

ASK- Amplitude Shift Keying


PSK- Phase Shift Keying

The Important parameter for digital modulation:

Capacity

Bits

Bit rate/ Baud rate

Bandwidth

Bit rate : number of data bits transmitted in one second in a

communication system.

Baud rate: number of times a signal in a communications

channel changes state or varies.

Bps = baud per second x number of bit per baud

1. ASK- Amplitude Shift Keying

The easiest digital modulation system compare to other modulation scheme.

Also can be called as DAM.

ASK signal can be represent as:

vask(t) = [ 1 + vm(t) ] [ (A/2)*cos(ωct) ]

Where

vask(t) = ASK wave

vm(t) = Digital modulating signal (Voltage)

A/2 = Unmodulation carrier/Amplitude (Voltage)

ωc = Analog carrier (radians per sec, 2fct)

1. ASK- Amplitude Shift Keying

ASK binary baseband represent signal

Modulating Signal

Modulated Signal

amplitude change

2. FSK- Frequency Shift Keying

Digital modulation with low performance level. Similar with FM concept.

Can also be called as BFSK (Binary FSK)

Representing by

vfsk(t) = vc cos { 2 [ fc + vm(t)f ]*t) }

Where

vfsk(t) = FSK wave

vc = Analog peak carrier amplitude (Voltage)

fc = Analog carrier frequenc (Hertz)

vm(t) = Binary input signal (Voltage)

f = Analog carrier peak frequency range (Voltage)

Teknik Pemodulasi Digit


(continue)...

f = | fm – fs | / 2

fm = mark frequency

fs = space freuency.

Bandwidth FSK, B = 2 ( f + fb )

where

fb = Input bit rate


FSK wave represent in time domain, where

fc= 4 kHz

fs fm fs fs fs fs fs fm fm fm


Binary Input Output

Frequency

‘0’ Space ( fs )

‘1’ Mark ( fm )

Truth table for FSK

Gaussian Minimum-Shift Keying A special case of FSK called Gaussian Minimum-Shift Keying (GMSK) is used in the GSM cellular radio and PCS systems to be described later. In a minimum shift system, the mark and space frequencies are separated by half the bit rate, that is,

0.5m s bf f f Here,

Frequency transmitted for mark (binary 1)

Frequency transmitted for space (binary 0)

Bit rate

mf

sf

bf

If we use the conventional FM terminology (refer to FM slides),

we see that GMSK has a deviation each way from the center

(carrier) frequency of,

0.25 bf Which corresponds to modulation index of

f

m

mf

0.25 b

b

f

f

0.25

Example: The GSM cellular radio system uses GMSK in a 100 kHz

channel, with a channel data rate of 170 kb/s. Calculate:

(a) The frequency shift between mark and space

(b) The transmitted frequencies if the carrier (center) frequency is

exactly 880 MHz

(c) The bandwidth efficiency of the scheme in b/s/Hz.

Answer:

(a) The frequency shift is

0.5 0.5 170 85m s bf f f kHz kHz

(b) The shift each way from the carrier frequency is half that found in (a), so the maximum frequency is

And the minimum frequency is

(c) The GSM system has a bandwidth efficiency of

170/100=1.7 b/s/Hz, comfortably under the theoretical maximum of 2 b/s/Hz for a two-level code.

max 0.25 880 0.25 170 922.5c bf f f MHz kHz MHz

min 0.25 880 0.25 170 837.5c bf f f MHz kHz MHz

Shannon-Hartley Theorem There is a theoretical limit to the maximum data rate that

can be transmitted in a channel with a given bandwidth.

The Shannon-Hartley theorem states:

22 logC B M

Here,

C=information capacity in bits per second

B=bandwidth n hertz

M=number of possible states per symbol

Shannon Limit The information capacity of a channel cannot be increased

without limit by increasing the number of states because

noise makes it difficult to distinguish between signal

states. The ultimate limit is called the Shannon limit:

2log (1 / )C B S N

Here,

C=information capacity in bits per second

B=bandwidth n hertz

S/N=signal to noise ratio (as a power ratio, not in decibels)

Example: A radio channel has a bandwidth of 12 kHz and a signal to

noise ratio of 20 dB. What is the maximum data rate that can be

transmitted:

(a) Using any system?

(b) Using a code with four possible states?

Answer:

(a) We need the signal to noise ratio as a power ratio.

We can convert the given decibel value as follows:

1 20

log10

S

N

100

Using equation for shannon limit:

2log (1 / )C B S N

3

212 10 log 1 100 312 10 6.658211

79.89 /kb s

(b) We can use the equation derived for Shannon-Hartley theorem, to

find the maximum possible bit rate given the specified code and

bandwidth. (a). From the Shannon-Hartley equation:

22 logC B M3

22 12 10 log 4 32 12 10 2

48 /kb s

Since this is less than the maximum possible for this channel, it should be possible to transmit over this channel, with a four-level scheme, at 48 kb/s. A more elaborate modulation scheme would be required to attain the maximum data rate of 79.89 kb/s for the channel.

We will then have to compare this answer with that of part

Example: A typical dial-up telephone connection has a bandwidth of 2 kHz

and a signal to noise ratio of 20 dB. Calculate the Shannon limit.

Answer:

We need the signal to noise ratio as a power ratio. We

can convert the given decibel value as follows:

1 20

log10

S

N

100

2log (1 / )C B S N

3

22 10 log 101

13.316 /kb s

3. PSK- Phase Shift Keying

One of the angle modulation form, the amplitude is fixed but in term of binary representation.

Is used when the FSK modulation cannot be accommodate for high data rate in limited band channel.

Is one of M-ary digital modulation scheme, similar to phase modulation. The different at input PSK, which is binary digital signal and limited output phase.

M-ary encoding: N = log2 M,

where

N = required number of bit

M = possible number of level, condition or combination with bit N.


BPSK is the easiest form of PSK, where N = 1 and M =

2.

Therefore, BPSK only has 2 phase at carrier, which are

logic ‘1’ phase and logic ‘0’ phase.

Can be called as Phase Reversal Keying (PRK) and

Biphase Modulation

Advantages: Improvement of the BER performance

Disadvantages: Spectral is not efficient due to rapid

phase with the presence of bit 1


BPSK wave representation in time domain

Rising point and every 1

Phase different


The others PSK types:

Delta-Phase Shift Keying, DPSK

Quadrature-Phase Shift Keying, QPSK or

DQPSK

Offset QPSK

/4 Delta-Phase Shift Keying

8-Phase Shift Keying

16-Phase Shift Keying

M-ary Modulation/BPSK • Signals of this type are called quaternary/quadrature PSK

(QPSK) signals. They are a special case of multi-PSK (MPSK)

signals. Binary PSK signals are often labeled as BPSK.

BPSK (M=2)

ψ (t)

2

“0” “1”

s s

8PSK (M=8)

ψ2(t)

1

− E E

2 ψ(t) “010”

s

3 “011” 001”

b b 1

QPSK (M=4)

s

4

E

s

“

2

“000”

ψ 2

(t

)

s

“110”

1

“01”

“00”

ψ

(t

)

s

s

s 1

2

E

1 5

“111” “100”

s

s

ψ(t

1

s

s )

s

6 8

“101”s

7

3

“11”

“10”

4

4. QAM- Quadrature Amplitude

Modulation

Similar to PSK, additional on carrier amplitude.

The technique is used to obtain high data rate

in a band limited channel.

The elements position in constellation diagram

is optimized so that:

The distance between element is maximized

(dynamic range increased)

Low error possibility

4. QAM- Quadrature Amplitude

Modulation

Advantage: High data rate and more bandwidth efficient as compared to FSK or QPSK

Disadvantage: Easier to be influenced by noise and the amplitude is always changing.

Types of QAM: 4-QAM

8-QAM

16-QAM

....

Quadrature Amplitude Modulation (QAM) • More general types of multi-symbol signaling schemes may be

generated by letting ai and bi take on multiple values themselves.

• The resultant signals are QAM signals. Therefore QAM is a

combined multi-phase/multi-amplitude signaling scheme.

16-QAM

“0000”

s

ψ

“0001” s

2

(t)

“0011” s

“0010”

s

1 2

3

3 4

“1000”

s

“1001” “1011” “1010”

s s s 5 6

1

-3 -1

s s

7 8

1 3

ψ s s

1

(t)

9

10

-1

11

12 “1100” “1101”

s s

“1111” “1110”

s s

13 14

-3

15 16 “0100”

“0101”

“0111”

“0110”

QAM- Quadrature Amplitude

Modulation

Constellation diagram of QAM symbol,

for M= 4,16 dan 64

16-QAM

http://en.wikipedia.org/wiki/File:16QAM_Gray_Coded.svg

http://en.wikipedia.org/wiki/File:16QAM_Gray_Coded.svg

QPSK: Without Pulse Shaping

Data

0

0

1

1

Data

0

1

0

1

Data

00

01

180o

10

11

M-ary Modulation/ Error

M-ary Modulation: Error Performance

M=2

M=4

M=8

M=16

PE

Note!

“The same average symbol

energy for different sizes of

signal space”

Eb

/N

0

dB

Probability of symbol error for M-PSK

Quadrature Amplitude Modulation (QAM)

• As the number of constellation size increases, the phase spacing

between signals reduces correspondingly.

• The channel noise and phase jitter makes it more difficult to

distinguish individual points in a constellation as the number of

point increases. This will produce more errors at the receiver.

• There is a limit on the number of QAM states that may be used.

• Shannon channel capacity theorem:

⎛

S

⎞

C

=

B

log

2

1+ ⎝ N

⎠

C = channel capacity (bits/s)

5. CPM- Continuous Phase

Modulation

The phase of carrier signal is continously

modulated.

The signal power is mostly homogeneous;

advantages of CPM as compared to other

digital modulation schemes.

Memory phase; phase for every signal is

determined by total of cumulative phase of the

prior signal.

5. CPM- Continuous Phase

Modulation

Transmitted CPM signal-memory types transmission

No Phase Change for Continuous bit

Minimum-Shift-Keying (MSK) MSK: wider mainlobe, but

better energy compaction,

hence more bandwidth

efficient

QPSK: energy spreading out,

hence not bandwidth efficient

MSK: lower sidelobes

6. MSK- Minimum Shift Keying

MSK encoding bit is implemented with

bits alternating between quadrature

components & every bit is coded to half

sinuisoidal wave– reduce the distortion.

Represented by


continue...

Where

Therefore, s(t) can be coded as



Modem in telephone line system use 3 technique of modulation: FSK, PSK and QAM

The good features of Modem:

High immunity to noise

low bandwidth consumption

Low power consumption

Low cost


Dual tone multi frequency (DTMF) use

the MFSK technique

16/64-Q digital terrestrial television

modulation in AM is used for UK and

64/256-QAM in US for digital cable


Standard Wireless LAN, IEEE 802.11x use

various of PSK method depends to the

required data rate.

Example, QPSK technique is used to obtain

data rate 11 Mbit/s for IEEE 802.11b.


Bluetooth uses /4-DQPSK at low data

rate 2 Mbits/s, and 8-DPSK at high data

rate 3 Mbits/s.

BPSK is used for RFID which utilized for

biometric passport & credit card


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