COMM702: Modulation II

Lecture 7

- M-ary Modulations

: Timing diagram for QPSKRemember

: Timing diagram for QPSKRemember

In QPSK

-The 180 change in phase of QPSK results in variation of the

envelope. Also the filtering operation of QPSK to limit its band

before transmission makes variation in the envelope.

-Such variations require Linear power Amplifiers to avoid spectral

re-growth.

-Linear power amplifiers are less efficient than non-linear power

amplifiers (for 40% efficiency, it consumes 2.5 W).

- Solution use Offset QPSK (OQPSK).

Variant of QPSK: Offset QPSK (OQPSK)

Odd-numbered

sequence

Even-numbered

sequence

QPSK

OR

10 00

11 01

00 10

Offset QPSK • Offset QPSK can be used in place of QPSK to achieve the non-

zero envelope in the modulated signal.

• Idea: OQPSK is implemented by offsetting (staggering) the timing of the odd or even bits by one bit-period, or half a symbol-period, the in-phase and quadrature components will never change at the same time.

• In the constellation diagram shown below, it can be seen that this will limit the phase-shift to be no more than 90° at a time. This yields much lower amplitude fluctuations than non-offset QPSK and is sometimes preferred in practice.

Timing Diagram of Offset QPSK

Timing Diagram of Offset QPSK

Transmitter of Offset QPSK

Receiver of Offset QPSK

Is the receiver different from the receiver of QPSK????

Suggest a receiver

Signal Space diagram of OQPSK

Advantages of OQPSK

OQPSK has the same probability of error as QPSK

and the same bandwidth

QPSK 4/• The maximum phase change is limited to as

compared to 180 for QPSK and 90 for OQPSK. Hence, the band limited QPSK preserves the constant envelope property better than band limited QPSK but is more susceptible to envelope variations than OQPSK.

• QPSK signal is generated by alternating between two QPSK constellations that are rotated by with respect to each other.

4/3

4/

4/

4/

Idea of QPSK 4/

• The idea is: the four symbol set is rotated by pi/4 (45) at every new symbol transition such that the phase transition from one symbol to the next are restricted to

4/34/ or

Generation of QPSK 4/

Quadrature Amplitude Modulation (QAM)

Combining two modulation types could

give improved performance expected

trade off between bandwidth efficiency

and noise performance

c

-

+

Time domain representation of QAM

is the min. distance between

any two message points in the

Constellation.

ai and bi

are

integers

16Example: QAM

oEoEoE3 oE3

QAM Demodulation

X1

X2

LPF

LPF

Si(t)

y1

y2

T

EbX

tT

Ebt

T

Ea

tT

Ebtt

T

Eay

T

EaX

tT

Ebt

T

Ea

T

Ea

tT

Ebt

T

Ea

ttbT

Eta

T

Ey

i

cici

cicci

i

cicii

cici

ccici

0

2

00

200

2

0

1

000

00

020

1

)]2cos(1[)2sin(

)(sin2

)sin()cos(2

)2sin()2cos(

)2sin()]2cos(1[

)cos()sin(2

)2(cos2

)2sin(2

)2cos(2

)( 00 tfT

Ebtf

T

Eats cicii

QAM constellation

n

nM 2

n

n

QAM square constellation • In case of QAM square constellation, the ordered pairs of coordinates

naturally form a square matrix, as shown:

• Example: For M=16, then L=4, thus the square constellation becomes:

QAM cross constellation • The constellation for odd number of bits per symbol n is performed

as follows:

- Start with a QAM square constellation with n-1 bits per symbol.

- Extend each side of the QAM square constellation by adding

- Ignore the corners in the extension.

32 n

Constellation of QAM for Different M

Performance of QAM

For High SNR

Bandwidth of QAM

MBW

RThen

M

RRBW bb

s 2

2

log2

1

log

22

0

0

0

12

6114

12

3112

:aswrittenisyprobabiliterrorsymboltheThen

3

)1(2

)N(M

EQ

M

)N(M

Eerfc

MP

EME

av

ave

av

Proof See Text Book

Page 371

ary Amplitude & Phase Keying)-Circular QAM (M

Circular QAM

Adaptive QAM Modulation

Adaptive QAM Modulation

Adaptive QAM Modulation

Approximated formula:

𝛾_

Adaptive Modulation