1. Chapter 5 Digital Modulation Systems
Multilevel Modulated Bandpass Signalling
Representation in the I-Q Plane
MPSK and QPSK
QAM
PSD of MPSK, QPSK and QAM
Huseyin Bilgekul
EEE 461 Communication Systems II
Department of Electrical and Electronic Engineering
Eastern Mediterranean University

2. Digital Modulation Carrier signal: Ac cos (2pfct + θ) Modulation: m(t)
Modulated signal: Ac (t) cos (2pfc(t) t + θ(t))
 m(t); discrete
Vary Vary
amplitude frequency & phase
Variations are discrete!!!!!
Binary
OOK
BPSK
DPSK
FSK
Multilevel
QPSK
MPSK
QAM

3. Multilevel Modulated Bandpass Signaling
Digital inputs with more than two levels are allowed on the transmitter output
Multilevel Digital Transmission System
Digital-to-
analog converter
l bits
Transmitter
Binary input
R bits/sec
M=2l – level multilevel signal
Modulated output
Multilevel signals can be generated by using a digital to analog converter (DAC). Multilevel signaling reduces the bandwidth requirement.

4. Signal Vector Representation
s(t) = Ac(t) cos (2pfct + θ(t)) Q
fixed!!!
θ = 90 S
t = t
Magnitude
Phase
t = 0
0 degrees I
θ = 0
I-Q
Plane

5. Signal Changes: Representation in the I-Q plane
Magnitude
Change
Phase
Change S2 Q Q S1 S1 S2 I I
I-Q Diagrams or
Constellations S1 S2 I Q
Magnitude
& Phase
Changes

6. M-ary Phase Shift Keying
If the transmitter is a PM transmitter with an M-level digital modulation signal, M-ary phase-shift keying (MPSK) is generated
The complex envelope is given by
The phase θ(t) is permitted to have only ‘M’ values
4 level M-ary signaling
Binary Seq.
DAC Value
PSK Phases 00
-3V 01
-1V
900 10
+1V
1800 11
+3V
2700
When M=4, the resulting signal is called Quadrature Phase Shift Keying (QPSK)

7. Quadrature Phase Shift Keying (QPSK)θ
g(t)
Imaginary (Quadrature)
Real
(In phase) θi
g(t)
Imaginary (Quadrature)
(In phase)
Real
π/4 -QPSK
QPSK

8. M-ary Phase Shift Keying
MPSK signal can also be generated using two quadrature carriers modulated by the x and y components of the complex envelope
Where the permitted values of x and y are
for the permitted phase angles θi , I = 1, 2, … M

9. QPSK signal

10. π/4 - QPSK signal p/4 Ts 0 0 0 1 1 0 1 1 Binary sequence
Binary sequence
4 – psk signal I Q 10 11 00 01
p/4
Gray Code

11. M-ary Phase Shift Keying (MPSK)Q I
Octophase
I-Q
Constellation
MPSK signal constellation (permitted values of the complex envelope)

12. Quadrature Amplitude Modulation (QAM)
QAM signal constellations are not restricted to having signaling points only on the circle of radius Ac (This is unlike M-PSK)
The general QAM signal
Where the complex envelope is
With
and
where
(xn,yn) denotes one of the permitted values of (xi,yi) during the
symbol time that is centered on

13. Quadrature Amplitude Modulation (QAM)
I-Q
Constellation
16 symbol QAM constellation (four symbols per dimension)

14. OPSK & π/4 QPSK
Offset Quadrature Phase-Shift Keying (OQPSK) is M=4 PSK in which allowed data transition times for the I and Q components are offset by a ½ symbol period
A π/4 Quadrature Phase-shift Keying (π/4 QPSK) signal is generated by alternating between two QPSK constellations that are rotated by π/4 with respect to each other

15. PSD for MPSK, QAM, OQPSK, and π/4 QPSK
The complex envelope is given by
The rectangular symbol pulse
Ts – Symbol period
Baud rate
And its fourier transform
where
PSD for the complex envelope of MPSK or QAM is
where
C – variance of cn

16. PSD for complex envelope of MPSK, QAM
Observations :
The PSD of MPSK or QAM is obtained by translating the PSD to the carrier frequency
For l =1  PSD for BPSK
For l =2  PSD for QPSK, OQPSK …
PSD for complex envelope of the bandpass multilevel signal is same as the PSD of baseband multilevel signals

17. llustrating the Gray encoding of the four quadrants and dibits in each quadrant for the V.32 modem. The dashed arrows illustrate the 90° rotational invariance.

18. (a) Signal constellation of V. 32 modem using nonredundant coding
(a) Signal constellation of V.32 modem using nonredundant coding. (b) Signal constellation of V.32 modem using trellis coding.

19. Quarter-superconstellation of V. 34 modem with 240 signal points
Quarter-superconstellation of V.34 modem with 240 signal points. The full superconstellation is obtained by combining the rotated versions of these points by 0, 90, 180, and 270 degrees. (Taken from Forney et al., 1996)

20. Decision Regions * * QPSK BPSK Imag Imag A Real A Realx x x x x * x * A x x
Real x
Received signal points without error
Transmitted signal point
Received signal points with error

21. Decision Regions and Noise Effects
What if the noise is not symmetric?
Adds a bias onto the signals
Asymmetric distribution
Decision surface moves over
Imag x x x x
p(n) A
Real x
Noise Amplitude

22. QAM Decision Regions Sketch the decision regions for QAM16
Assume uniform noise
Assume that you sent a “1101” symbol, what range should the in-phase and quadrature components be in?
What do you decide if:
(1.9,-1) is received?
(2.1,-1) is received due to noise?