Modulation (6):
Constellation Diagrams
Luiz DaSilva
Professor of Telecommunications
dasilval@tcd.ie
+353-1-8963660
Adapted from material by Dr Nicola Marchetti
Geometric representation of modulation signal
q  Digital Modulation involves
q Choosing a particular signal waveform for
transmission of a particular symbol
q For M possible symbols, we thus have M
possible waveforms
S = {s1 (t ), s2 (t ),..., sM (t )}
q For binary modulation, each bit is mapped to a
signal from a set of signals S, that has two
signals
q We can view the elements of S as points in a
vector space
2
Vector space
q We can represent the elements of S as linear
combination of basis signals
q The number of basis signals is the dimension of
the vector space
q Basis signals are orthogonal to each other
q Each basis is normalized to have unit energy:
∞
E = ∫ φi2 (t )dt = 1
−∞
th
φi (t ) is the i basis signal.
3
Example: BPSK
2 Eb
s1 (t ) =
cos( 2πf c t )
Tb
0 ≤ t ≤ Tb
2 Eb
s2 (t ) = −
cos( 2πf c t ) 0 ≤ t ≤ Tb
Tb
2
φ1 (t ) =
cos( 2πf c t )
Tb
S=
{ E φ (t ),−
b 1
Two signal
waveforms to
be used for
transmission
The basis signal
Q
}
Eb φ1 (t )
− Eb
Eb
I
Constellation Diagram
(Dimension = 1)
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Constellation diagram
q  Properties of modulation scheme can be inferred
from constellation diagram
q  Bandwidth occupied by the modulation decreases
as the number of signal points per dimension
increases (getting more dense)
q  Probability of bit error is inversely proportional to
the distance between the closest points in the
constellation
q  Bit error decreases as the distance increases
(sparse)
5
Demodulation
q  In ideal coherent detection, prototypes of the
possible arriving signals are available at the
receiver
q  These prototype waveforms exactly replicate
the signal set
q  The receiver is then said to be phase-locked to
the transmitter
q  During detection, the receiver multiplies and
integrates (correlates) the incoming signal with
each of its prototype replicas, and then decides for
the most correlated replica among those available
6
Amplitude and phase
q  Amplitude and phase can be modulated
simultaneously and separately, but this is difficult to
generate, and especially difficult to detect
q  Instead, in practical systems the signal is
separated into another set of independent
components: I (Inphase) and Q (Quadrature)
q  These components are orthogonal and do not
interfere with each other
q  For representation of these components, we use
phasors
7
Phasor representation
q  A sine wave can also be represented as
a phasor (equivalent to a vector in polar form)
A
time t = 0
A
A
φ
time t = t1
8
Phasor representation (cont’d)
q  A phasor is a rotating vector
A
φ2
time t = t2
9
Back to modulation
q  We can think of modulation using phasor/polar
format, rather than
10
“Speed”
withwhich
onewalks
thewhole
circle
11
In-phase and quadrature
12
In-phase and quadrature (cont’d)
13
Constellation points
q  Most digital modulations map the data to a
number of discrete points on the I/Q plane
q  These are known as constellation points
14
PSK
15
QAM
16
I/Q modulator
q I/Q diagrams are particularly useful because they
mirror the way most digital communications
signals are created using an I/Q modulator
q In the transmitter, I and Q signals are mixed with
the same local oscillator (LO)
q A 90 degree phase shifter is placed in one of the
LO paths
q Signals that are separated by 90 degrees are
also known as being orthogonal to each other
or in quadrature
17
I/Q modulator block diagram
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I/Q demodulator
q The composite signal with magnitude and phase
(or I and Q) information arrives at the receiver
input
q The input signal is mixed with the local oscillator
signal at the carrier frequency in two forms
q One is at an arbitrary zero phase
q The other has a 90 degree phase shift
19
I/Q demodulator (cont’d)
q Signals that are in quadrature do not interfere
with each other
q They are two independent components of the
signal
q The main advantage of I/Q modulation is the
ease of combining independent signal
components into a single composite signal and
later splitting such a composite signal into its
independent component parts
q Exploitation of the symmetry due to the
trigonometric identities
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