<s>
A	O
constellation	B-Application
diagram	I-Application
is	O
a	O
representation	O
of	O
a	O
signal	O
modulated	B-Application
by	O
a	O
digital	O
modulation	B-Application
scheme	O
such	O
as	O
quadrature	B-Device
amplitude	I-Device
modulation	I-Device
or	O
phase-shift	B-General_Concept
keying	I-General_Concept
.	O
</s>
<s>
It	O
displays	O
the	O
signal	O
as	O
a	O
two-dimensional	O
xy-plane	O
scatter	B-Application
diagram	I-Application
in	O
the	O
complex	O
plane	O
at	O
symbol	O
sampling	O
instants	O
.	O
</s>
<s>
In	O
a	O
manner	O
similar	O
to	O
that	O
of	O
a	O
phasor	O
diagram	O
,	O
the	O
angle	O
of	O
a	O
point	O
,	O
measured	O
counterclockwise	O
from	O
the	O
horizontal	O
axis	O
,	O
represents	O
the	O
phase	O
shift	O
of	O
the	O
carrier	O
wave	O
from	O
a	O
reference	O
phase	O
;	O
the	O
distance	O
of	O
a	O
point	O
from	O
the	O
origin	O
represents	O
a	O
measure	O
of	O
the	O
amplitude	B-Application
or	O
power	O
of	O
the	O
signal	O
.	O
</s>
<s>
In	O
a	O
digital	O
modulation	B-Application
system	O
,	O
information	O
is	O
transmitted	O
as	O
a	O
series	O
of	O
samples	B-Algorithm
,	O
each	O
occupying	O
a	O
uniform	O
time	O
slot	O
.	O
</s>
<s>
During	O
each	O
sample	O
,	O
the	O
carrier	O
wave	O
has	O
a	O
constant	O
amplitude	B-Application
and	O
phase	O
,	O
which	O
is	O
restricted	O
to	O
one	O
of	O
a	O
finite	O
number	O
of	O
values	O
.	O
</s>
<s>
Each	O
symbol	O
is	O
encoded	O
as	O
a	O
different	O
combination	O
of	O
amplitude	B-Application
and	O
phase	O
of	O
the	O
carrier	O
,	O
so	O
each	O
symbol	O
is	O
represented	O
by	O
a	O
point	O
on	O
the	O
constellation	B-Application
diagram	I-Application
,	O
called	O
a	O
constellation	O
point	O
.	O
</s>
<s>
The	O
constellation	B-Application
diagram	I-Application
shows	O
all	O
the	O
possible	O
symbols	O
that	O
can	O
be	O
transmitted	O
by	O
the	O
system	O
as	O
a	O
collection	O
of	O
points	O
.	O
</s>
<s>
In	O
a	O
frequency	B-Application
or	O
phase	B-Device
modulated	I-Device
signal	O
,	O
the	O
signal	O
amplitude	B-Application
is	O
constant	O
,	O
so	O
the	O
points	O
lie	O
on	O
a	O
circle	O
around	O
the	O
origin	O
.	O
</s>
<s>
Thus	O
each	O
symbol	O
can	O
be	O
represented	O
by	O
a	O
complex	O
number	O
,	O
and	O
the	O
constellation	B-Application
diagram	I-Application
can	O
be	O
regarded	O
as	O
a	O
complex	O
plane	O
,	O
with	O
the	O
horizontal	O
real	O
axis	O
representing	O
the	O
I	O
component	O
and	O
the	O
vertical	O
imaginary	O
axis	O
representing	O
the	O
Q	O
component	O
.	O
</s>
<s>
A	O
coherent	O
detector	O
is	O
able	O
to	O
independently	O
demodulate	B-Device
these	O
carriers	O
.	O
</s>
<s>
This	O
principle	O
of	O
using	O
two	O
independently	O
modulated	B-Application
carriers	O
is	O
the	O
foundation	O
of	O
quadrature	B-Device
modulation	I-Device
.	O
</s>
<s>
In	O
pure	O
phase	B-General_Concept
modulation	I-General_Concept
,	O
the	O
phase	O
of	O
the	O
modulating	O
symbol	O
is	O
the	O
phase	O
of	O
the	O
carrier	O
itself	O
and	O
this	O
is	O
the	O
best	O
representation	O
of	O
the	O
modulated	B-Application
signal	O
.	O
</s>
<s>
A	O
'	O
signal	O
space	O
diagram	O
 '	O
is	O
an	O
ideal	O
constellation	B-Application
diagram	I-Application
showing	O
the	O
correct	O
position	O
of	O
the	O
point	O
representing	O
each	O
symbol	O
.	O
</s>
<s>
After	O
passing	O
through	O
a	O
communication	O
channel	O
,	O
due	O
to	O
electronic	O
noise	O
or	O
distortion	O
added	O
to	O
the	O
signal	O
,	O
the	O
amplitude	B-Application
and	O
phase	O
received	O
by	O
the	O
demodulator	B-Device
may	O
differ	O
from	O
the	O
correct	O
value	O
for	O
the	O
symbol	O
.	O
</s>
<s>
When	O
plotted	O
on	O
a	O
constellation	B-Application
diagram	I-Application
the	O
point	O
representing	O
that	O
received	O
sample	O
will	O
be	O
offset	O
from	O
the	O
correct	O
position	O
for	O
that	O
symbol	O
.	O
</s>
<s>
An	O
electronic	O
test	O
instrument	O
called	O
a	O
vector	O
signal	O
analyzer	O
can	O
display	O
the	O
constellation	B-Application
diagram	I-Application
of	O
a	O
digital	O
signal	O
by	O
sampling	O
the	O
signal	O
and	O
plotting	O
each	O
received	O
symbol	O
as	O
a	O
point	O
.	O
</s>
<s>
Measured	O
constellation	B-Application
diagrams	I-Application
can	O
be	O
used	O
to	O
recognize	O
the	O
type	O
of	O
interference	O
and	O
distortion	O
in	O
a	O
signal	O
.	O
</s>
<s>
A	O
diagram	O
with	O
four	O
points	O
,	O
for	O
example	O
,	O
represents	O
a	O
modulation	B-Application
scheme	O
that	O
can	O
separately	O
encode	O
all	O
4	O
combinations	O
of	O
two	O
bits	O
:	O
00	O
,	O
01	O
,	O
10	O
,	O
and	O
11	O
,	O
and	O
so	O
can	O
transmit	O
two	O
bits	O
per	O
sample	O
.	O
</s>
<s>
Thus	O
in	O
general	O
a	O
modulation	B-Application
with	O
constellation	O
points	O
transmits	O
bits	O
per	O
sample	O
.	O
</s>
<s>
After	O
passing	O
through	O
the	O
communication	O
channel	O
the	O
signal	O
is	O
decoded	O
by	O
a	O
demodulator	B-Device
.	O
</s>
<s>
The	O
function	O
of	O
the	O
demodulator	B-Device
is	O
to	O
classify	O
each	O
sample	O
as	O
a	O
symbol	O
.	O
</s>
<s>
The	O
set	O
of	O
sample	O
values	O
which	O
the	O
demodulator	B-Device
classifies	O
as	O
a	O
given	O
symbol	O
can	O
be	O
represented	O
by	O
a	O
region	O
in	O
the	O
plane	O
drawn	O
around	O
each	O
constellation	O
point	O
.	O
</s>
<s>
If	O
noise	O
causes	O
the	O
point	O
representing	O
a	O
sample	O
to	O
stray	O
into	O
the	O
region	O
representing	O
another	O
symbol	O
,	O
the	O
demodulator	B-Device
will	O
misidentify	O
that	O
sample	O
as	O
the	O
other	O
symbol	O
,	O
resulting	O
in	O
a	O
symbol	O
error	O
.	O
</s>
<s>
Most	O
demodulators	B-Device
choose	O
,	O
as	O
its	O
estimate	O
of	O
what	O
was	O
actually	O
transmitted	O
,	O
the	O
constellation	O
point	O
which	O
is	O
closest	O
(	O
in	O
a	O
Euclidean	O
distance	O
sense	O
)	O
to	O
that	O
of	O
the	O
received	O
sample	O
;	O
this	O
is	O
called	O
maximum	O
likelihood	O
detection	O
.	O
</s>
<s>
On	O
the	O
constellation	B-Application
diagram	I-Application
these	O
detection	O
regions	O
can	O
be	O
easily	O
represented	O
by	O
dividing	O
the	O
plane	O
by	O
lines	O
equidistant	O
from	O
each	O
adjacent	O
pair	O
of	O
points	O
.	O
</s>
<s>
One	O
half	O
the	O
distance	O
between	O
each	O
pair	O
of	O
neighboring	O
points	O
is	O
the	O
amplitude	B-Application
of	O
additive	O
noise	O
or	O
distortion	O
required	O
to	O
cause	O
one	O
of	O
the	O
points	O
to	O
be	O
misidentified	O
as	O
the	O
other	O
,	O
and	O
thus	O
cause	O
a	O
symbol	O
error	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
further	O
the	O
points	O
are	O
separated	O
from	O
one	O
another	O
,	O
the	O
greater	O
the	O
noise	O
immunity	O
of	O
the	O
modulation	B-Application
.	O
</s>
<s>
Practical	O
modulation	B-Application
systems	O
are	O
designed	O
to	O
maximize	O
the	O
minimum	O
noise	O
needed	O
to	O
cause	O
a	O
symbol	O
error	O
;	O
on	O
the	O
constellation	B-Application
diagram	I-Application
this	O
means	O
that	O
the	O
distance	O
between	O
each	O
pair	O
of	O
adjacent	O
points	O
is	O
equal	O
.	O
</s>
<s>
The	O
received	O
signal	O
quality	O
can	O
be	O
analyzed	O
by	O
displaying	O
the	O
constellation	B-Application
diagram	I-Application
of	O
the	O
signal	O
at	O
the	O
receiver	O
on	O
a	O
vector	O
signal	O
analyzer	O
.	O
</s>
<s>
A	O
constellation	B-Application
diagram	I-Application
visualises	O
phenomena	O
similar	O
to	O
those	O
an	O
eye	O
pattern	O
does	O
for	O
one-dimensional	O
signals	O
.	O
</s>
<s>
The	O
eye	O
pattern	O
can	O
be	O
used	O
to	O
see	O
timing	O
jitter	O
in	O
one	O
dimension	O
of	O
modulation	B-Application
.	O
</s>
