Digital Signal Processing Reference
In-Depth Information
and
Q
derive from the historical names for the cosine carrier (the
in-phase
carrier) and the sine carrier which is the
quadrature
(i.e. the orthogonal car-
rier). Using complex symbols for the description of the internal signals in
the transmitter is an abstraction which simplifies the overall notation and
highlights the usefulness of complex discrete-time signal models.
l
g
r
,
y
i
d
.
,
©
,
L
s
Im
4
3
2
1
Re
-4
-3
-2
-1
1
2
3
4
-1
-2
-3
-4
Figure 12.10
16-point QAM constellations (
M
=
4).
Constellations.
The 2
M
symbols in the alphabet can be represented as
points in the complex plane and the geometrical arrangement of all such
points is called the signaling
constellation
. The simplest constellations are
upright square lattices with points on the odd integer coordinates; for
M
even, the 2
M
constellation points
hk
form a square shape with 2
M
/
2
points
α
per side:
2
M
/
2
−
1
2
M
/
2
−
1
α
hk
=(
2
h
−
1
)+
j
(
2
k
−
1
)
,
−
<
h
,
k
≤
