Digital Signal Processing Reference
In-Depth Information
−
(
M
−
1)
A
−
A
(
M
−
1)
A
−
3
A
A
3
A
0
2
A
Figure 2.3
.A
PAM
constellation with
M
codewords.
Im
2
A
codewords
2
A
Re
0
Figure 2.4
. A 4-bit
QAM
constellation with 2
4
= 16 codewords.
2.2.1 Average energy in a PAM constellation
It is useful to have an expression for the average energy in the symbols. In a
PAM constellation, the words are real numbers of the form (2
n
+1)
A,
where
n
is an integer. The energy of a symbol is simply (2
n
+1)
2
A
2
. Note that for every
positive codeword there is a corresponding negative codeword with the same
magnitude. So the average energy of a
b
-bit PAM constellation (with
M
=2
b
words) is
1
2
+3
2
+5
2
+
...
+(
M
1)
2
.
E
ave,P AM
=
2
A
2
M
−
(2
.
1)
If the
M
codewords are equally likely, then this represents the average energy
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