Digital Signal Processing Reference
In-Depth Information
10
0
10
-1
10
-2
10
-3
10
-4
4-QAM (2 bits)
16-QAM (4 bits)
64-QAM (6 bits)
256-QAM(8 bits)
10
-5
0
5
10
15
20
25
30
SNR (dB)
10
0
10
-2
10
-4
4-QAM (2 bits)
16-QAM (4 bits)
64-QAM (6 bits)
256-QAM(8 bits)
10
-6
10
-8
10
-10
0
20
40
60
SNR (dB)
Figure 2.16
. The symbol error probability for QAM. The top plot shows an SNR
range from 0 to 30 dB; the bottom plot shows a wider range of SNR.
As a reminder, note that (2.32) holds under two assumptions: (a) the Gray
code has been used for the binary representation, and (b) the SNR at the detector
input is large enough to justify the approximation (2.25). Both of these are very
reasonable assumptions. In simulations and examples that arise in the topic, we
shall always show the
symbol
error rates for consistency. The plots can readily be
converted to BER plots by using the relation (2.30). As the reader can see, the
expression for BER involves a few assumptions which may not hold accurately
in practice. More exact expressions for BER tend to be very complicated. The
reader wishing to investigate this topic further should read Cho and Yoon [2002]
and references therein.
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