This in turn means the
noise immunity vector remains constant as M increases. In other words, adding new signal vectors
to the FSK alphabet does not make the signals vulnerable to small noise vectors [74].
Let us discuss the rate conversions as we introduce the M-ary modulation scheme in Fig. 2.88.
n S M-ary
Modulator
Rb
Rb Rs log2M
=
No
Eb
No
Eb
No
Es . = log2M
FIGURE 2.88 Data rate conversions for M-ary modulation.
If we were to plot the symbol error rate (SER) versus the SNR, we would observe as more modulation
schemes levels are used, the performance degrades (i.e., the error rate performance curve
shifts to the right), as shown in Fig. 2.89. Also note the following relationship: M 2k.
The reason this occurs is that as Mincreases, there are more neighboring decision regions and thus
more ways to make a symbol error. In specific, there are M 1 ways to make a symbol error.
Now to observe the error rate performance improvement, we must use the normalized SNR or
Eb/No. Recall the following relationship:
(2.56)
(2.57)
(2.58)
We notice as the bandwidth W increases, the symbol time decreases and their product remains
approximately equal to 1. With this observation, we can now show the improvement as the number of
modulation levels increases [23].
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