Here we see a tremendous improvement when going
from M 1 to M 2 antennas. The improvement continues with each additional antenna; however,
PM(gs) a1 e
gs
bM
P[gicgM gs] P[gi gs]M
p(gi)
1
# e
gi
264 CHAPTER FIVE
CDF of SNR for M Branch Selection Diversity System
0.01%
0.10%
1.00%
10.00%
100.00%
??“40 ??“35 ??“30 ??“25 ??“20 ??“15 ??“10 ??“5 0 5 10
10*log(SNR)
Probability Amplitude < Abscissa
M = 1
M = 2
M = 16
M = 8
M = 4
FIGURE 5.51 CDF SNR for a selective diversity system.
it diminishes as M grows. For a single antenna case, we see that approximately 1% of the time the
SNR is less than or equal to 20 dB. In going to M 2 antennas, this value decreases to approximately
0.01% of the time. Hence increasing the number of antennas used in the receiver increases the
SNR and in doing so reduces the system??™s BER.
This can also be looked at under a different light, as the more antennas that are used in the receiver
the less visible are the deep fades and thus reducing the variability of the received SNR.
The mean SNR of the selected signal is
(5.91)
PDF of the mean SNR of the selected signal is given as
(5.92)
We have purposely omitted the steps used to derive the above equations; they can be found in [55].
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