5.57 for M1 to 4 antennas. It is clearly shown by adding another antenna performance
Pb a1 m
2 bM aM1
k0 aM 1 k
k b # a1 m
2 bk
m
g
g 1
g M # Eb /No
g Eb/No
m ?„ g
g 1
Pb
1
2 c1
m 22 m2 aM1
k0 Q2k
k R# a 1 m2
4 2m2bk d
PERFORMANCE IMPROVEMENT TECHNIQUES 269
BPSK Performance for MRC in Rayleigh Fading Channel
1.E??“01
1.E??“02
1.E??“03
1.E??“04
1.E??“05
1.E??“06
0 10 20 30 40 50
Eb/No (dB)
BER
Pb(BPSK) (M = 1)
Pb(BPSK) (M = 2)
Pb(BPSK) (M = 3)
Pb(BPSK) (M = 4)
FIGURE 5.57 BPSK BER performance for MRC combining.
improvement can be obtained. Moreover, with each additional antenna, the performance improvement
becomes smaller and smaller. In any case, for the M 2 antenna example there is more than 10
dB in improvement in Eb/No for a BER 1E-3.
An interesting observation from Fig. 5.57 shows the BER performance is linearly, dependent on
the inverse of the SNR raised to the power of the diversity order.
Next we plot the DPSK modulation scheme BER performance (see Fig. 5.58). The mathematical
equations provided earlier have variables that can be changed to plot the performance for either BPSK
or DPSK modulation scheme. This family of curves also shows the performance improvement gradually
increases as more and more antennas are added to the receiver.
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