MIMO Wireless Systems
Andreas Constantinides Assaf Shacham
May 14, 2004
1 Introduction
Communication in a slow flat Rayleigh fading channel with AWGN is not reliable as the channel frequently
enters into deep fades, (i.e., the channel attenuation is large). More specifically, as seen in class, Rayleigh
fading converts an exponential dependency of bit error probability on the signal-to-noise ratio (SNR) into
an inverse relationship. For BPSK, the probability of bit error in an AWGN channel is P
e
= Q
³
q
2E
b
N
0
´
,
where E
b
/N
0
is the SNR per bit. However, with Rayleigh fading the average probability of bit error is
P
e
=
1
2
·
Ã
1 −
s
β
1 + β
!
, where β =
E
b
N
0
· E(α
2
), and α is Rayleigh distributed
Figure 1 shows clearly this severe degradation in the probability of bit error for BPSK in a Rayleigh
fading channel for E(α
2
) = 1.
0 5 10 15 20 25 30 35 40 45
10
−6
10
−5
10
−4
10
−3
10
−2
10
−1
10
0
SNR per bit (dB)
Probability of bit error for BPSK vs SNR per bit
Probability of bit error
AWGN channel
Rayleigh fading channel
Figure 1: Effect of Rayleigh fading on the probability of bit error for BPSK
In this report, we will be mostly talking about QAM. So for completeness, in Fig. 2, we plot MAT-
LAB simulation results for the probability of symbol error of 16-QAM. As it can be seen, the performance
degradation is as severe as in the BPSK case.
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