EE 5505
Prof. Jindal
Wireless Communication
March 2, 2010
Homework 5
Due: Tuesday, March 9, 11:15 AM
Please turn in your MATLAB scripts in addition to your solutions and plots.
1. In this problem we will investigate performance with simple ARQ (i.e., packets are re
transmitted when they are decoded incorrectly), and particularly will focus on ﬁnding
the transmission rate/packet error probability that maximizes the goodput when ARQ
is used. For the sake of simplicity we will focus on a scenario where there is no time
or frequency diversity during transmission of a codeword (i.e., an ARQ round).
(a) The outage probability (i.e., the probability a packet is decoded correctly) for
transmitted rate
R
(with no diversity) is given by:
P
out
(
R
) =
P
£
log
2
(1 +

h

2
SNR)
< R
/
Assuming Rayleigh fading, show that the transmitted rate that achieves an outage
probability equal to
²
is:
R
²
= log
2
±
1 + log
e
±
1
1

²
¶
SNR
¶
.
(1)
(b) In class, we found that the longterm average (successful) rate with simple ARQ
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 Spring '08
 Jindal,N
 Gate, Diversity scheme, Rayleigh fading, QPSK, outage probability, optimal outage probability

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