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ECE 402: Communications Engineering
Homework 7 (Fall 2009)
Due: Tuesday 11/24
1. Suppose 64QAM is used to transmit data over an AWGN channel with the Nyquist pulse
g
(
t
) =
(1
/
√
T
)sinc(
t/T
).
(a)
What is the spectral eﬃciency
η
of 64QAM?
(b)
Find the
E
b
/N
0
in dB required to achieve an error probability of 10

8
. Use the approximate
M
QAM BER formula
P
b
≈
4
log
2
M
±
1

1
√
M
¶
Q
ˆs
3
PT
(
M

1)
N
0
!
.
Hint:
At some point, you’ll need to solve an equation of the form
Q
(
x
) =
b
for
x
. You can use
the MATLAB function
qfuncinv
to solve this:
x=qfuncinv(b)
.
(c)
According to Shannon’s Formula, what is the minimum
E
b
/N
0
in dB required by any reliable
communication system with this spectral eﬃciency
η
?
2. A microwave transmitter has an output power of 0.1 W at a frequency of 2 GHz. Assume that
this transmitter is used in a microwave communication system where the transmitting and receiving
antennas are parabolic dishes, each 1.22 m in diameter.
(a)
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 Fall '08
 Townsend

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