Lecture 13  EE 359: Wireless Communications  Fall 2004
MIDTERM
This exam is open book and notes, and calculators are needed. Graded exams and solutions will be available
next week. Good Luck!
Problem 1 (30 points): Wireless Channels.
This problem illustrates the impact of delay spread and doppler on wireless system performance. Consider
a channel with power delay profile
A
c
(
τ
) = 10
6
e

10
6
τ
and Doppler power spectrum
S
c
(
ρ
) =
(
(10

ρ
)
/
10
0
≤
ρ
≤
10 Hz
.
0
else
.
(a) Find the rms delay spread and Doppler spread for this channel.
(b) Assume a BPSK modulated voice signal is transmitted over this channel at 30 Kbps. Is outage
probability or average probability of error a better performance metric and why?
(c) Assume the channel exhibits a Rayleigh fading signal envelope. What is the average length of
time that the channel SNR is below its average value? For an MPSK system with a data rate
of 20 Kilosymbols per second, on average how many consecutive symbols have SNR below the
average SNR?
(d) Assume a DPSK modulated signal is transmitted over this channel.
For what range of data
rates will the average probability of error be below 10

3
at high SNR.
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 Spring '08
 Goldsmith
 Rayleigh fading, MRC

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