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EE 359: Wireless Communications  Fall 2005
SECOND EXAM
This exam is open book and notes, and calculators and the textbook are needed. Graded exams and solutions
will be available within the next week. Good luck!
Problem 1 (25 points): Short Answer.
(a) Name one advantage and one disadvantage of having a DSSS system whose spreading codes
have an autocorrelation approximately equal to a delta function?
(b) Consider a MIMO system with 10 transmit antennas and 6 receive antennas with matrix
H
describing the antenna gains from each transmit to each receive antenna. If the SVD of
H
has
4 nonzero singular values, then how many singular values are zero and what is the rank of
H
?
(c) Why are precoding and frequency equalization ineﬀective techniques for treating subcarrier
fading in OFDM systems?
(d) Consider an adaptive system with instantaneous SNR at the transmitter ˆ
γ
that is not necessarily
equal to the true SNR
γ
. Assume ˆ
γ
has the same distribution as
γ
,so
p
(ˆ
γ
)=
p
(
γ
). For the
variablerate variablepower MQAM scheme described in Section 9.3 of the text, suppose that
the transmit power and rate is adapted relative to ˆ
γ
instead of
γ
. Will the average transmitted
data rate and power be larger, smaller, or the same as under perfect channel estimates (ˆ
γ
=
γ
),
and why?
Problem 2 (25 points): MIMOOFDM Systems
MIMO techniques can be applied to systems with ISI as well as ﬂat fading. In this problem we illustrate
how to combine MIMO and OFDM. Consider a 2x2 MIMO system, where the channel from transmit
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 Spring '08
 Goldsmith

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