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ECEN 661 Modulation Theory
Spring 2006
Practice Midterm Exam #1
Problem 1.
The signal constellation shown is known as
the 32point cross (32CR) constellation.
In
all parts of this question, assume that all 32
points in the constellation are equally likely.
(a) On the plot of the signal constellation
given, carefully sketch the boundaries of the
decision region for the ML receiver.
(b) Find the relationship between the mini
mum squared Euclidean distance,
, and
the average energy per symbol,
, in this
constellation.
(c) Find the average number of nearest
neighbors,
, for this constellation as
well as the asymptotic expression for the
probability of symbol error for the ML receiver is an AWGN channel.
Leave your answer in
terms of
, where
is the average energy per bit.
(d) Find the asymptotic relative efficiency of this modulation format relative to QPSK and express
your answer in decibels.
(e) Derive a union bound for the probability of symbol error for the ML receiver for the 32CR
constellation.
Problem 2.
A zeromean bandpass noise process,
, whose PSD is as shown is passed through the system
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 Fall '11
 Miller

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