University of Illinois
Spring 2011
ECE 361:
Problem Set 3
M
ary Amplitude Shift Keying; Repetition Coding
Due:
Tuesday February 15 at 9:30 a.m.
Reading:
Lecture Notes: Lectures 26
1.
[Average energy in
M
ary amplitude shift keying]
In class, it was stated that the maximum energy in
M
ary amplitude shift keying was
E
max
= (
M

1)
2
E
while the average energy was
¯
E
= ((
M
2

1)
/
3)
E
. Prove the latter claim. Remember to consider both
the cases
M
odd and
M
even.
2.
[Bit error probabilities in 4ASK systems]
Consider a 4ASK system operating in additive white Gaussian noise with twosided power spectral
density
N
0
/
2. The (equally likely) numbers 0, 1, 2, 3 are (Gray)coded into data bits 00, 01, 11, and
10 and produce signal levels +3
√
E
,
√
E
,

√
E
, and

3
√
E
at the output of the receiver filter.
As
usual, the noise variance at the filter output is
N
0
/
2. Let
A
i
denote the event that the number
i
is
transmitted, and
E
the event that the number transmitted is received incorrectly.
(a) Find
P
(
E

A
i
), 0
≤
i
≤
3 and then use the law of total probability to find
P
(
E
).
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 Spring '09
 Probability theory, error probability, ary amplitude shift, suboptimum receiver

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