University of Illinois
Spring 2011
ECE 361:
Problem Set 10
Receivers for Passband Signals
Due:
Tuesday
May 3, 9:30 a.m.
1.
[Phase error in BPSK communication]
Antipodal signaling over an AWGN channel with bit energy
E
achieves bit error probability
Q
(
p
2
E
/N
0
)
with an optimum receiver. Now consider antipodal BPSK signaling with signals
±
p
2
E
/T
cos(2
πf
c
t
)
of duration
T
, and assume that the local oscillator (LO) is not perfectly synchronized to the carrier
in the incoming signal. Thus, instead of the LO signal being
√
2 cos(2
πf
c
t
), it is
√
2 cos(2
πf
c
t
+
θ
)
instead. Everything else is unchanged.
Show that the bit error probability is increased from
Q
(
p
2
E
b
/N
0
) to
Q
(cos
θ
p
2
E
b
/N
0
).
2.
[Phase error in QPSK communication]
The transmitted symbol in a QPSK communication system is
X
I
+
j
X
Q
where
X
I
,
X
Q
∈ {
+
√
E
b
,

√
E
b
}
are independent and equally likely to take on both values. Because of a phase error in the receiver, the
received symbol is (
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This document was uploaded on 01/24/2012.
 Spring '09

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