EE 230B Final Examination,
Spring 2008
NAME:_______________________
UCLA Electrical Engineering Department
Prof. G. Pottie
Instructions:
Attempt all five questions; they are of equal weight but not necessarily of equal
difficulty.
A sheet of useful formulae and other facts is attached.
1. Phase Error in QAM
Suppose a persistent phase error of
θ
occurs.
a) By what factor is the effective minimum distance reduced for 4QAM compared to
perfect synchronism?
Write an expression for
P
(
e

θ
).
Solution:
d
1
d
r
θ
d
2
+
d
2
=
r
2
;
d
=
r
/
2
=
r
sin(
π
/4)
sin(
π
/4
−
θ
)
=
d
1
/
r
;
d
1
=
r
sin(
π
/4
−
θ
)
P
(
e

θ
)
=
2
Q
2
r
sin(
π
/4
−
θ
)
2
N
0
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
b) Repeat for the worstcase signal point in 16QAM.
Soln:
Here, things are much the same except now there is a new boundary located at
2
r
/3.
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