EE132A, Spring 2007
Communication Systems
Prof. John Villasenor
Handout # 14
TA: Choo Chin (Jeffrey) Tan
Homework 6
Assigned: Monday, May 14, 2007
Due: Monday, May 21, 2007
Reading Assignment:
Chapter 8 (8.5), Chapter 10 (10.1 – 10.3), Chapter 9 (9.1, 9.2)
1.
Consider the signal space depicted below:
Assume that each symbol has transmitted energy
E
and that
( )
t
1
ϕ
and
( )
t
2
ϕ
are given by
( )
<
≤
=
elsewhere
,
0
0
,
2
cos
/
2
1
T
t
t
f
T
t
c
π
ϕ
,
( )
<
≤
=
elsewhere
,
0
0
,
2
sin
/
2
2
T
t
t
f
T
t
c
π
ϕ
(a)
Find the time domain expressions for the 8 signals
( )
t
s
i
,
8
,
,
1
midhorizellipsis
=
i
.
(b)
Determine the bit error probability (as a function of
E
b
/
N
0
), considering only the nearest
neighbors.
(c)
Provide a labeling using Gray coding.
2.
Consider an 8-PSK system and a 16-PSK system.
(a)
Find an expression for the probability of symbol (not bit) error for the 8-PSK system, as a
function of
E
and
N
0
, where
E
is the transmitted symbol energy.
(b)
Give an expression for the BER, as a function of
E
b
and
N
0
.
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- Spring '08
- Walker
- Frequency, S6, Zürich Hauptbahnhof, Communication Systems Handout, John Villasenor TA
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