Homework 7 of Elec 430
2.3
2002/01/11
2004/01/07 10:17:04.124 US/Central
Behnaam
Aazhang
aaz@ece.rice.edu
Dinesh
Rajan
dinesh@ece.rice.edu
Mohammad
Jaber
Borran
mohammad@ece.rice.edu
Behnaam
Aazhang
aaz@ece.rice.edu
Shawn
Stewart
mrshawn@alumni.rice.edu
Roy
Ha
rha@rice.edu
homework
(Blank Abstract)
Consider an On-Off Keying system where
s
1
t
A
2
f
c
t
θ
for
0
t
T
and
s
2
t
0
for
0
t
T
.
The channel is ideal AWGN with zero mean and spectral height
N
0
2
.
- Assume θ is known at
the receiver. What is the average probability of bit-error using an
optimum receiver?
- Assume that we estimate the receiver phase to be
θ
^
and that
θ
^
θ
.
Analyze the performance of the matched filter with the wrong phase,
that is, examine
P
e
¯
as a function of the phase error.
- When does noncoherent become preferable? (You can find an
expression for the
P
e
¯
of noncoherent receivers for OOK in your textbook.) That is, how
big should the phase error be before you would switch to
noncoherent?
Proakis and Salehi, Problems 9.4 and 9.14
A coherent phase-shift keyed system operating over
an AWGN channel with two sided power spectral density
N
0
2
uses
s
0
t
A
p
T
t
ω
c
t
θ
0
and
s
1
t
A
p
T
t
ω
c
t
θ
1
where
i
i
0
1
θ
i
3
, are constants and that
f
c
T
integer
with
ω
c
2
f
c
.
- Suppose
θ
0
and
θ
1
are known constants and that the optimum
receiver uses filters matched to
s
0
t
and
s
1
t
.
What are the values of
P
e
0
and
P
e
1
?
- Suppose
θ
0
and
θ
1
are unknown constants and that the
receiver filters are matched to
s
^
0
t
A
p
T
t
ω
c
t
and
s
^
1
t
A
p
T
t
ω
c
t
and the threshold is zero.
Use a correlation receiver structure.
What are
P
e
0
and
P
e
1
now? What are the minimum values of
P
e
0
and
P
e
1
(as a function of
θ
0
and
θ
1
)?