Digital Signal Processing Reference
In-Depth Information
q
(
n
)
s
(
n
)
x
(
n
)
y
(
n
)
F
(
z
)
0
C
(
z
)
M
P
z
channel
F
(
z
)
1
M
P
z
s
(
n
)
H
(
z
)
0
P
M
z
z
−1
F
(
z
)
M
H
(
z
)
1
M
P
P
M
1
transmitter filters
−
z
−1
z
−1
H
(
z
)
M
P
M
−
1
receiver filters
Figure P7.6(b).
7.7.
Multiuser systems.
Figure P7.7 shows a multiuser system where the
k
th
user sends a signal
s
k
(
n
) (modulated by the transmitting filter
F
k
(
z
))
through a channel
C
k
(
z
). You can imagine that each user uses a single
antenna to transmit the waveform. The signals from all
M
users are col-
lected by a receiver with a single antenna. The receiver uses
M
filters
H
k
(
z
) to separate out the different users. Let the filters be expressed in
the polyphase forms
P−
1
P−
1
z
−i
R
i,m
(
z
P
)
,H
k
(
z
)=
z
i
E
k,i
(
z
P
)
.
F
m
(
z
)=
(P7
.
7)
i
=0
i
=0
Using the pseudocirculant theory of Sec. 3.9, show that the path from
s
m
(
n
)to
s
k
(
n
) is an LTI system with transfer function
⎡
⎤
R
0
,m
(
z
)
R
1
,m
(
z
)
.
R
P−
1
,m
(
z
)
⎣
⎦
T
km
(
z
)=[
E
k,
0
(
z
)
E
k,
1
(
z
)
...
E
k,P−
1
(
z
)]
C
m
(
z
)
,
where
C
m
(
z
)isthe
P
P
pseudocirculant (blocked version) associated with
C
m
(
z
). From this expression we see that the system in general suffers from
multiuser interference
(MUI) because
×
s
k
(
n
) can be affected by
s
m
(
)
,m
=
k.
There is also
intersymbol interference
(ISI) because
s
k
(
n
) can be affected
by
s
k
(
)
,
=
n
(more generally by
s
m
(
)
,
=
n
).
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