Digital Signal Processing Reference
In-Depth Information
In the multiuser case, the MF receiver (8.62) is no longer the optimal ML decoder,
and the complexity of the optimal ML decoding technique grows exponentially with
the number of users. Therefore, in this case suboptimal but simple linear receivers are of
particular interest [57, 59, 60].
As before, we assume without any loss of genera lit y that the first transmitter is the user
of interest. Then, using (8.60), we can express the output vector of a linear receiver as
ˆ
1
=
T
sWX
,
(8.65)
where for each user of interest, a separate matrix
W
should be used.
Given the matrix
W
, the information symbols of the user of interest can be estimated as
ˆ
]
ˆ
,
sIIs
1
=,
j
[
(8.66)
1
where the dimension of the identity matrices in (8.66) is
J
×
J
. Using the linear estimate
(8.66), the
l
th
information symbol can be detected as the nearest to the
l
th
entry of the
ˆ
1
signal constellation point.
Using the concept of MV beamforming, the receiver weight matrix
W
can be designed
to maximally suppress interference while preserving a distortionless response toward the
signal of the transmitter-of-interest. Specifically, for each entry of
s
1
, the receiver output
power has to be minimized while preserving the distortionless response for that particu-
lar entry of
s
1
. This is equivalent to solving the following optimization problem [59]:
ˆ
T
T
min
ww
R
subjectto
aw
=
1
for all
l
= ,, ,, 2
J
,
1 2
…
(8.67)
l
l
1
,
l
l
w
l
where
N
1
∑
ˆ
T
R
=
X
()
()
t
(8.68)
X
t
N
t
=
1
is the sample estimate of the 2
M
r
T
× 2
M
r
T
correlation matrix
R
E
{
X
X
T
} of the vector-
ized data, and
X
(
t
) denotes the
t
th
data block.
Taking into account that problem (8.67) can be solved independently for each
l
, the
solution to (8.67) can be written as [59]
1
ˆ
−
1
w
=
R
a
, =,, , .
l
12
…J
2
(8.69)
MV,
l
ˆ
1
,
l
a
T
R
−
1
a
1
,
l
1
,
l
Although the MV receiver (8.69) is able to suppress MAI, it does not completely can-
cel
self-interference
that, for the
l
th
entry of
s
1
, is caused by entries of
s
1
other than the
l
th
one. Clearly, self-interference is treated in (8.67) in the same way as MAI. Thus, when
the MAI component is strong, self-interference may not be sufficiently rejected. Note,
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