Digital Signal Processing Reference
In-Depth Information
2
J
MU-FPC
J
FPC
N
N
r
ij
,
2
,
W
k
(
n
)
=
W
k
(
n
)
+
γ
(
n
)
(5.115)
i
=
1
j
=
1
=−
2
j
=
i
where
E
y
i
(
y
j
(
r
ij
,
=
n
)
n
−
)
(5.116)
is the cross-correlation between the
i
th and
j
th outputs of the space-time
receivers for a lag
,and
2
is the maximum lag for which the output signals
of the different filters must be decorrelated.
The MU-FPA, for space-time processing, is then given by [62]
J
FPC
W
k
(
n
+
1
)
=
W
k
(
n
)
−
μ
∇
W
k
(
n
)
2
N
−
γ
(
n
)
r
ik
,
(
n
)
p
i
,
(
n
)
(5.117)
i
=
1
=−
2
i
=
k
y
H
R
y
,
(
n
+
1
)
=
ς
R
y
,
(
n
)
+
(
1
−
ς
)
y
(
n
)
(
n
−
)
(5.118)
y
H
P
(
n
+
1
)
=
ς
P
(
n
)
+
(
1
−
ς
)
X
(
n
)
(
n
−
)
(5.119)
−
)
=
y
1
(
−
)
T
y
(
n
n
−
)
···
y
K
(
n
(5.120)
=−
2
,
,
2
,
...
(5.121)
where
r
ik
,
(
n
)
is the cross-correlation between the
i
th and
j
th user estimates with
lag
at time index
n
, given by the
(
i
,
j
)
th element of matrix
R
y
,
(
n
)
p
i
,
(
)
α is a smoothing factor related to the process of learning the involved
statistics
n
)
is the
i
th column of matrix
P
(
n
5.4.2 Multiuser Detection Methods Based on Orthogonalization Criteria
Another family of algorithms tries to replace the direct decorrelation of the
equalizer outputs with an alternative condition that guarantees the correct
recovery of the source signals even in the presence of the near-far effect.
The approach is based on a constrained optimization procedure in which the
global response is subject to preserving the structure of a perfect recovery
condition [75]. Let us present two strategies that use this approach in the
sequel.
