Digital Signal Processing Reference
In-Depth Information
Accordingly, the adaptation for spatial processing is given by the follow-
ing expression:
μ
1
2
y
k
(
N
y
k
(
x
∗
(
w
k
(
n
+
1
)
=
w
k
(
n
)
+
−
n
)
n
)
n
)
−
γ
r
ik
(
n
)
p
i
(
n
)
, (5.98)
i
=
1
i
=
k
where
th element of the matrix
R
y
(
r
ik
(
n
)
is the
(
i
,
k
)
n
)
is the
i
th column of matrix
P
p
i
(
n
)
(
n
)
, given in (5.97)
To take the effect of ISI into account, we have to modify the equations in
order that the decorrelation term comprises the different time instants and
mitigate the replication of a sequence of the same source signal with different
delays. We can then write the following:
2
K
K
r
ij
2
,
J
MU-CMA
(
W
k
)
=
J
CMA
(
W
k
)
+
(
)
γ
(5.99)
i
=
1
j
=
1
=−
2
j
=
i
where
E
y
i
(
−
)
r
ij
()
=
n
)
y
j
(
n
(5.100)
is the cross-correlation between the signals from the
i
th and
j
th outputs of
the space-time MIMO equalizer with lag
,and
2
is the maximum esti-
mated delay for which the signals associated with multiple users must be
uncorrelated.
Making use of the points of contact between spatial and space-time
processing, we can write
2
μ
1
2
y
k
(
K
y
k
(
W
k
(
n
+
1
)
=
W
k
(
n
)
+
−
n
)
n
)X(
n
)
−
γ
r
ik
,
(
n
)
p
i
,
(
n
)
,
i
=
1
=−
2
i
=
k
(5.101)
and
y
T
R
y
,
(
n
+
1
)
=
ς
R
y
,
(
n
)
+
(
1
−
ς
)
y
(
n
)
(
n
−
)
(5.102a)
y
T
P
(
n
+
1
)
=
ς
P
(
n
)
+
(
1
−
ς
)X(
n
)
(
n
−
)
(5.102b)
