
14
n
m
(ka)
= (n
1
(ka)
, n
2
(ka)
, . . . , n
L
(ka)
)T and stacked noise matrix is
(17)
N
m
= [
n
m
(1)
,
n
m
(2)
, … ,
n
m
(ka)
]
(18)
We define
h
(k,ka)
as the W-tap channel impulse response between the user k and antenna
k
a
h
(k,ka)
= (h
1
(k,ka)
, h
2
(k,ka)
, . . . , h
W
(k,ka)
)
T
(19)
Then the channel impulse response matrix for user k is stacked matrix from all Ka
antennas:
H
(k)
= [
h
(k,1)
,
h
(k,2)
, … ,
h
(k,ka)
]
H
= [
H
(1)T
,
H
(2)T
, … ,
K
(K)T
]
T
(20)
The key to estimate the channel matrix A is to estimate the channel’s impulse response
based on the given midamble training code sequence. Thus we build up the midamble
matrix:
G
(k)
is a L x W Toeplitz matrix of the midamble training code sequence for kth user. And
G
= [
G
(1)
,
G
(2)
, … ,
G
(K)
] stacked midamble training code matrix for all users
(21)
.Then, we have
E
m
=
GH
+
N
m
(22)
e
m
=
vec{
E
m
} = vec{
GH
+
N
m
} = vec{
GH
} + vec{
N
m
} = (
I
(Ka)
U
G
)vec{
H
} +
n
m
(23)
= (
I
(ka)
U
G
)
h
+
n
m
where
I
(Ka)
is a K
a
x K
a
identity matrix.
Then the ML estimator of vector
h
is
m
1
t
H
1
1
t
H
(Ka)
}
)
(
{
h
e
R
G
G
R
G
I
=
(24)
Where
R
m
= E{
n
m
n
m
Then, we have
H
}=
R
d
U
R
t
(ka)
m
1
t
H
1
1
t
H
(ka)
)
(
h
e
R
G
G
R
G
=
(25)
Since
R
t
is the temporal covariance, we will assume that
R
t
=
I
, Then
(ka)
m
(ka)
m
H
1
H
(ka)
)
(
h
Me
e
G
G
G
=
=
(26)
where
M
= (
G
H
G
)
–1
G
H
F
Freescale Semiconductor, Inc.
For More Information On This Product,
Go to: www.freescale.com
n
.