
11
[
]
T
ka
W
NQ
ka
ka
ka
n
n
n
)
(
1
)
(
2
)
(
1
)
(
+
=
K
n
(5)
and
[
]
T
Ka
)
(
)
2
(
)
n
n
n
N
K
=
n = vec [
N
]
(6)
The transmission of the block on N symbols can be modeled by a system of linear
equations that relates the spreading codes, the channel’s input response and the impact of
noise in the signal.
3.2.
Received Signal Model
The received sequence received at chip rate from the k
a
e
(ka)
= (e
1
th
antenna is:
(ka)
, e
2
(ka)
, . . . , e
NQ+W-1
(ka)
)
T
(7)
where Q again is the spreading factor of the data symbol and W is the number of taps in
channel.
[
.
,
e
e
e
E
K
From Figure 3-1 we can see that
(
1
2
1
,
,
W
Q
b
b
b
b
+
K
Is the convolution of the channel input response with the corresponding spreading code.
(
h
is the channel impulse response between the user k and antenna k
a
, c(k) is the
spreading code of the user k.)
]
T
Ka
)
(
)
(
)
=
e
= vec[
E
]
(8)
)
)
,
(
)
,
(
)
,
(
)
,
(
)
,
(
*
)
(
ka
k
T
ka
k
ka
k
ka
k
ka
k
k
h
c
=
=
(9)
)
,
(
ka
k
Then the we can see that the signal arriving at the receiver can be described by a linear
system of equations that relate the user’s signal and the receiver input:
N
d
I
A
E
+
=
)
(
)
Ka
(10)
Where,
U
is the Kronecker product .
Or
n
Ad
e
+
=
(11)
The matrix
A
is called channel matrix and is defined as
[
A
A
A
A
K
]
Ka
)
(
)
(
)
=
(12)
F
Freescale Semiconductor, Inc.
For More Information On This Product,
Go to: www.freescale.com
n
.