Digital Signal Processing Reference
In-Depth Information
a data-dependent component is added to the superimposed training such that interfer-
ence due to data (information sequence) is greatly reduced in channel estimation at the
receiver. This method is applicable to time-invariant channels only, and it requires “data
blocking” for block transmissions and insertion of a cyclic prefix in each data block. Its
extension to a class of time-variant channels is given in [59]. The UTRA specification
for third-generation (3G) systems [21] allows for a spread pilot (superimposed) sequence
in the base station's common pilot channel, suitable for downlinks. Periodic superim-
posed training for channel estimation via first-order statistics for SISO systems has been
discussed in [39, 41, 57, 58, 63]. In [8], performance bounds for training and superim-
posed training-based semiblind SISO channel estimation for time-varying flat fading
channels have been discussed.
Suppose that the superimposed training sequence
c
(
n
) =
c
(
n
+
mP
) ∀
m
,
n
is a non-
random periodic sequence with period
P
. Since
c
(
n
) is
P
periodic, we have
−
∑
0
P
1
()
=
j
α
n
cn
ce
,∀, :=
n
απ /
2
mP
,
(2.49)
m
m
m
m
=
where
∑
1
P
−
:=
()
=
−
j
α
m
c
c ne
/.
P
m
n
Suppose that we use the Slepian (DPS) sequences
u
q
(
n
) (≡ϕ
q
(
n
)) in the BEM. Then, by
(2.20) and (2.49),
Q
P
−
1
L
∑∑ ∑
1
({
=
=
()
()
.
−
j
α
m
j
α
n
En
y
c
h
l e
une
q
(2.50)
m
mq
q
==
m
0
l
=
0
=:
d
mq
It follows that
−
∑∑
1
Q
P
1
()
=
()
+
()
j
α
m
y
n
d
u ne
e
n
,
(2 . 51)
mq
q
q
==
m
0
where {
e
(
n
)} is a zero-mean random sequence.
Define the cost function
T
=
()
.
=
−
∑
0
1
2
J
e
n
(2.52)
n
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