Digital Signal Processing Reference
In-Depth Information
( )
∑
()
L
2
1
L
t
t
1
is the ML estimate of
E
ħ
(
t
)[
ħ
2
(
t
)] [24], and
E
ħ
(
t
)[
ħ
4
(
t
)] can be estimated simply as
( )
∑
()
L
4
1
L
t
t
1
[25]. Exactly in the same manner, one can show that Ω
k,q
and
E
q
[
H
k
4
(
t
)], and thus γ
k,q
, can
be estimated as follows:
−
( )
+
( )
2
1
∑
ˆ
4
Ω
ML
Ht
()
kq
,
k
L
tP
∈
ˆ
q
q
γ
kq
=
,
(7. 33)
,
2
ˆ
ML
Ω
kq
,
where
ˆ
ML
k,q
denotes the ML estimate of Ω
k,q
, which is given by
1
∑
ˆ
Ω
k
ML
=
Ht
2
().
(7. 3 4)
,
k
L
q
tP
∈
q
It follows that the
K
-factors are estimated as follows:
Q
Q
ˆ
1
−
γ
1
∑∑
1
ˆ
ˆ
kq
,
K
=
K
=
.
(7. 35)
k
k q
,
Q
Q
ˆ
11
−−
γ
q
=
1
q
=
1
kq
,
By analytically deriving the Cramer-Rao lower bound (CRLB) of the
K
-factors {
K
k
}
k
=1
, it
has been demonstrated that this is a good estimator [17].
7.4
Performance Evaluation
In this section, the performance of the ML estimator of DOAs, the Ricean
K
-factor esti-
mation algorithm, and the adaptive opportunistic beamforming scheme based on DOAs
and the
K
-factor estimation are numerically evaluated.
7.4.1 ML Estimation of Users' DOAs
In order to concentrate on the performance evaluation of the DOA estimation, the true
values of the Ricean
K
-factor are assumed to be known at the base station.
Figure 7.7
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