Digital Signal Processing Reference
In-Depth Information
2.5
2
Estimation Variance
Accurate CRLB
Approximate CRLB
1.5
1
0.5
0
0
1
2
3
4
5
6
7
8
9
10
Ricean K−factor of the physical channels, K
k
FIgure 7.9
Comparison of the CRLB and the estimation variance of the
K
-factor estimator of
the physical channels
h
nk
(
t
),
N
= 8,
M
= 1,
Q
= 50,
L
q
= 20. (Reproduced from Kim et al., 2006. ©
2006, IEEE. With permission.)
toward +∞. This implies that the maximum channel gain exploited by multiuser diversity
has increased significantly, and thus, the multiuser diversity gain can be notable. As can
be seen from (7.18), adaptive opportunistic beamforming achieves more improvement
when the number
N
of transmission antennas grows. This is because the value of
H
k
(
t
)
increases with
N
when
ϕ
(
t
)
−
θ
k
, and in turn, the value of H
M
(
t
)
increases with
N.
7.4.3 Estimation of
K
-Factors of the Physical Channels
In order to evaluate the performance of the
K
-factor estimator, the estimation variance
and the CRLB are compared in Figure 7.9 when
ϕ
q
= (
q
/
Q
)2
π.
One can see that the differ-
ence between the CRLB and the actual variance grows with the
K
-factor.* However, the
difference itself is not very large. For example, when
K
k
= 10, the difference is approxi-
mately 2, and thus the standard deviation is approximately 1.4, which is 14%
of the true
K
k
value. From the numerical results in the next section, it turns out that the effect of the
K
-factor estimation errors on the throughput performance is negligible.
7.4.4 Throughput
The final performance measure is the throughput obtained by different schemes. In slow
fading channels, the length
t
c
of the past window is
t
c
= +∞, and hence, the propor-
tional fair scheduling algorithm converges to select the user with the highest
R
k
(
t
).
he
*
In many previous
K
-factor estimators for SISO systems, the estimation variance also increases
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