Digital Signal Processing Reference
In-Depth Information
K
K
1
ht
,
=
()
k
exp(
jn
θ
)
+
bt
( )
,
(7.10)
nk
k
nk
1
+
1
+
K
k
k
where
K
k
is the Ricean
K
-factor and θ
k
is related to the DOA of the user. The first term in
(7.10) denotes the line-of-sight (LOS) component of the channel. The second term is the
diffused component and
b
nk
(
t
) ~ C N (0, 1). Then the equivalent channel gain becomes
N
N
∑
1
α
()
tK
K
∑
+
α
t
K
()
exp(
(
)
+
()
h
t
=
k
k
exp(
jn
θφ
+
()
t
n
j
φ
())()
t bt
.
(7.11)
k
n
n
nk
k
1
+
1
k
k
n
=
n
=
1
It can be seen that the randomization of α
n
(
t
) and ϕ
n
(
t
) will not change the dynamic
range of the diffused term, which is the same as in the Rayleigh fading environment.
However, the randomization of α
n
(
t
) and ϕ
n
(
t
) induces t he fluctuation of t he LOS compo-
nent significantly, which leads to performance improvement. Therefore, if the LOS com-
ponent is more dominant than the diffused path, larger fluctuation will be created by
opportunistic beamforming and more performance gain can be achieved. To an extreme
case that
K
k
→ ∞, the channel reduces to the slow fading case and opportunistic beam-
forming can improve the performance considerably, as we have seen in section 7.3.1.
Figure 7.6 shows the total throughput for Ricean fading channels with
K
k
= 10. There is
an impressive improvement in performance after using opportunistic beamforming. For
comparison, the performance curve for the Rayleigh fading channels is plotted.
2.6
2.4
2.2
Rayleigh
2
1.8
2 antenna, Ricean, opp. BF
1.6
1 antenna, Ricean
1.4
1.2
1
0.8
0
5
10
15
20
25
30
35
Number of users
FIgure 7.6
Total throughput as a function of the number of users under Ricean fading, with
and without opportunistic beamforming. The power allocations α
n
(
t
) are uniformly distributed
in [0, 1] and the phases θ
n
(
t
) are uniform in [0,2π]. (Reproduced from Viswanath et al., 2002. ©
2002, IEEE. With permission.)
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