Digital Signal Processing Reference
In-Depth Information
2.6
2.4
2.2
2
Mobile
1.8
Fixed opp. BF
1.6
1.4
Fixed
1.2
1
Equal time scheduling
0.8
0
5
10
15
20
25
30
35
Number of users
FIgure 7.3
Amplification in multiuser diversity gain with opportunistic beamforming in a
fixed environment. (Reproduced from Viswanath et al., 2002. © 2002, IEEE. With permission.)
For a particular user
k
, it is well known that coherent transmit beamforming can
maximize γ˜
n
(
t
) by setting [13]
2
| |
h
nk
,
α
n
=
,
(7. 6)
∑
N
| |
h
2
nk
,
n
=
1
φ
n
=−
arg(
h
) ,
(7.7)
nk
,
which is called the beamforming configuration. In this case, however, the base station
needs to know
h
n,k
, for
n
= 1,
…
,
N
, and hence, this amount of feedback information
might be prohibitive. On the other hand, opportunistic beamforming selects the user
when its equivalent SNR is at the peak. Therefore, opportunistic beamforming may
achieve the performance of coherent transmit beamforming, while only requiring the
feedback of γ˜
k
(
t
). This is confirmed by the following theorem.
heorem
7.
1
[13] “Suppose the slow fading states of the users are i.i.d and are discrete, and the joint
stationary distribution of
(α
1
(
t
), …, α
N
(
t
), ϕ
1
(
t
), …, ϕ
2
(
t
))
is the same as that of
2
2
,,
| |
| |
h
| |
h
1
k
nk
,
,−
arg()
h
1
,−
arg(
h
)
(7. 8)
k
nk
,
N
N
∑∑
2
2
| |
h
h
nk
,
nk
,
n
=
1
n
=
1
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