Digital Signal Processing Reference
In-Depth Information
In order to solve the fairness and delay problem, the proportional fair scheduling algo-
rithm has been developed in [12]. In this algorithm, the
k
t h
user feeds back the requested
data rate
R
k
(
t
) to the base station, where
R
k
(
t
) is the data rate the user can support at time
slot
t
. The proportional fair scheduling algorithm also stores the average throughput
T
k
(
t
) of every user in a past window of length
t
c
. At any time slot
t
, the proportional fair
scheduling algorithm transmits data to the user with the largest
Rt
Tt
()
()
.
k
k
(7. 2)
In order to see how the proportional fair scheduling algorithm works, we consider a
system with only two users. If the two users have identical fading statistics, the average
throughput
T
k
(
t
) of each user will converge to the same value. Thus, the proportional
fair scheduling algorithm just picks the user with the highest
R
k
(
t
), and it is fair for every
user in the long term. It is possible that the first user's channel is better than that of the
second user on average. Always transmitting to the user with the highest
R
k
(
t
) implies
that the first user will be served for most of the time and the second user will not be
served in a resource fair manner. This problem is solved by using the proportional fair
scheduling algorithm. Because the proportional fair scheduling algorithm selects the
user based on
R
k
(
t
)/
T
k
(
t
), a user is selected when its instantaneous channel condition is
high relative to its own average channel condition over the time scale
t
c
. To an extreme
case, if the second user is not served in the past window of length
t
c
,
T
2
(
t
) becomes zero
and the base station will transmit data to the second user immediately.
7.3
Opportunistic Beamforming
As we have seen in section 7.2, the dynamic range and the variation rate of the chan-
nel fluctuation determine the performance gain of multiuser diversity. Thus, if one can
induce larger and faster channel fluctuation, higher gain will be achieved. This can be
realized by opportunistic beamforming [13]. In this scheme,
N
antennas are deployed at
the base station and there are
M
users in the system. Let
h
n,k
(
t
) denote the channel coef-
ficient from the
n
th
antenna to the
k
t h
user at time slot
t
. The transmitted signal
s
(
t
) is first
multiplied by a complex weight coefficient
j
φ
()
t
wt
()
=α
()
te
n
n
n
and then transmitted by the
n
th
antenna, for
n
= 1,
…
,
N
. In order to satisfy the power
constraint, it is assumed that
∑
=
1
N
α ()
n
t
1
.
n
=
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