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Proactive Proportional Fair: A Novel Scheduling Algorithm Based on Future Channel Information in OFDMA Systems
ju.edu.cn, {tianyu.alex.wang, wangsw}@nj
Abstract—Radio resource scheduling is one of the most important issues in OFDMA systems, in which real-time and
historical channel information are utilized to schedule the current
radio resource allocation, such that system throughput can be
maximized while user fairness is guaranteed. Recently, some
studies have shown that wireless channel parameters can be
predicted by exploiting the time dependence of fading channels.
In this paper, we exploit this new degree of freedom and propose a
novel scheduling algorithm, proactive proportional fair (PPF), in
which future channel information is jointly considered with the
past and current channel parameters. Simulation results show
that the proposed PPF algorithm outperforms the generalized
proportional fair algorithm in terms of system throughput by
more than 40% when high user fairness is guaranteed.
Index Terms—Channel prediction, OFDMA, radio resource
scheduling.
I. INTRODUCTION
Radio resource scheduling is one of the most important
issues in OFDMA systems [1–3], which determines how the
time-frequency resource blocks are allocated to each user
in each transmission time interval (TTI) [4]. Among all the
metrics that are utilized to evaluate the performance of radio
resource scheduling, system throughput and user fairness are
mostly considered. Network operators always need to increase
the system throughput, such that the service capacity is maximized, while at the same time, guarantee the user fairness
since all mobile users are charged at the same price. Therefore,
the trade-off between system throughput and user fairness is
crucial for the performance of a scheduling algorithm.
A variety of scheduling algorithms have been proposed to
achieve the best trade-off between system throughput and user
fairness in OFDMA systems as can be found in the literature.
Max-rate (MR) only focuses on the aggregate throughput of
the entire system, which allocates radio resources to the user
with the highest channel parameter in the current TTI [5].
Max-min fairness (MMF) has a strict fairness criterion that
gives the highest priority to the user with the lowest average
This work was partially supported by the National Natural Science Foundation of China (61801208, 61671233), the Jiangsu Science Foundation
(BK20170650), the Postdoctoral Science Foundation of China (BX201700118,
2017M621712), and the Jiangsu Postdoctoral Science Foundation(1701118B),
and the open research fund of National Mobile Communications Research
Laboratory (2019D02).
data rate in the past [6]. Proportional fair (PF) achieves a tradeoff between system throughput and user fairness by jointly
considering the instantaneous data rate in the current TTI and
the average throughput in the past [7]. Generalized proportional fair (GPF) extends the PF algorithm by introducing
two hyperparameters, such that the trade-off between system
throughput and user fairness can be adjusted in a flexible way
[8].
The existing scheduling algorithms utilize the past and
the current channel information to decide the current radio
resource allocation. Recently, some studies have shown that
small-scale channel parameters can be predicted by exploiting
the time dependency of fading channels [9, 10], which provides
a new degree of freedom for radio resource scheduling. In fact,
some studies have utilized the predicted channel parameters
to schedule radio resources. In [11] the authors proposed a
scheduling algorithm that estimates users’ average throughput
in the future by iteration, and in [12] the authors introduced
a joint algorithm that is effective when channel quality information is predicted imperfectly.
In this paper, we assume the channel parameters can be
predicted, and propose a novel scheduling algorithm, proactive
proportional fair (PPF), in which future channel information is
jointly utilized with the past and current channel information to
decide the current radio resource allocation. Simulation results
show that the proposed PPF algorithm outperforms the GPF
algorithm in terms of system throughput by more than 40%
when high user fairness is guaranteed.
The rest of the paper is organized as follows. In section II
the system model of packet scheduling for an OFDMA system
is provided, and key issues regarding to the design of packet
scheduler are presented. In section III the existing scheduling
algorithms are elaborated and analyzed, which shows that
future channel information can be utilized to improve the
performance of the system. In section IV simulation results are
shown to compare the proposed algorithm with the existing
algorithms in terms of both system throughput and user
fairness. Finally, in section V we draw our conclusion, and
discuss some directions of the future work.
II. SYSTEM MODEL
In OFDMA systems, radio resources are abstracted into
time-frequency resource blocks (RBs), as shown in Fig. 1.
Each RB represents a subchannel with bandwidth w within a
TTI τ. We consider a network with N users and K subchannels. In order to avoid co-channel interference, each RB can
be allocated to at most one user. A scheduling algorithm is to
decide how to allocate the K RBs to the N users at TTI t
[13]. We denote by hi,k(t) as the channel parameter of user
i ∈ N under subchannel k ∈ K at TTI t, and the signal to
interference plus noise of user i under subchannel k at TTI t
can be given by
SINRi,k(t) = Pi,k(t)∣hi,k(t)∣2
∑k′≠K Pi,k′(t)∣hi,k′(t)∣2 + wn0 , (1)
where Pi,k(t) is the transmission power of user i on subchannel k at TTI t, w denotes the bandwidth of each subchannel
and n0 denotes the thermal noise density of white Gaussian
noise.
Fig. 1. Radio resource scheduling in OFDMA systems.
For any TTI t, we denote by xi,k(t) the indicator for
subchannel k ∈ K and user i ∈ N , in which xi,k(t) = 1
represents that subchannel k is allocated to user i in TTI
t and xi,k(t) = 0 represents the opposite. Most scheduling
algorithms can be presented in a general framework, in which
a weight factor mi,k(t) is assigned to each user i for each
subchannel k, and the subchannels are allocated to the user
with the largest weight factor, i.e.,
xi,k(t) = { 1 0, mi,k(t) = maxj,∈Notherwise mj,k(t),. (2)
Here, mi,k(t) can be seen as the preference of subchannel
k for user i at TTI t, and the subchannel is allocated to the
user that is most preferred. Therefore, the difference between
scheduling algorithms is how the preferences mi,k(t) are
determined.
To decide the optimal weight factors, a variety of performance metrics have been considered in the literature. Some of
the most popular metrics are presented as follows:
● Real-time Throughput: Let di,k(t) denote the real-time
throughput of user i in subchannel k at TTI t. This metric
can be directly calculated by using the current channel
parameters, given by
di,k(t) = w log[1 + SINRi,k(t)], (3)
where SINRi,k(t) denotes the signal to interference plus
noise ratio of user i in subchannel k at TTI t.
● Average Throughput: Let ri(t) denote the average
throughput of user i for TTI t [14], which can be given
by
ri(t) = (1 − 1
NT
)ri(t − 1) + 1
NT
ri(t), (4)
where ri(t) denotes the data throughput that user i
achieves at TTI t and NT denotes the time window over
which the average throughput is calculated. ri(t) can be
calculated as follows:
ri(t) =
K∑k=1
xi,k(t)di,k(t). (5)
● Fairness Index: User fairness is one of the most important issues in wireless communication networks, for
which various fairness indexes have been proposed. The
most famous fairness index is the Jain’s fairness index
[15], which is defined as:
F(T) =
(∑N i=1 Ri(T))2
N ∑N i=1 Ri(T)2 , (6)
where Ri(T) denotes the total throughput received by
user i within the considered time period T, given by
Ri(T) =
T∑t=1
ri(t). (7)
The value of Jain’s fairness index is between 0 and 1.
The user fairness increases as the value of Jain index
approaches 1. When the total throughput of each user is
equal to each other, we have F(t) = 1.
III. PROACTIVE SCHEDULING USING FUTURE CHANNEL
INFORMATION
We first show how the current scheduling algorithms decide
weight factors. Then we propose a novel PPF algorithm, which
introduces a new degree of freedom by using future channel
information.
A. Existing Scheduling Algorithms
The MR algorithm aims at maximizing the overall throughput by allocating each RB to the user that achieves the largest
throughput in the current TTI. Formally, the weight factors of
the MR algorithm are given by
mM R
i,k (t) = di,k(t). (8)
The MMF algorithm seeks for absolute fairness by allocating each RB to the user that has achieved the lowest throughput
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Proactive Proportional Fair: A Novel Scheduling Algorithm Based on Future Channel Information in OFDMA Systems
ju.edu.cn, {tianyu.alex.wang, wangsw}@nj
Abstract—Radio resource scheduling is one of the most important issues in OFDMA systems, in which real-time and
historical channel information are utilized to schedule the current
radio resource allocation, such that system throughput can be
maximized while user fairness is guaranteed. Recently, some
studies have shown that wireless channel parameters can be
predicted by exploiting the time dependence of fading channels.
In this paper, we exploit this new degree of freedom and propose a
novel scheduling algorithm, proactive proportional fair (PPF), in
which future channel information is jointly considered with the
past and current channel parameters. Simulation results show
that the proposed PPF algorithm outperforms the generalized
proportional fair algorithm in terms of system throughput by
more than 40% when high user fairness is guaranteed.
Index Terms—Channel prediction, OFDMA, radio resource
scheduling.
I. INTRODUCTION
Radio resource scheduling is one of the most important
issues in OFDMA systems [1–3], which determines how the
time-frequency resource blocks are allocated to each user
in each transmission time interval (TTI) [4]. Among all the
metrics that are utilized to evaluate the performance of radio
resource scheduling, system throughput and user fairness are
mostly considered. Network operators always need to increase
the system throughput, such that the service capacity is maximized, while at the same time, guarantee the user fairness
since all mobile users are charged at the same price. Therefore,
the trade-off between system throughput and user fairness is
crucial for the performance of a scheduling algorithm.
A variety of scheduling algorithms have been proposed to
achieve the best trade-off between system throughput and user
fairness in OFDMA systems as can be found in the literature.
Max-rate (MR) only focuses on the aggregate throughput of
the entire system, which allocates radio resources to the user
with the highest channel parameter in the current TTI [5].
Max-min fairness (MMF) has a strict fairness criterion that
gives the highest priority to the user with the lowest average
This work was partially supported by the National Natural Science Foundation of China (61801208, 61671233), the Jiangsu Science Foundation
(BK20170650), the Postdoctoral Science Foundation of China (BX201700118,
2017M621712), and the Jiangsu Postdoctoral Science Foundation(1701118B),
and the open research fund of National Mobile Communications Research
Laboratory (2019D02).
data rate in the past [6]. Proportional fair (PF) achieves a tradeoff between system throughput and user fairness by jointly
considering the instantaneous data rate in the current TTI and
the average throughput in the past [7]. Generalized proportional fair (GPF) extends the PF algorithm by introducing
two hyperparameters, such that the trade-off between system
throughput and user fairness can be adjusted in a flexible way
[8].
The existing scheduling algorithms utilize the past and
the current channel information to decide the current radio
resource allocation. Recently, some studies have shown that
small-scale channel parameters can be predicted by exploiting
the time dependency of fading channels [9, 10], which provides
a new degree of freedom for radio resource scheduling. In fact,
some studies have utilized the predicted channel parameters
to schedule radio resources. In [11] the authors proposed a
scheduling algorithm that estimates users’ average throughput
in the future by iteration, and in [12] the authors introduced
a joint algorithm that is effective when channel quality information is predicted imperfectly.
In this paper, we assume the channel parameters can be
predicted, and propose a novel scheduling algorithm, proactive
proportional fair (PPF), in which future channel information is
jointly utilized with the past and current channel information to
decide the current radio resource allocation. Simulation results
show that the proposed PPF algorithm outperforms the GPF
algorithm in terms of system throughput by more than 40%
when high user fairness is guaranteed.
The rest of the paper is organized as follows. In section II
the system model of packet scheduling for an OFDMA system
is provided, and key issues regarding to the design of packet
scheduler are presented. In section III the existing scheduling
algorithms are elaborated and analyzed, which shows that
future channel information can be utilized to improve the
performance of the system. In section IV simulation results are
shown to compare the proposed algorithm with the existing
algorithms in terms of both system throughput and user
fairness. Finally, in section V we draw our conclusion, and
discuss some directions of the future work.
II. SYSTEM MODEL
In OFDMA systems, radio resources are abstracted into
time-frequency resource blocks (RBs), as shown in Fig. 1.
Each RB represents a subchannel with bandwidth w within a
TTI τ. We consider a network with N users and K subchannels. In order to avoid co-channel interference, each RB can
be allocated to at most one user. A scheduling algorithm is to
decide how to allocate the K RBs to the N users at TTI t
[13]. We denote by hi,k(t) as the channel parameter of user
i ∈ N under subchannel k ∈ K at TTI t, and the signal to
interference plus noise of user i under subchannel k at TTI t
can be given by
SINRi,k(t) = Pi,k(t)∣hi,k(t)∣2
∑k′≠K Pi,k′(t)∣hi,k′(t)∣2 + wn0 , (1)
where Pi,k(t) is the transmission power of user i on subchannel k at TTI t, w denotes the bandwidth of each subchannel
and n0 denotes the thermal noise density of white Gaussian
noise.
Fig. 1. Radio resource scheduling in OFDMA systems.
For any TTI t, we denote by xi,k(t) the indicator for
subchannel k ∈ K and user i ∈ N , in which xi,k(t) = 1
represents that subchannel k is allocated to user i in TTI
t and xi,k(t) = 0 represents the opposite. Most scheduling
algorithms can be presented in a general framework, in which
a weight factor mi,k(t) is assigned to each user i for each
subchannel k, and the subchannels are allocated to the user
with the largest weight factor, i.e.,
xi,k(t) = { 1 0, mi,k(t) = maxj,∈Notherwise mj,k(t),. (2)
Here, mi,k(t) can be seen as the preference of subchannel
k for user i at TTI t, and the subchannel is allocated to the
user that is most preferred. Therefore, the difference between
scheduling algorithms is how the preferences mi,k(t) are
determined.
To decide the optimal weight factors, a variety of performance metrics have been considered in the literature. Some of
the most popular metrics are presented as follows:
● Real-time Throughput: Let di,k(t) denote the real-time
throughput of user i in subchannel k at TTI t. This metric
can be directly calculated by using the current channel
parameters, given by
di,k(t) = w log[1 + SINRi,k(t)], (3)
where SINRi,k(t) denotes the signal to interference plus
noise ratio of user i in subchannel k at TTI t.
● Average Throughput: Let ri(t) denote the average
throughput of user i for TTI t [14], which can be given
by
ri(t) = (1 − 1
NT
)ri(t − 1) + 1
NT
ri(t), (4)
where ri(t) denotes the data throughput that user i
achieves at TTI t and NT denotes the time window over
which the average throughput is calculated. ri(t) can be
calculated as follows:
ri(t) =
K∑k=1
xi,k(t)di,k(t). (5)
● Fairness Index: User fairness is one of the most important issues in wireless communication networks, for
which various fairness indexes have been proposed. The
most famous fairness index is the Jain’s fairness index
[15], which is defined as:
F(T) =
(∑N i=1 Ri(T))2
N ∑N i=1 Ri(T)2 , (6)
where Ri(T) denotes the total throughput received by
user i within the considered time period T, given by
Ri(T) =
T∑t=1
ri(t). (7)
The value of Jain’s fairness index is between 0 and 1.
The user fairness increases as the value of Jain index
approaches 1. When the total throughput of each user is
equal to each other, we have F(t) = 1.
III. PROACTIVE SCHEDULING USING FUTURE CHANNEL
INFORMATION
We first show how the current scheduling algorithms decide
weight factors. Then we propose a novel PPF algorithm, which
introduces a new degree of freedom by using future channel
information.
A. Existing Scheduling Algorithms
The MR algorithm aims at maximizing the overall throughput by allocating each RB to the user that achieves the largest
throughput in the current TTI. Formally, the weight factors of
the MR algorithm are given by
mM R
i,k (t) = di,k(t). (8)
The MMF algorithm seeks for absolute fairness by allocating each RB to the user that has achieved the lowest throughput
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