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A Proportional Fairness Scheduling Algorithm with QoS constraints for OFDMA Systems Tien-Dzung Nguyen and Youngnam Han School of Engineering, Information and Communications University Email: {dungnt, ynhan}@icu.ac.kr Abstract In this work, we propose a Proportional Fairness

subcarrier is flat. Denote gk,n as the channel gain and pk,n as the allocated power of user k to subcarrier n.

scheduling algorithm with QoS constraints to achieve

The channel capacity of user k on subcarrier n with

the tradeoff between throughput and fairness in

BER requirement is given by

OFDMA systems. Numerical results reveal that good

rk , n = f ( BER, g k , n , pk , n ) ,

tradeoff is achieved.

(1)

where f(.) is a nonlinear function that depends on the 1 Introduction OFDM technique is suitable to support high speed

type of constellation used. Equation (1) yields the throughput of user k N

data rate services of the next generation wireless net-

Rk = ∑ ρ k , n rk , n ,

works [1]. In multiuser OFDMA systems, there are diverse channel patterns between the Base-Station (BS)

(2)

n =1

and the overall system throughput K

and users. The probability that all users experience a

N

T = ∑∑ ρ k , n rk , n ,

deep fade in a particular subcarrier is very low.

(3)

k =1 n =1

Therefore, subcarrier and power allocation to different

where ρk,n(t) is defined as assignment indicator

users makes further efficient use of scarce radio

variable to user k using subcarrier n: ρk,n(t) is 1 when

resource.

subcarrier n is assigned to user k; otherwise it is 0. In

Throughput maximization in previous works may

OFDMA systems, no more than one user is allowed to

cause the starvation of getting services due to the lack

transmit on a subcarrier.

of system fairness. Users who have constantly good

B. Proposed Algorithm

channels will be more likely to be serviced, and vice

1) Proportional Fairness Scheduling

versa. In this paper, we propose a practical and

The

Proportional

Fairness

(PF) Scheduling

efficient algorithm to enhance system throughput and

algorithm is suitable to obtain the tradeoff between

maintain system fairness under constraints of users'

system throughput and fairness. Like in [2], for

QoS. Numerical results show that our proposed

OFDMA systems, we define the scheduling utility

algorithm can achieve a good tradeoff of throughput

function for each user: uk = wkrk/Rkavg (for all k), where

and fairness. System fairness is high while system

wk is weighted factor which plays the role of resource

throughput is slightly degraded. Moreover, the

utilization, rk is the minimum data rate and Rkavg(t) is

probability of outage is significantly reduced.

the average rate of user k up to time t on the average

2 Experiment

window size Tc

A. System Model Consider a downlink configuration of single-cell multiuser OFDMA systems. Assume that there are K users moving in the cell, sharing N subcarriers. Each user experiences independent fading and each

Rkavg (t + 1) = (1 − 1/ Tc ) Rkavg (t ) + Rk / Tc

(4)

The priority of users pk are then defined proportional to the order of uk. 2) Subcarrier-and-Bit Allocation

We propose a practical and efficient algorithm to

applying water-filling algorithm on Sk for single user k

guarantee users’ minimum data rate and maintain the

with total power Pk = |Sk|Ptot/N. Additional complexity

fairness.

will be added, but this complexity is not significant because

water-filling

algorithm

is

performed

concurrently for each user. C. Performance Evaluation 1) Simulation environment Cells' radius is 1km. We divide the cell into two zones: inner and outer zones. The distance between two zones is 0.5 km; and the number of users in each zone is 50% of the total users, respectively. Users' position is uniformly distributed in each zone and their moving speed is uniformly distributed over the range [0-100] km/h. The COST 231 Hata urban propagation model is used for the link gain between BS and users: - Path loss:

{

31.5 + 3.5 log( d ), if d > 0.035km 31.5 + 3.5 log(0.035), if d < 0.035km

- Shadowing: lognormal distribute ℵ(0, 8dB) Other parameters to be mentioned are: BER of 10-4, minimum data rate of 2[Mbps], system Fig. 1: Subcarrier Allocation

a.

Subcarrier Allocation

Assume that equal power Ptot/N is distributed to all subcarriers. We allocate the smallest number of the subcarriers to users according to their priority, from the highest to the lowest one, to satisfy their minimum

bandwidth of 10[MHz], subcarriers of 512, carrier frequency of 1.9 [GHz], transmitter power of 10[W] and noise power of -100[dB]. 2) Fairness measure We use the Fairness Index proposed in [5] to measure system fairness

data rate. Thus, the remaining subcarriers are reserved

2

 K   K  Fairness Index =  ∑ xk  /  K ∑ xk2  ,  i = k   k =1 

to lower priority users. To do so, we use following criterion: n* = argminn{abs(Rk + rk,n – rk)}.

(5)

The allocation process will take several steps for

where xk is the resource portion allocated to user k. In

each user. When the minimum data rate is not satisfied

this paper, we define xk as the fraction of demand, or xk

yet, the user chooses the best subcarriers. Finally, the

= Rkavg /rk. If all users get the same amount, xk’s are all

user chooses the subcarrier which makes his/her data

equal, then the Fairness Index is 1, and the system is

rate just over the minimum data rate. The allocation

100% fair. As the disparity increases, fairness

process repeats until no subcarrier remains or no user

decreases to 0.

unserviced. The detailed algorithm is depicted in the Fig. 1, where U and S are denoted as sets of users’ index and subcarriers’ index respectively. If subcarriers remain, they will be allocated to the set of serviced-users (UA) by max SNR criterion [3]. b.

Bit Loading

Denote Sk as the set of subcarriers allocated to user k. We can increase system throughput further by

3) Performance evaluation We compare following algorithms: water-filling (in [3]), max-min (in [2]) and our proposed algorithm with two weighted factors, wk = 1 and wk = average SNR. Fig. 2 shows the comparison of system fairness. Max-min algorithm provides nearly perfect fairness. Our proposed algorithm yields better fairness when

comparing to water- filling algorithm, especially when

accommodation. The performance of probability of

the number of users increases.

outage is shown in Fig. 4. By applying the new subcarrier-allocation strategy, the probability of outage

1.0 System Fairness (Fairness Index)

is significantly reduced. 0.9

In conclusion, our proposed algorithm enhances system performance. It improves system fairness and

0.8

reduces the outage probability while incurred slight 0.7

degradation in throughput

water-filling max-min proposed algorithm (w=1) proposed algorithm (w=average SNR)

0.6

D. Conclusion In this paper, we propose an efficient power and

0.5 0

10

20

30

40

50

60

Number of users

subcarrier allocation algorithm to achieve the tradeoff between system throughput and fairness. The key

Fig. 2. System fairness vs. number of users 20

issue is to design priority and an appropriate utility

15

behavior. We apply the Proportional Fairness concept

Average R/B (bit/s/Hz)

function for each user to control the transmission to design such the utility function to guarantee the 10

fairness among users as well as improve system throughput. The simulation results show that our

5

water-filling max-min proposed algorithm (w=1) proposed algorithm (w=average SNR)

proposed algorithm can achieve a good tradeoff of system throughput and fairness. To get better system

0 0

10

20

30 Number of users

40

50

60

optimization and fairness problems are left to the

Fig.3: System throughput vs. number of users 0.4

future studies. water-filling max-min proposed algorithm (w=1) proposed algorithm (w=average SNR)

0.3 Probability of Outage

performance, further investigations of combined

3

Acknowledgement

This work was supported in part by the Institute of Information Technology Assessment (IITA) through

0.2

the Ministry of Information and Communication (MIC), Korea.

0.1

4

References

[1] R. van Nee and R. Prasad, “OFDM for Wireless

0.0 0

10

20

30

40

50

60

Multimedia Communications”. Boston: Artech House, 2000.

Number of users

Fig. 4: Probability of outage vs. number of users

[2] Jalali et al "Data throughput of CDMA-HDR a high

Fig. 3 shows the comparison of system

efficiency-high data rate personal communication wireless

throughput. The optimal throughput is performed by

system" VTC 51st Volume 3, 15-18 May 2000.

water-filling algorithm. Our proposed algorithm has

[3] Keunyoung Kim et al "Subcarrier and power allocation

slight

in OFDMA systems", VTC2004-Fall.

throughput

degradation

while

max-min

algorithm that provides nearly perfect fairness is

[4] Rhee, W.; Cioffi, J.M., "Increase in capacity of multiuser

significantly incurred in throughput.

OFDM system using dynamic subchannel allocation", VTC

In this simulation, if a user's data rate is less than

2000-Spring Tokyo.

2Mbps, the outage will occur. The probability of

[5] R.Jain et al. "A Quantitative measure of fairness and

outage is defined as the ratio of the number of users

discrimination for resource allocation in shared computer

whose data rate is less than 2Mpbs over total users in

systems," Technical Report TR-301, DEC Research Report,

the system. It measures inversely the ability of system

1984.