An Adaptive Sub-carrier and Power Allocation Algorithm with QoS Guarantee for OFDMA System

Anding Wang1,3, Yuyang Qiu2, Lili Lin1, Shiju Li3 1. College of Information and Electronics, Zhejiang Gongshang University Hangzhou, China 2. College of Statistics and Mathematics, Zhejiang Gongshang University Hangzhou, China

3. Dept. of Information and Electronics, Zhejiang University Hangzhou, China anding_704@hotmail.com YuyangQiu@gmail.com sunshine@hzcnc.com

leesj@cise.zju.edu.cn

Abstract

This paper presents an adaptive sub-carrier and

power allocation scheme for orthogonal frequency division multiple access (OFDMA) systems according to their different quality of service (QoS) requirements and traffic type. The algorithm maximized the transmission data rate while satisfying total power constraint and a certain bit error rate (BER) requirement. A greedy algorithm known to be the most efficient algorithm for this problem can provide a high quality optimal solution, but has the disadvantage of incurring a long computation time. This problem should be solved in a real-time environment. The proposed algorithm not only avoids the high complexity but also provides considerable universality and flexibility for both the fixed rate voice data and variable rate multimedia data of the broadband wireless communication. It mainly consists of two steps. The first is the allocation of sub-carriers and power alternately to the real-time user. The second is the residual resource distribution to the non-real-time users. The simulation results demonstrate that the

scheme has computational advantages over the conventional algorithms while providing the QoS guarantee.

1. Introduction

The broadband wireless system will be required to provide efficient and flexible solution to high-speed communications and to support a variety of services utilizing advanced multiple access techniques. This means that the network will have to accommodate users with different traffic classes and QoS requirements. OFDMA is one of the best candidates Because it resists the inter-symbol interference and

frequency selecting fading effectively. Therefore, appropriately assigning sub-carriers and power to users with different data rate requirements becomes important issues.

Several algorithms in the literatures have been proposed to implement the optimal sub-carrier and power allocation, of which the most basic algorithm used is “multiuser water-filling” algorithm under the capacity-achieving principle [1]. Another algorithm is the multiuser greedy algorithm [2]. It assumes that the sub-carrier allocation of the different users have been accomplished in advance and on the base of which we apply the single user greedy algorithm to different users according to the certain data rate requirement. However, although the water-filling and greedy algorithms indeed yield the optimal solution, they are often difficult to be computed and realized. The Rhee adaptive resource allocation algorithm [3], allocating sub-carriers and power with the fairness guarantee, obtains the very low complexity but its performance is not optimal.

Moreover, these adaptive algorithms haven’t taken into account the impact of resource allocation scheme on different class users. It is no doubt that voice service and data service coexist in both current systems and future mobile communication system. They have quite different traffic characteristics and QoS requirements. Voice traffic requires a real-time transmission，but it can tolerate a moderate bit error rate. On the contrary, data traffic can accept the varied transmission delay, but it requires a lower BER.

Based on these reasons, we propose a novel algorithm of significant flexibility whose objective is to maximize each user data rate with the total transmission power constraint. It consists of two steps. The first is the sub-carrier and power assignment to the real-time user with the target rate requirement. The second is the non-real-time user’s resource allocation. The simulation results demonstrate that the proposed scheme has computational advantages and better performance.

The 10th IEEE International Conference on High Performance Computing and Communications

978-0-7695-3352-0/08 $25.00 © 2008 IEEE

DOI 10.1109/HPCC.2008.64

492

The 10th IEEE International Conference on High Performance Computing and Communications

978-0-7695-3352-0/08 $25.00 © 2008 IEEE

DOI 10.1109/HPCC.2008.64

492

The 10th IEEE International Conference on High Performance Computing and Communications

978-0-7695-3352-0/08 $25.00 © 2008 IEEE

DOI 10.1109/HPCC.2008.64

492

2. System model

We consider an OFDMA system’s downlink with N sub-carriers which are assigned to K users. At the base station, the adaptive algorithm allocated the sub-carriers and power to the different users dynamically according to the Channel State Information (CSI). We assume there are two preconditions: 1. The transmitter knows the CSI of different users completely. 2. Only one user occupies each sub-carrier at certain time. At transmitter, the data first are modulated by multiple quadrature amplitude modulation (MQAM) which is a composite modulator consisting of amplitude and phase modulation. Then they are transformed by Inverse Fast Fourier Transform (IFFT) which converts signal in frequency domain into signal in the time domain. Finally they compose the OFDMA symbol and are loaded to each sub-carrier through the independent time variable frequency selective Rayleigh fading channel. At receiver different users extract data on their own sub-carriers according to the information of sub-carrier and power allocation of the transmitter. The received data symbol of user k over the sub-carrier n can be expressed as:

nknknknknk zhpby ,,,,, += (1)

Where nkb , and nkp , denote the source data and power

of user k over the sub-carrier n respectively, nkh , is the

channel gain of user k on sub-carrier n, nkz , is the Additive White Gaussian Noise (AWGN) with zero mean and B/NNσ 0

2 = variance, N0 denotes the single-sided noise power spectral density of AWGN and B is the system bandwidth. Then the signal-to-noise Ratio (SNR) of the receiver is written as:

nknknknk

nk HpNBN

hp,,

0

2,,

, /SNR == (2)

We define the kth user’s channel gain-to-noise ratio (CNR) on the sub-carrier n as nkH , = 22

, /σnkh . The

information of the allocated sub-carriers is fed back to the different receivers by an independent control channel for each user to obtain its own information.

In order to satisfy a given BER (Bit Error Ratio) requirement, we can derive the formula from the document [4], the correlation of the MQAM’s BER, the receiver’s SNR and the bit number nkq , can be expressed as follows:

⎟⎟⎠

⎞⎜⎜⎝

⎛

−−

≈12

5.1exp

51BER

,

,nkq

nkMQAM

SNR (3)

From the equation (3), if the BER requirement is given, we can obtain the largest bit number which is transmitted on the nth sub-carrier of user k in one OFDMA symbol:

SNR

1log ,2, ⎟⎟

⎠

⎞⎜⎜⎝

⎛Γ

+= nknkq bits/symbol (4)

Where 5.1/)BER5ln( MQAM−=Γ is a constant, which

is defined as SNR gap. The total data rate of user k is the sum of all its sub-carriers’ data rate.

⎟⎟⎠

⎞⎜⎜⎝

⎛Γ

+== ∑ ∑∈ ∈

nknk

n n

nkk

HpNB

Tq

rk k

,,2

, 1logΩ Ω

bps (5)

Where kΩ denotes the sub-carrier set of the user k, T is the duration time of one OFDMA signal block i.e. T=N/B second. We assume the front K1 users is the real-time user and the behind K-K1 users is the non-real-time user. We formulate the optimization principle of the resource adaptive allocation as follows:

1. Assume the total power is at the constraint of Ptotal

2. Each real-time user’s data rate must reach the certain value Rk

3. The BER requirement: real-time user is BER1 and the non- real-time user is BER2.

4. Maximize the total date rate of the non-real-time users and allocate the power to each user according to the proportional fairness principle.

The optimization problem is mathematically formulated as follows:

∑ ∑+= =

⎟⎟⎠

⎞⎜⎜⎝

⎛Γ

+K

Kk

N

n

nknknkcp

HpNBc

nknk 1 1 2

,,2,,

1,,

1logmax (6)

C1： k

N

n

nknknkk R

HpNBcr ≥⎟⎟

⎠

⎞⎜⎜⎝

⎛Γ

+=∑=1 1

,,2, 1log

（ 1,2,1 Kk …= ）

∑=

⎟⎟⎠

⎞⎜⎜⎝

⎛Γ

+=N

n

nknknkk

HpNBcr

1 2

,,2, 1log

（ 111 ,2,1 KKKk …++= ）

C2： nkc nk , 1,0, ∀∈ ∑=

∀=K

knk nc

1, 1

C3：∑∑= =

≤K

k

N

ntotalnk Pp

1 1,

C4： nkp nk , 0, ∀≥ C5： KKKKKK rrr γγγ :::::: 2121 1111

…… ++++ = Where 5.1/)BER5ln( 11 −=Γ , 5.1/)BER5ln( 22 −=Γ

is the SNR gap of the real-time user and non-real-time user respectively. ,,2,1, 11 KKKkk …++=γ is the predetermined data rate of the different non real-time user. Where nkC , is defined as the indicator of allocating the nth sub-carrier to the kth user. That is, 1, =nkρ when the nth sub-

carrier is assigned to the kth user, while 0, =nkρ , otherwise.

Because the real-time users share the high priority, we should first satisfy the real-time users’ rate and target BER

493493493

requirements, then allocate the remaining resource to other ordinary users according to the proportional fairness principle. C1 is the data rate requirements of the real-time users, C2 reflects the state of sub-carrier’s allocation, C3 is the total power’s constraint, C4 denotes the power condition of user k over the sub-carrier n and C5 is the data rate proportion requirements of the non real-time users. 3. The resource allocation of the real-time user

We allocate the sub-carrier and power alternately for the real-time users. The main idea is that we assume each user’s power is proportional to its sub-carrier number. Once a user achieves one sub-carrier, it will obtain the corresponding power NPtotal / . Then each user accomplishes the power assignment in terms of the water-filling principle to reach the optimal data rate. After updating the users’ data rates a round, we choose the minimum data rate user to start the next round allocation until all users reach their data rate requirements. The algorithm is described in detail as follows:

1. Initialization: 0, =nkc , ,,2,1 1Kk …∈∀ , ,,2,1 Nn …∈

0=kr , 0=kP , φ=kΩ , ,,2,1 1Kk …∈ ,,2,1 N…=A . Where kΩ is the sub-carriers set

of the user k. 2. for k = 1 : 1K

Find the n that satisfies jknk HH ,, ≥ , A∈∀j

1, =nkc , nkk ∪ΩΩ = , n−= AA , NPPP totalkk /+=

Update kr : )1(log1

,2 Γ

+= nkkk

HP

NBr

3. while φ≠A and 1KKdone <

Find the k that satisfies ik rr ≤ , ,,2,1 1Ki …∈∀ To k, find the n that satisfies jknk HH ,, ≥ , A∈∀j

1, =nkc , nkk ∪ΩΩ = , n−= AA , NPPP totalkk /+=

Update kr : )1(log1

,,2 Γ

++= nknkkk

Hp

NBrr

if kk Rr ≥ , 1+= donedone KK

Where doneK is the number of the real-time users who already reached their data rate requirements,

+−= ]1[,

,nk

nk Hp λ is the power of each sub-carrier

according to the water-filling algorithm kn

nk Ppk

=∑∈Ω

, [1].

We can see that this sub-carrier allocation is similar to the Rhee algorithm. The main difference is that the Rhee algorithm assumes the power is distributed averagely while this proposed algorithm allocates the power proportional to the obtained sub-carrier number and applies the water-filling principle to assign the power on each sub-carrier in one user. This method takes the advantage of the frequency diversity fully to reach the higher user data rate. 4. The resource allocation of the non-real-time user

After satisfying the QoS requirement of the real-time user, we allocate the remaining resource to the non-real-time users. The non- real-time users’ resource allocation can be converted to the optimization problem as follows:

∑ ∑+= ∈

⎟⎟⎠

⎞⎜⎜⎝

⎛Γ

+K

Kk n

nknk

pk

nk

HpNB

1 2

,,2

1,

1logmaxΩ

(7)

C1: ∑∈

⎟⎟⎠

⎞⎜⎜⎝

⎛Γ

+=kn

nknkk

HpNBr

Ω 2

,,2 1log

（ KKKk ,,2,1 11 …++= ）

C2: ∑ ∑∑ ∑= ∈+= ∈

−=′≤1

1 1,

1,

K

k nnktotal

K

Kk nnk

kk

pPPpΩΩ

C3: ,2,,1 0 11, KKKkp nk …++∈∀≥ C4: KKK ΩΩΩ …,, 21 11 ++

,,2,1

1

11 2121

K

KKK N

Ω

ΩΩΩΩΩ

∪…∪∪…∪…∪∪ −⊆++

C5: KKKKKK rrr γγγ :::::: 2121 1111

…… ++++ = Where C1 is the different data rate of the non real-

time users, C2 is the remaining power’s constraint for the non real-time users, C3 denotes the power condition of user k over the sub-carrier n, C4 is the two sub-carrier set for the real-time users and non real-time users respectively and C5 is the data rate proportion requirements of the non real-time users. We can resolute this problem using the Shen [5] algorithm. However this has the computing complexity because of the iterative method to solute the non-linear equations. Wong [6] proposes an improved algorithm which linearizes the power allocation problem and guarantees the data rate’s proportional fairness of the different users approximately. Moreover, it reduces the computing complexity greatly.

Step 1: Make certain the sub-carrier number of each non-real-time user

From [7], we know the sub-carrier number each user obtained is approximately proportional to its final data rate ratio.

KKKKKK NNN γγγ ::::::2121…… ≈ (8)

494494494

So we compute each user’s sub-carrier number according to the predetermined user data rate ratio.

⎥⎥⎥⎥

⎦

⎥

⎢⎢⎢⎢

⎣

⎢

′=∑

+=

• K

Kkk

kk NN

11

γ

γ ),,2,1( 11 KKKk …++=

(9) The residual sub-carrier number that are not allocated is

∑+=

−′=K

KkkNNN

1

*

1

(10)

Where N ′ is the total sub-carrier number that are allocated to the non-real-time user。

Step 2: The sub-carrier allocation of non-real-time users

The objective of the sub-carrier allocation is to maximize the total data rate, at the same time guarantee the rate proportional fairness among the users. We adopt the modified Rhee algorithm to allocate the N ′ sub-carriers to the non-real-time users completely.

1. Initialization： ,,2,1 N…=A ，

,,2,1 11 KKK …++=K

0=kr , φ=kΩ , K∈∀k NPp total ′′= /

2. for k = KK :11 +

Find the n that satisfies jknk HH ,, ≥ , A∈∀j

nkk ∪ΩΩ = , 1−= kk NN , n−= AA

Update kr : )1(log2

,2 Γ

+= nkk

Hp

NBr

while *N>A

Find the k that satisfies iikk rr γγ // ≤ , K∈∀i To k，Find the n that satisfies jknk HH ,, ≥ , A∈∀j

if 0>kN

nkk ∪ΩΩ = , 1−= kk NN , n−= AA

Update kr : )1(log2

,2 Γ

++= nkkk

Hp

NBrr

else

k−= KK

3. ,,2,1 11 KKK …++=K

for *:1 Nn = To k, find the n that

satisfies nlnk HH ,, ≥ K∈∀l

nkk ∪ΩΩ = , n−= AA

Update kr : )1(log2

,2 Γ

++= nkkk

Hp

NBrr

k−= KK

Step 3: The power allocation of the non-real-time users From [5]，the power allocation relation of the non-real-

time users is as follows ：

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛ −Γ

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛ −Γ

+

kk

kkkk

k

WN

VPHNN

WN

VPHNN

22

1,2

121

11

2

1,12

1

1

log1log1

log1log1

γ

γ (1

1) Where,

22 1,,

1,, Γ−

= ∑=

kN

n knk

knkk HH

HHV (12)

kk NN

n k

nkk H

HW

1

2 1,

,

⎟⎟⎠

⎞⎜⎜⎝

⎛= ∏

=

),,2,1( 11 KKKk …++= (13)

After simplifying the equation we can obtain the linearized matrix equations as follows:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ ′

=⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

++

+

++

K

K

total

K

K

K

K

KK

b

bP

P

PP

a

a 22

1

2,2 11

1

11

01

01111

(14)

Where

11,1

1,1,

11

1

++

+−=KK

kk

K

Kkk WH

WHN

Na (15)

⎟⎟⎠

⎞⎜⎜⎝

⎛

Γ−

Γ+−Γ=

+

++++

++ k

kkk

K

KKKKk

KKk N

WVHN

WVHWW

WHb

2

1,

12

111,11

11,1

2

1

111

1

11

),,3,2( 11 KKKk …++= (16)

We decompose the coefficient matrix through LU, and deal with the fore and post iterative, then we easily obtain the total power of the different non-real-time users.

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛−′= ∑∑

+=+=+

K

Kk kk

K

Kk kk

ktotalK aa

bPP

2 ,2 ,1

11

1

11/ (17)

kkkk aPbP ,1 /)( −= ， ( KKKk ,,3,2 11 …++= ) (18)

Step 4: The power allocation in each non-real-time user We adopt the water-filling algorithm to allocate the

power of the different sub-carriers in the non-real-time user.

495495495

21,,

1,,1,, Γ

−+=

knk

knkknk HH

HHpp (19)

Where k

kkk N

VPp −=1, , KKKk ,,3,2 11 …++= .

5. Simulation and performance analysis

In this section, several results will be presented to verify the better performance using the proposed adaptive algorithm with QoS guarantee. The following parameters have been considered for the simulations: The required BER of the ordinary user is Pe=

310− and the high priority user is 510− respectively. We assume the real-time users have the same data rate requirement of 0.3bps/Hz and the different ordinary users share the equal priority i.e. their data rate ratio is set to 1::1:1:: 21 11

… =++ KKK γγγ .The total

allocated power equals to 1 watt and the overall bandwidth is 1 MHz. The number of sub-carriers N =256, the number of users K=4~16. The independent Rayleigh fading channel model with 6 paths and 5ms delay spread is considered for our simulation. The largest Doppler frequency shift is 30Hz, and the Gaussian white noise PSD is -80dBw/Hz.

The performance of the real-time user’s allocation algorithm:

In the resource allocation of the real-time user, we compare this paper’s algorithm which allocated the sub-carrier and power alternately to the Rhee algorithm and the traditional adaptive TDMA mode. Figure 1 shows the correlation between total data rate and the user number. Distinguishingly this paper’s alternate and Rhee algorithm have better performance than the TDMA system greatly. And the alternate algorithm is the best because the Rhee algorithm distributes the power to each sub-carrier averagely. However, the alternate algorithm allocates the power to each user proportional to its sub-carrier number and utilizes the water-filling to each user which maximize the total data rate at the constraint of power.

Figure 1. The correlation between data rate and user

number

Figure 2 shows the alternate algorithm’s data rate gain compared with the Rhee algorithm. We observe that as the number of users increases, the data rate gain is also increasing. We can explain this phenomenon as the effect of multiuser diversity i.e. the users of the system is more, the probability becomes less of each user which subjects to the deep fading on the same sub-carrier.

Figure 2. The correlation between data rate gain

and user number The performance of the non-real-time user’s allocation algorithm:

In the non-real-time user’s resource allocation, we linearized the optimization problem approximately using the Wong algorithm and then compare the algorithm with the Shen algorithm.

Figure 3 reflects the total data rate while utilizing the Wong and Shen algorithm respectively. Similarly, because of the multiuser diversity effect, along with the users more, these two algorithms’ data rate both increase. Moreover, the Wong algorithm has the better performance than the Shen algorithm at the cost of broaden the data rate proportional fairness requirement.

2 4 6 8 10 12 14 164.25

4.3

4.35

4.4

4.45

4.5

4.55

4.6

number of users

capa

city

(bp

s/H

z)

Wong

Shen

Figure 3 The correlation between data rate and user

number

At the computing complexity, Figure 4 shows that the Wong algorithm has the absolute advantages because it

496496496

linearizes the equation approximately. It avoids the iterative computing of the Shen algorithm.

2 4 6 8 10 12 14 1610

-3

10-2

10-1

number of users

Ave

CP

U t

ime

(s)

Wong

Shen

Figure 4.The correlation between complexity and user

number

From Figure 5, we observe that the data rate proportional fairness is at our expectance at the condition of randomly producing the users’ data rate ratio.

0 2 4 6 8 10 12 14 16 180

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

number of users

norm

aliz

ed r

ate

prop

ortio

n

Gamma

WongShen

Figure 5. The proportional fairness of 16 users

6. Conclusion

This paper studies the adaptive sub-carrier and bit allocation in wireless OFDMA system with heterogeneous services. The algorithm first allocates sub-carriers and bits to high priority users according to theirs rate and BER requirement, then distributes the residual resources to the ordinary users in terms of the proportional fairness principle. The algorithm supports the QoS of real-time users and provides rate proportionality among non-real-time users. The simulation demonstrates that the proposed method has better performance than the existing algorithms. Also, considering the resource allocation for heterogeneous services, this algorithm achieves approximately the optimal performances. References [1] R. S. Cheng, S. Verdli, “Gaussian Multi-Access Channels with ISI: Capacity Region and Multiuser Water-

Filling,” IEEE Trans Information Theory, vol. 39, May 1993, pp. 773-785. [2] Inhyong Kim, Hae Leem Lee, Beomsup Kim, Yong H.Lee, “On the Use of Linear Programming for Dynamic Subchannel and Bit Allocation in Multiuser OFDM”, Global Telecommunications Conference, 2001. GLOBECOM '01. IEEE, Vol.6, 25-29 Nov. 2001, pp: 3648 – 3652 [3] W. Rhee, J. M. Cioffi, “Increase in Capacity of Multiuser OFDM System Using Dynamic Subchannel Allocation,” in Proc. IEEE Vehic.Tech. Conf., Tokyo, Japan, May 2000, pp. 1085-1089. [4] A. J. Goldsmith, S.-G. Chua, “Variable-rate Variable-power MQAM for Fading Channels,” IEEE Trans. Commun., vol. 45, Oct. 1997, pp. 1218–1230. [5] Z. Shen, J. G. Andrews, and B. L. Evans, “Adaptive Resource Allocation in Multiuser OFDM Systems With Proportional Fairness,” IEEE Trans. Wireless Commun., Vol. 4, Issue 6, Nov. 2005, pp. 2726 – 2737 [6] I.C Wong, Z. Shen, B.L Evans and J.G Andrews, “A Low Complexity Algorithm for Proportional Resource Allocation in OFDMA Systems,” Signal Processing Systems, SIPS 2004. IEEE Workshop on, 2004, pp. 1-6. [7] H. Yin and H. Liu, “An Efficient Multiuser Loading Algorithm for OFDM based Broadband Wireless Systems,” in Proc. IEEE Global Telecommunications Conference, vol. 1, 2000, pp. 103-107.

497497497