1) The document proposes a non-cooperative resource allocation game algorithm using Adaptive Modulation and Coding (AMC) schemes in multi-cell OFDMA systems. 2) The algorithm aims to maximize utility while reducing co-channel interference and improving power efficiency through AMC. 3) Simulation results show the proposed algorithm achieves maximum capacity within AMC levels and reduces system power compared to an algorithm without AMC.

1. A Resource Allocation Using Game Theory
Adopting AMC Scheme in Multi-cell OFDMA System
1
Seung Hyun Paik, 2Sungkwang Kim, and 1Hong Bae Park
1
Electrical Engineering and Computer Science
Kyungbook National Univ., Daegu, Korea
white@ee.knu.ac.kr
2
Wizntec, Daegu, Korea
kimsg@wizntec.com
Abstract—In this paper, we consider a downlink resource However, in [5], the proposed algorithm is not considered
allocation algorithm in multi-cell Orthogonal Frequency the Adaptive Modulation & Coding (AMC) scheme.
Division Multiple access (OFDMA) systems. The resource In this paper, we present a non-cooperative resource
allocation problem is modeled as a non-cooperative game. We allocation game algorithm using AMC scheme in multi-cell
define a specific utility function that can represent the capacity OFDMA system. We expect to reduce the co-channel
maximizing against co-channel interference in multi-cell. Then interference while maximizing the utility and to improve
we present the resource allocation game that employs an power efficiency by using AMC scheme, because the power
Adaptive Modulation & Coding (AMC) scheme. The proposed is allocated to possible maximum AMC level. In the other
algorithm is to maximize a discrete capacity that precisely
word, since AMC scheme uses discrete level of Modulation
characterizes the AMC levels. As a result of adopting AMC
scheme, we expect co-channel interference to be more reduced.
and Coding Scheme (MCS), capacity doesn’t increase even
though power increase in a range of each level, thus the
Keywords-component; Resource allocation, power control, power can be limited in a range of AMC level. Hence, co-
game theory, AMC, and OFDMA. channel interference can be more reduced while holding the
maximized utility.
I. INTRODUCTION
In view of the multiple channel access techniques for
high data rate transmission, Orthogonal Frequency Division II. SYSTEM MODEL
Multiplexing Access (OFDMA) have attracted a lot of work We consider the OFDMA system consisting of N co-
in next wireless network standard. Many papers have shown channel cells serving K users who are randomly located over
that resource allocation in OFDMA systems improve the the wireless networks, where total bandwidth B and L sub-
performance. In particular, the resource allocation problem channel are reused in the system. The total transmission
in a multi-cell OFDMA system becomes more important and power of each base station is constrained as
more complicated, because the co-channel interferences
‫ܮ‬
among cells affect the performance and the distributive
topology of the system requires distributive implementations. ෍ ‫݌‬ln = ‫ܘ‬n ൑ ‫۾‬max . (1)
In single-cell environment, the water filling algorithm is a ݈=1
good solution. However, in multi-cell environment, all
possible combinations of the co-channel interference by We assume that each sub-channel can be assigned to only
power allocation must be considered to determine the best one user. The SINR of the sub-channel l of user k’s in cell n
resource allocation. Hence, the water filling algorithm is not is expressed as
suitable for the multi-cell OFDMA system. On the other
hand, it is difficult for each a cells to know the channel
݊
|݄݈݇ |2 ‫݈݊݌‬
݊
conditions of the users in the other cells. Thus the cells ߛ݈݇ = , (2)
σ݉ ്݊ |݄݈݇ |2 ‫0ܰ + ݈݉݌‬
ܰ ݉
cannot cooperate with the other cells. Each a cells allocate
resource to maximize their own performances.
The resource allocation by a game theoretical approach ݉
have been worked in papers [1]-[5], because the game theory where ܰ0 is the noise power and |݄݈݇ |2 denotes channel gain
is widely recognized as a useful and powerful tool in the of sub-channel l between the user k in cell n and the cell m.
distributed systems [1]. In [5], the proposed algorithm is a The data rate of the sub-channel l of user k is as follows
non-cooperative game for the downlink resource allocation
in multi-cell OFDMA systems that maximize the system ݊
‫ܤ‬ ݊
‫= ݈݇ݎ‬ log 2 (1 + ߚߛ݈݇ ), (3)
performance while minimizing the co-channel interference. ‫ܮ‬
978-1-4244-5824-0/$26.00 c 2010 IEEE V2-344

2. where ߚ = െ1.5/݈݊༌ (5BER) is a parameter related to bit
݊
error rate (BER)[6]. Therefore, the channel capacity of the ݊
|݄݈݇ |2
ߩ݇ = , (8)
user k is as follows σ݉ ്݊ |݄݈݇ |2 ‫2 ߪ + ݈݉݌‬
݉
L
‫ݔ ݔ‬൒0
݊ ݊ ݊ (‫ = +)ݔ‬ቄ ,
ܴ݇ (‫ ۱ , ࢔ܘ‬n ) = ෍ ݈ܿ݇ ‫, ݈݇ݎ‬ (4) 0 ‫0<ݔ‬ (9)
݈=1 ‫ܮ‬
ߣ‫ ݊כ‬൭෍ ‫ ݊כ݈݌‬െ ܲ݉ܽ‫ ݔ‬൱ = 0, ߣ‫ ݊כ‬൒ 0, (10)
where ۱ n is the sub-channel assignment matrix, if the sub-
݊ ݈=1
channel l is assigned to the user k then ݈ܿ݇ is 1, and 0
otherwise. where ‫ ݊כ݈݌‬is the best response of the cell n’s sub-channel l
III. NON-COOPERATIVE RESOURCE ALLOCATION and ߣ‫ ݊כ‬is the Lagrangian multiplier for the maximum power
ALGORITHM constraint[8].
We define the utility function based on system capacity We can achieve the power set according to (7). Thus we
and the cost of the system power is as follows can estimate the SINR. The discrete capacity is determined
by AMC level according to the estimated SINR. So the
ܷ݊ (‫ = ) ݊ۯ , ݊ܘ‬෍ ܴ݇ ( ‫ ) ݊ۯ , ݊ܘ‬െ ߜ ෍ ‫, ݈݊݌‬ (5) maximum data rates of each sub-channel can be determined.
K ‫ܮ‬ If the SINR is bigger than the AMC level requirement, the
power can be decreased. Hence ߜ of each cell can be
where ߜ is the price per the system power unit making the changed as following
co-channel interference in the neighboring cells.
We use an alternative notation ܷ݊ (‫ ۾ , ݊ܘ‬െ݊ , ‫ ۾ ,) ݊ۯ‬െ݊ = ‫ܤ‬ 1
(‫݊ܘ , ڮ , 2ܘ , 1ܘ‬െ1 , ‫ ) ܰܘ , ڮ , 1+݊ܘ‬is the total power set except ෍ቆ െ ݊ ቇ = ‫ܘ = ܲܮ‬nƍ , (11)
(ߜ Ԣ +ߣ‫ ܮ) ݊כ‬ln 2 ߚߩ݇
on ‫ . ݊ܘ‬This notation emphasizes that the cell n has control L
over its own system power ‫ ݊ܘ‬only. We are interested in the
non-cooperative power control game (NPG) is expressed as where ‫ܘ‬nƍ = ‫כܘ‬n െ ‫ܘ‬െ‫ܘ , ܚ‬െ‫ ܚ‬is can be reduce power
NPG: max ‫ ۾ , ݊ܘ( ܷ݊ ݊ܘ‬െ݊ , ‫ ) ݊ۯ‬for all n = 1, 2, ‫ , ڮ‬N. 1 ln 2 1 1
= ൭ܲ + ෍ ݊ ൱ . (12)
(ߜ Ԣ + ߣ‫) ݊כ‬ ‫ܤ‬ ‫ܮ‬ ߚߩ݇
‫ܮ‬
In the NPG, each cell optimizes its own system power
unit based utility depending on the system power unit of the We have the new price ߜ Ԣ , thus co-channel interference
other cells in system. It is necessary to characterize a set of can be reduced and the power efficiency can be enhanced.
powers where the cells are satisfied with the own utility.
Such an operating point is the Nash equilibrium. IV. SYSTEM RESULTS
Definition 1: A Nash equilibrium for the non-cooperative We evaluate the performance of proposed the resource
power control game is a power matrix P such that no cells allocation algorithm by comparing it with the results of not
can improve its utility by a unilateral change in its power. If adopting AMC scheme. The OFDMA system, proposed by
cells all choose appropriate strategy to maximize their own IEEE 802.16 WMANS standard [9]-[10], is considered with
utility, the NPG converges to the Nash equilibrium[7]. 3 cells, 10 sub-channels, 5 users in a cell and 7 AMC levels.
We represent the necessary condition for the Nash
equilibrium as TABLE I. SIMULATION PARAMETERS
Parameters value
߲ܷ݊ (6)
= 0, (݈ = 1, 2, ‫.)ܮ , ڮ‬ ‫ܮ/ܤ‬ 0.1 MHz
߲‫݈݊݌‬
Cell radius 1km
Maximum transmission power 10W
In here,
+ Path loss exponent 3.76
‫ܤ‬ 1
‫݊כ݈݌‬ =ቆ െ ݊ቇ , (7) Noise power density -174dBm/Hz
(ߜ + ߣ‫ ܮ) ݊כ‬ln 2 ߚߩ݇
Target BER 10-5
ߜ0 1
where
[Volume 2] 2010 2nd International Conference on Future Computer and Communication V2-345

3. TABLE II. MODULATION AND CODING PARAMETERS FOR
IEEE802.16 WMAN
Rate at
Modulation
Level 5MHz Requiired
(coding rate)
(Mbps)
1 QPSK(1/2) 4.03 5
2 QPSK(3/4) 6.04 8
3 16-QAM(1/2) 8.06 10.5
4 16-QAM(3/4) 12.09 14
5 64-QAM(1/2) 12.09 16
6 64-QAM(2/3) 16.12 18
7 64-QAM(3/4) 18.14 20
Figure 2. The comparison of the system power.
V. CONCLUSION
Fig. 1 shows the comparison of system capacity In this paper, we proposed the resource allocation game
accoding to different two algorithms, since there is the algorithm adopting AMC scheme. We showed that the
fundamental difference. The algorithm adopting AMC proposed algorithm maximize the system capacity in AMC
schemea decide a discrete capacity depending on AMC level through simulation results. The performance in term of
level. On the other hands, the capacity of the resource capacity was not better than excluding AMC in simulation.
allocation algorithm excluding AMC scheme is a However, it was possible to reduce extra power and to
continuous value. Therefore we estimate that the capacity of enhance power effieciency. And we estimated co-channel
proposed algorithm is not better than the other. However, interference to be reduced more than before adopting AMC.
proposed algorithm achive a maximum capacity in AMC As a result, we achieved opitmization power set to improve
level. And in Fig. 2, we can make certain that the proposed performance of the OFDMA system in multi-cell by
algorithm reduce the system power. Since the power proposed algorithm.
reduced, SINR could be decreased. But, in the other cells,
co-channel interference is reduced as much as power, so the ACKNOWLEDGMENT
SINR can be increased. Hence we estimate additional This work was supported by the Research &
decrease of co-channel interference. Development Center program of Small & Medium Business
Administration.[000366620209]
REFERENCES
[1] A. B. MacKenzie and S. B. Wicker, “Game theory in
communications: motivation, explanation, and application to power
control,” in Proc. IEEE Globecom 2001, San Antonio, Texas, Nov.
2001.
[2] G. Li and H. Liu, “Downlink dynamic resource allocation for multi-
cell OFDMA system,” in Proc. IEEE VTC 2003, Orlando, Oct. 2003.
[3] T. K. Chee, C. Lim, and J. Choi “A cooperative game theoretic
framework for resource allocation in OFDMA systems,” in Proc.
IEEE ICCS 2006, Singapore, Oct. 2006.
[4] Zhu Han, Zhu Ji, and K. J. R. Liu, “Power minimization for multi-cell
OFDM networks using distributed non-cooperative game approach”,
in Proc. IEEE Global Telecommunications Conf. (GLOBECOM
2004), vol.6, pp. 3742-3747, Nov. 2004.
[5] H. j. Kwon and B. G. Lee, “Distributed Resource Allocation through
Noncooperative Game Approach in Multi-cell OFDMA Systems”, in
Proc. ICC 2006, Turkey, Jun. 2006.
[6] A. J. Goldsmith and S.-G. Chua, “Variable-rate variable-power
Figure 1. The comparison of the system capacity. MQAM for fading channels,” IEEE Trans. Commun., vol. 45, pp.
1218–1230, Oct. 1997.
V2-346 2010 2nd International Conference on Future Computer and Communication [Volume 2]

4. [7] D. Fugenberg and J. Tirole, Game Theory, MIT Press, Cambridge,
MA, 1991.
[8] S. Boyd and L. Vandenberghe, Convex Optimization, New York:
Cambridge University Press, 2004.
[9] S.H. Ali, Lee Ki-Dong, and V.C.M. Leung, “Dynamic resource
allocation in OFDMA wireless metropolitan area networks,” IEEE
Wireless Communications, vol. 14, issue 1, pp. 6-13, Feb. 2007.
[10] S. K. Kim and C. G. Kang, “Throughput analysis of band AMC
schem in broadband wireless OFDMA system”, in Proc. WCNC 2006,
New Orleans, April, 2006.
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