A Resource Allocation Using Game Theory                           Adopting AMC Scheme in Multi-cell OFDMA System          ...
where ߚ = െ1.5/݈݊༌   (5BER) is a parameter related to bit                                                                 ...
TABLE II.     MODULATION AND CODING PARAMETERS FOR                 IEEE802.16 WMAN                                Rate at ...
[7]  D. Fugenberg and J. Tirole, Game Theory, MIT Press, Cambridge,     MA, 1991.[8] S. Boyd and L. Vandenberghe, Convex O...
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05497433

  1. 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.comAbstract—In this paper, we consider a downlink resource However, in [5], the proposed algorithm is not consideredallocation 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 resourceallocation problem is modeled as a non-cooperative game. We allocation game algorithm using AMC scheme in multi-celldefine a specific utility function that can represent the capacity OFDMA system. We expect to reduce the co-channelmaximizing against co-channel interference in multi-cell. Then interference while maximizing the utility and to improvewe present the resource allocation game that employs an power efficiency by using AMC scheme, because the powerAdaptive Modulation & Coding (AMC) scheme. The proposed is allocated to possible maximum AMC level. In the otheralgorithm is to maximize a discrete capacity that precisely word, since AMC scheme uses discrete level of Modulationcharacterizes the AMC levels. As a result of adopting AMCscheme, 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 forhigh data rate transmission, Orthogonal Frequency Division II. SYSTEM MODELMultiplexing 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 overthat 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 transmissionin a multi-cell OFDMA system becomes more important and power of each base station is constrained asmore complicated, because the co-channel interferences ‫ܮ‬among cells affect the performance and the distributivetopology of the system requires distributive implementations. ෍ ‫݌‬ln = ‫ܘ‬n ൑ ‫۾‬max . (1)In single-cell environment, the water filling algorithm is a ݈=1good solution. However, in multi-cell environment, allpossible combinations of the co-channel interference by We assume that each sub-channel can be assigned to onlypower allocation must be considered to determine the best one user. The SINR of the sub-channel l of user k’s in cell nresource allocation. Hence, the water filling algorithm is not is expressed assuitable for the multi-cell OFDMA system. On the otherhand, 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 allocateresource 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 gainis 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 followsnon-cooperative game for the downlink resource allocationin multi-cell OFDMA systems that maximize the system ݊ ‫ܤ‬ ݊ ‫= ݈݇ݎ‬ log 2 (1 + ߚߛ݈݇ ), (3)performance while minimizing the co-channel interference. ‫ܮ‬978-1-4244-5824-0/$26.00 c 2010 IEEE V2-344
  2. 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. 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 gameaccoding to different two algorithms, since there is the algorithm adopting AMC scheme. We showed that thefundamental difference. The algorithm adopting AMC proposed algorithm maximize the system capacity in AMCschemea decide a discrete capacity depending on AMC level through simulation results. The performance in term oflevel. 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 tocontinuous value. Therefore we estimate that the capacity of enhance power effieciency. And we estimated co-channelproposed 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 improvelevel. And in Fig. 2, we can make certain that the proposed performance of the OFDMA system in multi-cell byalgorithm 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 ACKNOWLEDGMENTSINR 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. 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.[Volume 2] 2010 2nd International Conference on Future Computer and Communication V2-347

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