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...l results of transmit power sufficient to satisfy the network connectivity has been proposed. In recent years there has been a growing interest in applying game theory to study wireless systems. [6], =-=[7]-=- used game theory to investigate power control and rate control for wireless data. In [8], the authors provide motivations for using game theory to study communication systems, and in particular power...

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...y problems in multiagent systems, in particular congestion problems on networks [2], and more recently, power control problems, channel selection problems and scheduling problems in wireless networks =-=[3, 4]-=-, as well as target assignment problems [5] and job scheduling [6]. We now formally define a potential game.sDefinition 2 (Potential Games). A function P : S → R is a potential for a game if: P(si,s−i...

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...user’s power to the minimum power [2, 9, 14-16, 23, 24], and as optimization-based approaches [7]. Much of this previous work deals with static time invariant channel models. The scheme introduced in =-=[7, 11]-=-, whereby the statistics of the received SIR are used to allocate power, rather than an instantaneous SIR. Therefore, the allocation decisions can be made on a much slower time scale. Previous attempt...

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...s on the channel capacity and decouples lower layer decisions like modulation and coding is proposed. Research in the area of joint rate and power control is emerging and related work can be found in =-=[5]-=-, [9]. In [5], joint rate and power control is approached from a gametheoretic perspective, and modeled as two distinct games. The algorithm in [5] requires that all terminals find first the rate of t...

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...ι − = ≠ ι = − −s−( −s= − − + + +s−( − ∑s(8)swheres2 0 2 0 1 i N j j G G ωι = = ∑sis the weighted coefficient and iP−srepresents the actions for all players except i. Note thatsthe utility function in =-=[7]-=- only considers the QoS of CUsswithout guaranteeing the protection of PU. In Equations(8), β ≥1 is a constant, and the interference constraintsof PU can be easily satisfied by increasing the value ofs...

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...ithms were developed to improve system performance by controlling power allocation and data rate. There has also been a growing interest in applying game theory to study wireless systems. [15], [16], =-=[17]-=- used game theory to investigate power control and rate control for wireless data. A game theoretic perspective on interference avoidance in ad hoc networks was provided in [18]. III. ROBUST MATHEMATI...

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...n to power control, and this has resulted in the need for joint rate and power control in wireless systems. We note that very little work has been done in this field, and related work can be found in =-=[4]-=-, [8]. In [4], joint rate and power control is approched from a game-theoretic perspective, and modeled as two different games. One disadvantage of the algorithm in [4] is that all terminals must firs...

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... detection, beamforming and adaptive modulation [5], [6]. In [7], [8] adaptive algorithms were developed to improve system performance by controlling power allocation and data rate. As the use of MIMO technology in ad hoc networks grows, MIMO interference systems have attracted a great deal of attention. [9], [10] studied the interactions and capacity dependencies of MIMO interference systems and [11], [12] explored methods for power management and interference avoidance in MIMO systems. In recent years there has been a growing interest in applying game theory to study wireless systems. [13], [14] used game theory to investigate power control and Manuscript received February 11, 2005; revised August 5, 2005, August 19, 2006, and December 7, 2006; accepted January 19, 2007. The associate editor coordinating the review of this paper and approving it for publication was W. Yu. This material is based upon work supported by the National Science Foundation under Grant No. 0322797 and 0435041. The authors are with the Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA 19104-2875 (e-mail: {lch, dandekar}@ece.drexel.edu). Digital Object Identifier 10.1109/TWC...