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A gametheoretic approach to energyefficient power control in multicarrier CDMA systems
 IEEE Journal on Selected Areas in Communications (JSAC
, 2006
"... Abstract—A gametheoretic model for studying power control in multicarrier codedivision multipleaccess systems is proposed. Power control is modeled as a noncooperative game in which each user decides how much power to transmit over each carrier to maximize its own utility. The utility function co ..."
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Cited by 89 (8 self)
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Abstract—A gametheoretic model for studying power control in multicarrier codedivision multipleaccess systems is proposed. Power control is modeled as a noncooperative game in which each user decides how much power to transmit over each carrier to maximize its own utility. The utility function considered here measures the number of reliable bits transmitted over all the carriers per joule of energy consumed and is particularly suitable for networks where energy efficiency is important. The multidimensional nature of users ’ strategies and the nonquasiconcavity of the utility function make the multicarrier problem much more challenging than the singlecarrier or throughputbasedutility case. It is shown that, for all linear receivers including the matched filter, the decorrelator, and the minimummeansquareerror detector, a user’s utility is maximized when the user transmits only on its “best ” carrier. This is the carrier that requires the least amount of power to achieve a particular target signaltointerferenceplusnoise ratio at the output of the receiver. The existence and uniqueness of Nash equilibrium for the proposed power control game are studied. In particular, conditions are given that must be satisfied by the channel gains for a Nash equilibrium to exist, and the distribution of the users among the carriers at equilibrium is characterized. In addition, an iterative and distributed algorithm for reaching the equilibrium (when it exists) is presented. It is shown that the proposed approach results in significant improvements in the total utility achieved at equilibrium compared with a singlecarrier system and also to a multicarrier system in which each user maximizes its utility over each carrier independently. Index Terms—Energy efficiency, game theory, multicarrier codedivision multipleaccess (CDMA), multiuser detection, Nash equilibrium, power control, utility function. I.
BAn energyefficient approach to power control and receiver design in wireless data networks,[
 IEEE Trans. Commun.,
, 2005
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Energyefficient resource allocation in wireless networks: An overview of gametheoretic approaches
 IEEE Signal Process. Magazine
, 2007
"... A gametheoretic model is proposed to study the crosslayer problem of joint power and rate control with quality of service (QoS) constraints in multipleaccess networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own ..."
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Cited by 55 (8 self)
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A gametheoretic model is proposed to study the crosslayer problem of joint power and rate control with quality of service (QoS) constraints in multipleaccess networks. In the proposed game, each user seeks to choose its transmit power and rate in a distributed manner in order to maximize its own utility while satisfying its QoS requirements. The user’s QoS constraints are specified in terms of the average source rate and an upper bound on the average delay where the delay includes both transmission and queuing delays. The utility function considered here measures energy efficiency and is particularly suitable for wireless networks with energy constraints. The Nash equilibrium solution for the proposed noncooperative game is derived and a closedform expression for the utility achieved at equilibrium is obtained. It is shown that the QoS requirements of a user translate into a “size ” for the user which is an indication of the amount of network resources consumed by the user. Using this competitive multiuser framework, the tradeoffs among throughput, delay, network capacity and energy efficiency are studied. In addition, analytical expressions are given for users ’ delay profiles and the delay performance of the users at Nash equilibrium is quantified.
The waterfilling game in fading multipleaccess channels
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2008
"... A gametheoretic framework is developed to design and analyze the resource allocation algorithms in fading multipleaccess channels (MACs), where the users are assumed to be selfish, rational, and limited by average power constraints. The maximum sumrate point on the boundary of the MAC capacity ..."
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Cited by 47 (0 self)
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A gametheoretic framework is developed to design and analyze the resource allocation algorithms in fading multipleaccess channels (MACs), where the users are assumed to be selfish, rational, and limited by average power constraints. The maximum sumrate point on the boundary of the MAC capacity region is shown to be the unique Nash equilibrium of the corresponding waterfilling game. This result sheds a new light on the opportunistic communication principle. The base station is then introduced as a player interested in maximizing a weighted sum of the individual rates. A Stackelberg formulation is proposed in which the base station is the designated game leader. In this setup, the base station announces first its strategy defined as the decoding order of the different users, in the successive cancellation receiver, as a function of the channel state. In the second stage, the users compete conditioned on this particular decoding strategy. This formulation is shown to be able to achieve all the corner points of the capacity region, in addition to the maximum sumrate point. On the negative side, it is shown that there does not exist a base station strategy in this formulation that achieves the rest of the boundary points. To overcome this limitation, a repeated game approach, which achieves the capacity region of the fading MAC, is presented. Finally, the study is extended to vector channels highlighting interesting differences between this scenario and the scalar channel case.
ARC: An Integrated Admission and Rate Control Framework for CDMA Data Networks Based on Noncooperative Games
, 2003
"... The competition among wireless data service providers brings in an option for the customers to switch their providers, due to unsatisfactory service or otherwise. However, the existing resource management algorithms for wireless networks fail to fully capture the farreaching impact of this competit ..."
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Cited by 32 (10 self)
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The competition among wireless data service providers brings in an option for the customers to switch their providers, due to unsatisfactory service or otherwise. However, the existing resource management algorithms for wireless networks fail to fully capture the farreaching impact of this competitiveness. From this perspective, we propose an integrated admission and rate control (ARC) framework for CDMA based wireless data networks. The admission control is at the session (macro) level while the rate control is at the link layer packet (micro) level. The ARC framework is based on a novel game theoretic formulation which defines noncooperative games between the service providers and the customers. A user’s decision to leave or join a provider is based on a finite set of strategies. A service provider can also construct its game strategy set so as to maximize the utility (revenue) yet attaining
A hybrid systems model for power control in multicell wireless data networks, Performance Evaluation 57(4
, 2004
"... Abstract — We present a power control scheme based on noncooperative game theory, using a fairly broad class of convex cost functions. The multicell CDMA wireless data network is modeled as a switched hybrid system where handoffs of mobiles between different cells correspond to discrete switching ev ..."
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Cited by 29 (10 self)
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Abstract — We present a power control scheme based on noncooperative game theory, using a fairly broad class of convex cost functions. The multicell CDMA wireless data network is modeled as a switched hybrid system where handoffs of mobiles between different cells correspond to discrete switching events between different subsystems. Under a set of sufficient conditions, we prove the existence of a unique Nash equilibrium for each subsystem, and prove global exponential stability of an update algorithm. We also establish the global convergence of the dynamics of the multicell power control game to a convex superset of Nash equilibria for any switching (handoff) scheme satisfying a mild condition on average dwelltime. Robustness of these results to feedback delays as well as to quantization is investigated. In addition, we consider a quantization scheme to reduce the communication overhead between mobiles and the base stations. Finally, we illustrate the proposed power control scheme through simulations. I.
The waterfilling game in fading multiple access channels
 Online]. Available
, 2005
"... We adopt a game theoretic approach for the design and analysis of distributed resource allocation algorithms in fading multiple access channels. The users are assumed to be selfish, rational, and limited by average power constraints. We show that the sumrate optimal point on the boundary of the mul ..."
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Cited by 18 (0 self)
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We adopt a game theoretic approach for the design and analysis of distributed resource allocation algorithms in fading multiple access channels. The users are assumed to be selfish, rational, and limited by average power constraints. We show that the sumrate optimal point on the boundary of the multipleaccess channel capacity region is the unique Nash Equilibrium of the corresponding waterfilling game. This result sheds a new light on the opportunistic communication principle and argues for the fairness of the sumrate optimal point, at least from a game theoretic perspective. The basestation is then introduced as a player interested in maximizing a weighted sum of the individual rates. We propose a Stackelberg formulation in which the basestation is the designated game leader. In this setup, the basestation announces first its strategy defined as the decoding order of the different users, in the successive cancellation receiver, as a function of the channel state. In the second stage, the users compete conditioned on this particular decoding strategy. We show that this formulation allows for achieving all the corner points of the capacity region, in addition to the sumrate optimal point. On the negative side, we prove the nonexistence of a basestation strategy in this formulation that achieves the rest of the boundary points. To overcome this limitation, we present a repeated game approach which achieves the capacity region of the fading multiple access channel. Finally, we extend our study to vector channels highlighting interesting differences between this scenario and the scalar channel case. 1
Distributed Resource Allocation Schemes: Pricing Algorithms for Power Control and Beamformer Design in Interference Networks
"... Achieving high spectral efficiencies in wireless networks requires the ability to mitigate and manage the associated interference. This becomes especially important in networks where many transmitters and receivers are randomly placed, so that in the absence of coordination a particular receiver is ..."
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Cited by 16 (0 self)
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Achieving high spectral efficiencies in wireless networks requires the ability to mitigate and manage the associated interference. This becomes especially important in networks where many transmitters and receivers are randomly placed, so that in the absence of coordination a particular receiver is likely to encounter significant interference from a neighboring transmitter. A challenge is then to provide a means
A noncooperative power control game for multicarrier CDMA systems
 In Proc. IEEE Wireless Communications and Networking Conference (WCNC
, 2005
"... A gametheoretic model for studying power control in multicarrier CDMA systems is proposed. Power control is modeled as a noncooperative game in which each user must decide how much power to transmit over each carrier to maximize its own utility. The utility function considered here measures the n ..."
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Cited by 9 (1 self)
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A gametheoretic model for studying power control in multicarrier CDMA systems is proposed. Power control is modeled as a noncooperative game in which each user must decide how much power to transmit over each carrier to maximize its own utility. The utility function considered here measures the number of reliable bits transmitted over all the carriers per joule of energy consumed and is particularly suitable for networks where energy efficiency is important. The multidimensional nature of users ’ strategies and nonquasiconcavity of the utility function make the multicarrier problem much more challenging than the singlecarrier case. It is shown that, for all linear receivers including the matched filter, decorrelating and minimum mean square error (MMSE) detectors, a user’s utility is maximized when the user transmits only on its “best ” carrier. This is the carrier that requires the least amount of power to achieve a particular target signal to interference plus noise ratio (SIR) at the output of the receiver. The existence and uniqueness of Nash equilibrium for the proposed power control game are studied. In particular, we give conditions that must be satisfied by the channel gains for a Nash equilibrium to exist and also characterize the distribution of the users among the carriers at equilibrium. In addition, an iterative and distributed algorithm for reaching the equilibrium (when it exists) is presented. It is shown that the proposed approach results in a significant improvement in the total utility achieved at equilibrium compared to the case in which each user maximizes its utility over each carrier independently.
A noncooperative power control game in delayconstrained multipleaccess networks
 Proceedings of the IEEE International Symposium on Information Theory (ISIT
, 2005
"... Abstract — A gametheoretic approach for studying power control in multipleaccess networks with transmission delay constraints is proposed. A noncooperative power control game is considered in which each user seeks to choose a transmit power that maximizes its own utility while satisfying the user ..."
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Cited by 7 (6 self)
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Abstract — A gametheoretic approach for studying power control in multipleaccess networks with transmission delay constraints is proposed. A noncooperative power control game is considered in which each user seeks to choose a transmit power that maximizes its own utility while satisfying the user’s delay requirements. The utility function measures the number of reliable bits transmitted per joule of energy and the user’s delay constraint is modeled as an upper bound on the delay outage probability. The Nash equilibrium for the proposed game is derived, and its existence and uniqueness are proved. Using a largesystem analysis, explicit expressions for the utilities achieved at equilibrium are obtained for the matched filter, decorrelating and minimum mean square error multiuser detectors. The effects of delay constraints on the users ’ utilities (in bits/Joule) and network capacity (i.e., the maximum number of users that can be supported) are quantified. I.