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39
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 22 (6 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.
Coalition games with cooperative transmission: A cure for the curse of boundary nodes in selfish packetforwarding wireless networks
 IEEE Trans. Comm
, 2009
"... Abstract — In wireless packetforwarding networks with selfish nodes, applications of a repeated game can induce the nodes to forward each others ’ packets, so that the network performance can be improved. However, the nodes on the boundary of such networks cannot benefit from this strategy, as the ..."
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Cited by 18 (6 self)
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Abstract — In wireless packetforwarding networks with selfish nodes, applications of a repeated game can induce the nodes to forward each others ’ packets, so that the network performance can be improved. However, the nodes on the boundary of such networks cannot benefit from this strategy, as the other nodes do not depend on them. This problem is sometimes known as the curse of the boundary nodes. To overcome this problem, an approach based on coalition games is proposed, in which the boundary nodes can use cooperative transmission to help the backbone nodes in the middle of the network. In return, the backbone nodes are willing to forward the boundary nodes’ packets. The stability of the coalitions is studied using the concept of a core. Then two types of fairness, namely, the minmax fairness using nucleolus and the average fairness using the Shapley function are investigated. Finally, a protocol is designed using both repeated games and coalition games. Simulation results show how boundary nodes and backbone nodes form coalitions together according to different fairness criteria. The proposed protocol can improve the network connectivity by about 50%, compared with pure repeated game schemes. I.
Introducing Hierarchy in Energy Games
, 2009
"... In this work we introduce hierarchy in wireless networks that can be modeled by a decentralized multiple access channel and for which energyefficiency is the main performance index. In these networks users are free to choose their power control strategy to selfishly maximize their energyefficiency ..."
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Cited by 15 (10 self)
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In this work we introduce hierarchy in wireless networks that can be modeled by a decentralized multiple access channel and for which energyefficiency is the main performance index. In these networks users are free to choose their power control strategy to selfishly maximize their energyefficiency. Specifically, we introduce hierarchy in two different ways: 1. Assuming singleuser decoding at the receiver, we investigate a Stackelberg formulation of the game where one user is the leader whereas the other users are assumed to be able to react to the leader’s decisions; 2. Assuming neither leader nor followers among the users, we introduce hierarchy by assuming successive interference cancellation at the receiver. It is shown that introducing a certain degree of hierarchy in noncooperative power control games not only improves the individual energy efficiency of all the users but can also be a way of insuring the existence of a nonsaturated equilibrium and reaching a desired tradeoff between the global network performance at the equilibrium and the requested amount of signaling. In this respect, the way of measuring the global performance of an energyefficient network is shown to be a critical issue.
Discrete power control: Cooperative and noncooperative optimization
 in INFOCOM
, 2007
"... Abstract — We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a ..."
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Cited by 13 (3 self)
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Abstract — We consider an uplink power control problem where each mobile wishes to maximize its throughput (which depends on the transmission powers of all mobiles) but has a constraint on the average power consumption. A finite number of power levels are available to each mobile. The decision of a mobile to select a particular power level may depend on its channel state. We consider two frameworks concerning the state information of the channels of other mobiles: (i) the case of full state information and (ii) the case of local state information. In each of the two frameworks, we consider both cooperative as well as noncooperative power control. We manage to characterize the structure of equilibria policies and, more generally, of bestresponse policies in the noncooperative case. We present an algorithm to compute equilibria policies in the case of two noncooperative players. Finally, we study the case where a malicious mobile, which also has average power constraints, tries to jam the communication of the other mobile. Our results are illustrated and validated through various numerical examples. I.
Are, “Nonatomic games for multiuser systems
 IEEE JSAC, issue on Game Theory in Communication Systems
, 2008
"... Abstract—In this contribution, the performance of a multiuser system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect ..."
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Cited by 12 (6 self)
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Abstract—In this contribution, the performance of a multiuser system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). This scenario illustrates the case of decentralized schemes, where limited information on the network is available at the terminal. Various receivers are considered, namely the matched filter, the MMSE filter and the optimum filter. The goal of this paper is to extend previous work, and to derive simple expressions for the noncooperative Nash equilibrium as the number of mobiles becomes large and the spreading length increases. To that end two asymptotic methodologies are combined. The first is asymptotic random matrix theory which allows us to obtain explicit expressions of the impact of all other mobiles on any given tagged mobile. The second is the theory of nonatomic games which computes good approximations of the Nash equilibrium as the number of mobiles grows. Index Terms—Game theory, random matrix theory, CDMA, resource allocation, MMSE. I.
Dynamic discrete power control in cellular networks
 IEEE Trans. on Automatic Control
, 2009
"... cellular networks ..."
Wardrop Equilibrium for CDMA Systems
"... Abstract — In this contribution, the performance of an uplink CDMA system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while per ..."
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Cited by 6 (2 self)
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Abstract — In this contribution, the performance of an uplink CDMA system is analyzed in the context of frequency selective fading channels. Using game theoretic tools, a useful framework is provided in order to determine the optimal power allocation when users know only their own channel (while perfect channel state information is assumed at the base station). We consider the realistic case of frequency selective channels. This scenario illustrates the case of decentralized schemes and aims at reducing the downlink signaling overhead. Various receivers are considered, namely the Matched filter, the MMSE filter and the optimum filter. The goal of this paper is to derive simple expressions for the noncooperative Nash equilibrium as the number of mobiles becomes large. To that end we combine two asymptotic methodologies. The first is asymptotic random matrix theory which allows us to obtain explicit expressions for the impact of all other mobiles on any given tagged mobile. The second is the theory of nonatomic games along with the Wardrop equilibrium concept which allows us to compute good approximations of the Nash equilibrium as the number of mobiles grow. 1 I.
Energyefficient power control in impulse radio UWB wireless networks
"... In this paper, a gametheoretic model for studying power control for wireless data networks in frequencyselective multipath environments is analyzed. The uplink of an impulseradio ultrawideband system is considered. The effects of interframe interference and multipleaccess interference on the per ..."
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Cited by 5 (5 self)
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In this paper, a gametheoretic model for studying power control for wireless data networks in frequencyselective multipath environments is analyzed. The uplink of an impulseradio ultrawideband system is considered. The effects of interframe interference and multipleaccess interference on the performance of generic Rake receivers are investigated for synchronous systems. Focusing on energy efficiency, a noncooperative game is proposed in which users in the network are allowed to choose their transmit powers to maximize their own utilities, and the Nash equilibrium for the proposed game is derived. It is shown that, due to the frequency selective multipath, the noncooperative solution is achieved at different signaltointerferenceplusnoise ratios, depending on the channel realization and the type of Rake receiver employed. A largesystem analysis is performed to derive explicit expressions for the achieved utilities. The Paretooptimal (cooperative) solution is also discussed and compared with the noncooperative approach.
A new decentralized power allocation strategy in singlehop wireless networks
 HOPKINS UNIVERSITY
, 2006
"... In this paper, a simple decentralized power allocation strategy is proposed, which relies on the local information in a singlehop wireless network with n links. The main goal of the strategy is to improve the average sumrate. We first define a new utilitybased framework, in which each user takes ..."
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Cited by 5 (4 self)
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In this paper, a simple decentralized power allocation strategy is proposed, which relies on the local information in a singlehop wireless network with n links. The main goal of the strategy is to improve the average sumrate. We first define a new utilitybased framework, in which each user takes into account the negative impact of its power increment on the other users performance. For large n and by knowing only the direct channel gain hii, the optimum strategy for user i is to transmit with full power or remain silent. The transmission policy is to compare hii with a prespecified threshold τn that is a function of n. Under a Rayleigh fading channel condition, it is demonstrated that among n pairs of nodes, the average number of active links is of order log n. Also, the average sumrate scales as Θ(log n). The performance of the proposed strategy is compared with that of the centralized power allocation scheme and the noncooperative power control games through simulation and the analytical arguments. The proposed onoff power allocation scheme has the advantage of not requiring a central controller. The proposed strategy relies on a one shot game with a simple structure, rather than the iterative mechanism used in the pricing algorithm. These properties make our scheme more practical in timevarying networks.
A repeated game formulation of energyefficient decentralized power control
 IEEE TRANS. ON WIRELESS COMMUNICATIONS
, 2010
"... Decentralized multiple access channels where each transmitter wants to selfishly maximize his transmission energyefficiency are considered. Transmitters are assumed to choose freely their power control policy and interact (through multiuser interference) several times. It is shown that the correspo ..."
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Cited by 4 (3 self)
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Decentralized multiple access channels where each transmitter wants to selfishly maximize his transmission energyefficiency are considered. Transmitters are assumed to choose freely their power control policy and interact (through multiuser interference) several times. It is shown that the corresponding conflict of interest can have a predictable outcome, namely a finitely or discounted repeated game equilibrium. Remarkably, it is shown that this equilibrium is Paretoefficient under reasonable sufficient conditions and the corresponding decentralized power control policies can be implemented under realistic information assumptions: only individual channel state information and a public signal are required to implement the equilibrium strategies. Explicit equilibrium conditions are derived in terms of minimum number of game stages or maximum discount factor. Both analytical and simulation results are provided to compare the performance of the proposed power control policies with those already existing and exploiting the same information assumptions namely, those derived for the oneshot and Stackelberg games.