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176
Distributed interference compensation for wireless networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2006
"... We consider a distributed power control scheme for wireless ad hoc networks, in which each user announces a price that reflects compensation paid by other users for their interference. We present an asynchronous distributed algorithm for updating power levels and prices. By relating this algorithm ..."
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Cited by 177 (33 self)
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We consider a distributed power control scheme for wireless ad hoc networks, in which each user announces a price that reflects compensation paid by other users for their interference. We present an asynchronous distributed algorithm for updating power levels and prices. By relating this algorithm to myopic best response updates in a fictitious game, we are able to characterize convergence using supermodular game theory. Extensions of this algorithm to a multichannel network are also presented, in which users can allocate their power across multiple frequency bands.
Auctionbased spectrum sharing
 WiOpt '04
, 2004
"... Abstract. We study auctionbased mechanisms for sharing spectrum among a group of users, subject to a constraint on the interference temperature at collocated receivers. The users access the channel using spread spectrum signaling and thus generate interference with each other. Each user receives a ..."
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Cited by 119 (18 self)
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Abstract. We study auctionbased mechanisms for sharing spectrum among a group of users, subject to a constraint on the interference temperature at collocated receivers. The users access the channel using spread spectrum signaling and thus generate interference with each other. Each user receives a utility that is a function of the received signaltointerference plus noise ratio. We propose two auction mechanisms for allocating the received power. The first is an SINRbased auction, which, when combined with logarithmic utilities, leads to a weighted maxmin fair SINR allocation. The second is a powerbased auction that maximizes the total utility when the bandwidth is large enough. Both auction mechanisms achieve social optimality in a large system limit where bandwidth, power and the number of users are increased in a fixed proportion. We also give sufficient conditions for global convergence of a distributed updating algorithm and discuss the convergence speed. 1
Nash Equilibria of Packet Forwarding Strategies in Wireless Ad Hoc Networks
, 2006
"... In selforganizing ad hoc networks, all the networking functions rely on the contribution of the participants. As a basic example, nodes have to forward packets for each other in order to enable multihop communication. In recent years, incentive mechanisms have been proposed to give nodes incentive ..."
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Cited by 101 (10 self)
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In selforganizing ad hoc networks, all the networking functions rely on the contribution of the participants. As a basic example, nodes have to forward packets for each other in order to enable multihop communication. In recent years, incentive mechanisms have been proposed to give nodes incentive to cooperate, especially in packet forwarding. However, the need for these mechanisms was not formally justified. In this paper, we address the problem of whether cooperation can exist without incentive mechanisms. We propose a model based on game theory and graph theory to investigate equilibrium conditions of packet forwarding strategies. We prove theorems about the equilibrium conditions for both cooperative and noncooperative strategies. We perform simulations to estimate the probability that the conditions for a cooperative equilibrium hold in randomly generated network scenarios. As the problem is involved, we deliberately restrict ourselves to a static configuration. We conclude that in static ad hoc networks— where the relationships between the nodes are likely to be stable—cooperation needs to be encouraged.
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.
Optimal linear precoding strategies for wideband noncooperative systems based on game theory – Part II: Algorithms
 IEEE Trans. Signal Process
, 2008
"... In this twoparts paper we propose a decentralized strategy, based on a gametheoretic formulation, to find out the optimal precoding/multiplexing matrices for a multipointtomultipoint communication system composed of a set of wideband links sharing the same physical resources, i.e., time and band ..."
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Cited by 86 (10 self)
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In this twoparts paper we propose a decentralized strategy, based on a gametheoretic formulation, to find out the optimal precoding/multiplexing matrices for a multipointtomultipoint communication system composed of a set of wideband links sharing the same physical resources, i.e., time and bandwidth. We assume, as optimality criterion, the achievement of a Nash equilibrium and consider two alternative optimization problems: 1) the competitive maximization of mutual information on each link, given constraints on the transmit power and on the spectral mask imposed by the radio spectrum regulatory bodies; and 2) the competitive maximization of the transmission rate, using finite order constellations, under the same constraints as above, plus a constraint on the average error probability. In Part I of the paper, we start by showing that the solution set of both noncooperative games is always nonempty and contains only pure strategies. Then, we prove that the optimal precoding/multiplexing scheme for both games leads to a channel diagonalizing structure, so that both matrixvalued problems can be recast in a simpler unified vector power control game, with no performance penalty. Thus, we study this simpler game and derive sufficient conditions ensuring the uniqueness of the Nash equilibrium. Interestingly, although derived under stronger constraints,
BAn energyefficient approach to power control and receiver design in wireless data networks,[
 IEEE Trans. Commun.,
, 2005
"... ..."
Power Control in TwoTier Femtocell Networks
, 2008
"... Two tier cellular networks, comprising of a central macrocell underlaid with short range femtocell hotspots offer an economical way to improve cellular capacity. With shared spectrum and lack of coordination between tiers, crosstier interference limits overall capacity. To quantify nearfar effects ..."
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Cited by 74 (6 self)
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Two tier cellular networks, comprising of a central macrocell underlaid with short range femtocell hotspots offer an economical way to improve cellular capacity. With shared spectrum and lack of coordination between tiers, crosstier interference limits overall capacity. To quantify nearfar effects with universal frequency reuse, this paper derives a fundamental relation providing the largest feasible macrocell SignaltoInterferencePlusNoise Ratio (SINR), given any set of feasible femtocell SINRs. A distributed utilitybased SINR adaptation at femtocells is proposed in order to alleviate crosstier interference at the macrocell from overlaid femtocell infrastructure. The FoschiniMiljanic (FM) algorithm is a special case of the adaptation. Each femtocell maximizes its individual utility consisting of a SINR based reward less an incurred cost (interference to the macrocell). Numerical results show greater than 30 % improvement in mean femtocell SINRs relative to FM. In the event that crosstier interference prevents a macrouser from obtaining its SINR target, an algorithm is proposed that adaptively curtails transmission powers of the strongest femtocell interferers. The algorithm ensures that a macrouser achieves its SINR target even with 100 femtocells/cellsite, and requires a worst case SINR reduction of only 16 % at femtocells. These results motivate design of power control schemes requiring minimal network overhead in twotier networks with shared spectrum.
On selfish behavior in CSMA/CA networks
 In Proc. of IEEE Infocom
, 2005
"... Abstract — CSMA/CA protocols rely on the random deferment of packet transmissions. Like most other protocols, CSMA/CA was designed with the assumption that the nodes would play by the rules. This can be dangerous, since the nodes themselves control their random deferment. Indeed, with the higher pro ..."
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Cited by 61 (7 self)
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Abstract — CSMA/CA protocols rely on the random deferment of packet transmissions. Like most other protocols, CSMA/CA was designed with the assumption that the nodes would play by the rules. This can be dangerous, since the nodes themselves control their random deferment. Indeed, with the higher programmability of the network adapters, the temptation to tamper with the software or firmware is likely to grow; by doing so, a user could obtain a much larger share of the available bandwidth at the expense of other users. We use a gametheoretic approach to investigate the problem of the selfish behavior of nodes in CSMA/CA networks, specifically geared towards the most widely accepted protocol in this class of protocols, IEEE 802.11. We characterize two families of Nash equilibria in a single stage game, one of which always results in a network collapse. We argue that this result provides an incentive for cheaters to cooperate with each other. Explicit cooperation among nodes is clearly impractical. By applying the model of dynamic games borrowed from game theory, we derive the conditions for the stable and optimal functioning of a population of cheaters. We use this insight to develop a simple, localized and distributed protocol that successfully guides multiple selfish nodes to a Paretooptimal Nash equilibrium. I.
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.