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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.
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.
Crosslayer optimization for energyefficient wireless communications: a survey,” to be published
"... Abstract—Since battery technology has not progressed as rapidly as semiconductor technology, power efficiency has become increasingly important in wireless networking, in addition to the traditional quality and performance measures, such as bandwidth, throughput, and fairness. Energyefficient desi ..."
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Cited by 45 (7 self)
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Abstract—Since battery technology has not progressed as rapidly as semiconductor technology, power efficiency has become increasingly important in wireless networking, in addition to the traditional quality and performance measures, such as bandwidth, throughput, and fairness. Energyefficient design requires a cross layer approach as power consumption is affected by all aspects of system design, ranging from silicon to applications. This article presents a comprehensive overview of recent advances in crosslayer design for energyefficient wireless communications. We particularly focus on a systembased approaches towards energy optimal transmission and resource management across time, frequency, and spatial domains. Details related to energyefficient hardware implementations are also covered. Index Terms – energy efficiency, crosslayer, wireless communications, energy aware I.
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 42 (7 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.
Adaptation, coordination, and distributed resource allocation in interferencelimited wireless networks.
 Proceeding of the IEEE,
, 2007
"... ABSTRACT  A sensible design of wireless networks involves striking a good balance between an aggressive reuse of the spectral resource throughout the network and managing the resulting cochannel interference. Traditionally, this problem has been tackled using a Bdivide and conquer[ approach. The ..."
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Cited by 34 (3 self)
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ABSTRACT  A sensible design of wireless networks involves striking a good balance between an aggressive reuse of the spectral resource throughout the network and managing the resulting cochannel interference. Traditionally, this problem has been tackled using a Bdivide and conquer[ approach. The latter consists in deploying the network with a static or semidynamic pattern of resource reutilization. The chosen reuse factor, while sacrificing a substantial amount of efficiency, brings the interference to a tolerable level. The resource can then be managed in each cell so as to optimize the per cell capacity using an advanced air interface design. In this paper, we focus our attention on the overall network capacity as a measure of system performance. We consider the problem of resource allocation and adaptive transmission in multicell scenarios. As a key instance, the problem of joint scheduling and power control simultaneously in multiple transmitreceive links, which employ capacityachieving adaptive codes, is studied. In principle, the solution of such an optimization hinges on tough issues such as the computational complexity and the requirement for heavy receivertotransmitter feedback and, for cellular networks, celltocell channel state information (CSI) signaling. We give asymptotic properties pertaining to ratemaximizing power control and scheduling in multicell networks. We then present some promising leads for substantial complexity and signaling reduction via the use of newly developed distributed and game theoretic techniques.
EnergyEfficient Precoding for MultipleAntenna Terminals
, 2011
"... The problem of energyefficient precoding is investigated when the terminals in the system are equipped with multiple antennas. Considering static and fastfading multipleinput multipleoutput (MIMO) channels, the energyefficiency is defined as the transmission rate to power ratio and shown to be ..."
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Cited by 26 (10 self)
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The problem of energyefficient precoding is investigated when the terminals in the system are equipped with multiple antennas. Considering static and fastfading multipleinput multipleoutput (MIMO) channels, the energyefficiency is defined as the transmission rate to power ratio and shown to be maximized at low transmit power. The most interesting case is the one of slow fading MIMO channels. For this type of channels, the optimal precoding scheme is generally not trivial. Furthermore, using all the available transmit power is not always optimal in the sense of energyefficiency [which, in this case, corresponds to the communicationtheoretic definition of the goodputtopower (GPR) ratio]. Finding the optimal precoding matrices is shown to be a new open problem and is solved in several special cases: 1. when there is only one receive antenna; 2. in the low or high signaltonoise ratio regime; 3. when uniform power allocation and the regime of large numbers of antennas are assumed. A complete numerical analysis is provided to illustrate the derived results and stated conjectures. In particular, the impact of the number of antennas on the energyefficiency is assessed and shown to be significant.
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 18 (7 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.
Lowcomplexity energyefficient scheduling for uplink ofdma
 IEEE Trans. Commun
, 2012
"... Abstract—Energyefficient wireless communication is very important for batteryconstrained mobile devices. For mobile devices in a cellular system, uplink power consumption dominates the wireless power budget because of RF power requirements for reliable transmission over long distances. Our previ ..."
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Cited by 17 (1 self)
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Abstract—Energyefficient wireless communication is very important for batteryconstrained mobile devices. For mobile devices in a cellular system, uplink power consumption dominates the wireless power budget because of RF power requirements for reliable transmission over long distances. Our previous work in this area focused on optimizing energy efficiency by maximizing the instantaneous bitsperJoule metric through iterative approaches, which resulted in significant energy savings for uplink cellular OFDMA transmissions. In this paper, we develop energy efficient schemes with significantly lower complexity when compared to iterative approaches, by considering timeaveraged bitsperJoule metrics. We consider an uplink OFDMA system where multiple users communicate to a central scheduler over frequencyselective channels with high energy efficiency. The scheduler allocates the system bandwidth among all users to optimize energy efficiency across the whole network. Using timeaveraged metrics, we derive energy optimal techniques in “closed forms ” for peruser link adaptation and resource scheduling across users. Simulation results show that the proposed schemes not only have low complexity but also perform close to the globally optimum solutions obtained through exhaustive search. Index Terms—Energy efficiency, OFDMA, bits per Joule, link adaptation, resource allocation. I.
NonAtomic Games for MultiUser Systems
"... 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 ..."
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Cited by 16 (6 self)
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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.
Joint receiver and transmitter optimization for energyefficient CDMA communications
 IEEE J. Sel. Areas Commun., Special Issue on Multiuser Detection for Advanced Communications Systems and Networks
, 2008
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