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44
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.
Adaptive resource allocation in jamming teams using game theory, in Modeling and Optimization
 in Mobile, in Proceedings of the International Symposium on Ad Hoc and Wireless Networks (WiOpt
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Power Allocation in Team Jamming Games in Wireless Ad Hoc Networks
"... In this work, we study the problem of power allocation in teams. Each team consists of two agents who try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The co ..."
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Cited by 4 (4 self)
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In this work, we study the problem of power allocation in teams. Each team consists of two agents who try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function is the difference between the rates of erroneously transmitted bits of each team. We model the problem as a zerosum differential game between the two teams and use Isaacs ’ approach to obtain the necessary conditions for the optimal trajectories. This leads to a continuouskernel power allocation game among the players. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy Nash equilibrium (PSNE). Finally, we present simulation results for the case when the agents are holonomic. 1.
InterOperator Spectrum Sharing from a Game Theoretical Perspective
, 2009
"... We address the problem of spectrum sharing where competitive operators coexist in the same frequency band. First, we model this problem as a strategic noncooperative game where operators simultaneously share the spectrum according to the Nash Equilibrium (NE). Given a set of channel realizations, s ..."
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Cited by 4 (1 self)
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We address the problem of spectrum sharing where competitive operators coexist in the same frequency band. First, we model this problem as a strategic noncooperative game where operators simultaneously share the spectrum according to the Nash Equilibrium (NE). Given a set of channel realizations, several Nash equilibria exist which renders the outcome of the game unpredictable. Then, in a cognitive context with the presence of primary and secondary operators, the interoperator spectrum sharing problem is reformulated as a Stackelberg game using hierarchy where the primary operator is the leader. The Stackelberg Equilibrium (SE) is reached where the best response of the secondary operator is taken into account upon maximizing the primary operator’s utility function. Moreover, an extension to the multiple operators spectrum sharing problem is given. It is shown that the Stackelberg approach yields better payoffs for operators compared to the classical waterfilling approach. Finally, we assess the goodness of the proposed distributed approach by comparing its performance to the centralized approach. Copyright © 2009 Mehdi Bennis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Green Power Control in Cognitive Wireless Networks
, 2013
"... Abstract—A decentralized network of cognitive and noncognitive transmitters where each transmitter aims at maximizing his energyefficiency is considered. The cognitive transmitters are assumed to be able to sense the transmit power of their noncognitive counterparts and the former have a cost for s ..."
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Cited by 2 (1 self)
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Abstract—A decentralized network of cognitive and noncognitive transmitters where each transmitter aims at maximizing his energyefficiency is considered. The cognitive transmitters are assumed to be able to sense the transmit power of their noncognitive counterparts and the former have a cost for sensing. The Stackelberg equilibrium analysis of this 2−level hierarchical game is conducted, which allows us to better understand the effects of cognition on energyefficiency. In particular, it is proven that the network energyefficiency is maximized when only a given fraction of terminals are cognitive. Then, we study a sensing game where all the transmitters are assumed to take the decision whether to sense (namely to be cognitive) or not. This game is shown to be a weighted potential game and its set of equilibria is studied. Playing the sensing game in a first phase (e.g., of a timeslot) and then playing the power control game is shown to be more efficient individually for all transmitters than playing a game where a transmitter would jointly optimize whether to sense and his power level, showing the existence of a kind of Braess paradox. The derived results are illustrated by numerical results and provide some insights on how to deploy cognitive radios in heterogeneous networks in terms of sensing capabilities. Index Terms—Power Control, Stackelberg Equilibrium, EnergyEfficiency.
1Promoting Cooperation in Wireless Relay Networks through Stackelberg Dynamic Scheduling
"... Abstract—This paper discusses a new perspective for the application of game theory to wireless relay networks, namely, how to employ it not only as an analytical evaluation instrument, but also in constructively deriving practical network management policies. We focus on the problem of medium shari ..."
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Cited by 1 (1 self)
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Abstract—This paper discusses a new perspective for the application of game theory to wireless relay networks, namely, how to employ it not only as an analytical evaluation instrument, but also in constructively deriving practical network management policies. We focus on the problem of medium sharing in wireless networks, which is often seen as a case where game theory just proves the inefficiency of distributed access, without proposing any remedy. Instead, we show how, by properly modeling the agents involved in such a scenario, and enabling simple but effective incentives towards cooperation for the users, we obtain a resource allocation scheme which is meaningful from both perspectives of game theory and network engineering. Such a result is achieved by introducing throughput redistribution as a way to transfer utilities, which enables cooperation among the users. Finally, a Stackelberg formulation is proposed, involving the network access point as a further player. Our approach is also able to take into account power consumption of the terminals, still without treating it as an insurmountable hurdle to cooperation, and at the same time to drive the network allocation towards an efficient cooperation level.