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74
Efficient power control via pricing in wireless data networks
 IEEE Transactions on Communication
, 2000
"... A major challenge in operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With increasing demand for wireless data servic ..."
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Cited by 201 (6 self)
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A major challenge in operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With increasing demand for wireless data services, it is necessary to establish power control algorithms for information sources other than voice. We present a power control solution for wireless data in the analytical setting of a game theoretic framework. In this context, the quality of service (QoS) a wireless terminal receives is referred to as the utility and distributed power control is a noncooperative power control game where users maximize their utility. The outcome of the game results in a Nash equilibrium that is ine#cient. We introduce pricing of transmit powers in order to obtain Pareto improvement of the noncooperative power control game, i.e. to obtain improvements in user utilities relative to the case with no pricing. Specifically, we consider a pricing function that is a linear function of the transmit power. The simplicity of the pricing function allows a distributed implementation where the price can be broadcast by the base station to all the terminals. We see that pricing is especially helpful in a heavily loaded system.
Distributed Multiuser Power Control for Digital Subscriber Lines
, 2002
"... This paper considers the multiuser power control problem in a frequencyselective interference channel. The interference channel is modeled as a noncooperative game, and the existence and uniqueness of a Nash equilibrium are established for a twoplayer version of the game. An iterative waterfillin ..."
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Cited by 170 (22 self)
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This paper considers the multiuser power control problem in a frequencyselective interference channel. The interference channel is modeled as a noncooperative game, and the existence and uniqueness of a Nash equilibrium are established for a twoplayer version of the game. An iterative waterfilling algorithm is proposed to efficiently reach the Nash equilibrium. The iterative waterfilling algorithm can be implemented distributively without the need for centralized control. It implicitly takes into account the loop transfer functions and cross couplings, and it reaches a competitively optimal power allocation by offering an opportunity for loops to negotiate the best use of power and frequency with each other. When applied to the upstream power backoff problem in veryhigh bitrate digital subscriber lines and the downstream spectral compatibility problem in asymmetric digital subscriber lines, the new power control algorithm is found to give a significant performance improvement when compared with existing methods.
CDMA Uplink Power Control as a Noncooperative Game
, 2002
"... We present a gametheoretic treatment of distributed power control in CDMA wireless systems. ..."
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Cited by 115 (22 self)
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We present a gametheoretic treatment of distributed power control in CDMA wireless systems.
A utilitybased powercontrol scheme in wireless cellular systems
 IEEE/ACM TRANS. ON NETWORKING
, 2003
"... Distributed powercontrol algorithms for systems with hard signaltointerference ratio (SIR) constraints may diverge when infeasibility arises. In this paper, we present a powercontrol framework called utilitybased power control (UBPC) by reformulating the problem using a softened SIR requirement ..."
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Cited by 54 (3 self)
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Distributed powercontrol algorithms for systems with hard signaltointerference ratio (SIR) constraints may diverge when infeasibility arises. In this paper, we present a powercontrol framework called utilitybased power control (UBPC) by reformulating the problem using a softened SIR requirement (utility) and adding a penalty on power consumption (cost). Under this framework, the goal is to maximize the net utility, defined as utility minus cost. Although UBPC is still noncooperative and distributed in nature, some degree of cooperation emerges: a user will automatically decrease its target SIR (and may even turn off transmission) when it senses that traffic congestion is building up. This framework enables us to improve system convergence and to satisfy heterogeneous service requirements (such as delay and bit error rate) for integrated networks with both voice users and data users. Fairness, adaptiveness, and a high degree of flexibility can be achieved by properly tuning parameters in UBPC.
Downlink Power Allocation for Multiclass CDMA Wireless Networks
, 2002
"... In this paper we consider the downlink power allocation problem for multiclass CDMA wireless networks. We use a utility based power allocation framework to treat multiclass services in a unified way. The goal of this paper is to obtain a power allocation which maximizes the total system utility. I ..."
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Cited by 48 (4 self)
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In this paper we consider the downlink power allocation problem for multiclass CDMA wireless networks. We use a utility based power allocation framework to treat multiclass services in a unified way. The goal of this paper is to obtain a power allocation which maximizes the total system utility. In the wireless context, natural utility functions for each mobile are nonconcave. Hence, we cannot use existing techniques on convex optimization problems to derive a social optimal solution. We propose a simple distributed algorithm to obtain an approximation to the social optimal power allocation. The proposed distributed algorithm is based on dynamic pricing and allows partial cooperation between mobiles and the base station. The algorithm consists of two stages. At the mobile selection stage, the base station selects mobiles to which power is allocated, considering the partialcooperative nature of mobiles. This is called partialcooperative optimal selection, since in a partialcooperative setting and pricing scheme considered in this paper, this selection is optimal and satisfies system feasibility. At the power allocation stage, the base station allocates power to the selected mobiles. This power allocation is a social optimal power allocation among mobiles in the partialcooperative optimal selection, thus, we call it a partialcooperative optimal power allocation. We compare the partialcooperative optimal power allocation with the social optimal power allocation for the single class case. From these results, we infer that the system utility obtained by the partialcooperative optimal power allocation is quite close to the system utility obtained by the social optimal allocation.
An energyefficient approach to power control and receiver design in wireless data networks
 IEEE TRANSACTIONS ON COMMUNICATIONS
, 2005
"... In this work, the crosslayer design problem of joint multiuser detection and power control is studied using a gametheoretic approach that focuses on energy efficiency. The uplink of a directsequence code division multiple access (DSCDMA) data network is considered and a noncooperative game is ..."
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Cited by 45 (14 self)
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In this work, the crosslayer design problem of joint multiuser detection and power control is studied using a gametheoretic approach that focuses on energy efficiency. The uplink of a directsequence code division multiple access (DSCDMA) data network is considered and a noncooperative game is proposed in which users in the network are allowed to choose their uplink receivers as well as their transmit powers to maximize their own utilities. The utility function measures the number of reliable bits transmitted by the user per joule of energy consumed. Focusing on linear receivers, the Nash equilibrium for the proposed game is derived. It is shown that the equilibrium is one where the powers are SIRbalanced with the minimum mean square error (MMSE) detector as the receiver. In addition, this framework is used to study power control games for the matched filter, the decorrelator, and the MMSE detector; and the receivers’ performance is compared in terms of the utilities achieved at equilibrium (in bits/Joule). The optimal cooperative solution is also discussed and compared with the noncooperative approach. Extensions of the results to the case of multiple receive antennas are also presented. In addition, an admission control scheme based on maximizing the total utility in the network is proposed.
UtilityBased Power Control in Cellular Wireless Systems
 In Proc. of IEEE INFOCOM’01
, 2001
"... Distributed power control algorithms for systems with hard SIR constraints may diverge when infeasibility arises. In this paper, we present a power control framework called utilitybased power control (UBPC) by reformulating the problem using a softened SIR requirement (utility) and adding a penalty ..."
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Cited by 43 (2 self)
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Distributed power control algorithms for systems with hard SIR constraints may diverge when infeasibility arises. In this paper, we present a power control framework called utilitybased power control (UBPC) by reformulating the problem using a softened SIR requirement (utility) and adding a penalty on power consumption (cost). Under this framework, the goal is to maximize the net utility, defined as utility minus cost. Although UBPC is still noncooperative and distributed in nature, some degree of cooperation emerges: a user will automatically decrease its target SIR (and may even turn off transmission) when it senses that traffic congestion is building up. This framework enables us to improve system convergence and to satisfy heterogeneous service requirements (such as delay and bit error rate) for integrated networks with both voice users and data users. Fairness, adaptiveness, and a high degree of flexibility can be achieved by properly tuning parameters in UBPC. Keywords Signaltointerference ratio (SIR), wireless, cellular system, power control, utility function, distributed algorithm. I.
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 42 (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.
SModular Games and Power Control in Wireless Networks
 IEEE Transactions on Automatic Control
, 2003
"... This note shows how centralized or distributed power control algorithms in wireless communications can be viewed as Smodular games coupled policy sets (coupling is due to the fact that the set of powers of a mobile that satisfy the signaltointerference ratio constraints depends on powers used by ..."
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Cited by 31 (4 self)
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This note shows how centralized or distributed power control algorithms in wireless communications can be viewed as Smodular games coupled policy sets (coupling is due to the fact that the set of powers of a mobile that satisfy the signaltointerference ratio constraints depends on powers used by other mobiles). This sheds a new light on convergence properties of existing synchronous and asynchronous algorithms, and allows us to establish new convergence results of power control algorithms. Furthermore, known properties of power control algorithms allow us to extend the theory of Smodular games and obtain conditions for the uniqueness of the equilibrium and convergence of best response algorithms independently of the initial state.