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Efficient power control via pricing in wireless data networks
 IEEE Trans. on Commun
, 2002
"... Abstract—A major challenge in the 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 the increasing demand for wir ..."
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Cited by 339 (8 self)
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Abstract—A major challenge in the 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 the 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 inefficient. 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. Index Terms—Game theory, Pareto efficiency, power control, pricing, wireless data. I.
Joint Scheduling and Power Control for Wireless Adhoc Networks
, 2002
"... In this pape we introduce powe r control as a solution tothe multiple accel proble in conte tionbase wirenb adhocne works.The motivation for this study is two fold, limiting multiuse intej toincre single hop throughput, andrej powe r consumption to increj batte life We focus onne ne bor transmi ..."
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Cited by 283 (6 self)
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In this pape we introduce powe r control as a solution tothe multiple accel proble in conte tionbase wirenb adhocne works.The motivation for this study is two fold, limiting multiuse intej toincre single hop throughput, andrej powe r consumption to increj batte life We focus onne ne bor transmissions whes node are rej tose information packe  tothe re e e re e sub jej to a constraint on the signaltointealtoinjj ratio.The multiple acce  proble is solve via twoaltej phase name schej and powe r control.The sche algorithm isej tial to coordinate the transmissions ofinde ede t use inorde toejj strong intej (e.g selfinterference) that can not be ove by powe r control. On the othe hand, powe r control isej in adistribute fashion to dej the admissible powe r ve ifone ene that can be use bythe sche use to satisfy thei singlej transmissionrensmissi ts. This isdone for two type s ofne works, namej TDMA and TDMA/CDMA wire/CD adhocne works.
Resource allocation and crosslayer control in wireless networks
 Foundations and Trends in Networking
, 2006
"... Information flow in a telecommunication network is accomplished through the interaction of mechanisms at various design layers with the end goal of supporting the information exchange needs of the applications. In wireless networks in particular, the different layers interact in a nontrivial manner ..."
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Cited by 276 (59 self)
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Information flow in a telecommunication network is accomplished through the interaction of mechanisms at various design layers with the end goal of supporting the information exchange needs of the applications. In wireless networks in particular, the different layers interact in a nontrivial manner in order to support information transfer. In this text we will present abstract models that capture the crosslayer interaction from the physical to transport layer in wireless network architectures including cellular, adhoc and sensor networks as well as hybrid wirelesswireline. The model allows for arbitrary network topologies as well as traffic forwarding modes, including datagrams and virtual circuits. Furthermore the time varying nature of a wireless network, due either to fading channels or to changing connectivity due to mobility, is adequately captured in our model to allow for state dependent network control policies. Quantitative performance measures that capture the quality of service requirements in these systems depending on the supported applications are discussed, including throughput maximization, energy consumption minimization, rate utility function maximization as well as general performance functionals. Crosslayer control algorithms with optimal or suboptimal performance with respect to the above measures are presented and analyzed. A detailed exposition of the related analysis and design techniques is provided. 1
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 271 (23 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.
Multiaccess Fading Channels  Part I: Polymatroid Structure, Optimal Resource Allocation and Throughput Capacities
 IEEE Trans. Inform. Theory
"... In multiaccess wireless systems, dynamic allocation of resources such as transmit power, bandwidths, and rates is an important means to deal with the timevarying nature of the environment. In this twopart paper, we consider the problem of optimal resource allocation from an informationtheoretic p ..."
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Cited by 224 (10 self)
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In multiaccess wireless systems, dynamic allocation of resources such as transmit power, bandwidths, and rates is an important means to deal with the timevarying nature of the environment. In this twopart paper, we consider the problem of optimal resource allocation from an informationtheoretic point of view. We focus on the multiaccess fading channel with Gaussian noise, and define two notions of capacity depending on whether the traffic is delaysensitive or not. In part I, we characterize the throughput capacity region which contains the longterm achievable rates through the timevarying channel. We show that each point on the boundary of the region can be achieved by successive decoding. Moreover, the optimal rate and power allocations in each fading state can be explicitly obtained in a greedy manner. The solution can be viewed as the generalization of the waterfilling construction for singleuser channels to multiaccess channels with arbitrary number of users, and exploits the underlying polymatroid structure of the capacity region. In part II, we characterize a delaylimited capacity region and obtain analogous results.
Power Control for Wireless Data
 IEEE Personal Communications
, 2000
"... Abstract With cellular phones massmarket consumer items, the next frontier is mobile multimedia communications. This situation raises the question of how to do power control for information sources other than voice. To explore this issue, we use the concepts and mathematics of microeconomics and g ..."
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Cited by 213 (13 self)
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Abstract With cellular phones massmarket consumer items, the next frontier is mobile multimedia communications. This situation raises the question of how to do power control for information sources other than voice. To explore this issue, we use the concepts and mathematics of microeconomics and game theory. In this context, the Quality of Service of a telephone call is referred to as the "utility " and the distributed power control problem for a CDMA telephone is a "noncooperative game". The power control algorithm corresponds to a strategy that has a locally optimum operating point referred to as a "Nash equilibrium. " The telephone power control algorithm is also "Pareto efficient, " in the terminology of game theory. When we apply the same approach to power control in
A Tutorial on Decomposition Methods for Network Utility Maximization
 IEEE J. SEL. AREAS COMMUN
, 2006
"... A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison ..."
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Cited by 185 (4 self)
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A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison across architectural alternatives of modularized network design. Decomposition theory naturally provides the mathematical language to build an analytic foundation for the design of modularized and distributed control of networks. In this tutorial paper, we first review the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss–Seidel iterations, and implication of different time scales of variable updates. Then, we introduce primal, dual, indirect, partial, and hierarchical decompositions, focusing on network utility maximization problem formulations and the meanings of primal and dual decompositions in terms of network architectures. Finally, we present recent examples on: systematic search for alternative decompositions; decoupling techniques for coupled objective functions; and decoupling techniques for coupled constraint sets that are not readily decomposable.
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 176 (22 self)
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We present a gametheoretic treatment of distributed power control in CDMA wireless systems.
Linear precoding via conic optimization for fixed mimo receivers
 IEEE Trans. on Signal Processing
, 2006
"... We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two different design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maxi ..."
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Cited by 154 (3 self)
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We consider the problem of designing linear precoders for fixed multiple input multiple output (MIMO) receivers. Two different design criteria are considered. In the first, we minimize the transmitted power subject to signal to interference plus noise ratio (SINR) constraints. In the second, we maximize the worst case SINR subject to a power constraint. We show that both problems can be solved using standard conic optimization packages. In addition, we develop conditions for the optimal precoder for both of these problems, and propose two simple fixed point iterations to find the solutions which satisfy these conditions. The relation to the well known downlink uplink duality in the context of joint downlink beamforming and power control is also explored. Our precoder design is general, and as a special case it solves the beamforming problem. In contrast to most of the existing precoders, it is not limited to full rank systems. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders. 1