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159
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 29 (3 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,
Maximizing Capacity in Arbitrary Wireless Networks in the SINR Model: Complexity and Game Theory
"... Abstract—In this paper we consider the problem of maximizing the number of supported connections in arbitrary wireless networks where a transmission is supported if and only if the signaltointerferenceplusnoise ratio at the receiver is greater than some threshold. The aim is to choose transmissi ..."
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Cited by 28 (2 self)
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Abstract—In this paper we consider the problem of maximizing the number of supported connections in arbitrary wireless networks where a transmission is supported if and only if the signaltointerferenceplusnoise ratio at the receiver is greater than some threshold. The aim is to choose transmission powers for each connection so as to maximize the number of connections for which this threshold is met. We believe that analyzing this problem is important both in its own right and also because it arises as a subproblem in many other areas of wireless networking. We study both the complexity of the problem and also present some game theoretic results regarding capacity that is achieved by completely distributed algorithms. We also feel that this problem is intriguing since it involves both continuous aspects (i.e. choosing the transmission powers) as well as discrete aspects (i.e. which connections should be supported).
Methodologies for analyzing equilibria in wireless games
 IEEE Signal Processing Magazine, Special issue on Game Theory for Signal Processing
, 2009
"... Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure s ..."
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Cited by 27 (16 self)
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Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure such states at which the network will effectively operate. In this article, we provide nonexhaustive methodologies for characterizing equilibria in wireless games in terms of existence, uniqueness, selection and efficiency.
Pricebased spectrum management in cognitive radio networks
 Selected Topics in Signal Processing
, 2008
"... Abstract — Cognitive radios (CRs) have a great potential to improve spectrum utilization by enabling users to access the spectrum dynamically without disturbing licensed primary radios (PRs). A key challenge in operating these radios as a network is how to implement an efficient medium access contro ..."
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Cited by 27 (2 self)
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Abstract — Cognitive radios (CRs) have a great potential to improve spectrum utilization by enabling users to access the spectrum dynamically without disturbing licensed primary radios (PRs). A key challenge in operating these radios as a network is how to implement an efficient medium access control (MAC) mechanism that can adaptively and efficiently allocate transmission powers and spectrum among CRs according to the surrounding environment. Most existing works address this issue via suboptimal heuristic approaches or centralized solutions. In this paper, we propose a novel joint power/channel allocation scheme that improves the performance through a distributed pricing approach. In this scheme, the spectrum allocation problem is modeled as a noncooperative game, with each CR pair acting as a player. A pricebased iterative waterfilling (PIWF) algorithm is proposed, which enables CR users to reach a good Nash equilibrium (NE). This PIWF algorithm can be implemented distributively with CRs repeatedly negotiating their best transmission powers and spectrum. Simulation results show that the social optimality of the NE solution is dramatically improved through pricing. Depending on the different orders according to which CRs take actions, we study sequential and parallel versions of the PIWF algorithm. We show that the parallel version converges faster than the sequential version. We then propose a corresponding MAC protocol to implement our resource management schemes. The proposed MAC allows multiple CR pairs to be first involved in an admission phase, then iteratively negotiate their transmission powers and spectrum via controlpacket exchanges. Following the negotiation phase, CRs proceed concurrently with their data transmissions. Simulations are used to study the performance of our protocol and demonstrate its effectiveness in terms of improving the overall network throughput and reducing the average power consumption. I.
Resource Control for Elastic Traffic in CDMA Networks
 Proceedings of MOBICOM’02
, 2002
"... We present a framework for resource control in CDMA networks carrying elastic tra#c, considering both the uplink and the downlink direction. The framework is based on microeconomics and congestion pricing, and seeks to exploit the joint control of the transmission rate and the signal quality in orde ..."
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Cited by 26 (6 self)
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We present a framework for resource control in CDMA networks carrying elastic tra#c, considering both the uplink and the downlink direction. The framework is based on microeconomics and congestion pricing, and seeks to exploit the joint control of the transmission rate and the signal quality in order to achieve e#cient utilization of network resources, in a distributed and decentralized manner. An important feature of the framework is that it incorporates both the congestion for shared resources in wireless and wired networks, and the cost of battery power at mobile hosts. We prove that for elastic tra#c, where users value only their average throughput, the user's net utility maximization problem can be decomposed into two simpler problems: one involving the selection of the optimal signal quality, and one involving the selection of the optimal transmission rate. Based on this result, the selection of signal quality can be performed as done today using outer loop power control, while rate adaptation can be integrated with rate adaptation at the transport layer.
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 23 (6 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.
Distributed relay selection and power Control for multiuser cooperative communication networks using stackelberg game
 IEEE Trans. on Mobile Computing
, 2009
"... Abstract — The performances in cooperative communications depend on careful resource allocation such as relay selection and power control, but traditional centralized resource allocation needs considerable overhead and signaling to exchange the information for channel estimations. In this paper, we ..."
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Cited by 20 (5 self)
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Abstract — The performances in cooperative communications depend on careful resource allocation such as relay selection and power control, but traditional centralized resource allocation needs considerable overhead and signaling to exchange the information for channel estimations. In this paper, we propose a distributed buyer/seller game theoretic framework over multiuser cooperative communication networks to stimulate cooperation and improve the system performance. By employing a twolevel game to jointly consider the benefits of source nodes as buyers and relay nodes as sellers, the proposed approach not only helps the source smartly find the relays at relatively better locations and buy optimal amount of power from them, but also helps the competing relays maximize their own utilities by asking the reasonable prices. The game is proved to converge to a unique optimal equilibrium. From the simulation results, the relays in good locations can play more important roles in increasing source node’s utility, so the source would like to buy more power from these preferred relays. On the other hand, the relays have to set the proper prices to attract the source’s buying because of competition from other relays and selections from the source. Moreover, the distributed game resource allocation can achieve comparable performance compared with the centralized one. I.
Distributed opportunistic scheduling for ad hoc communications with imperfect channel information,” Submitted to
 V. CONCLUSION In
"... Abstract — Distributed opportunistic scheduling is studied for wireless adhoc networks, where many links contend for one channel using random access. In such networks, distributed opportunistic scheduling (DOS) involves a process of joint channel probing and distributed scheduling. It has been show ..."
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Cited by 19 (7 self)
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Abstract — Distributed opportunistic scheduling is studied for wireless adhoc networks, where many links contend for one channel using random access. In such networks, distributed opportunistic scheduling (DOS) involves a process of joint channel probing and distributed scheduling. It has been shown that under perfect channel estimation, the optimal DOS for maximizing the network throughput is a pure threshold policy. In this paper, this formalism is generalized to explore DOS under noisy channel estimation, where the transmission rate needs to be backed off from the estimated rate to reduce the outage. It is shown that the optimal scheduling policy remains to be thresholdbased, and that the rate threshold turns out to be a function of the variance of the estimation error and be a functional of the backoff rate function. Since the optimal backoff rate is intractable, a suboptimal linear backoff scheme that backs off the estimated signaltonoise ratio (SNR) and hence the rate is proposed. The corresponding optimal backoff ratio and rate threshold can be obtained via an iterative algorithm. Finally, simulation results are provided to illustrate the tradeoff caused by increasing training time to improve channel estimation at the cost of probing efficiency. I.
ARC: An Integrated Admission and Rate Control Framework for CDMA Data Networks Based on Noncooperative Games
, 2003
"... The competition among wireless data service providers brings in an option for the customers to switch their providers, due to unsatisfactory service or otherwise. However, the existing resource management algorithms for wireless networks fail to fully capture the farreaching impact of this competit ..."
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Cited by 18 (6 self)
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The competition among wireless data service providers brings in an option for the customers to switch their providers, due to unsatisfactory service or otherwise. However, the existing resource management algorithms for wireless networks fail to fully capture the farreaching impact of this competitiveness. From this perspective, we propose an integrated admission and rate control (ARC) framework for CDMA based wireless data networks. The admission control is at the session (macro) level while the rate control is at the link layer packet (micro) level. The ARC framework is based on a novel game theoretic formulation which defines noncooperative games between the service providers and the customers. A user’s decision to leave or join a provider is based on a finite set of strategies. A service provider can also construct its game strategy set so as to maximize the utility (revenue) yet attaining
Improved results for Stackelberg scheduling strategies
 Proc. 29th ICALP
, 2002
"... We continue the study initiated in [Ro01] on Stackelberg Scheduling Strategies. We are given a set of ¡ independent parallel machines or equivalently a set of ¡ parallel edges on which certain flow has to be sent. Each edge ¢ is endowed with a latency function £¥¤§¦© ¨ �. The setting is that of a n ..."
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Cited by 17 (0 self)
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We continue the study initiated in [Ro01] on Stackelberg Scheduling Strategies. We are given a set of ¡ independent parallel machines or equivalently a set of ¡ parallel edges on which certain flow has to be sent. Each edge ¢ is endowed with a latency function £¥¤§¦© ¨ �. The setting is that of a noncooperative game: players choose edges so as minimize their individual latencies. Additionally, there is a single player who control as fraction � of the total flow. The goal is to find a strategy for the leader (i.e. an assignment of flow to indivual links) such that the selfish users react so as to minimize the total latency of the system. Building on the recent results in [Ro01, RT00], we show the following: 1. We devise a fully polynomial approximate Stackelberg scheme: given a performance ¦©������ � requirement, the stackelberg scheme runs in time polynomial ¡ in and and produces an assignment of flows such that the cost of the induced Nash equilibrium is within a ����� factor of the optimum stackelberg �§ � strategy. The result is extended to obtain a polynomialapproximation scheme when instances are restricted to layered directed graphs in which each layer has a bounded number of vertices. 2. We then consider a two round Stackelberg strategy (denoted 2SS). In this strategy, the game consists of three rounds: a move by the leader followed by the moves of all the followers folowed again by a move by the leader who possibly reassigns some of the flows. We show that 2SS always dominates the one round scheme, and for some classes of latency functions, is guaranteed to be closer to the global social optimum. We also consider the variant where the leader plays after the selfish users have routed themselves, and observe that this dominates the oneround scheme. Extensions of the results to the special case when all the latency functions are linear are also presented. Our results extend the earlier results and answer an open question posed by Roughgarden [Ro01].