Non-cooperative Feedback Rate Control Game for Channel State Information in Wireless Networks

It has been well recognized that channel state information (CSI) feedback is of great importance for dowlink transmissions of closed-loop wireless networks. However, the existing work typically researched the CSI feedback problem for each individual mobile station (MS), and thus, cannot efficiently model the interactions among self-interested mobile users in the network level. To this end, in this paper, we propose an alternative approach to investigate the CSI feedback rate control problem in the analytical setting of a game theoretic framework, in which a multiple-antenna base station (BS) communicates with a number of co-channel MSs through linear precoder. Specifically, we first present a non-cooperative feedback-rate control game (NFC), in which each MS selects the feedback rate to maximize its performance in a distributed way. To improve efficiency from a social optimum point of view, we then introduce pricing, called the non-cooperative feedback-rate control game with price (NFCP). The game utility is defined as the performance gain by CSI feedback minus the price as a linear function of the CSI feedback rate. The existence of the Nash equilibrium of such games is investigated, and two types of feedback protocols (FDMA and CSMA) are studied. Simulation results show that by adjusting the pricing factor, the distributed NFCP game results in close optimal performance compared with that of the centralized scheme.Comment: 26 pages, 10 figures; IEEE Journal on Selected Areas in Communications, special issue on Game Theory in Wireless Communications, 201

Truthful Mechanisms for Secure Communication in Wireless Cooperative System

To ensure security in data transmission is one of the most important issues for wireless relay networks, and physical layer security is an attractive alternative solution to address this issue. In this paper, we consider a cooperative network, consisting of one source node, one destination node, one eavesdropper node, and a number of relay nodes. Specifically, the source may select several relays to help forward the signal to the corresponding destination to achieve the best security performance. However, the relays may have the incentive not to report their true private channel information in order to get more chances to be selected and gain more payoff from the source. We propose a Vickey-Clark-Grove (VCG) based mechanism and an Arrow-d'Aspremont-Gerard-Varet (AGV) based mechanism into the investigated relay network to solve this cheating problem. In these two different mechanisms, we design different "transfer payment" functions to the payoff of each selected relay and prove that each relay gets its maximum (expected) payoff when it truthfully reveals its private channel information to the source. And then, an optimal secrecy rate of the network can be achieved. After discussing and comparing the VCG and AGV mechanisms, we prove that the AGV mechanism can achieve all of the basic qualifications (incentive compatibility, individual rationality and budget balance) for our system. Moreover, we discuss the optimal quantity of relays that the source node should select. Simulation results verify efficiency and fairness of the VCG and AGV mechanisms, and consolidate these conclusions.Comment: To appear in IEEE Transactions on Wireless Communication

Game Theory and Microeconomic Theory for Beamforming Design in Multiple-Input Single-Output Interference Channels

In interference-limited wireless networks, interference management techniques are important in order to improve the performance of the systems. Given that spectrum and energy are scarce resources in these networks, techniques that exploit the resources efficiently are desired. We consider a set of base stations operating concurrently in the same spectral band. Each base station is equipped with multiple antennas and transmits data to a single-antenna mobile user. This setting corresponds to the multiple-input single-output (MISO) interference channel (IFC). The receivers are assumed to treat interference signals as noise. Moreover, each transmitter is assumed to know the channels between itself and all receivers perfectly. We study the conflict between the transmitter-receiver pairs (links) using models from game theory and microeconomic theory. These models provide solutions to resource allocation problems which in our case correspond to the joint beamforming design at the transmitters. Our interest lies in solutions that are Pareto optimal. Pareto optimality ensures that it is not further possible to improve the performance of any link without reducing the performance of another link. Strategic games in game theory determine the noncooperative choice of strategies of the players. The outcome of a strategic game is a Nash equilibrium. While the Nash equilibrium in the MISO IFC is generally not efficient, we characterize the necessary null-shaping constraints on the strategy space of each transmitter such that the Nash equilibrium outcome is Pareto optimal. An arbitrator is involved in this setting which dictates the constraints at each transmitter. In contrast to strategic games, coalitional games provide cooperative solutions between the players. We study cooperation between the links via coalitional games without transferable utility. Cooperative beamforming schemes considered are either zero forcing transmission or Wiener filter precoding. We characterize the necessary and sufficient conditions under which the core of the coalitional game with zero forcing transmission is not empty. The core solution concept specifies the strategies with which all players have the incentive to cooperate jointly in a grand coalition. While the core only considers the formation of the grand coalition, coalition formation games study coalition dynamics. We utilize a coalition formation algorithm, called merge-and-split, to determine stable link grouping. Numerical results show that while in the low signal-to-noise ratio (SNR) regime noncooperation between the links is efficient, at high SNR all links benefit in forming a grand coalition. Coalition formation shows its significance in the mid SNR regime where subset link cooperation provides joint performance gains. We use the models of exchange and competitive market from microeconomic theory to determine Pareto optimal equilibria in the two-user MISO IFC. In the exchange model, the links are represented as consumers that can trade goods within themselves. The goods in our setting correspond to the parameters of the beamforming vectors necessary to achieve all Pareto optimal points in the utility region. We utilize the conflict representation of the consumers in the Edgeworth box, a graphical tool that depicts the allocation of the goods for the two consumers, to provide closed-form solution to all Pareto optimal outcomes. The exchange equilibria are a subset of the points on the Pareto boundary at which both consumers achieve larger utility then at the Nash equilibrium. We propose a decentralized bargaining process between the consumers which starts at the Nash equilibrium and ends at an outcome arbitrarily close to an exchange equilibrium. The design of the bargaining process relies on a systematic study of the allocations in the Edgeworth box. In comparison to the exchange model, a competitive market additionally defines prices for the goods. The equilibrium in this economy is called Walrasian and corresponds to the prices that equate the demand to the supply of goods. We calculate the unique Walrasian equilibrium and propose a coordination process that is realized by the arbitrator which distributes the Walrasian prices to the consumers. The consumers then calculate in a decentralized manner their optimal demand corresponding to beamforming vectors that achieve the Walrasian equilibrium. This outcome is Pareto optimal and lies in the set of exchange equilibria. In this thesis, based on the game theoretic and microeconomic models, efficient beamforming strategies are proposed that jointly improve the performance of the systems. The gained results are applicable in interference-limited wireless networks requiring either coordination from the arbitrator or direct cooperation between the transmitters