Coalitional Games for Transmitter Cooperation in MIMO Multiple Access Channels

Cooperation between nodes sharing a wireless channel is becoming increasingly necessary to achieve performance goals in a wireless network. The problem of determining the feasibility and stability of cooperation between rational nodes in a wireless network is of great importance in understanding cooperative behavior. This paper addresses the stability of the grand coalition of transmitters signaling over a multiple access channel using the framework of cooperative game theory. The external interference experienced by each TX is represented accurately by modeling the cooperation game between the TXs in \emph{partition form}. Single user decoding and successive interference cancelling strategies are examined at the receiver. In the absence of coordination costs, the grand coalition is shown to be \emph{sum-rate optimal} for both strategies. Transmitter cooperation is \emph{stable}, if and only if the core of the game (the set of all divisions of grand coalition utility such that no coalition deviates) is nonempty. Determining the stability of cooperation is a co-NP-complete problem in general. For a single user decoding receiver, transmitter cooperation is shown to be \emph{stable} at both high and low SNRs, while for an interference cancelling receiver with a fixed decoding order, cooperation is stable only at low SNRs and unstable at high SNR. When time sharing is allowed between decoding orders, it is shown using an approximate lower bound to the utility function that TX cooperation is also stable at high SNRs. Thus, this paper demonstrates that ideal zero cost TX cooperation over a MAC is stable and improves achievable rates for each individual user.Comment: in review for publication in IEEE Transactions on Signal Processin

Coalitional Games in MISO Interference Channels: Epsilon-Core and Coalition Structure Stable Set

The multiple-input single-output interference channel is considered. Each transmitter is assumed to know the channels between itself and all receivers perfectly and the receivers are assumed to treat interference as additive noise. In this setting, noncooperative transmission does not take into account the interference generated at other receivers which generally leads to inefficient performance of the links. To improve this situation, we study cooperation between the links using coalitional games. The players (links) in a coalition either perform zero forcing transmission or Wiener filter precoding to each other. The $\epsilon$-core is a solution concept for coalitional games which takes into account the overhead required in coalition deviation. We provide necessary and sufficient conditions for the strong and weak $\epsilon$-core of our coalitional game not to be empty with zero forcing transmission. Since, the $\epsilon$-core only considers the possibility of joint cooperation of all links, we study coalitional games in partition form in which several distinct coalitions can form. We propose a polynomial time distributed coalition formation algorithm based on coalition merging and prove that its solution lies in the coalition structure stable set of our coalition formation game. Simulation results reveal the cooperation gains for different coalition formation complexities and deviation overhead models.Comment: to appear in IEEE Transactions on Signal Processing, 14 pages, 14 figures, 3 table

Coalitions in Cooperative Wireless Networks

Cooperation between rational users in wireless networks is studied using coalitional game theory. Using the rate achieved by a user as its utility, it is shown that the stable coalition structure, i.e., set of coalitions from which users have no incentives to defect, depends on the manner in which the rate gains are apportioned among the cooperating users. Specifically, the stability of the grand coalition (GC), i.e., the coalition of all users, is studied. Transmitter and receiver cooperation in an interference channel (IC) are studied as illustrative cooperative models to determine the stable coalitions for both flexible (transferable) and fixed (non-transferable) apportioning schemes. It is shown that the stable sum-rate optimal coalition when only receivers cooperate by jointly decoding (transferable) is the GC. The stability of the GC depends on the detector when receivers cooperate using linear multiuser detectors (non-transferable). Transmitter cooperation is studied assuming that all receivers cooperate perfectly and that users outside a coalition act as jammers. The stability of the GC is studied for both the case of perfectly cooperating transmitters (transferrable) and under a partial decode-and-forward strategy (non-transferable). In both cases, the stability is shown to depend on the channel gains and the transmitter jamming strengths.Comment: To appear in the IEEE Journal on Selected Areas in Communication, Special Issue on Game Theory in Communication Systems, 200

A Distributed Merge and Split Algorithm for Fair Cooperation in Wireless Networks

This paper introduces a novel concept from coalitional game theory which allows the dynamic formation of coalitions among wireless nodes. A simple and distributed merge and split algorithm for coalition formation is constructed. This algorithm is applied to study the gains resulting from the cooperation among single antenna transmitters for virtual MIMO formation. The aim is to find an ultimate transmitters coalition structure that allows cooperating users to maximize their utilities while accounting for the cost of coalition formation. Through this novel game theoretical framework, the wireless network transmitters are able to self-organize and form a structured network composed of disjoint stable coalitions. Simulation results show that the proposed algorithm can improve the average individual user utility by 26.4% as well as cope with the mobility of the distributed users.Comment: This paper is accepted for publication at the IEEE ICC Workshop on Cooperative Communications and Networkin

Improving Macrocell - Small Cell Coexistence through Adaptive Interference Draining

The deployment of underlay small base stations (SBSs) is expected to significantly boost the spectrum efficiency and the coverage of next-generation cellular networks. However, the coexistence of SBSs underlaid to an existing macro-cellular network faces important challenges, notably in terms of spectrum sharing and interference management. In this paper, we propose a novel game-theoretic model that enables the SBSs to optimize their transmission rates by making decisions on the resource occupation jointly in the frequency and spatial domains. This procedure, known as interference draining, is performed among cooperative SBSs and allows to drastically reduce the interference experienced by both macro- and small cell users. At the macrocell side, we consider a modified water-filling policy for the power allocation that allows each macrocell user (MUE) to focus the transmissions on the degrees of freedom over which the MUE experiences the best channel and interference conditions. This approach not only represents an effective way to decrease the received interference at the MUEs but also grants the SBSs tier additional transmission opportunities and allows for a more agile interference management. Simulation results show that the proposed approach yields significant gains at both macrocell and small cell tiers, in terms of average achievable rate per user, reaching up to 37%, relative to the non-cooperative case, for a network with 150 MUEs and 200 SBSs

Mathematical optimization and game theoretic techniques for multicell beamforming

The main challenge in mobile wireless communications is the incompatibility between limited wireless resources and increasing demand on wireless services. The employment of frequency reuse technique has effectively increased the capacity of the network and improved the efficiency of frequency utilization. However, with the emergence of smart phones and even more data hungry applications such as interactive multimedia, higher data rate is demanded by mobile users. On the other hand, the interference induced by spectrum sharing arrangement has severely degraded the quality of service for users and restricted further reduction of cell size and enhancement of frequency reuse factor. Beamforming technique has great potential to improve the network performance. With the employment of multiple antennas, a base station is capable of directionally transmitting signals to desired users through narrow beams rather than omnidirectional waves. This will result users suffer less interference from the signals transmitted to other co-channel users. In addition, with the combination of beamforming technique and appropriate power control schemes, the resources of the wireless networks can be used more efficiently. In this thesis, mathematical optimization and game theoretic techniques have been exploited for beamforming designs within the context of multicell wireless networks. Both the coordinated beamforming and the coalitional game theoretic based beamforming techniques have been proposed. Initially, coordinated multicell beamforming algorithms for mixed design criteria have been developed, in which some users are allowed to achieve target signal-to-interference- plus-noise ratios (SINRs) while the SINRs of rest of the users in all cells will be balanced to a maximum achievable SINR. An SINR balancing based coordinated multicell beamforming algorithm has then been proposed which is capable of balancing users in different cells to different SINR levels. Finally, a coalitional game based multicell beamforming has been considered, in which the proposed coalition formation algorithm can reach to stable coalition structures. The performances of all the proposed algorithms have been demonstrated using MATLAB based simulations

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

Coalitional Game Theory for Communication Networks: A Tutorial

Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and autonomic networks, it has become imperative to seek suitable game theoretical tools that allow to analyze and study the behavior and interactions of the nodes in future communication networks. In this context, this tutorial introduces the concepts of cooperative game theory, namely coalitional games, and their potential applications in communication and wireless networks. For this purpose, we classify coalitional games into three categories: Canonical coalitional games, coalition formation games, and coalitional graph games. This new classification represents an application-oriented approach for understanding and analyzing coalitional games. For each class of coalitional games, we present the fundamental components, introduce the key properties, mathematical techniques, and solution concepts, and describe the methodologies for applying these games in several applications drawn from the state-of-the-art research in communications. In a nutshell, this article constitutes a unified treatment of coalitional game theory tailored to the demands of communications and network engineers.Comment: IEEE Signal Processing Magazine, Special Issue on Game Theory, to appear, 2009. IEEE Signal Processing Magazine, Special Issue on Game Theory, to appear, 200

Cooperative Interference Alignment in Femtocell Networks

International audienceUnderlay femtocells have recently emerged as a key technology that can significantly improve the coverage and performance of next-generation wireless networks. In this paper, we propose a novel approach for interference management that enables a number of femtocells to cooperate and improve their downlink rate, by sharing spectral resources and suppressing intra-tier interference using interference alignment. We formulate a coalitional game in partition form among the femtocells and propose a distributed algorithm for coalition formation. Using our approach, the femtocell access points can make individual decisions on whether to cooperate or not, while maximizing a utility function that captures the cooperative gains and the costs in terms of transmit power for information exchange. We show that, using the proposed coalition formation algorithm, the femtocells can self-organize into a network partition composed of disjoint femtocell coalitions, which constitutes the recursive core of the game. Simulation results show significant gains in terms of average payoff per femtocell, reaching up to 30% relative to the non-cooperative scheme