The MIMO Iterative Waterfilling Algorithm

This paper considers the non-cooperative maximization of mutual information in the vector Gaussian interference channel in a fully distributed fashion via game theory. This problem has been widely studied in a number of works during the past decade for frequency-selective channels, and recently for the more general MIMO case, for which the state-of-the art results are valid only for nonsingular square channel matrices. Surprisingly, these results do not hold true when the channel matrices are rectangular and/or rank deficient matrices. The goal of this paper is to provide a complete characterization of the MIMO game for arbitrary channel matrices, in terms of conditions guaranteeing both the uniqueness of the Nash equilibrium and the convergence of asynchronous distributed iterative waterfilling algorithms. Our analysis hinges on new technical intermediate results, such as a new expression for the MIMO waterfilling projection valid (also) for singular matrices, a mean-value theorem for complex matrix-valued functions, and a general contraction theorem for the multiuser MIMO watefilling mapping valid for arbitrary channel matrices. The quite surprising result is that uniqueness/convergence conditions in the case of tall (possibly singular) channel matrices are more restrictive than those required in the case of (full rank) fat channel matrices. We also propose a modified game and algorithm with milder conditions for the uniqueness of the equilibrium and convergence, and virtually the same performance (in terms of Nash equilibria) of the original game.Comment: IEEE Transactions on Signal Processing (accepted

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201

Game theoretic aspects of distributed spectral coordination with application to DSL networks

In this paper we use game theoretic techniques to study the value of cooperation in distributed spectrum management problems. We show that the celebrated iterative water-filling algorithm is subject to the prisoner's dilemma and therefore can lead to severe degradation of the achievable rate region in an interference channel environment. We also provide thorough analysis of a simple two bands near-far situation where we are able to provide closed form tight bounds on the rate region of both fixed margin iterative water filling (FM-IWF) and dynamic frequency division multiplexing (DFDM) methods. This is the only case where such analytic expressions are known and all previous studies included only simulated results of the rate region. We then propose an alternative algorithm that alleviates some of the drawbacks of the IWF algorithm in near-far scenarios relevant to DSL access networks. We also provide experimental analysis based on measured DSL channels of both algorithms as well as the centralized optimum spectrum management

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 Game-Theoretic View of the Interference Channel: Impact of Coordination and Bargaining

This work considers coordination and bargaining between two selfish users over a Gaussian interference channel. The usual information theoretic approach assumes full cooperation among users for codebook and rate selection. In the scenario investigated here, each user is willing to coordinate its actions only when an incentive exists and benefits of cooperation are fairly allocated. The users are first allowed to negotiate for the use of a simple Han-Kobayashi type scheme with fixed power split. Conditions for which users have incentives to cooperate are identified. Then, two different approaches are used to solve the associated bargaining problem. First, the Nash Bargaining Solution (NBS) is used as a tool to get fair information rates and the operating point is obtained as a result of an optimization problem. Next, a dynamic alternating-offer bargaining game (AOBG) from bargaining theory is introduced to model the bargaining process and the rates resulting from negotiation are characterized. The relationship between the NBS and the equilibrium outcome of the AOBG is studied and factors that may affect the bargaining outcome are discussed. Finally, under certain high signal-to-noise ratio regimes, the bargaining problem for the generalized degrees of freedom is studied.Comment: 43 pages, 11 figures, to appear on Special Issue of the IEEE Transactions on Information Theory on Interference Networks, 201

Alternating-Offer Bargaining Games over the Gaussian Interference Channel

This paper tackles the problem of how two selfish users jointly determine the operating point in the achievable rate region of a two-user Gaussian interference channel through bargaining. In previous work, incentive conditions for two users to cooperate using a simple version of Han-Kobayashi scheme was studied and the Nash bargaining solution (NBS) was used to obtain a fair operating point. Here a noncooperative bargaining game of alternating offers is adopted to model the bargaining process and rates resulting from the equilibrium outcome are analyzed. In particular, it is shown that the operating point resulting from the formulated bargaining game depends on the cost of delay in bargaining and how bargaining proceeds. If the associated bargaining problem is regular, a unique perfect equilibrium exists and lies on the individual rational efficient frontier of the achievable rate region. Besides, the equilibrium outcome approaches the NBS if the bargaining costs of both users are negligible.Comment: 8 pages, 6 figures, to appear in Proceedings of Forty-Eighth Annual Allerton Conference on Communication, Control, and Computin