Asynchronous Iterative Waterfilling for Gaussian Frequency-Selective Interference Channels

This paper considers the maximization of information rates for the Gaussian frequency-selective interference channel, subject to power and spectral mask constraints on each link. To derive decentralized solutions that do not require any cooperation among the users, the optimization problem is formulated as a static noncooperative game of complete information. To achieve the so-called Nash equilibria of the game, we propose a new distributed algorithm called asynchronous iterative waterfilling algorithm. In this algorithm, the users update their power spectral density in a completely distributed and asynchronous way: some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference. The proposed algorithm represents a unified framework that encompasses and generalizes all known iterative waterfilling algorithms, e.g., sequential and simultaneous versions. The main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the (unique) Nash equilibrium of the game.Comment: Submitted to IEEE Transactions on Information Theory, August 22, 2006. Revised September 25, 2007. Accepted January 14, 2008. To appear on IEEE Transactions on Information Theory, 200

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

Competitive Design of Multiuser MIMO Systems based on Game Theory: A Unified View

This paper considers the noncooperative maximization of mutual information in the Gaussian interference channel in a fully distributed fashion via game theory. This problem has been studied in a number of papers during the past decade for the case of frequency-selective channels. A variety of conditions guaranteeing the uniqueness of the Nash Equilibrium (NE) and convergence of many different distributed algorithms have been derived. In this paper we provide a unified view of the state-of-the-art results, showing that most of the techniques proposed in the literature to study the game, even though apparently different, can be unified using our recent interpretation of the waterfilling operator as a projection onto a proper polyhedral set. Based on this interpretation, we then provide a mathematical framework, useful to derive a unified set of sufficient conditions guaranteeing the uniqueness of the NE and the global convergence of waterfilling based asynchronous distributed algorithms. The proposed mathematical framework is also instrumental to study the extension of the game to the more general MIMO case, for which only few results are available in the current literature. The resulting algorithm is, similarly to the frequency-selective case, an iterative asynchronous MIMO waterfilling algorithm. The proof of convergence hinges again on the interpretation of the MIMO waterfilling as a matrix projection, which is the natural generalization of our results obtained for the waterfilling mapping in the frequency-selective case.Comment: To appear on IEEE Journal on Selected Areas in Communications (JSAC), September 200

Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems based on Game Theory-Part II: Algorithms

In this two-part paper, we address the problem of finding the optimal precoding/multiplexing scheme for a set of non-cooperative links sharing the same physical resources, e.g., time and bandwidth. We consider two alternative optimization problems: P.1) the maximization of mutual information on each link, given constraints on the transmit power and spectral mask; and P.2) the maximization of the transmission rate on each link, using finite order constellations, under the same constraints as in P.1, plus a constraint on the maximum average error probability on each link. Aiming at finding decentralized strategies, we adopted as optimality criterion the achievement of a Nash equilibrium and thus we formulated both problems P.1 and P.2 as strategic noncooperative (matrix-valued) games. In Part I of this two-part paper, after deriving the optimal structure of the linear transceivers for both games, we provided a unified set of sufficient conditions that guarantee the uniqueness of the Nash equilibrium. In this Part II, we focus on the achievement of the equilibrium and propose alternative distributed iterative algorithms that solve both games. Specifically, the new proposed algorithms are the following: 1) the sequential and simultaneous iterative waterfilling based algorithms, incorporating spectral mask constraints; 2) the sequential and simultaneous gradient projection based algorithms, establishing an interesting link with variational inequality problems. Our main contribution is to provide sufficient conditions for the global convergence of all the proposed algorithms which, although derived under stronger constraints, incorporating for example spectral mask constraints, have a broader validity than the convergence conditions known in the current literature for the sequential iterative waterfilling algorithm.Comment: Paper submitted to IEEE Transactions on Signal Processing, February 22, 2006. Revised March 26, 2007. Accepted June 5, 2007. To appear on IEEE Transactions on Signal Processing, 200

Robust game-theoretic algorithms for distributed resource allocation in wireless communications

The predominant game-theoretic solutions for distributed rate-maximization algorithms in Gaussian interference channels through optimal power control require perfect channel knowledge, which is not possible in practice due to various reasons, such as estimation errors, feedback quantization and latency between channel estimation and signal transmission. This thesis therefore aims at addressing this issue through the design and analysis of robust gametheoretic algorithms for rate-maximization in Gaussian interference channels in the presence of bounded channel uncertainty. A robust rate-maximization game is formulated for the single-antenna frequency-selective Gaussian interference channel under bounded channel uncertainty. The robust-optimization equilibrium solution for this game is independent of the probability distribution of the channel uncertainty. The existence and uniqueness of the equilibrium are studied and sufficient conditions for the uniqueness of the equilibrium are provided. Distributed algorithms to compute the equilibrium solution are presented and shown to have guaranteed asymptotic convergence when the game has a unique equilibrium. The sum-rate and the price of anarchy at the equilibrium of this game are analyzed for the two-user scenario and shown to improve with increase in channel uncertainty under certain conditions. These results indicate that the robust solution moves closer to a frequency division multiple access (FDMA) solution when uncertainty increases. This leads to a higher sum-rate and a lower price of anarchy for systems where FDMA is globally optimal. A robust rate-maximization game for multi-antenna Gaussian interference channels in the presence of channel uncertainty is also developed along similar principles. It is shown that this robust game is equivalent to the nominal game with modified channel matrices. The robust-optimization equilibrium for this game and a distributed algorithm for its computation are presented and characterized. Sufficient conditions for the uniqueness of the equilibrium and asymptotic convergence of the algorithm are presented. Numerical simulations are used to confirm the behaviour of these algorithms. The analytical and numerical results of this thesis indicate that channel uncertainty is not necessarily detrimental, but can indeed result in improvement of performance of networks in particular situations, where the Nash equilibrium solution is quite inefficient and channel uncertainty leads to reduced greediness of users.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A game-theoretic approach to transmitter covariance matrix design for broadband MIMO Gaussian interference channels

A game-theoretic approach to transmitter covariance matrix design for broadband MIMO Gaussian interference channels Anandkumar, A.J.G. Lambotharan, S. Chambers, J.A. Dept of Electron. & Electr. Eng., Loughborough Univ., Loughborough, UK This paper appears in: Statistical Signal Processing, 2009. SSP '09. IEEE/SP 15th Workshop on Publication Date: Aug. 31 2009-Sept. 3 2009 On page(s): 301 - 304 E-ISBN: 978-1-4244-2711-6 Location: Cardiff ISBN: 978-1-4244-2709-3 INSPEC Accession Number:10961923 Digital Object Identifier: 10.1109/SSP.2009.5278580 Current Version Published: 2009-10-06 Abstract A game-theoretic approach to the maximization of the information rates of broadband multi-input-multi-output (MIMO) Gaussian interference channels is proposed. The problem is cast as a strategic noncooperative game with the MIMO links as players and the information rates as payoff functions. The Nash equilibrium solution of this game is a waterfilling operation and sufficient conditions for its existence and uniqueness are presented. A distributed algorithm which requires no cooperation among the users is presented along with conditions for guaranteed global convergence of the proposed algorithm. The efficacy of the proposed scheme is confirmed through a design example

Real and Complex Monotone Communication Games

Noncooperative game-theoretic tools have been increasingly used to study many important resource allocation problems in communications, networking, smart grids, and portfolio optimization. In this paper, we consider a general class of convex Nash Equilibrium Problems (NEPs), where each player aims to solve an arbitrary smooth convex optimization problem. Differently from most of current works, we do not assume any specific structure for the players' problems, and we allow the optimization variables of the players to be matrices in the complex domain. Our main contribution is the design of a novel class of distributed (asynchronous) best-response- algorithms suitable for solving the proposed NEPs, even in the presence of multiple solutions. The new methods, whose convergence analysis is based on Variational Inequality (VI) techniques, can select, among all the equilibria of a game, those that optimize a given performance criterion, at the cost of limited signaling among the players. This is a major departure from existing best-response algorithms, whose convergence conditions imply the uniqueness of the NE. Some of our results hinge on the use of VI problems directly in the complex domain; the study of these new kind of VIs also represents a noteworthy innovative contribution. We then apply the developed methods to solve some new generalizations of SISO and MIMO games in cognitive radios and femtocell systems, showing a considerable performance improvement over classical pure noncooperative schemes.Comment: to appear on IEEE Transactions in Information Theor

Distributed Power Control in Multiuser MIMO Networks with Optimal Linear Precoding

Contractive interference functions introduced by Feyzmahdavian et al. is the newest approach in the analysis and design of distributed power control laws. This approach can be extended to several cases of distributed power control. One of the distributed power control scenarios wherein the contractive interference functions have not been employed is the power control in MIMO systems. In this paper, this scenario will be analyzed. In addition, the optimal linear precoder is employed in each user to achieve maximum point-to-point information rate. In our approach, we use the same amount of signaling as the previous methods did. However, we show that the uniqueness of Nash equilibria is more probable in our approach, suggesting that our proposed method improves the convergence performance of distributed power control in MIMO systems. We also show that the proposed power control algorithm can be implemented asynchronously, which gives a noticeable flexibility to our algorithm given the practical communication limitations.Comment: 6 pages, 3 figures, Presented in 7th International Symposium on Telecommunications (IST 2014