795 research outputs found
Optimal Linear Precoding Strategies for Wideband Non-Cooperative Systems based on Game Theory-Part I: Nash Equilibria
In this two-parts paper we propose a decentralized strategy, based on a
game-theoretic formulation, to find out the optimal precoding/multiplexing
matrices for a multipoint-to-multipoint 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 matrix-valued 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, incorporating for example spectral mask constraints, our
uniqueness conditions have broader validity than previously known conditions.
Finally, we assess the goodness of the proposed decentralized strategy by
comparing its performance with the performance of a Pareto-optimal centralized
scheme. To reach the Nash equilibria of the game, in Part II, we propose
alternative distributed algorithms, along with their convergence conditions.Comment: Paper submitted to IEEE Transactions on Signal Processing, September
22, 2005. Revised March 14, 2007. Accepted June 5, 2007. To be published on
IEEE Transactions on Signal Processing, 2007. To appear on IEEE Transactions
on Signal Processing, 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
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
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
Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems
We propose a novel decomposition framework for the distributed optimization
of general nonconvex sum-utility functions arising naturally in the system
design of wireless multiuser interfering systems. Our main contributions are:
i) the development of the first class of (inexact) Jacobi best-response
algorithms with provable convergence, where all the users simultaneously and
iteratively solve a suitably convexified version of the original sum-utility
optimization problem; ii) the derivation of a general dynamic pricing mechanism
that provides a unified view of existing pricing schemes that are based,
instead, on heuristics; and iii) a framework that can be easily particularized
to well-known applications, giving rise to very efficient practical (Jacobi or
Gauss-Seidel) algorithms that outperform existing adhoc methods proposed for
very specific problems. Interestingly, our framework contains as special cases
well-known gradient algorithms for nonconvex sum-utility problems, and many
blockcoordinate descent schemes for convex functions.Comment: submitted to IEEE Transactions on Signal Processin
Inclusion of a Parental Component in a Sports-Based HIV Prevention Program for Dominican Youth
Background: Underprivileged youth in the Dominican Republic (DR) are at high risk of acquiring the human immunodeficiency virus (HIV). Protective parenting practices may inhibit sexual risk-taking. Objective: We investigated whether parental involvement in a sports-based HIV prevention program increased self-efficacy to prevent HIV and safe sex behavior among Dominican youth. Method: The study had a quasi-experimental design with repeated measures. N = 90 participants between 13 and 24 years of age participated in the program through two different trainings, UNICA and A Ganar, both of which had an experimental (i.e., program with parental component) and a control (i.e., program without parental component) condition. Results: Self-efficacy to prevent HIV significantly increased among participants in the experimental condition of UNICA. Self-efficacy for safe sex increased among sexually active participants in the experimental condition of A Ganar. Implications for Impact: These findings are important to meet the United Nations’ Sustainable Development Goal of good health and wellbeing, as they suggest that parental involvement in sports-based HIV prevention programs can enhance their positive effects for increasing youth’s self-efficacy to practice HIV-preventive behaviors. Randomized control trials and longitudinal studies are needed.</p
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
Cognitive MIMO Radio: A Competitive Optimality Design Based on Subspace Projections
Cognitive MIMO Radio: A Competitive Optimality Design Based on Subspace
Projection
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
- …