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 noncooperative links sharing the same physical resources, e.g., time and bandwidth. We consider two alternative optimization problems: P.l) the maximization of mutual information on each...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 56; no. 3; pp. 1250 - 1267
Main Authors: Scutari, G., Palomar, D.P., Barbarossa, S.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.03.2008
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Bandwidth
Coding, codes
Competitive optimality
Constraint optimization
Convergence
distributed algorithms
Economic models
Error probability
Exact sciences and technology
Game theory
Information, signal and communications theory
Iterative algorithms
iterative waterfilling
Miscellaneous
Multiplexing
Mutual information
Nash equilibrium
Signal and communications theory
Signal processing
Studies
Sufficient conditions
Telecommunications and information theory
Wideband
Multiplexing
Error probability
Nash equilibrium
Iterative method
Optimization
Transceiver
Optimal strategy
Wide band
iterative waterfilling
Coding
Sequential method
Optimal planning
Gradient method
Competitive optimality
Cooperative systems
Game theory
Sufficient condition
Decentralized system
distributed algorithms
Distributed algorithm
Signal processing
Optimality criterion
Transmission rate
Mutual information
Power spectrum
ISSN:1053-587X, 1941-0476
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this two-part paper, we address the problem of finding the optimal precoding/multiplexing scheme for a set of noncooperative links sharing the same physical resources, e.g., time and bandwidth. We consider two alternative optimization problems: P.l) 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.l, 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.l 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 of the paper, 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 and 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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
content type line 23
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2007.907808