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...

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Vydané v:	IEEE transactions on signal processing Ročník 56; číslo 3; s. 1250 - 1267
Hlavní autori:	Scutari, G., Palomar, D.P., Barbarossa, S.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY IEEE 01.03.2008 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	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
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Popis
Shrnutí:	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.
Bibliografia:	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