Optimal Linear Precoding Strategies for Wideband Noncooperative Systems Based on Game Theory—Part I: Nash Equilibria

By Gesualdo Scutari, D. P. Palomar, Sergio Barbarossa. IEEE Transactions on Signal Processing, 2007

300 citations recorded by the source corpus.

In this two-part 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 this first part 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.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/8129c109ac21be98ea4a73dbdbe95b0482eea43c

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Citations in the corpus

Competition Versus Cooperation on the MISO Interference Channel (2008, background): “The MIMO IFC has also been studied from a noncooperative game-theoretic perspective in [13] and [14], which presented results on equilibrium rates and proposed distributed algorithms.”
Learning to Optimize: Training Deep Neural Networks for Interference Management (2017, unknown): “dressing wireless resource management problems. Well-known optimization-based algorithms for such purposes include those developed for power control (e.g., iterative water-ﬁlling type algorithms [4], [5], interference pricing [6], SCALE [7]), transmit/receive beamformer design (e.g., the WMMSE algor”
A Distributed, Asynchronous and Incremental Algorithm for Nonconvex Optimization: An ADMM Based Approach (2014, background): “In [5], [6], the authors show that the well-known iterative water-ﬁlling algorithm [8], [9] can be implemented in a totally asynchronous manner, as long as the interference among the users are weak enough.”
Game Theory in Wireless and Communication Networks (2008, unknown): “The proof is based on the KKT condition [431, 139].”
Learning to optimize: Training deep neural networks for wireless resource management (2017, methodology): “…optimization-based algorithms for such purposes include those developed for power control (e.g., iterative water-ﬁlling type algorithms [3], [4], interference pricing [5], SCALE [6]), transmit/receive beamformer design (e.g., the WMMSE algorithm [7], pricing-based schemes [8], semideﬁnite…”
Convex Optimization in Signal Processing and Communications (2009, background): “When problem (1.1) is not separable, dual decomposition approach will not lead to distributed methods.”