## Optimal linear precoding strategies for wideband noncooperative systems based on game theory – Part II: Algorithms (2008)

Venue: | IEEE Trans. Signal Process |

Citations: | 29 - 3 self |

### BibTeX

@ARTICLE{Palomar08optimallinear,

author = {Gesualdo Scutari Daniel P. Palomar and Sergio Barbarossa},

title = {Optimal linear precoding strategies for wideband noncooperative systems based on game theory – Part II: Algorithms},

journal = {IEEE Trans. Signal Process},

year = {2008},

pages = {1250--1267}

}

### OpenURL

### Abstract

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,