Competitive Design of Multiuser MIMO Systems based on Game Theory: A Unified View

TL;DR

This paper unifies and extends game-theoretic approaches to multiuser MIMO systems, providing a mathematical framework that guarantees the uniqueness of Nash Equilibria and convergence of distributed algorithms, including in the more complex MIMO case.

Contribution

It offers a unified interpretation of waterfilling as a projection, enabling a general framework for analyzing convergence and uniqueness in multiuser MIMO game-theoretic systems.

Findings

Unified framework for frequency-selective and MIMO channels

Conditions guaranteeing Nash Equilibrium uniqueness

Convergence proofs for distributed waterfilling algorithms

Abstract

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.