Competitive resource allocation in MIMO networks : a game-theoretic approach

The growing number of connected devices and machine-to-machine connections challenges the traditional orthogonal multiple access schemes for wireless communications. Simultaneously, the emergence of smart devices able to sense their environment and update their communications accordingly opens the way for decentralized solutions. This master thesis therefore analyzes the competitive allocation of radio resources in a point-to-point multi-antenna (MIMO) interfering network, for pairs of transmitter-receiver maximizing either their rate or their energy efficiency. The interaction between the competing users is modeled in the framework of game theory, each pair acting as a rational and intelligent player. The Nash equilibria of the considered games are studied on the one hand from the properties of contraction mappings, and on the other hand from the framework of (quasi)-variational inequalities. The best response dynamics is proven to converge towards a Nash equilibrium under conditions tightening existing ones in case of users maximizing their rate, while this work is the first to consider a point-to-point MIMO network with energy efficiency objectives. A novel framework, which we call pseudo-variational inequalities, is furthermore developed as well as associated unicity conditions. This theoretical analysis paves the way for fully decentralized resource allocation schemes in practical wireless networks.