Equilibrium Efficiency Improvement in MIMO Interference Systems: A Decentralized Stream Control Approach

We consider a multi-link MIMO interference system in which each link wishes to maximize its own mutual information by choosing its own signal vector, which leads to a multi-player game. We show the existence of a Nash equilibrium and obtain sufficient conditions for the uniqueness of equilibrium. We consider two decentralized link adjustment algorithms called best-response process (a.k.a. iterative water- filling) and gradient-play (an autonomous and non-cooperative version of the well-known gradient ascent algorithm). Under our uniqueness conditions, we establish the convergence of these algorithms to the unique equilibrium provided that the links use some inertia. To improve the efficiency of an equilibrium with respect to the total mutual information by imposing limits on the number of independent data streams, we present a stream control approach using linear transformation of the link covariance matrices. We then show how to decentralize our stream control approach by allowing the links to negotiate the limits on the number of independent data streams that they are willing to impose upon themselves. To achieve this, we introduce a variation of a learning algorithm called "adaptive play" that has desirable convergence properties in potential games with reduced computation.