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Power games in MIMO interference systems

We consider a multi-link and multi-input-multi-output (MIMO) interference system in which each link wishes to minimize its own power by choosing its own signal vector subject to an information theoretic Quality-of-Service (QoS) requirement. Our setup leads to a multi-link game, referred to as a “power game”, in which the feasible strategy set of an individual link depends on the strategies of the other links. We characterize the rates for which an equilibrium solution exists in a power game in terms of the equilibria of “capacity games” introduced in our earlier work [1]. We provide an example where the set of equilibrium rates is properly contained in the set of achievable rates. We provide a conservative estimate of the region of equilibrium rates using a minmax approach. We discuss the uniqueness of equilibrium as well as the convergence of best response dynamics (a.k.a. iterative water-filling) for all rates when the interference is sufficiently small and some other mild conditions are met. Finally, we extend our results to the case where the QoS requirements are softened.