Competitive Downlink Beamforming Design in Multiuser Multicell Wireless Systems

This paper is concerned with the game-theory approach in designing the multiuser downlink beamformers in multicell systems. Sharing the same physical resource, the base station of each cell wishes to minimize its transmit power subject to a set of target signal-to-interference-plus-noise ratios (SINRs) at the multiple users in the cell. In that process, each base station determines its optimal downlink beamformer strategy in a distributed manner, without any coordination between the cells. Via the game-theory framework, we examine the conditions guaranteeing the existence and uniqueness of the Nash Equilibrium (NE). We establish the best response strategy of a cell, given the beamforming strategies from other cells. Such best response strategy is shown to be a standard function, which then guarantees the uniqueness of the NE and the convergence of the distributed algorithm. A sufficient condition for the existence of the NE is also presented.