Dynamic Coalition Formation for Network MIMO in Small Cell Networks

Abstract

In this paper, we apply the concepts of network multiple-input-multiple-output (MIMO) to small cell networks. To do so, the issue of imperfect channel state information (CSI) at the transmitter is considered when frequency-division duplexing is used, for which the feedback channel is limited. We first introduce a regret based learning approach to optimize the transmit beamforming parameters for the cases when the feedback channel is temporarily unavailable during deep fades. We then propose a coalition formation game model to cluster the small cell base stations so that they can perform cluster-wise joint beamforming. We take the \tit{recursive core} as the solution concept of the coalition formation game. To obtain the recursive core, we first consider a typical merge-split algorithm. However, we show that this algorithm can be unstable. Alternatively, we adopt the merge-only algorithm which guarantees the formation stability and show that its outcome belongs to the recursive core. Finally, we analyze the average number and the average size of coalitions that can form during such a coalition formation process. Numerical simulations are given to illustrate the behavior of the coalition formation among small cell base stations.