Stackelberg-type channel state information feedback control game for energy efficiency in wireless networks

Efficient use of energy has recently become an essential research topic for wireless communications. Channel state information (CSI) feedback has been well recognised to have great significances for the energy-efficiency (EE) of the closed-loop wireless networks. However, works on EE focus mostly on the feed-forward data link by performing precoding and upper layer resource allocation and scheduling approaches. Unlike traditional work, the authors propose to study the EE by controlling the CSI feedback, where the mobile transmitter and receiver pairs exchange data by precoding for co-channel interference reduction. The EE maximisation problem can be formulated in the analytical settings of a game-theoretic framework by a two-level Stackelberg-type CSI feedback control game (SCFC), which can balance the power consumptions and the bandwidth. Specifically, the leader maximises the EE objective by introducing a price factor in the higher level. In lower level, multiple mobile receivers compete for the feedback channel utilisation to maximise their own utilities. The existence of the equilibriums is corroborated and the convergence behaviour is discussed. Simulation results demonstrate that the proposed distributed SCFC game can greatly enhance the EE performance by adjusting the pricing factor which can achieve close optimal performances in comparison with the centralised scheme.