Pricing-Based Distributed Energy-Efficient Beamforming for MISO Interference Channels

In this paper, we consider the problem of maximizing the weighted sum energy efficiency (WS-EE) for multi-input single-output (MISO) interference channels (ICs), which are well acknowledged as general models of heterogeneous networks (HetNets), multicell networks, etc. To address this problem, we develop an efficient distributed beamforming algorithm based on a pricing mechanism. Specifically, we carefully introduce a price metric for distributed beamforming design, which fortunately allows efficient closed-form solutions to the per-user beam-vector optimization problem. The convergence of the distributed pricing-based beamforming design is theoretically proven. Furthermore, we present an implementation strategy of the proposed distributed algorithm with limited information exchange. Numerical results show that our algorithm converges much faster than existing algorithms, while yielding comparable, sometimes even better performance in terms of the WS-EE. Finally, by taking the backhaul power consumption into account, it is interesting to show that the proposed algorithm with limited information exchange achieves better WS-EE than the full information exchange-based algorithm in some special cases.