Dynamic Base Station Sleep Control via Submodular Optimization for Green mmWave Networks

This paper proposes a dynamic millimeter-wave (mmWave) base station (BS) sleep control scheme for green mmWave networks. The typical coverage radius of mmWave BS is short due to high propagation and shadowing loss, thus large number of BSs are required to be deployed densely. A network consisting of many BSs consumes large energy. Sleep and activation control is a promising technique to reduce energy consumption. However, to select a set of BSs to sleep from large number of BSs to maximize total throughput under on condition that the total energy consumption of the network is limited is a NP-hard problem and it requires huge computation time. This paper formulates sleep control based on submodular optimization which can be solved quickly by using a greedy algorithm and the performance in the worst case is guaranteed to be \((1-\mathrm {e}^{-1})\)-approximation. We design a utility function defined as total expected rate for mmWave access networks in consideration of the characteristics of mmWave communication, and prove that it is submodular and monotone. The sleep and activation control of mmWave BSs is formulated as a combinatorial optimization problem to maximize a monotone submodular function under the constraint that the number of BSs to be activated is limited due to energy constraints. Simulation results confirmed that the proposed scheme obtains a BS set achieving higher throughput than random selection and the scheme is polynomial time algorithm.