Energy-efficient beamforming for two-tier massive MIMO downlink

Heterogeneous networks (HetNets) consisting of macro cells with very large antenna arrays and a secondary tier of small cells with a few antennas each can well tackle the contradiction of large coverage of the network and high data rate at the hot spots. However, it is not permissible to assign orthogonal pilot sequences for all the supported users due to the large number. Hence, we propose a pilot reduction scheme based on the heterogeneous system configurations and the unique topology of this HetNet. The reusing of pilot sequences causes the presence of the contaminated channel state information (CSI) and results in receivers´ Quality of Service (QoS) outage. With the contaminated CSI, we provide an energy-efficient beamforming based on minimizing the total power consumption while keeping the QoS constraints satisfied and restricting the QoS outage probability below a given specification. By applying the approach of Bernstein approximation and semi-definite relaxation, we transform the original intractable chance constrained program to a convex problem conservatively. Numerical results show that the average power consumption of the proposed beamforming for our pilot reduction scheme is close to that of the perfect CSI case. Since our scheme will greatly compress the length of pilot sequence especially for those highly densified network with large number of small cells, it will be crucially helpful to put such two-tier massive multiple-input and multiple-output (MIMO) systems into practice.