Outage Constrained Robust Hybrid Coordinated Beamforming for Massive MIMO Enabled Heterogeneous Cellular Networks

Heterogeneous network (HetNet), employing massive multiple-input multiple-output (MIMO), has been recognized as a promising technique to enhance network capacity, and to improve energy efficiency for the fifth generation of wireless communications. However, most existing schemes for coordinated beamforming (CoBF) for a massive MIMO HetNet unrealistically assume the availability of perfect channel state information (CSI) on one hand, and cascade of each antenna with a distinct radio-frequency chain in massive MIMO is neither power nor cost-efficient on the other hand. In this paper, we consider a massive MIMO-enabled HetNet framework, consisting of one macrocell base station (MBS) equipped with an analog beamformer, followed by a digital beamformer, and one femtocell base station (FBS) equipped with a digital beamformer. In the presence of Gaussian CSI errors, we propose a robust hybrid CoBF (HyCoBF) design, including an analog beamforming design for MBS, and a digital CoBF design for both MBS and FBS. To this end, an outage probability-constrained robust HyCoBF problem is formulated by minimizing the total transmit power. The analog beamforming mechanism at MBS is a newly devised low-complexity beam selection scheme by selecting analog beams from a discrete Fourier transform matrix codebook. Then, a conservative approximate CoBF solution is obtained via semidefinite relaxation and an extended Bernstein type inequality. Furthermore, a distributed implementation for the obtained CoBF solution using alternating direction method of multipliers is proposed. Finally, numerical simulations are provided to demonstrate the efficacy of the proposed robust HyCoBF algorithm.