Outage constrained robust hybrid coordinated beamforming for massive MIMO enabled heterogeneous cellular networks

Heterogeneous network (HetNet), employing massive multiple-input multiple-output (MEMO), has been recognized as a promising technique to enhance network capacity, and to improve energy efficiency for fifth generation (5G) 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 (CSQ on one hand, and cascade of each antenna with a distinct radio frequency (RF) chain in massive MEMO is neither power nor cost efficient on the other hand. In this paper, we consider a massive MEMO 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 (DFT) matrix codebook. Then a conservative approximate CoBF solution is obtained via semidefinite relaxation (SDR) and an extended Bernsteintype inequality. Finally, numerical simulations are provided to demonstrate the efficacy of the proposed HyCoBF algorithm.