From Sparse Channel to Sparse Beamforming: A 3D-MIMO Case

This paper investigates the beamforming for three- dimensional multiple input multiple output (3D-MIMO) systems with inaccurate channel state information (CSI). From the view of angle-domain, the 3D-MIMO channel is sparse on the high 3D resolution provided by planar antenna array with large number of antenna elements at the base station (BS) in 3D-MIMO systems. Prior knowledge of sparsity is not only beneficial to channel estimation in literature, but also implies more efficient beamforming with inaccurate CSI at transmitters as discussed in this paper. We prove that the optimal beamforming vector is correspondingly sparse in angle-domain with a sparse channel. Therefore, we add the ℓ₁-norm penalty to the beamforming vector in optimization design in angle-domain, which can fight against the perturbation due to inaccurate CSI. Technically, the problem is reformulated as a second order cone program (SOCP) form that can be solved efficiently. Simulation results demonstrate that the proposed beamforming method can achieve considerable system sum-rate improvement with high CSI error.