  In this paper, a novel robust beamforming scheme is proposed in three
dimensional multi-input multi-output (3D-MIMO) systems. As one of the typical
deployments of massive MIMO, a 3D-MIMO system owns sparse channels in angular
domain. Thus, various of sparse channel estimation algorithms produce sparse
channel estimation errors which can be utilized to narrow down the perturbation
region of imperfect CSI. We investigate a $l_1$-norm bounded channel
uncertainty model for the robust beamforming problems, which captures the
sparse nature of channel errors. Compared with the conventional spherical
uncertainty, we prove that the scheme with $l_1$-norm bounded uncertainty
consumes less beamforming power with the same signal to interference and noise
ratio (SINR) thresholds. The proposed scheme is reformulated as a second-order
cone programming (SOCP) and simulation results verify the effectiveness of our
algorithm.
