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In this paper, a novel robust beamforming scheme is proposed in threedimensional multi-input multi-output (3D-MIMO) systems. As one of the typicaldeployments of massive MIMO, a 3D-MIMO system owns sparse channels in angulardomain. Thus, various of sparse channel estimation algorithms produce sparsechannel estimation errors which can be utilized to narrow down the perturbationregion of imperfect CSI. We investigate a $l_1$-norm bounded channeluncertainty model for the robust beamforming problems, which captures thesparse nature of channel errors. Compared with the conventional sphericaluncertainty, we prove that the scheme with $l_1$-norm bounded uncertaintyconsumes less beamforming power with the same signal to interference and noiseratio (SINR) thresholds. The proposed scheme is reformulated as a second-ordercone programming (SOCP) and simulation results verify the effectiveness of ouralgorithm.

Robust Beamforming for Downlink 3D-MIMO Systems with $l_1$-norm Bounded CSI Uncertainty