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

## TL;DR

This paper introduces a robust beamforming method for 3D-MIMO systems that leverages sparse channel error models with $l_1$-norm bounds, reducing power consumption while maintaining SINR levels.

## Contribution

It proposes a novel $l_1$-norm bounded uncertainty model for robust beamforming in 3D-MIMO, improving power efficiency over traditional spherical models.

## Key findings

- Less beamforming power required for the same SINR
- Effective reformulation as SOCP
- Simulation confirms improved performance

## Abstract

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.