# Robust Beamforming for Downlink Multi-Cell Systems: A Bilevel Optimization Perspective

arXiv: https://arxiv.org/abs/2401.11409 · HTML: https://mlsanity.com/paper/2401.11409/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2024.

## Built on by (most cited first, 2 of 2)

- [Argus: Federated Non-convex Bilevel Learning over 6G Space-Air-Ground Integrated Network](https://mlsanity.com/paper/2505.09106/) (2025)
- [Synergistic Localization and Sensing in MIMO-OFDM Systems via Mixed-Integer Bilevel Learning](https://mlsanity.com/paper/2507.07118/) (2025)

## Abstract (arXiv)

Utilization of inter-base station cooperation for information processing has shown great potential in enhancing the overall quality of communication services (QoS) in wireless communication networks. Nevertheless, such cooperations require the knowledge of channel state information (CSI) at base stations (BSs), which is assumed to be perfectly known. However, CSI errors are inevitable in practice which necessitates beamforming techniques that can achieve robust performance in the presence of channel estimation errors. Existing approaches relax the robust beamforming design problems into semidefinite programming (SDP), which can only achieve a solution that is far from being optimal. To this end, this paper views robust beamforming design problems from a bilevel optimization perspective. In particular, we focus on maximizing the worst-case weighted sum-rate (WSR) in the downlink multi-cell multi-user multiple-input single-output (MISO) system considering bounded CSI errors. We first reformulate this problem into a bilevel optimization problem and then develop an efficient algorithm based on the cutting plane method. A distributed optimization algorithm has also been developed to facilitate the parallel processing in practical settings. Numerical results are provided to confirm the effectiveness of the proposed algorithm in terms of performance and complexity, particularly in the presence of CSI uncertainties.