# Learning Robust Beamforming for MISO Downlink Systems

arXiv: https://arxiv.org/abs/2103.01602 · HTML: https://mlsanity.com/paper/2103.01602/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 14 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 4 of 4)

- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Deep Learning for Distributed Optimization: Applications to Wireless Resource Management](https://mlsanity.com/paper/1905.13378/) (2019)
- [Deep Learning Methods for Universal MISO Beamforming](https://mlsanity.com/paper/2007.00841/) (2020)
- [Regularized Zero-Forcing for Multiantenna Broadcast Channels with User Selection](https://mlsanity.com/paper/2003.09923/) (2020)

## Built on by (most cited first, 5 of 5)

- [A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimization](https://mlsanity.com/paper/2207.05364/) (2022)
- [Uncertainty Injection: A Deep Learning Method for Robust Optimization](https://mlsanity.com/paper/2302.12304/) (2023)
- [Hierarchical ML Codebook Design for Extreme MIMO Beam Management](https://mlsanity.com/paper/2312.02178/) (2023)
- [Channel-Feedback-Free Transmission for Downlink FD-RAN: A Radio Map based Complex-valued Precoding Network Approach](https://mlsanity.com/paper/2312.02184/) (2023)
- [BERT4beam: Large AI Model Enabled Generalized Beamforming Optimization](https://mlsanity.com/paper/2509.11056/) (2025)

## Abstract (arXiv)

This paper investigates a learning solution for robust beamforming optimization in downlink multi-user systems. A base station (BS) identifies efficient multi-antenna transmission strategies only with imperfect channel state information (CSI) and its stochastic features. To this end, we propose a robust training algorithm where a deep neural network (DNN), which only accepts estimates and statistical knowledge of the perfect CSI, is optimized to fit to real-world propagation environment. Consequently, the trained DNN can provide efficient robust beamforming solutions based only on imperfect observations of the actual CSI. Numerical results validate the advantages of the proposed learning approach compared to conventional schemes.