# Twenty-Five Years of Advances in Beamforming: From Convex and Nonconvex Optimization to Learning Techniques

arXiv: https://arxiv.org/abs/2211.02165 · HTML: https://mlsanity.com/paper/2211.02165/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2022.

## Built on by (most cited first, 7 of 7)

- [Machine Learning for Large-Scale Optimization in 6G Wireless Networks](https://mlsanity.com/paper/2301.03377/) (2023)
- [LVM4CSI: Enabling Direct Application of Pre-Trained Large Vision Models for Wireless Channel Tasks](https://mlsanity.com/paper/2507.05121/) (2025)
- [Learning minimal volume uncertainty ellipsoids](https://mlsanity.com/paper/2405.02441/) (2024)
- [Sparse Array Design for Direction Finding using Deep Learning](https://mlsanity.com/paper/2308.04615/) (2023)
- [Reducing the Environmental Impact of Wireless Communication via Probabilistic Machine Learning](https://mlsanity.com/paper/2311.12807/) (2023)
- [Rapid and Power-Aware Learned Optimization for Modular Receive Beamforming](https://mlsanity.com/paper/2408.00439/) (2024)
- [Multi-perspective Imbalance-Conscious 6G Beamforming Optimization and Performance](https://mlsanity.com/paper/2608.12929/) (2026)

## Abstract (arXiv)

Beamforming is a signal processing technique to steer, shape, and focus an electromagnetic wave using an array of sensors toward a desired direction. It has been used in several engineering applications such as radar, sonar, acoustics, astronomy, seismology, medical imaging, and communications. With the advances in multi-antenna technologies largely for radar and communications, there has been a great interest on beamformer design mostly relying on convex/nonconvex optimization. Recently, machine learning is being leveraged for obtaining attractive solutions to more complex beamforming problems. This article captures the evolution of beamforming in the last twenty-five years from convex-to-nonconvex optimization and optimization-to-learning approaches. It provides a glimpse of this important signal processing technique into a variety of transmit-receive architectures, propagation zones, paths, and conventional/emerging applications.