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.

翻译：波束成形是一种利用传感器阵列对电磁波进行导向、整形和聚焦的信号处理技术，使其指向期望方向。该技术已广泛应用于雷达、声纳、声学、天文学、地震学、医学成像和通信等工程领域。随着主要面向雷达和通信的多天线技术发展，基于凸/非凸优化的波束成形器设计受到广泛关注。近年来，机器学习被用于获取更复杂波束成形问题的理想解决方案。本文梳理了波束成形技术在过去二十五年中从凸优化到非凸优化、从优化方法到学习方法的演进历程，展示了这一重要信号处理技术在不同收发架构、传播区域、路径及传统/新兴应用中的发展全貌。