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：波束成形是一种信号处理技术，通过传感器阵列对电磁波进行导向、赋形和聚焦，使其朝向期望方向传播。该技术已广泛应用于雷达、声纳、声学、天文学、地震学、医学成像和通信等多个工程领域。随着主要面向雷达与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备受关注。近年来，机器学习被用于为更复杂的波束成形问题提供具有吸引力的解决方案。本文系统梳理了过去二十五年间波束成形技术从凸优化到非凸优化、从优化方法到学习方法的演进历程，揭示了这一重要信号处理技术在多种发射-接收架构、传播区域、传播路径以及传统/新兴应用中的发展全貌。