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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.
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