  This paper studies analog beamforming in active sensing applications, such as
millimeter-wave radar or ultrasound imaging. Analog beamforming architectures
employ a single RF-IF chain connected to all array elements via inexpensive
phase shifters. This can drastically lower costs compared to fully-digital
beamformers having a dedicated RF-IF chain for each sensor. However,
controlling only the element phases may lead to elevated side-lobe levels and
degraded image quality. We address this issue by image addition, which
synthesizes a high resolution image by adding together several lower resolution
component images. Image addition also facilitates the use of sparse arrays,
which can further reduce array costs. To limit the image acquisition time, we
formulate an optimization problem for minimizing the number of component
images, subject to achieving a desired point spread function. We propose a
gradient descent algorithm for finding a locally optimal solution to this
problem. We also derive an upper bound on the number of component images needed
for achieving the traditional fully-digital beamformer solution.
