# Analog Beamforming for Active Imaging using Sparse Arrays

## TL;DR

This paper explores analog beamforming with sparse arrays for active imaging, proposing an optimization approach to reduce image acquisition time and costs while maintaining high resolution.

## Contribution

It introduces an optimization framework and a gradient descent algorithm for minimizing component images in analog beamforming with sparse arrays.

## Key findings

- Proposed a gradient descent algorithm for image synthesis optimization.
- Derived an upper bound on the number of component images needed.
- Demonstrated cost reduction potential with sparse array configurations.

## Abstract

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.