# Trading beams for bandwidth: Imaging with randomized beamforming

## TL;DR

This paper introduces a broadband imaging technique that reduces the number of spatial measurements needed by using randomized beamforming, leveraging the scene's range-limited structure to improve efficiency and cost-effectiveness.

## Contribution

It proposes a novel trade-off allowing fewer array measurements through broadband illumination and randomized beamforming, supported by theoretical analysis and simulations.

## Key findings

- Significant reduction in spatial measurements needed for imaging
- Theoretical validation of the measurement trade-off
- Improved imaging speed and cost efficiency

## Abstract

We study the problem of actively imaging a range-limited far-field scene using an antenna array. We describe how the range limit imposes structure in the measurements across multiple wavelengths. This structure allows us to introduce a novel trade-off: the number of spatial array measurements (i.e., beams that have to be formed) can be reduced significantly lower than the number array elements if the scene is illuminated with a broadband source. To take advantage of this trade-off, we use a small number of "generic" linear combinations of the array outputs, instead of the phase offsets used in conventional beamforming. We provide theoretical justification for the proposed trade-off without making any strong structural assumptions on the target scene (such as sparsity) except that it is range limited. In proving our theoretical results, we take inspiration from the sketching literature. We also provide simulation results to establish the merit of the proposed signal acquisition strategy. Our proposed method results in a reduction in the number of required spatial measurements in an array imaging system and hence can directly impact their speed and cost of operation.