The Best Radar Ranging Pulse to Resolve Two Reflectors

TL;DR

This paper identifies optimal radar waveforms for resolving two identical reflectors with high precision, providing algorithms and experimental validation that surpass traditional resolution limits and approach theoretical bounds.

Contribution

It introduces explicit algorithms for optimizing waveforms to achieve superresolution in radar ranging and extends the analysis to multi-parameter estimation methods.

Findings

Optimal waveforms improve resolution beyond traditional limits.

Experimental results demonstrate sub-tenth inverse bandedge resolution.

Uncertainties approach the Cramér-Rao bound.

Abstract

Previous work established fundamental bounds on subwavelength resolution for the radar range resolution problem, called superradar [Phys. Rev. Appl. 20, 064046 (2023)]. In this work, we identify the optimal waveforms for distinguishing the range resolution between two reflectors of identical strength. We discuss both the unnormalized optimal waveform as well as the best square-integrable pulse, and their variants. Using orthogonal function theory, we give an explicit algorithm to optimize the wave pulse in finite time to have the best performance. We also explore range resolution estimation with unnormalized waveforms with multi-parameter methods to also independently estimate loss and time of arrival. These results are consistent with the earlier single parameter approach of range resolution only and give deeper insight into the ranging estimation problem. Experimental results are presented using radio pulse reflections inside coaxial cables, showing robust range resolution smaller than a tenth of the inverse bandedge, with uncertainties close to the derived Cram\'er-Rao bound.