Fundamental Limits on Subwavelength Range Resolution

TL;DR

This paper establishes fundamental information-theoretic bounds on subwavelength resolution in radar ranging, analyzing the limits of target discrimination and separation precision for different measurement methods.

Contribution

It introduces a theoretical framework for understanding the ultimate limits of subwavelength resolution using information metrics and explores optimal estimation strategies.

Findings

Discriminability vanishes quadratically as target separation approaches zero.

Robust subwavelength estimation remains possible despite fundamental bounds.

Maximum likelihood estimation can enhance range precision.

Abstract

We establish fundamental bounds on subwavelength resolution for the radar ranging problem, ``super radar''. Information theoretical metrics are applied to probe the resolution limits for the case of both direct electric field measurement and photon-counting measurements. To establish fundamental limits, we begin with the simplest case of range resolution of two point targets from a metrology perspective. These information-based metrics establish fundamental bounds on both the minimal discrimination distance of two targets as well as the precision on the separation of two subwavelength resolved targets. For the minimal separation distance, both the direct field method and photon counting method show that the discriminability vanishes quadratically as the target separation goes to zero, and is proportional to the variance of the second derivative of the electromagnetic field profile. Nevertheless, robust subwavelength estimation is possible. Several different band-limited function classes are introduced to optimize discrimination. We discuss the application of maximum likelihood estimation to improve the range precision with optimal performance. The general theory of multi-parameter estimation is analyzed, and a simple example of estimating both the separation and relative strength of the two point reflectors is presented.