On the Sample Complexity of Super-Resolution Radar

TL;DR

This paper identifies and corrects a flaw in the proof of a key lemma related to the sample complexity in super-resolution radar, clarifying the true relationship between sample size and delay-Doppler pair recovery.

Contribution

It provides a corrected proof for the sample complexity lemma in super-resolution radar, resolving an incorrect quadratic relation claim.

Findings

Corrected the proof of the key lemma on sample complexity

Clarified the true linear relation between sample size and delay-Doppler pairs

Resolved a critical issue affecting theoretical guarantees in radar super-resolution

Abstract

We point out an issue with Lemma 8.6 of [1]. This lemma specifies the required sample complexity for recovering the delay-Doppler pairs in radar systems. In this lemma, it is claimed that the required sample complexity is linearly related to the number of delay-Doppler pairs. However, the way this result is proved seems to be wrong and leads to a quadratic relation. In this work, we provide a correction to the proof of this lemma.