Disproving Sum-Difference Co-Array Property

TL;DR

This paper critically examines the sum-difference co-array property used in sparse array design, revealing that its foundational assumption is valid only under very limited conditions, thus challenging prior claims.

Contribution

It provides a necessary and sufficient condition for the SDCA property, clarifying its limited applicability and correcting previous misconceptions.

Findings

The SDCA property holds only under specific rare conditions.

Previous assumptions about SDCA's general validity are incorrect.

The paper refines the theoretical understanding of sparse array co-arrays.

Abstract

The recently published paper by Gupta and Agrawal [1] exploited the sum-difference co-array (SDCA) to enhance the virtual aperture of sparse arrays. We argue that the key SDCA property established in [1] requires a critical necessary and sufficient condition that is valid for a very rare case only.