Expected RIP: Conditioning of The Modulated Wideband Converter

TL;DR

This paper introduces the expected restricted isometry property to evaluate the conditioning of the modulated wideband converter's sensing matrix, providing practical rate requirements for stable sparse signal recovery.

Contribution

It proposes a new conditioning criterion for the modulated wideband converter and derives theoretical guarantees applicable to common binary sequences.

Findings

The expected restricted isometry property offers a realistic measure of matrix conditioning.

Theoretical guarantees are established for the converter's performance.

Practical rate requirements are derived for binary sequences like Gold codes.

Abstract

The sensing matrix of a compressive system impacts the stability of the associated sparse recovery problem. In this paper, we study the sensing matrix of the modulated wideband converter, a recently proposed system for sub-Nyquist sampling of analog sparse signals. Attempting to quantify the conditioning of the converter sensing matrix with existing approaches leads to unreasonable rate requirements, due to the relatively small size of this matrix. We propose a new conditioning criterion, named the expected restricted isometry property, and derive theoretical guarantees for the converter to satisfy this property. We then show that applying these conditions to popular binary sequences, such as maximal codes or Gold codes, leads to practical rate requirements.