Expected RIP: Conditioning of The modulated wideband converter

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 conditi...

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Bibliographic Details
Main Authors: Mishali, M., Eldar, Y.C.
Format: Conference Proceeding
Language:eng ; jpn
Subjects:
Binary sequences
Compressed sensing
Conferences
expected restricted isometry property
Frequency conversion
Gold
Information theory
Matrix converters
modulated wideband converter
multiband sampling
Sampling methods
Sparse matrices
Stability
Wideband
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Summary: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.
DOI:10.1109/ITW.2009.5351492