A restricted isometry property for structurally-subsampled unitary matrices

Waheed U. Bajwa, Akbar M. Sayeed, Robert Nowak

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Scopus citations

Abstract

Subsampled (or partial) Fourier matrices were originally introduced in the compressive sensing literature by Candès et al. Later, in papers by Candès and Tao and Rudelson and Vershynin, it was shown that (random) subsampling of the rows of many other classes of unitary matrices also yield effective sensing matrices. The key requirement is that the rows of U, the unitary matrix, must be highly incoherent with the basis in which the signal is sparse. In this paper, we consider acquisition systems that - despite sensing sparse signals in an incoherent domain - cannot randomly subsample rows from U. We consider a general class of systems in which the sensing matrix corresponds to subsampling of the rows of matrices of the form Φ = RU (instead of U), where R is typically a low-rank matrix whose structure reflects the physical/technological constraints of the acquisition system. We use the term "structurally-subsampled unitary matrices" to describe such sensing matrices. We investigate the restricted isometry property of a particular class of structurally-subsampled unitary matrices that arise naturally in application areas such as multiple-antenna channel estimation and sub-nyquist sampling. In addition, we discuss an immediate application of this work in the area of wireless channel estimation, where the main results of this paper can be applied to the estimation of multiple-antenna orthogonal frequency division multiplexing channels that have sparse impulse responses.

Original languageEnglish (US)
Title of host publication2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Pages1005-1012
Number of pages8
DOIs
StatePublished - Dec 1 2009
Externally publishedYes
Event2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States
Duration: Sep 30 2009Oct 2 2009

Publication series

Name2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

Other

Other2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
CountryUnited States
CityMonticello, IL
Period9/30/0910/2/09

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Control and Systems Engineering
  • Communication

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    Bajwa, W. U., Sayeed, A. M., & Nowak, R. (2009). A restricted isometry property for structurally-subsampled unitary matrices. In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 (pp. 1005-1012). [5394883] (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). https://doi.org/10.1109/ALLERTON.2009.5394883