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Compressive Detection of Random Subspace Signals

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Details

Original languageEnglish
Pages (from-to)4166-4179
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume64
Issue number16
DOIs
Publication statusPublished - 15 Aug 2016
Publication typeA1 Journal article-refereed

Abstract

The problem of compressive detection of random subspace signals is studied. We consider signals modeled as s = Hx where H is an N × K matrix with K ≤ N and x ~ N(0K,12IK). We say that signal s lies in or leans toward a subspace if the largest eigenvalue of HHT is strictly greater than its smallest eigenvalue. We first design a measurement matrix Φ = [ΦsT, ΦoT]T comprising of two sub-matrices Φs and Φo where Φs projects the signal to the strongest left-singular vectors, i.e., the left-singular vectors corresponding to the largest singular values, of subspace matrix H and Φo projects it to the weakest left-singular vectors. We then propose two detectors that work based on the difference in energies of the samples measured by the two sub-matrices Φs and Φo and provide theoretical proofs for their optimality. Simplified versions of the proposed detectors for the case when the variance of noise is known are also provided. Furthermore, we study the performance of the detector when measurements are imprecise and show how imprecision can be compensated by employing more measurement devices. The problem is then re-formulated for the generalized case when the signal lies in the union of a finite number of linear subspaces instead of a single linear subspace. Finally, we study the performance of the proposed methods by simulation examples.

Keywords

  • Compressive detection, F -distribution, hypothesis testing, random subspace signals, unknown noise variance

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