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,1,σ∞2IK). 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.
Original language | English |
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Pages (from-to) | 4166-4179 |
Number of pages | 14 |
Journal | IEEE Transactions on Signal Processing |
Volume | 64 |
Issue number | 16 |
DOIs | |
Publication status | Published - 15 Aug 2016 |
Publication type | A1 Journal article-refereed |
Keywords
- Compressive detection
- F -distribution
- hypothesis testing
- random subspace signals
- unknown noise variance
Publication forum classification
- Publication forum level 3
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Signal Processing