On the detection of low rank matrices in the high-dimensional regime

Autor: Antoine Chevreuil, Philippe Loubaton
Přispěvatelé: Electronique, Systèmes de communication et Microsystèmes (ESYCOM), Université Paris-Est Marne-la-Vallée (UPEM)-ESIEE Paris-Conservatoire National des Arts et Métiers [CNAM] (CNAM), Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Chevreuil, Antoine, Conservatoire National des Arts et Métiers [CNAM] (CNAM), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Université Paris-Est Marne-la-Vallée (UPEM)-ESIEE Paris, Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Université Paris-Est Marne-la-Vallée (UPEM)-ESIEE Paris
Jazyk: angličtina
Rok vydání: 2018
Předmět:
Signal Processing (eess.SP)
Rank (linear algebra)
Index Terms—statistical detection tests
Mathematics - Statistics Theory
large deviation principle
02 engineering and technology
Statistics Theory (math.ST)
Lambda
01 natural sciences
Upper and lower bounds
large random matrices
Combinatorics
010104 statistics & probability
Matrix (mathematics)
0202 electrical engineering
electronic engineering
information engineering
FOS: Electrical engineering
electronic engineering
information engineering
FOS: Mathematics
0101 mathematics
Electrical Engineering and Systems Science - Signal Processing
[SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
Physics
020206 networking & telecommunications
Complex normal distribution
Singular value
Random matrix
Random variable
[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Zdroj: EUSIPCO
EUSIPCO, Sep 2018, Rome, Italy
Popis: We address the detection of a low rank $n\times n$deterministic matrix $\mathbf{X}_{0}$ from the noisy observation ${\bf X}_{0}+{\bf Z}$ when $n\to\infty$, where ${\bf Z}$ is a complex Gaussian random matrix with independent identically distributed $\mathcal{N}_{c}(0,\frac{1}{n})$ entries. Thanks to large random matrix theory results, it is now well-known that if the largest singular value $\lambda_{1}$ of ${\bf X}_{0}$ verifies $\lambda_{1}>1$, then it is possible to exhibit consistent tests. In this contribution, we prove a contrario that under the condition $\lambda_{1}
Comment: 7 pages, 2 figures, submitted to EUSIPCO2018
Databáze: OpenAIRE
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