Robust random matrix theory and applications to radar detection

Robust random matrix theory and applications to radar detection

Frédéric Pascal Abla Kammoun 

Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506) CentraleSupélec-CNRS-Université Paris-Sud, 91192 Gif-sur-Yvette, France

Computer, Electrical, and Mathematical Sciences and Engineering (CEMSE) Division, KAUST, Thuwal, Makkah Province, Saudi Arabia

Corresponding Author Email: 
frederic.pascal@centralesupelec.fr
Page: 
321-349
|
DOI: 
https://doi.org/10.3166/TS.33.321-349
Received: 
7 May 2015
| |
Accepted: 
18 December 2015
| | Citation
Abstract: 

This article presents recent results obtained from both Random Matrix Theory and Robust Estimation Theory, and applied to radar detection problems. More precisely, to answer the problem of high dimensional data, we focus on a regularized version of the Tyler’s cova- riance matrix estimator (Tyler, 1987 ; Pascal, Chitour et al., 2008). Thus, it is shown thanks to the statistical analysis of this estimator, i.e. first and second-order behavior in high dimensional regime (N/n → c ∈ (0, 1] when N, n → ∞), that an optimal design of a robust detector, namely the adaptive normalized matched filter (ANMF) can be derived. The optimality consi- dered in this paper refers to the maximisation (resp. minimization) of the detection probability (resp. probability of false alarm). Finally, Monte-Carlo simulations are conducted to highlight the improvement brought by the proposed approach compared to classical techniques of the literature.

Keywords: 

 random matrix theory, robust estimation theory, regularization, radar detection, ANMF.

Extended Abstract
1. Introduction
2. Etat de l’art et problèmes étudiés
3. Design optimal du ANMF-RSCM dans le cas d’un bruit gaussien
4. Design optimal du ANMF-RTE : bruit non-gaussien
5. Simulations
6. Conclusion
Remerciements
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