Performances of Low Rank Detectors Based on Random Matrix Theory with Application to STAP

Alice Combernoux (1) , Frédéric Pascal (1) , Marc Lesturgie (1) , Guillaume Ginolhac (2)

1 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay (COmUE)
2 LISTIC - Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance

The paper addresses the problem of target detection embedded in a disturbance composed of a low rank Gaussian clutter and a white Gaussian noise. In this context, it is interesting to use an adaptive version of the Low Rank Normalized Matched Filter detector, denoted LR-ANMF, which is a function of the estimation of the projector onto the clutter subspace. In this paper, we show that the LR-ANMF detector based on the sample covariance matrix is consistent when the number of secondary data K tends to infinity for a fixed data dimension m but not consistent when m and K both tend to infinity at the same rate, i.e. m/K → c ∈ (0, 1]. Using the results of random matrix theory, we then propose a new version of the LR-ANMF which is consistent in both cases and compare it to a previous version, the LR-GSCM detector. The application of the detectors from random matrix theory on STAP (Space Time Adaptive Processing) data shows the interest of our approach.

Mots clés: Low rank detection; Random matrix theory; G-MUSIC estimator; Spike-MUSIC estimator; STAP processing; Adaptive Normalized Matched Filter

Domaines: Traitement du signal et de l'image [eess.SP]

Alice Combernoux, Frédéric Pascal, Marc Lesturgie, Guillaume Ginolhac. Performances of Low Rank Detectors Based on Random Matrix Theory with Application to STAP. 2014 International Radar Conference , Oct 2014, Lille, France. ⟨10.1109/RADAR.2014.7060457⟩. ⟨hal-01084420⟩