Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals

A central limit theorem for bilinear forms of the type a∗ ˆCN (ρ)−1 b, where a, b ∈ CN are unit norm deterministic vectors and ˆCN (ρ) a robust-shrinkage estimator of scatter parametrized by ρ and built upon n independent elliptical vector observations, is presented. The fluctuations of a∗ ˆCN (ρ)−1 b are found to be of order N− 1 2 and to be the same as those of a∗ ˆSN (ρ)−1 b for ˆSN (ρ) a matrix of a theoretical tractable form. This result is exploited in a classical signal detection problem to provide an improved detector which is both robust to elliptical data observations (e.g., impulsive noise) and optimized across the shrinkage parameter ρ.

• Type: Journal
• Year: 2016
• Where: MA
• Authors: Romain Couillet, Abla Kammoun, Frédéric Pascal 0001
• Keywords: Communications, MA 2016