TY - JOUR

T1 - Fluctuations of the SNR at the output of the MVDR with Regularized Tyler Estimators

AU - Elkhalil, Khalil

AU - Kammoun, Abla

AU - Al-Naffouri, Tareq Y.

AU - Alouini, Mohamed-Slim

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2016/12/27

Y1 - 2016/12/27

N2 - This paper analyzes the statistical properties of the signal-to-noise ratio (SNR) at the output of the Capon's minimum variance distortionless response (MVDR) beamformers when operating over impulsive noises. Particularly, we consider the supervised case in which the receiver employs the regularized Tyler estimator in order to estimate the covariance matrix of the interference-plus-noise process using n observations of size N×1N×1. The choice for the regularized Tylor estimator (RTE) is motivated by its resilience to the presence of outliers and its regularization parameter that guarantees a good conditioning of the covariance estimate. Of particular interest in this paper is the derivation of the second order statistics of the SINR. To achieve this goal, we consider two different approaches. The first one is based on considering the classical regime, referred to as the n-large regime, in which N is assumed to be fixed while n grows to infinity. The second approach is built upon recent results developped within the framework of random matrix theory and assumes that N and n grow large together. Numerical results are provided in order to compare between the accuracies of each regime under different settings.

AB - This paper analyzes the statistical properties of the signal-to-noise ratio (SNR) at the output of the Capon's minimum variance distortionless response (MVDR) beamformers when operating over impulsive noises. Particularly, we consider the supervised case in which the receiver employs the regularized Tyler estimator in order to estimate the covariance matrix of the interference-plus-noise process using n observations of size N×1N×1. The choice for the regularized Tylor estimator (RTE) is motivated by its resilience to the presence of outliers and its regularization parameter that guarantees a good conditioning of the covariance estimate. Of particular interest in this paper is the derivation of the second order statistics of the SINR. To achieve this goal, we consider two different approaches. The first one is based on considering the classical regime, referred to as the n-large regime, in which N is assumed to be fixed while n grows to infinity. The second approach is built upon recent results developped within the framework of random matrix theory and assumes that N and n grow large together. Numerical results are provided in order to compare between the accuracies of each regime under different settings.

UR - http://hdl.handle.net/10754/622087

UR - http://www.sciencedirect.com/science/article/pii/S0165168416303760

UR - http://www.scopus.com/inward/record.url?scp=85008516865&partnerID=8YFLogxK

U2 - 10.1016/j.sigpro.2016.12.023

DO - 10.1016/j.sigpro.2016.12.023

M3 - Article

SN - 0165-1684

VL - 135

SP - 1

EP - 8

JO - Signal Processing

JF - Signal Processing

ER -