Fluctuations for linear spectral statistics of large random covariance matrices

The theory of large random matrices has proved to be an efficient tool to address many problems in wireless communication and statistical signal processing these last two decades. We provide hereafter a central limit theorem (CLT) for linear spectral statistics of large random covariance matrices, improving Bai and Silverstein's celebrated 2004 result. This fluctuation result should be of interest to study the fluctuations of important estimators in statistical signal processing.