Robust Estimation of Scatter Matrix, Random Matrix Theory and an Application to Spectrum Sensing

The covariance estimation is one of the most critical tasks in multivariate statistical analysis. In many applications, reliable estimation of the covariance matrix, or scatter matrix in general, is required. The performance of the classical maximum likelihood method relies a great deal on the validity of the model assumption. Since the assumptions are often approximately correct, many robust statistical methods have been proposed to be robust against the deviation from the model assumptions. M-estimator is an important class of robust estimator of the scatter matrix. The properties of these robust estimators under high dimensional setting, which means the number of dimensions has the same order of magnitude as the number of observations, is desirable. To study these, random matrix theory is a very important tool. With high dimensional properties of robust estimators, we introduced a new method for blind spectrum sensing in cognitive radio networks.