Spiked Models of Large Dimensional Random Matrices Applied to Wireless Communications and Array Signal Processing.

摘要

Worked performed during this period includes the investigation into eigenvalue behavior of several different classes of large dimensional random matrices. They are: 1) a class of random matrices important to array signal processing and wireless communications with the goal of proving exact separation of their eigenvalues; 2) an ensemble of random matrices used to estimate the powers transmitted by multiple signal sources in multi-antenna fading channels; 3) another ensemble whose eigenvalues yield the mutual information of a multiple antenna radio channel, for which a central limit theorem is proven; 4) ensembles which yield robust estimation of a population covariance matrix with application to array signal processing; and 5) a sample covariance matrix for which a CLT is studied on linear statistics of its eigenvalues, whose limiting empirical distribution of its eigenvalues is studied with application toward computing the power of a likelihood ratio test for determining the presence of spike eigenvalues in the population covariance matrix.