Complex Factor Analysis

Abstract

Many techniques for array processing assume either that the system has a calibrated array or that the noise covariance matrix is known. If the noise covariance matrix is unknown, training or other calibration techniques are used to find it. In this thesis another approach to the problem of unknown noise covariance is presented. The factor analysis (FA) model is used to model the data. In order to make the theory applicable in telecommunication and radio astronomy, the model is extended to the case of complex numbers. The necessary mathematical tools for estimation, detection and performance analysis are derived. The maximum likelihood estimator for the FA model in the case of proper complex Gaussian distributed noise and signals is given. Two different iterative algorithms for finding the MLE of the model parameters are presented. The necessary iteration steps for an alternating least squares algorithm are also presented. The Cramer–Rao bound for the FA model is found and the convergence of the estimated parameters to this bound are illustrated using simulations. The improved performance of some popular algorithms like ESPRIT and spatial filtering have been demonstrated using computer simulations. A general likelihood ratio test is presented as a tool to test the correctness of the estimated parameters. An especial case of this test is presented as a constant false alarm detector. This thesis is an initial attempt for developing the factor analysis as a tool for signal processing. The multivariate nature of the theory makes it a good candidate for solving many problems in telecommunication and radio astronomy.