A New Framework for Adaptive Subspace Filtering: Theory and Algorithms for Application to Wireless Communications

University Of Southern California, Los Angeles CA

Investigators

Abstract

This proposal is a continuation of the research on Reduced-rank Adaptive Subspace Filtering for Spread Spectrum Communications, Array Signal Processing and Detection, a research grant funded by the National Science Foundation under Contract No. MIP-9706215. During the current grant, the theoretical foundations of the cross-spectral metric (CSM) for reduced-rank were studied. The practical processing algorithms to apply the CSM to several related research areas are developed. Our research shows that the CSM method results in a better rank reduction than the principal components method in the sense of the minimum mean square error for filtering. The remaining problem with the CSM method is that the eigenvectors of the data covariance matrix, that are used to span the full-rank space, are unknown and have to be estimated from the observation data in most applications. The expensive computation needed for obtaining these eigenvectors will hinder the use of the CSM method in real-time processing. In addition, the strategy used by the CSM method for searching a desired rank-reducing subspace is not efficient: one has to compute all of the eigenvectors and their corresponding eigenvalues in order to rank order the cross-spectral items, but only a certain number of them are needed for the subspace filtering. A new framework for reduced rank subspace filtering, built on a non-eigenvector-based subspace representation, is now proposed to address these issues. In this new framework, a set of orthonormal vectors, which tridiagonalizes, rather than diagonalizes, the covariance matrix, is used to replace a set of eigenvectors as a basis of the full-rank space. Advantages of this replacement are (1) the computation of the tridiagonalization has a much lower complexity as compared to that of the diagonalization; (2) the rank reduction from the full-rank N to the lower rank K only requires computing K or less desired orthonormal basis vectors, instead of computing all N of them, and (3) the resulting subspace remains optimal in the sense of maximum signal-to-interference plus noise ratio. The proposed effort for this non-eigenvector-based subspace filtering framework includes studying the theoretical foundations, developing adaptive processing algorithms and their computation architectures, deriving a rank reduction optimization metric, and evaluating theoretical and implementation performances as compared to the eigenvector based approaches. New results in rank reduced adaptive filtering will be directly applicable to several new research areas currently under consideration such as space and time wireless systems and code addressed multiple access signaling. In these applications, and similar extensions, low dimension addressing signals are superimposed in larger 2-dimensional(frequency/time or space/time) signal spaces. Signal crosstalk in the form of address overlap must be removed by processing over the entire 2-D observation space. The ability to rank reduce data for efficient crosstalk rejection will be a major step in the development of practical processing algorithms. In addition, overlap interference will be time varying due to continual data modulation (in the multiple accessing case) and due to the spatial fading (in the space/time case). Hence adaptive updating processors will be necessary for maximum efficiency. The research developed in the newer study proposed here will significantly influence practical filtering solutions for these two dimensional cases.