Robust techniques and application of blind source separation
Abstract
Blind source separation (BSS) is a process to recover a set of unobserved source signals from their linear mixtures with unknown coefficients. Very little is assumed to be known about the sources, except that they are mutually independent and that at most one of them is Gaussian. The underlying principle in BSS is independent component analysis. In this dissertation, we explore a new application of BSS for digital communication systems, and new robust methods for BSS. In a digital communication system, digital information is transmitted to the receiver through a communication channel. In many applications, multiple-access protocols are used to provide a channel for multiple users, such as in Frequency Division Multiple Access (FDMA). The performance of the communication system can be greatly limited by various impairments which include additive noise, intersymbol interference (ISI), and adjacent channel interference (ACI). We show that FDMA systems with ACI and ISI can be modeled as a BSS problem. Simple BSS algorithms together with fractional sampling are shown to recover data in individual bands in the presence of ACI and ISI. For the FDMA overlapping channel, two approaches to improve the separation performance are also proposed, using prior information about the mixing matrix structure. We also compare the performances of different approaches for increasing the overall capacity. The performance of BSS adaptive algorithms greatly depends on some nonlinear functions. The optimum nonlinear functions depend on the distributions of the original source signals which may be unknown. If there is a mismatch between assumed and true source distribution, the performance of the adaptive algorithm may degrade significantly. Therefore, robust BSS is very desirable in such cases. We propose a new approach for robust BSS using ranks of observed signals. Two different ranking methods are introduced for rank computation. In addition, we consider nonlinear functions restricted to being piecewise linear for use in adaptive BSS. The general expressions for the optimum M -interval piecewise linear functions are obtained based on optimization of convergence and steady state error performance. A 3-interval adaptive piecewise linear function is proposed for separating sub/super-Gaussian sources. Simulation examples are presented showing good robust performance.
Recommended Citation
Lan Xiang,
"Robust techniques and application of blind source separation"
(January 1, 2004).
Dissertations from ProQuest.
Paper AAI3125923.
http://repository.upenn.edu/dissertations/AAI3125923
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