Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/16866
Title: Design and analysis of adaptive noise subspace estimation algorithms
Authors: LU YANG
Keywords: Signal processing, noise subspace estimation, PCA/MCA
Issue Date: 4-Aug-2009
Source: LU YANG (2009-08-04). Design and analysis of adaptive noise subspace estimation algorithms. ScholarBank@NUS Repository.
Abstract: In this thesis, several adaptive noise subspace estimation algorithms are ana-<br>lyzed and tested. Adaptive subspace estimation algorithms are of importance be-<br>cause many techniques in communications are based on subspace approaches. To<br>avoid the cubic-order computational complexity of the direct eigenvalue decompo-<br>sition which makes real-time implementation impossible, many adaptive subspace<br>algorithms which need much less computational eB.ort have been proposed. Among<br>them, there are only a few limited noise subspace estimation algorithms as com-<br>pared with signal subspace estimation algorithms. Moreover, many of the existing<br>noise subspace estimation algorithms are either unstable or nonrobust. Therefore,<br>the aim of this thesis is to develop and analyze stable low cost noise subspace<br>estimation algorithms.<br><br>To shed light on how to obtain stable results for noise subspace algorithms,<br>the propagation of orthogonality error for FRANS (fast Rayleigh's quotient based<br>adaptive noise subspace) algorithm is examined in the mean and in the mean-<br>square sense. It is shown that FRANS suB.ers from numerical instability since<br>its accumulated numerical errors grow geometrically. Then, an upper bound on<br>the orthogonality error is derived for the Householder based FRANS (HFRANS)<br>algorithm, which is numerically much more stable than FRANS algorithm.<br><br>To further improve the performance of HFRANS, a gradient adaptive step-size<br>strategy is proposed. One drawback of such a strategy is the diB1culty in choosing<br>a proper initial value and convergence rate for the step-size update. Hence, we<br>propose an optimal step-size strategy, which addresses the initialization issue. The<br>proposed step-size strategies can also be applied on other noise and signal subspace<br>estimation algorithms.<br><br>To speed up the convergence rate of adaptive subspace estimation algorithms,<br>a diagonal matrix step-size strategy is proposed, which leads to a set of decoupled<br>noise (or signal) subspace vectors that can be controlled individually. This results<br>in better performance of the algorithms.<br><br>Finally, a hardware friendly approach, which is free from square root or division<br>operations is proposed to stabilize FRANS while retaining its low computational<br>complexity. This approach is suitable for VLSI (very large scale integration) im-<br>plementation. An ordinary diB.erential equation (ODE) based analysis is provided<br>to examine the stability of the proposed algorithm. This analysis shows that the<br>proposed algorithm is stable on the manifold and bounded at the equilibrium point.
URI: http://scholarbank.nus.edu.sg/handle/10635/16866
Appears in Collections:Ph.D Theses (Open)

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