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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
Citation: 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-
lyzed and tested. Adaptive subspace estimation algorithms are of importance be-
cause many techniques in communications are based on subspace approaches. To
avoid the cubic-order computational complexity of the direct eigenvalue decompo-
sition which makes real-time implementation impossible, many adaptive subspace
algorithms which need much less computational eB.ort have been proposed. Among
them, there are only a few limited noise subspace estimation algorithms as com-
pared with signal subspace estimation algorithms. Moreover, many of the existing
noise subspace estimation algorithms are either unstable or nonrobust. Therefore,
the aim of this thesis is to develop and analyze stable low cost noise subspace
estimation algorithms.

To shed light on how to obtain stable results for noise subspace algorithms,
the propagation of orthogonality error for FRANS (fast Rayleigh's quotient based
adaptive noise subspace) algorithm is examined in the mean and in the mean-
square sense. It is shown that FRANS suB.ers from numerical instability since
its accumulated numerical errors grow geometrically. Then, an upper bound on
the orthogonality error is derived for the Householder based FRANS (HFRANS)
algorithm, which is numerically much more stable than FRANS algorithm.

To further improve the performance of HFRANS, a gradient adaptive step-size
strategy is proposed. One drawback of such a strategy is the diB1culty in choosing
a proper initial value and convergence rate for the step-size update. Hence, we
propose an optimal step-size strategy, which addresses the initialization issue. The
proposed step-size strategies can also be applied on other noise and signal subspace
estimation algorithms.

To speed up the convergence rate of adaptive subspace estimation algorithms,
a diagonal matrix step-size strategy is proposed, which leads to a set of decoupled
noise (or signal) subspace vectors that can be controlled individually. This results
in better performance of the algorithms.

Finally, a hardware friendly approach, which is free from square root or division
operations is proposed to stabilize FRANS while retaining its low computational
complexity. This approach is suitable for VLSI (very large scale integration) im-
plementation. An ordinary diB.erential equation (ODE) based analysis is provided
to examine the stability of the proposed algorithm. This analysis shows that the
proposed algorithm is stable on the manifold and bounded at the equilibrium point.
Appears in Collections:Ph.D Theses (Open)

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