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Variable matrix-type step-size affine projection algorithm with orthogonalized input vectors

서지혜 (JiHye Seo, 포항공과대학교)

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초록 moremore
This thesis proposes a variable matrix-type step-size affine projection algorithm (APA) with orthogonalized input vectors. We generate orthogonalized input vectors using the Gram-Schmidt process so as to implement the weight update equation of the APA using the sum of normalized least mean square (NLMS)-like updating equations. This method allows us to use individual step sizes corresponding to each NLMS-like equation. This is equivalent to adopting the step size in the form of a diagonal matrix in the APA. A variable step-size scheme is adopted to improve the performance of the filter. The individual step sizes are determined to minimize the mean square deviation of the APA. The experimental results show that the proposed algorithm has a faster convergence rate and a smaller steady-state estimation error than the existing APAs.
This thesis proposes a variable matrix-type step-size affine projection algorithm (APA) with orthogonalized input vectors. We generate orthogonalized input vectors using the Gram-Schmidt process so as to implement the weight update equation of the APA using the sum of normalized least mean square (NLMS)-like updating equations. This method allows us to use individual step sizes corresponding to each NLMS-like equation. This is equivalent to adopting the step size in the form of a diagonal matrix in the APA. A variable step-size scheme is adopted to improve the performance of the filter. The individual step sizes are determined to minimize the mean square deviation of the APA. The experimental results show that the proposed algorithm has a faster convergence rate and a smaller steady-state estimation error than the existing APAs.
목차 moremore
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Applications using adaptive filter . . . . . . . . . . . . . . . . . . . . . . . . . 2
...
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Applications using adaptive filter . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 System identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.3 Noise cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Issues for adaptive filtering algorithm . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 Convergence rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.2 Misadjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.3 Computational complexity . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.4 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Adaptive filtering algorithms 5
2.1 Linear estimation problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Steepest-descent algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 LMS-type algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Least mean square algorithm . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.2 Normalized least mean square algorithm . . . . . . . . . . . . . . . . . 8
2.3.3 Affine projection algorithm . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Variable matrix-type step-size ane projection algorithm with orthogonalized input vectors 9
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Affine projection algorithm with orthogonalized input vectors . . . . . . . . . 11
3.3 Variable Matrix-type Step-size Affine Projection Algorithm with Orthogonalized Input Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3.1 Variable matrix-type step-size APA with orthogonalized input vectors 13
3.3.2 Derivation of step size based on MSD analysis . . . . . . . . . . . . . 14
4 Experimental Results 18
4.0.3 System identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.0.4 Acoustic echo cancellation . . . . . . . . . . . . . . . . . . . . . . . . . 24
5 Conclusions 28
6 Appendix 29
Summary (in Korean) 30
References 31