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충격잡음에 강인한 ℓ1-norm 기반 가변 스텝사이즈 적응필터 알고리즘

Title
충격잡음에 강인한 ℓ1-norm 기반 가변 스텝사이즈 적응필터 알고리즘
Other Titles
ℓ1-norm based variable step-size adaptive filtering algorithms robust to impulsive noise
Author
김정희
Alternative Author(s)
Jung-Hee Kim
Advisor(s)
남상원
Issue Date
2016-02
Publisher
한양대학교 일반대학원
Degree
Doctor
Abstract
본 논문에서는 충격잡음 환경에서 세 가지의 사인 알고리즘(Affine Projection Sign Algorithm (APSA), Sign Subband Adaptive Filter (SSAF), Affine Projection SSAF (APSSAF))의 수렴 성능을 향상시키기 위한 새로운 ℓ1-norm 기반 가변 스텝사이즈 (variable step-size: VSS) 알고리즘을 제안한다. 구체적으로, 제안하는 가변스텝사이즈는 스텝사이즈의 box 제약 조건에서, 본래의 사인 알고리즘의 목적함수를 최소화하는 문제로부터 유도된다. 제안하는 ℓ1-norm 최소화 문제에서는 본래의 사인 알고리즘과 같은 목적함수를 사용하지만, 여기서는 다른 변수, 스텝사이즈에 대해 최소화한다.따라서 제안하는 목적함수는 스텝사이즈에 대해 1차원 piecewise 선형 볼록 함수로 해석할 수 있으며, 이는 제안하는 목적함수가 미분불능임을 의미한다. 이러한 문제점을 해결하기 위해, 최적의 해를 구할 수 있는 효율적인 수치해석적 절차도 제안한다. 제안하는 ℓ1-norm 최소화 절차는 제안하는 최소화 문제와 동일한 형식의 어떠한 최적화 문제에도 적용할 수 있다. 특히, 기존 SSAF 알고리즘은 필터뱅크로 인하여 신호의 전달 경로에 시간 지연이 발생하기 때문에 실시간 응용에 제한적으로 활용된다. 이러한 어려움을 극복하기 위해, 시간 지연이 없는 SSAF 구조를 제안한다. 또한, 각 부밴드에 ℓ1-norm 최소화 기법을 적용한 밴드별 가변 스텝사이즈 (band-dependent VSS: BDVSS) 알고리즘도 제안한다.그렇게함으로써,각 부밴드에 서로다른 스텝사이즈를 할당할 수 있으며, 기존 방법에 비해 향상된 수렴 성능을 기대할수 있다. 제안하는 알고리즘은 충격잡음이 포함되는 시스템 식별 환경의 다양한 컴퓨터시뮬레이션을 통해 테스트하였다. 또한, 제안하는알고리즘은 double-talk이 발생하는 음향반향신호제거 (Acoustic Echo Cancellation: AEC)와 능동충격소음제어 (Active Impulsive Noise Control: AINC) 등 충격잡음이 발생하는 다양한 시스템에도 적용하여 이에 대한 성능을 검증하였다. 그 결과, 제안하는 알고리즘은 충격잡음에 강인한 기존 적응필터 알고리즘에 비해 수렴속도와 정상상태오차 측면에서 우수한 성능을 보였다. 더욱이, 제안하는 알고리즘은 어떠한 사전 정보가 필요하지 않으면서도, 잡음 분산이나 사전에 결정된 상수의 정보가 필요한 최근의 가변 스텝사이즈 사인 알고리즘과 비슷한 수렴 성능을 보인다.|In this dissertation, a novel ℓ1-norm based variable step-size (VSS) algorithm is proposed to improve the convergence under impulsive interference in three sign algorithms: the affine projection sign algorithm (APSA), sign subband adaptive filter (SSAF), and affine projection SSAF (APSSAF). Each proposed VSS is obtained by employing the same ℓ1-norm based objective function as in the original sign algorithm, with a box-constraint on the step-size. In the proposed ℓ1-norm minimization problem for the step-size, the objective function is minimized with respect to a different scalar variable, i.e., the step-size. Accordingly, the proposed objective function can be interpreted as a one-dimensional piecewise linear convex one with respect to the step-size, which implies that it is non-differentiable. To resolve the non-differentiability problem, an efficient numerical procedure is presented for the optimal solution. Note that this numerical procedure can be further utilized to solve any optimization problem that can be formulated in the same form as the proposed minimization problem. In particular, the conventional SSAF introduces an undesirable signal path delay by the filter banks
therefore, it can be restrictively used in real-time applications. Thus, a delayless scheme for the SSAF is also developed. Furthermore, a band-dependent VSS (BDVSS) algorithm for the delayless SSAF is derived by applying the proposed ℓ1-norm minimization to each subband of the delayless SSAF. By doing so, a different step-size can be assigned to each subband, and improved performance compared with the conventional algorithms can be expected. The proposed approach is tested using extensive computer simulations in a system identification scenario with impulsive interference. In addition, its performance is also verified in various impulsive noise environments such as acoustic echo cancellation (AEC) with double-talk and active impulsive noise control (AINC). The results demonstrate that the proposed approach yields better performance in terms of the convergence rate and steady-state error than the existing adaptive algorithms robust against impulsive interference. Furthermore, although the proposed approach does not require any a priori information, it provides a good convergence performance compared with the most recent VSS sign algorithms, which require either the a priori information of noise variance or a carefully selected predefined constant.
In this dissertation, a novel ℓ1-norm based variable step-size (VSS) algorithm is proposed to improve the convergence under impulsive interference in three sign algorithms: the affine projection sign algorithm (APSA), sign subband adaptive filter (SSAF), and affine projection SSAF (APSSAF). Each proposed VSS is obtained by employing the same ℓ1-norm based objective function as in the original sign algorithm, with a box-constraint on the step-size. In the proposed ℓ1-norm minimization problem for the step-size, the objective function is minimized with respect to a different scalar variable, i.e., the step-size. Accordingly, the proposed objective function can be interpreted as a one-dimensional piecewise linear convex one with respect to the step-size, which implies that it is non-differentiable. To resolve the non-differentiability problem, an efficient numerical procedure is presented for the optimal solution. Note that this numerical procedure can be further utilized to solve any optimization problem that can be formulated in the same form as the proposed minimization problem. In particular, the conventional SSAF introduces an undesirable signal path delay by the filter banks
URI
https://repository.hanyang.ac.kr/handle/20.500.11754/126401http://hanyang.dcollection.net/common/orgView/200000428901
Appears in Collections:
GRADUATE SCHOOL[S](대학원) > ELECTRONICS AND COMPUTER ENGINEERING(전자컴퓨터통신공학과) > Theses (Ph.D.)
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