한국음향학회지 (The Journal of the Acoustical Society of Korea)

  • 제38권3호
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  • Pages.283-289
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  • 2019
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  • 1225-4428(pISSN)
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  • 2287-3775(eISSN)
한국음향학회 (The Acoustical Society of Korea)
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기울기 평균 벡터를 사용한 가변 스텝 최소 자승 알고리즘과 시변 망각 인자를 사용한 시변 음향 채널 추정

An time-varying acoustic channel estimation using least squares algorithm with an average gradient vector based a self-adjusted step size and variable forgetting factor

  • 임준석 (세종대학교 전자정보통신공학과)
  • Lim, Jun-Seok (Department of Electrical Engineering, Sejong University)
  • 투고 : 2019.03.08
  • 심사 : 2019.04.15
  • 발행 : 2019.05.31
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⟨ 이전 논문 다음 논문 ⟩

초록

RLS(Recursive-least-squares) 알고리즘은 수렴성이 좋고, 수렴 후 오차 수준도 우수한 것으로 알려져 있다. 그러나 알고리즘 내에 역행렬 계산이 포함되어 수치적 불안정성을 나타내는 단점도 있다. 본 논문에서는 언급한 불안정성을 회피하기 위해서 역행렬이 없지만 수렴성이 유사한 알고리즘을 제안한다. 이를 위해서 기울기 평균 벡터를 사용한 가변 스텝 최소 자승 알고리즘을 사용한다. 또 시변 채널 추정에 우수한 성능을 내기 위해서 계산량이 적은 가변 망각인자를 도입한다. 시뮬레이션을 통해서 기존 RLS와의 성능을 비교하고 그 유사성을 보인다. 또 시변 채널에서 가변 망각인자의 우수성도 보인다.

RLS (Recursive-least-squares) algorithm is known to have good convergence and excellent error level after convergence. However, there is a disadvantage that numerical instability is included in the algorithm due to inverse matrix calculation. In this paper, we propose an algorithm with no matrix inversion to avoid the instability aforementioned. The proposed algorithm still keeps the same convergence performance. In the proposed algorithm, we adopt an averaged gradient-based step size as a self-adjusted step size. In addition, a variable forgetting factor is introduced to provide superior performance for time-varying channel estimation. Through simulations, we compare performance with conventional RLS and show its equivalency. It also shows the merit of the variable forgetting factor in time-varying channels.

키워드

GOHHBH_2019_v38n3_283_f0001.png 이미지

Fig. 1. A structure of adaptive filtering system.

GOHHBH_2019_v38n3_283_f0002.png 이미지

Fig. 2. Convergence performance comparison in the time invariant channel (a) mean square error comparison (-○-: RLS, -△-: proposed algorithm with fixed forgetting factor, -◇-: proposed algorithm with variable forgetting factor method 1, -×-: proposed algorithm with variable forgetting factor method 2) (b) comparison between two variable forgetting factor methods.

GOHHBH_2019_v38n3_283_f0003.png 이미지

Fig. 3. Convergence performance comparison in the time invariant channel (a) mean square error comparison (-○-: RLS, -△-: proposed algorithm with fixed forgetting factor, -◇-: proposed algorithm with variable forgetting factor method 1, -×-: proposed algorithm with variable forgetting factor method 2) (b) comparison between two variable forgetting factor methods.

Table 1. Summary of the proposed algorithm.

GOHHBH_2019_v38n3_283_t0001.png 이미지

참고문헌

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