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A Study on the Modified RLS Algorithm Using Orthogonal Input Vectors

직교 입력 벡터를 이용하는 수정된 RLS 알고리즘에 관한 연구

  • Ahn, Bong Man (Industrial Cooperation Foundation, Chonbuk Nation University) ;
  • Kim, Kwang Woong (Institute of Sundertechnology) ;
  • Ahn, Hyun Gyu (Department of Mathematics Education, Graduate School of Education, Chonbuk Nation University) ;
  • Han, Byoung Sung (Industrial Cooperation Foundation, Chonbuk Nation University)
  • 안봉만 (전북대학교 산학협력단) ;
  • 김관웅 ((주)썬더테크놀로지 연구소) ;
  • 안현규 (전북대학교 교육대학원 수학교육과) ;
  • 한병성 (전북대학교 산학협력단)
  • Received : 2018.10.05
  • Accepted : 2018.10.18
  • Published : 2019.01.01

Abstract

This paper proposes an easy algorithm for finding tapped-delay-line (TDL) filter coefficients in an adaptive filter algorithm using orthogonal input signals. The proposed algorithm can be used to obtain the coefficients and errors of a TDL filter without using an inverse orthogonalization process for the orthogonal input signals. The form of the proposed algorithm in this paper has the advantages of being easy to use and similar to the familiar recursive least-squares (RLS) algorithm. In order to evaluate the proposed algorithm, system identification simulation of the $11^{th}$-order finite-impulse-response (FIR) filter was performed. It is shown that the convergence characteristics of the learning curve and the tracking ability of the coefficient vectors are similar to those of the conventional RLS analysis. Also, the derived equations and computer simulation results ensure that the proposed algorithm can be used in a similar manner to the Levinson-Durbin algorithm.

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Fig. 1. Structure of proposed algorithm.

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Fig. 2. Algorithm processing structure.

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Fig. 3. Learning curves for proposed algorithm with S/N=-20dB. (a) Learning curve of the proposed algorithm and the RLSL filter and (b) learning curve of RLS algorithm and RLSL filter.

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Fig. 4. E[ŵ] curves with S/N=-20 dB. (a) Proposed algorithmand (b) RLS algorithm.

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Fig. 5. The various curves with δ=100 and S/N=-20 dB. (a) Learning curves with δ=100 and (b) E[ŵ] curves of proposed algorithm with δ=100.

Table 1. Summary of the proposed algorithm.

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Table 2. Mean values of E[ŵ] with various S/N ratio.

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Table 3. The average value of E[ŵ] accord. to the filter order mismatch.

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Acknowledgement

Supported by : 전북태크노파크

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