A Study on the Convergence Characteristics Improvement of the Modified-Multiplication Free Adaptive Filer

변형 비적 적응 필터의 수렴 특성 개선에 관한 연구

In this paper, the structure of modified multiplication-free adaptive filter(M-MADF) and convergence analysis are presented. To evaluate the performance of proposed M-MADF algorithm, fractionally spaced equalizer (FSE) is used. The input signals are quantized using DPCM and the reference signals is processed using a first-order linear prediction filter, and the outputs are processed by a conventional adaptive filter. The filter coefficients are updated using the Sign algorithm. Under the assumption that the primary and reference signals are zero mean, wide-sense stationary and Gaussian, theoretical results for the coefficient misalignment vector and its autocorrelation matrix of the filter are driven. The convergence properties of Sign. MADF and M-MADF algorithm for updating of the coefficients of a digital filter of the fractionally spaced equalizer (FSE) are investigated and compared with one another. The convergence properties are characterized by the steady state error and the convergence speed. It is shown that the convergence speed of M-MADF is almost same as Sign algorithm and is faster that MADF in the condition of same steady error. Especially it is very useful for high correlated signals.

본 논문에서는 곱셈연산이 필요치 안은 변형 비적 적응필터(MMADF : Modified Multiplication-free adaptive Filter) 알고리즘을 제안하고 수렴특성을 해석하였다. 제안한 구조는 DPCM(Differential Pulse Code Modulation)과 Sign 알고리듬을 이용한 MADF 구조에서 1차 필터를 첨가한 구조이다. 해석방법은 계수 비정렬벡터와 그 자기상관행렬의 수렴을 유도하였다. 수렴특성을 평가하기 위하여 분할등기(FSE : Fractionally Spaced Equallizer)에 적용하였으며, Sign 알고리듬, MADF 알고리듬, MMADF 알고리듬을 사용하여 정상상태오차와 수렴속도로 특성을 비교평가 하였다. MMADF 알고리듬을 FSE에 적용한 결과 안정된 수렴특성을 나타내었으며, 동일한 정상상태오차를 갖는 조건에서 시뮬레이션한 결과 기존의 Sign 및 MADF 알고리듬에 비해 신호특성 및 수렴속도가 개선 되었다.