A Fast Block FIR Adaptive Digital Filtering Algorithm with Individual Adaption of Parameters

A general formulation for developing a fast-block least-mean-square (LMS) adaptive algorithm is presented. In this algorithm, a convergence factor is obtained that is tailored for each adaptive filter coefficient and is updated at each block iteration. These convergence factors are chosen to minimize the mean-squared error in the processed block and are easily computed from readily available signals. The algorithm is called the optimum block adaptive algorithm with individual adaptation of parameters (OBAI). It is shown that the new coefficient vector obtained from the OBAI algorithm is an estimate of the Wiener solution at each iteration. Implementation aspects of OBAI are examined and a technique is presented that eliminates matrix inversion by processing signals in overlapping blocks and applying the matrix inversion lemma. When the coefficients are updated once per input data sample, the resulting OBAI algorithm requires 7N/sup 2/-5N+9 multiplications and divisions (MAD) per iteration, where N is the number of estimated parameters. The convergence properties of OBAI are investigated and compared with several recently proposed algorithms. >

[1]  John M. Cioffi.  The block-processing FTF adaptive algorithm , 1986, IEEE Trans. Acoust. Speech Signal Process..

[2]  Leonid G. Kazovsky,et al.  Adaptive filters with individual adaptation of parameters , 1986 .

[3]  L. Ljung,et al.  Fast calculation of gain matrices for recursive estimation schemes , 1978 .

[4]  Giancarlo Prati,et al.  Self-Orthogonalizing Adaptive Equalization in the Discrete Frequency Domain , 1984, IEEE Trans. Commun..

[5]  Lennart Ljung,et al.  Application of Fast Kalman Estimation to Adaptive Equalization , 1978, IEEE Trans. Commun..

[6]  T. Kailath,et al.  Fast, recursive-least-squares transversal filters for adaptive filtering , 1984 .

[7]  Jae Chon Lee,et al.  Performance of transform-domain LMS adaptive digital filters , 1986, IEEE Trans. Acoust. Speech Signal Process..

[8]  M. L. Honig,et al.  Recursive fixed-order covariance Least-Squares algorithms , 1983, The Bell System Technical Journal.

[9]  Nasir Ahmed,et al.  Sequential regression considerations of adaptive filtering , 1977 .

[10]  L. Fransen,et al.  Optimum adaptive algorithms with applications to noise cancellation , 1984 .

[11]  Jont B. Allen,et al.  FIR system modeling and identification in the presence of noise and with band-limited inputs , 1978 .

[12]  S. Mitra,et al.  A unified approach to time- and frequency-domain realization of FIR adaptive digital filters , 1983 .

[13]  A. Gray,et al.  Unconstrained frequency-domain adaptive filter , 1982 .

[14]  Chong Kwan Un,et al.  A reduced structure of the frequency-domain block LMS adaptive digital filter , 1984 .

[15]  Sanjit K. Mitra,et al.  Block implementation of adaptive digital filters , 1981 .

[16]  C. Burrus.  Block implementation of digital filters , 1971 .

[17]  J.C. Lee,et al.  A frequency-weighted block LMS algorithm and its application to speech processing , 1985, Proceedings of the IEEE.

[18]  Lloyd J. Griffiths,et al.  An adaptive lattice structure for noise-cancelling applications , 1978, ICASSP.

[19]  W. Mikhael,et al.  Fast algorithms for block FIR adaptive digital filtering , 1987 .

[20]  S. Thomas Alexander,et al.  Adaptive Signal Processing , 1986, Texts and Monographs in Computer Science.

[21]  B. Widrow,et al.  Stationary and nonstationary learning characteristics of the LMS adaptive filter , 1976, Proceedings of the IEEE.

[22]  A. Peterson,et al.  Transform domain LMS algorithm , 1983 .

[23]  A.M. Peterson,et al.  Frequency domain least-mean-square algorithm , 1981, Proceedings of the IEEE.

[24]  H. Voelcker,et al.  Digital filtering via block recursion , 1970 .

[25]  George Carayannis,et al.  A fast sequential algorithm for least-squares filtering and prediction , 1983 .

[26]  C. Barnes,et al.  Block-shift invariance and block implementation of discrete-time filters , 1980 .