Abstract
We derive a new frequency-domain adaptive algorithm by using a frequency-domain recursive least squares criterion, minimizing an error signal in the frequency-domain. A similar criterion was proposed by Mansour and Gray by using mathematical expectations. Here, however, we propose to go one step further and derive an exact adaptive algorithm from the so-called normal equation. It is shown that the obtained algorithm is complex to implement, and to reduce the complexity we need to remove a constraint resulting in the unconstrained frequency-domain LMS (UFLMS) algorithm. We also give the optimal adaptation step size for the UFLMS. Most importantly, we generalize all this to the multi-channel case, thereby exploiting the cross-power spectra among all the channels which is very important (for a fast convergence rate) in multi-channel acoustic echo cancellation (AEC), where the input signals are highly correlated.
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References
M. Dentino, J. McCool, and B. Widrow, “Adaptive filtering in the frequency domain,” Proc. IEEE, vol. 66, pp. 1658–1659, Dec. 1978.
E. R. Ferrara, Jr., “Fast implementation of LMS adaptive filter,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-28, pp. 474–475, Aug. 1980.
D. Mansour and A. H. Gray, JR., “Unconstrained frequency-domain adaptive filter,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-30, pp. 726–734, Oct. 1982.
J. C. Lee and C. K. Un, “Performance analysis of frequency-domain block LMS adaptive digital filters,” IEEE Trans. Circuits Syst., vol. CAS-36, pp. 173–189, Feb. 1989.
J.-S. Soo and K. K. Pang, “Multidelay block frequency domain adaptive filter,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-38, pp. 373–376, Feb. 1990.
J. Benesty and P. Duhamel, “Fast constant modulus adaptive algorithm,” IEE Proc.-F, vol. 138, pp. 379–387, Aug. 1991.
J. Benesty and P. Duhamel, “A fast exact least mean square adaptive algorithm,” IEEE Trans. Signal Processing, vol. 40, pp. 2904–2920, Dec. 1992.
E. Moulines, O. Ait Amrane, and Y. Grenier, “The generalized multidelay adaptive filter: structure and convergence analysis,” IEEE Trans. Signal Processing, vol. 43, pp. 14–28, Jan. 1995.
J. Prado and E. Moulines, “Frequency-domain adaptive filtering with applications to acoustic echo cancellation,” Ann Télécommun., vol. 49, pp. 414–428, 1994.
J. Benesty, F. Amand, A. Gilloire, and Y. Grenier, “Adaptive filtering algorithms for stereophonic acoustic echo cancellation,” in Proc. IEEE ICASSP, 1995, pp. 3099–3102.
M. G. Bellanger, Adaptive Digital Filters and Signal Analysis. Marcel Dekker, 1987.
J. Benesty, D. R. Morgan, J. L. Hall, and M. M. Sondhi, “Synthesized stereo combined with acoustic echo cancellation for desktop conferencing,” Bell Labs Tech. J., vol. 3, pp. 148–158, Jul.-Sep. 1998.
M. M. Sondhi, D. R. Morgan, and J. L. Hall, “Stereophonic acoustic echo cancellatio—An overview of the fundamental problem,” IEEE Signal Processing Lett., vol. 2, pp. 148–151, Aug. 1995.
J. Benesty, D. R. Morgan, and M. M. Sondhi, “A better understanding and an improved solution to the specific problems of stereophonic acoustic echo cancellation,” IEEE Trans. Speech Audio Processing, vol. 6, pp. 156–165, Mar. 1998.
A. Gilloire, “Current issues in stereophonic and multi-channel acoustic echo cancellation,” in Proc. IWAENC, 1997, pp. K5–K8.
J. Benesty, D. R. Morgan, and M. M. Sondhi, “A hybrid mono/stereo acoustic echo canceler,” IEEE Trans. Speech Audio Processing, vol. 6, pp. 468–475, Sep. 1998.
J. Benesty, A. Gilloire, and Y. Grenier, “A frequency-domain stereophonic acoustic echo canceler exploiting the coherence between the channels and using nonlinear transformations,” in Proc. IWAENC, Sep. 1999, pp. 28–31.
J. Benesty, A. Gilloire, and Y. Grenier, “A frequency domain stereophonic acoustic echo canceler exploiting the coherence between the channels,” J. Acoust. Soc. Am., vol. 106, pp. L30–L35, Sep. 1999.
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Benesty, J., Morgan, D.R. (2000). Multi-Channel Frequency-Domain Adaptive Filtering. In: Gay, S.L., Benesty, J. (eds) Acoustic Signal Processing for Telecommunication. The Springer International Series in Engineering and Computer Science, vol 551. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8644-3_7
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DOI: https://doi.org/10.1007/978-1-4419-8644-3_7
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