×

zbMATH — the first resource for mathematics

A fast second-order signal separation algorithms with on-line capabilities. (English) Zbl 1011.93103
Authors’ abstract: In correlation-based signal separation algorithms, the received mixed signals are fed to a decoupling system designed to minimize the output cross-correlation functions. If minimization is perfect, each of the system’s outputs carries only one signal independent of the others. In these algorithms, the computational burden of the output cross-correlation functions normally slows down the separation algorithm. This paper describes a computationally efficient method for off-line pre-computation of the needed cross-correlation functions. Explicit formulas have been derived for the output cross-correlation functions in terms of the received input signals and the decoupling system parameters. Then, it is shown that signal separation amounts to the least-squares solution of a system of linear equations describing these output cross-correlation functions, evaluated over a batch of lags. Next, a fast RLS-type adaptive algorithm is devised for on-line signal separation. In this respect, an algorithm is derived for updating the decoupling parameters as data comes in. This update is achieved recursively along the negative of the steepest descent directions of an objective cost function describing the output cross-correlation functions over a batch of lags, subject to equal output power constraints. Illustrative examples are given to demonstrate the effectiveness of the proposed algorithms.
MSC:
93E10 Estimation and detection in stochastic control theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
93E24 Least squares and related methods for stochastic control systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Feder, IEEE Transactions on Speech, Audio Processing 1 pp 405– (1993)
[2] Yellin, IEEE Transactions on Signal Processing 42 pp 2158– (1994)
[3] Multichannel blind signal separation by decorrelation. Proceedings of IEEE Signal Processing Society 1995 Workshop on Applications of Signal Processing to Audio and Acoustics, Mohonk Mountain House: New York, October 1995; 15-18.
[4] Multi-channel signal separation. Proceedings of ICASSP’ 96, Atlanta, U.S.A., vol. II, May 1996; 649-652.
[5] El-Raheem GMA, El-Sallam AAA. Signal separation using high order statistics. Proceedings of the 16th National Radio Science Conference, NRSC’ 99, Cairo, Egypt C-37, Ain-Shams University, 23-25 February 1999.
[6] Two rapidly convergemt algorithms for signal separation. IEEE Symposium on Circuits and Systems ISCAS’ 99, Orlando, Florida, U.S.A., May 1999.
[7] Fahmy, International Journal of Circuit Theory and Application 28 pp 225– (2000)
[8] Fast on-line signal separation with maximum output power constraint. Proceedings of ISPACS’2001, International Symposium on Intelligent Signal Processing and Communication Systems, Nashville, Tennesse, U.S.A., November 2001.
[9] Adaptive Digital Filters and Signal Analysis. Marcel Dekker: New York, 1987.
[10] Gradient adaptation with unit-norm constraints. Technical Report # No. EE-99-003, Southern Methodist University, Dallas, TX, February 1999.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.