A fast second-order signal separation algorithms with on-line capabilities.

*(English)*Zbl 1011.93103Authors’ 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.

Reviewer: Pedro A.Morettin (São Paulo)

##### 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 |

##### Keywords:

off-line computation; signal separation; decoupling; output cross-correlation functions; adaptive algorithm
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\textit{M. F. Fahmy} and \textit{G. M. A. El-Raheem}, Int. J. Circuit Theory Appl. 30, No. 4, 425--439 (2002; Zbl 1011.93103)

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