Signal separation using second and high order statistics

Fahmy, Mahmoud; El-Raheem, G.M.A.; El-Sallam, Amar A.

doi:10.1109/nrsc.1999.760921

Cited by 1 publication

(7 citation statements)

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“…In literature [5][6][7][8], it has been shown that to retrieve n 0 independent signals from a set of n 0 received mixed signals, one has to minimize the objective function deÿned as…”

Section: A Fast Correlation-based Least-squares Signal Separation Algmentioning

confidence: 99%

“…(5) To overcome the colouring e ects made by the de-coupling matrix W , i.e. to recover the original received signals f 11 ⊗ s 1 (n); f 22 ⊗ s 2 (n), the following steps are followed [7]:…”

Section: A Fast Correlation-based Least-squares Signal Separation Algmentioning

confidence: 99%

“…In recent years, the ÿeld of blind de-convolution and signal separation has received considerable interest [1][2][3][4][5][6][7][8]. It ÿnds applications in various areas of signal processing such as noise cancellation, channel equalization, hearing aids and many others.…”

Section: Introductionmentioning

confidence: 99%

“…In References [5][6][7][8], it has been shown that, to recover the unknown signal sources s i (k), the unknown coupling matrix F has to be nonsingular. This condition is ensured if the received sources x i (k) are received from independent sensors.…”

Section: Introductionmentioning

confidence: 99%

“…In References [3,4], an iterative method is proposed for choosing the de-coupling matrix as the eigenvectors corresponding to the minimum eigenvalue of a certain positive deÿnite matrix derived from an objective function representing the sum of squared output cross-correlation functions evaluated over a batch of lags. In References [5][6][7][8], signal separation has been achieved through solving, in a least-squares sense a system of linear equations describing either the cross-correlation or cross-cumulant functions evaluated for the de-coupling system's outputs, over a batch of lags.…”

Section: Introductionmentioning

confidence: 99%

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A fast second‐order signal separation algorithms with on‐line capabilities

Fahmy

El-Raheem

2002

Circuit Theory & Apps

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SUMMARYIn correlation-based signal separation algorithms, the received mixed signals are fed to a de-coupling system designed to minimize the output cross-correlation functions. If minimizaion is perfect, each of the system's outputs carries only one signal independent of the others. In these algorithms, the computation burden of the output cross-correlation functions normally slows down the separation algorithm. This paper, describes a computationally e cient method for o -line pre-computation of the needed crosscorrelation functions. Explicit formulas have been derived for the output cross-correlation functions in terms of the received input signals and the de-coupling 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 de-coupling 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 e ectiveness of the proposed algorithms.

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“…In literature [5][6][7][8], it has been shown that to retrieve n 0 independent signals from a set of n 0 received mixed signals, one has to minimize the objective function deÿned as…”

Section: A Fast Correlation-based Least-squares Signal Separation Algmentioning

confidence: 99%

Section: A Fast Correlation-based Least-squares Signal Separation Algmentioning

confidence: 99%