Convergence analysis of decision-directed adaptive echo cancellers for baseband data transmission

Borrallo, José Manuel Páez; Speranzini, F.L.

doi:10.1109/26.380069

Cited by 5 publications

(6 citation statements)

References 6 publications

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“…Precisely, we will prove the following theorem: Proving that β is a solution of C for any α can be easily verified by substituting |g ij | by 1 √ 3 in system (13). The proof of Theorem 1 is based on the computation of the minimal discriminant variety (with respect to the projection on the α-axis) of the set of the complex vectors [|g 11 |, |g 12 |, |g 21 |, |g 22 …”

Section: Computation Of the Roots Distributionmentioning

confidence: 99%

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Using Computer Algebra to Certify the Global Convergence of a Numerical Optimization Process

Lazard

Rouillier

et al. 2007

Math.comput.sci.

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The basic objective of blind signal separation is to recover a set of source signals from a set of observations that are mixtures of the sources with no, or very limited knowledge about the mixture structure and source signals. To extract the original sources, many algorithms have been proposed; among them, the cross-correlation and constant modulus algorithm (CC-CMA) appears to be the algorithm of choice due to its computational simplicity.An important issue in CC-CMA algorithm is the global convergence analysis, because the cost function is not quadratic nor convex and contains undesirable stationary points. If these undesirable points are local minimums, the convergence of the algorithm may not be guaranteed and the CC-CMA would fail to separate source signals.The main result of this paper is to complete the classification of these stationary points and to prove that they are not local minimums unless if the mixing parameter is equal to 1. This is obtained by using the theory of discriminant varieties to determine the stationnary points as a function of the parameter and then to show that the Hessian matrix of the cost function is not positive semidefinite at these stationnay points, unless if the mixing parameter is 1.

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Section: Computation Of the Roots Distributionmentioning

confidence: 99%

“…We start from the range of α ∈]1, ∞[, for which we know by Theorem 1, that (13) has only the solution (|g 11 | = |g 12 | = |g 21 | = |g 22 this solution into (6), we can easily find the equations g * 11 g 21 + g * 12 g 22 = 0 g * 11 g 12 + g * 21 g 22 = 0 .…”

Section: Convergence Analysismentioning

confidence: 99%

Using Computer Algebra to Certify the Global Convergence of a Numerical Optimization Process

Lazard

Rouillier

et al. 2007

Math.comput.sci.

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“…En [Páez-Borrallo et al, 1995] y [Lorenzo-Speranzini, 1990] se analiza en detalle el comportamiento de los canceladores de ecos basados en estructuras de referencia no-cero, aplicados a los sistemas de comunicaciones con código de línea bipolar (2-PAM). En ellos se destaca que la principal problemática que surge es la alteración de la forma unimodal de la superficie de error( un sólo mínimo global), a una forma multimodal (con varios mínimos locales o puntos de ensilladura).…”

Section: El Efecto Enmascaramiento En El Algoritmo Lmaunclassified

“…Siguiendo un desarrollo equivalente a los realizados para los casos de referencia cero, las expresiones generales (2.3) y (2.11) se particularizan en [Páez-Borrallo et al, 1995 Determinar en este caso de forma analítica la naturaleza monótona, o no, de la expresión Si{n)/82(71) es extremadamente complejo. La alternativa es la representación gráfica de dicha relación jugando con los diferentes parámetros [Páez-Borrallo et al, 1995;Lorenzo-Speranzini, 1990]. En la figura 2.17 se representa uno de esos casos^.…”

Section: El Riesgo De Multimodalidad En El Algoritmo L2unclassified

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Técnicas adaptativas autorreferenciadas para la cancelación conjunta de eco e ISI aplicadas a los transceptores HDSL

Álvarez¹

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A la memoria de mi MadrePara finalizar, se muestra que las técnicas de autorreferencia pueden ser aplicadas de modo general. Las simulaciones en el entorno HDSL, usando canceladores de eco e ISI, apuntan unas buenas prestaciones trabajando en entornos de test CSA.También se muestra que esta nueva técnica puede ser aplicada a otro tipo de filtros adaptativos como son los igualadores CMA trabajando con modulaciones tipo PSK.

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Self-Reference Joint Echo Cancellation and Blind Equalization in High Bit-Rate Digital Subscriber Loops

Álvarez

Pàez-Borrallo

Zazo-Bello

1998

Signal Analysis and Prediction

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Convergence analysis of decision-directed adaptive echo cancellers for baseband data transmission

Cited by 5 publications

References 6 publications

Using Computer Algebra to Certify the Global Convergence of a Numerical Optimization Process

Using Computer Algebra to Certify the Global Convergence of a Numerical Optimization Process

Técnicas adaptativas autorreferenciadas para la cancelación conjunta de eco e ISI aplicadas a los transceptores HDSL

Self-Reference Joint Echo Cancellation and Blind Equalization in High Bit-Rate Digital Subscriber Loops

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