Publication: Técnicas de igualación no lineal vía estructuras en escalera
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1999-06
Defense date
1999-07-09
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Abstract
Los esquemas de igualación no lineal permiten aumentar significativamente la velocidad de transmisión de datos en canales dispersivos, y particularmente, en los que además hay no lineales. Sus inconvenientes más importantes son dos: su alta complejidad y su baja velocidad de convergencia. Los esquemas no lineales necesitan una gran potencia de cálculo para poder llevar a cabo el elevado número de operaciones necesarias por dato adquirido en el receptor. Por otra parte, algunos esquemas no lineales como el perceptrón multicapa necesitan de un gran número de datos para poder llegar a la convergencia y, además, corren el riesgo de caer en mínimos locales de convergencia, lo que los hace poco prácticos en comunicaciones. Otros esquemas, como los filtros de Volterra, son menos propensos (por su arquitectura) a caer en mínimos locales, pero son dificiles de ajustar para que converjan. En algunas situaciones no es necesario el uso de esquemas no lineales para alcanzar probabilidades de error razonablemente bajas. Muchas veces se puede considerar que el canal es localmente lineal. Si se utilizan esquemas basados en funciones lineales que actúen localmente e independientes unos de otros, se consiguen resultados satisfactorios. Incluso cuando el canal presenta no linealidades, es posible utilizar esquemas lineales que, actuando en paralelo, se especialicen en zonas diferentes del espacio. En esta Tesis se examinará un esquema de este tipo, que es el esquema en escalera. Este esquema se basa en una cadena de decisiones bit a bit a partir de las cuales se lleva a cabo la decisión multinivel. El procedimiento bit a bit del esquema en escalera permite introducir algoritmos de gradiente basados en objetivos binarios, lo que permite equilibrios en compromisos en prestaciones frente a velocidad. Sin embargo, algunos objetivos, como la Entropía Relativa, sólo convergen bajo ciertas condiciones iniciales, lo que dificulta el funcionamiento del sistema. Aquí se proponen maneras sencillas de facilitar la convergencia sin necesidad de introducir restricciones en el sistema. El esquema en escalera facilita la inserción de algoritmos no lineales sólo en las zonas del espacio que lo necesiten, dejando las otras para clasificación lineal. Por otro lado, se han desarrollado sistemas de clasificación inspirados en la Máquina de Vectores de Soporte, que ha dado muy buenos resultados en problemas de clasificación, pero que no es adaptativa. En esta Tesis desarrollamos variantes de este algoritmo basados en métodos de selección de muestras, que han proporcionado buenos resultados en velocidad de convergencia y capacidad de seguimiento de canales no estacionarios.
Nonlinear equalization schemes sigriificanfly enable data transmission speed to be increased in dispersive channeis, and particularly in those which are also nonhinear. Two are its rnost important drawbacks: its bigh complexity and its low convergence rate. Nonlinear schernes need high computational power so as to be able to carry out the big number of necessary cornputations per sample. On the other hand, sorne nonhinear schernes such as the multilayer perceptron not only need a large amount of data in order to reach convergence, but they also run the risk of failing down to local minima for convergence, which makes thern be little practical in cornrnunications. Other schernes, such as Volterra ftlters, are less prone to fail down to local rninima thanks because of their architecture, but they do not easily adjust for reaching convergence. In sorne situations, the use of nonhinear schernes for reaching reasonably low error probabilities is not necessary. In many cases one can consider that the channel is localy linear. When schernes based upon linear functions operating localy and independently from one another are used, one obtains satisfactory results. Even if the channel has nonlinearities, it is possible to use linear schemes which, operating in parallel, specialize in dlifferent areas of dic space. Iii this Thesis this kind of scherne, called staircare scheme, will be analysed. It is based on a bit by bit decisions chain from which one carnes out dic decision iii a communications multilevel. The bit by bit staircase scherne procedure allows gradient algorithms based upon binary objectives to be introduced, which enables balancing commitments performance and speed. Nevertheless, sorne objectives, such as Relative Entropy, only converge under certain iiiitial conditions which hinder the running of the system. Here they suggest easy ways of making convergence easy without the need of introducing any restrictions in the system. The staircase scherne makes nonhinear algorithm insertion easier only in those arcas of the space where it is needed, leaving the remaining nonlinear algorithms to linear classification. On dic other hand, classification systems inspired by the Support Vectors Machine have shown good results in classification problems tough they are not adaptative. In this thesis wc will develop variants of this algorithm based on sarnple selection methods which have fournished good resulta in speed convergence as wdll as iii their nonstationary channel tracking abilty.
Nonlinear equalization schemes sigriificanfly enable data transmission speed to be increased in dispersive channeis, and particularly in those which are also nonhinear. Two are its rnost important drawbacks: its bigh complexity and its low convergence rate. Nonlinear schernes need high computational power so as to be able to carry out the big number of necessary cornputations per sample. On the other hand, sorne nonhinear schernes such as the multilayer perceptron not only need a large amount of data in order to reach convergence, but they also run the risk of failing down to local minima for convergence, which makes thern be little practical in cornrnunications. Other schernes, such as Volterra ftlters, are less prone to fail down to local rninima thanks because of their architecture, but they do not easily adjust for reaching convergence. In sorne situations, the use of nonhinear schernes for reaching reasonably low error probabilities is not necessary. In many cases one can consider that the channel is localy linear. When schernes based upon linear functions operating localy and independently from one another are used, one obtains satisfactory results. Even if the channel has nonlinearities, it is possible to use linear schemes which, operating in parallel, specialize in dlifferent areas of dic space. Iii this Thesis this kind of scherne, called staircare scheme, will be analysed. It is based on a bit by bit decisions chain from which one carnes out dic decision iii a communications multilevel. The bit by bit staircase scherne procedure allows gradient algorithms based upon binary objectives to be introduced, which enables balancing commitments performance and speed. Nevertheless, sorne objectives, such as Relative Entropy, only converge under certain iiiitial conditions which hinder the running of the system. Here they suggest easy ways of making convergence easy without the need of introducing any restrictions in the system. The staircase scherne makes nonhinear algorithm insertion easier only in those arcas of the space where it is needed, leaving the remaining nonlinear algorithms to linear classification. On dic other hand, classification systems inspired by the Support Vectors Machine have shown good results in classification problems tough they are not adaptative. In this thesis wc will develop variants of this algorithm based on sarnple selection methods which have fournished good resulta in speed convergence as wdll as iii their nonstationary channel tracking abilty.
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Transmisión digital, Algoritmos, Igualación no lineal