Neste trabalho, são propostos e analisados algoritmos autodidatas eficientes para a equalização de canais de comunicação, considerando a transmissão de sinais QAM (quadrature amplitude modulation). Suas funções de erro são construídas de forma a fazer com que o erro de estimação seja igual a zero nas coordenadas dos símbolos da constelação. Essa característica os possibilita ter um desempenho similar ao de um algoritmo de equalização supervisionada como o NLMS (normalized least mean-square), independentemente da ordem da constelação QAM. Verifica-se analiticamente que, sob certas condições favoráveis para a equalização, os vetores de coeficientes dos algoritmos propostos e a correspondente solução de Wiener são colineares. Além disso, usando a informação da estimativa do símbolo transmitido e de seus símbolos vizinhos, esquemas de baixo custo computacional são propostos para aumentar a velocidade de convergência dos algoritmos. No caso do algoritmo baseado no critério do módulo constante, evita-se sua divergência através de um mecanismo que descarta estimativas inconsistentes dos símbolos transmitidos. Adicionalmente, apresenta-se uma análise de rastreio (tracking), que permite obter expressões analíticas para o erro quadrático médio em excesso dos algoritmos propostos em ambientes estacionários e não-estacionários. Através dessas expressões, verifica-se que com sobreamostragem, ausência de ruído e ambiente estacionário, os algoritmos propostos podem alcançar a equalização perfeita, independentemente da ordem da constelação QAM. Os algoritmos são estendidos para a adaptação conjunta dos filtros direto e de realimentação do equalizador de decisão realimentada, levando-se em conta um mecanismo que evita soluções degeneradas. Resultados de simulação sugerem que a utilização dos esquemas aqui propostos pode ser vantajosa na recuperação de sinais QAM, fazendo com que seja desnecessário o chaveamento para o algoritmo de decisão direta. / In this work, we propose efficient blind algorithms for equalization of communication channels, considering the transmission of QAM (quadrature amplitude modulation) signals. Their error functions are constructed in order to make the estimation error equal to zero at the coordinates of the constellation symbols. This characteristic enables the proposed algorithms to have a similar performance to that of a supervised equalization algorithm as the NLMS (normalized least mean-square), independently of the QAM order. Under some favorable conditions, we verify analytically that the coefficient vector of the proposed algorithms are collinear with the Wiener solution. Furthermore, using the information of the symbol estimate in conjunction with its neighborhood, we propose schemes of low computational cost in order to improve their convergence rate. The divergence of the constant-modulus based algorithm is avoided by using a mechanism, which disregards nonconsistent estimates of the transmitted symbols. Additionally, we present a tracking analysis in which we obtain analytical expressions for the excess mean-square error in stationary and nonstationary environments. From these expressions, we verify that using a fractionally-spaced equalizer in a noiseless stationary environment, the proposed algorithms can achieve perfect equalization, independently of the QAM order. The algorithms are extended to jointly adapt the feedforward and feedback filters of the decision feedback equalizer, taking into account a mechanism to avoid degenerative solutions. Simulation results suggest that the proposed schemes may be advantageously used to recover QAM signals and make the switching to the decision direct mode unnecessary.

Neste trabalho, são propostos e analisados algoritmos autodidatas eficientes para a equalização de canais de comunicação, considerando a transmissão de sinais QAM (quadrature amplitude modulation). Suas funções de erro são construídas de forma a fazer com que o erro de estimação seja igual a zero nas coordenadas dos símbolos da constelação. Essa característica os possibilita ter um desempenho similar ao de um algoritmo de equalização supervisionada como o NLMS (normalized least mean-square), independentemente da ordem da constelação QAM. Verifica-se analiticamente que, sob certas condições favoráveis para a equalização, os vetores de coeficientes dos algoritmos propostos e a correspondente solução de Wiener são colineares. Além disso, usando a informação da estimativa do símbolo transmitido e de seus símbolos vizinhos, esquemas de baixo custo computacional são propostos para aumentar a velocidade de convergência dos algoritmos. No caso do algoritmo baseado no critério do módulo constante, evita-se sua divergência através de um mecanismo que descarta estimativas inconsistentes dos símbolos transmitidos. Adicionalmente, apresenta-se uma análise de rastreio (tracking), que permite obter expressões analíticas para o erro quadrático médio em excesso dos algoritmos propostos em ambientes estacionários e não-estacionários. Através dessas expressões, verifica-se que com sobreamostragem, ausência de ruído e ambiente estacionário, os algoritmos propostos podem alcançar a equalização perfeita, independentemente da ordem da constelação QAM. Os algoritmos são estendidos para a adaptação conjunta dos filtros direto e de realimentação do equalizador de decisão realimentada, levando-se em conta um mecanismo que evita soluções degeneradas. Resultados de simulação sugerem que a utilização dos esquemas aqui propostos pode ser vantajosa na recuperação de sinais QAM, fazendo com que seja desnecessário o chaveamento para o algoritmo de decisão direta. / In this work, we propose efficient blind algorithms for equalization of communication channels, considering the transmission of QAM (quadrature amplitude modulation) signals. Their error functions are constructed in order to make the estimation error equal to zero at the coordinates of the constellation symbols. This characteristic enables the proposed algorithms to have a similar performance to that of a supervised equalization algorithm as the NLMS (normalized least mean-square), independently of the QAM order. Under some favorable conditions, we verify analytically that the coefficient vector of the proposed algorithms are collinear with the Wiener solution. Furthermore, using the information of the symbol estimate in conjunction with its neighborhood, we propose schemes of low computational cost in order to improve their convergence rate. The divergence of the constant-modulus based algorithm is avoided by using a mechanism, which disregards nonconsistent estimates of the transmitted symbols. Additionally, we present a tracking analysis in which we obtain analytical expressions for the excess mean-square error in stationary and nonstationary environments. From these expressions, we verify that using a fractionally-spaced equalizer in a noiseless stationary environment, the proposed algorithms can achieve perfect equalization, independently of the QAM order. The algorithms are extended to jointly adapt the feedforward and feedback filters of the decision feedback equalizer, taking into account a mechanism to avoid degenerative solutions. Simulation results suggest that the proposed schemes may be advantageously used to recover QAM signals and make the switching to the decision direct mode unnecessary.

Software radios (SWR) have been proposed for wireless communication systems to enable them to operate according to incompatible wireless communication standards by implementing most analog functions in the digital section on software-reprogrammable hardware. However, this significantly increases the required computations for SWR functionality, mainly because of the digital front-end computationally intensive filtering functions, such as sample rate conversion (SRC), channelization, and equalization. For increasing the computational efficiency of SWR systems, two new SRC methods with better performance than conventional SRC methods are presented. In the first SRC method, we modify the conventional CIC filters to enable them to perform SRC on slightly oversampled signals efficiently. We also describe a SRC method with high efficiency for SRC by factors greater than unity at which SRC in SWR systems may be computationally demanding. This SRC method efficiently increases the sample rate of wideband signals, especially in SWR base station transmitters, by applying Lagrange interpolation for evaluating output samples hierarchically using a low-rate signal that is computed with low cost from the input signal. A new channelizer/synthesizer is also developed for extracting/combining frequency multiplexed channels in SWR transceivers. The efficiency of this channelizer/synthesizer, which uses modulated perfect reconstruction (PR) filter banks, is higher than polyphase filter banks (when applicable) for processing few channels, and significantly higher than discrete filter banks for processing any number of variable-bandwidth channels where polyphase filter banks are inapplicable. Because the available methods for designing modulated PR filter banks are inapplicable due to the required number of subchannels and stopband attenuation of the prototype filters, a new design method for these filter banks is introduced. This method is reliable and significantly faster than the existing methods. Modulated PR filter banks are also considered for implementing a frequency-domain block blind equalizer capable of equalizing SWR signals transmitted though channels with long impulse responses and severe intersymbol interference (ISI). This blind equalizer adapts by using separate sets of weights to correct for the magnitude and phase distortion of the channel. The adaptation of this blind equalizer is significantly more reliable and its computational requirements increase at a lower rate compared to conventional time-domain equalizers making it efficient for equalizing long channels that exhibit severe ISI.

L'objet de ce document est de rapporter une partie des travaux de recherche auxquels j'ai contribué durant les cinq dernières années. Le but visé n'est pas de faire une synthèse exhaustive des travaux réalisés sur cette période mais d'en sélectionner certains d'entre eux pour leur pertinence et leur cohérence. Les travaux rapportés dans ce manuscrit concernent l'exploitation des représentations parcimonieuses dans les applications en télécommunication. Depuis mes travaux de thèse, où j'ai abordé le problème de la séparation aveugle de sources en exploitant le caractère parcimonieux des signaux audio, mes travaux gravitent autour des représentations parcimonieuses et leurs applications en communication numérique. En effet, après avoir exploité la propriété de parcimonie des signaux audio dans le domaine temps-fréquence d'un point de vue structurel, je me suis intéressé aux mesures de parcimonie et aux problèmes inverses régularisés. Cette réflexion m'a poussé à entreprendre l'étude sur l'exploitation de la parcimonie pour l'estimation aveugle de canaux de communication. En particulier, l'identification aveugle de canaux parcimonieux dans les systèmes Single-Input Multiple-Output (SIMO). Une extension de ces techniques a été développée pour les systèmes Multiple-Input Multiple-Output MIMO OFDM où le cas semi-aveugle a été traité. L'identification de canaux pour les communications étant étroitement liée aux signaux à alphabet fini. Je me suis par conséquent intéressé à l'exploitation de cette caractéristique des signaux de communication (signaux à alphabet fini) par le biais des représentations parcimonieuses afin de résoudre certains problèmes inverses difficiles. Enfin, j'ai abordé le problème de détection de signaux en utilisant des méthodes de tests statistiques basées sur l'hypothèse de parcimonie des signaux observés. Ces méthodes ont trouvés un cadre applicatif dans les communications sans fil, la guerre électronique et la séparation aveugle de sources.

L'objet de ce document est de rapporter une partie des travaux de recherche auxquels j'ai contribué durant les cinq dernières années. Le but visé n'est pas de faire une synthèse exhaustive des travaux réalisés sur cette période mais d'en sélectionner certains d'entre eux pour leur pertinence et leur cohérence. Les travaux rapportés dans ce manuscrit concernent l'exploitation des représentations parcimonieuses dans les applications en télécommunication. Depuis mes travaux de thèse, où j'ai abordé le problème de la séparation aveugle de sources en exploitant le caractère parcimonieux des signaux audio, mes travaux gravitent autour des représentations parcimonieuses et leurs applications en communication numérique. En effet, après avoir exploité la propriété de parcimonie des signaux audio dans le domaine temps-fréquence d'un point de vue structurel, je me suis intéressé aux mesures de parcimonie et aux problèmes inverses régularisés. Cette réflexion m'a poussé à entreprendre l'étude sur l'exploitation de la parcimonie pour l'estimation aveugle de canaux de communication. En particulier, l'identification aveugle de canaux parcimonieux dans les systèmes Single-Input Multiple-Output (SIMO). Une extension de ces techniques a été développée pour les systèmes Multiple-Input Multiple-Output MIMO OFDM où le cas semi-aveugle a été traité. L'identification de canaux pour les communications étant étroitement liée aux signaux à alphabet fini. Je me suis par conséquent intéressé à l'exploitation de cette caractéristique des signaux de communication (signaux à alphabet fini) par le biais des représentations parcimonieuses afin de résoudre certains problèmes inverses difficiles. Enfin, j'ai abordé le problème de détection de signaux en utilisant des méthodes de tests statistiques basées sur l'hypothèse de parcimonie des signaux observés. Ces méthodes ont trouvés un cadre applicatif dans les communications sans fil, la guerre électronique et la séparation aveugle de sources.

En la última década, los métodos kernel (métodos núcleo) han demostrado ser técnicas muy eficaces en la resolución de problemas no lineales. Parte de su éxito puede atribuirse a su sólida base matemática dentro de los espacios de Hilbert generados por funciones kernel ("reproducing kernel Hilbert spaces", RKHS); y al hecho de que resultan en problemas convexos de optimización. Además, son aproximadores universales y la complejidad computacional que requieren es moderada. Gracias a estas características, los métodos kernel constituyen una alternativa atractiva a las técnicas tradicionales no lineales, como las series de Volterra, los polinómios y las redes neuronales. Los métodos kernel también presentan ciertos inconvenientes que deben ser abordados adecuadamente en las distintas aplicaciones, por ejemplo, las dificultades asociadas al manejo de grandes conjuntos de datos y los problemas de sobreajuste ocasionados al trabajar en espacios de dimensionalidad infinita.En este trabajo se desarrolla un conjunto de algoritmos basados en métodos kernel para resolver una serie de problemas no lineales, dentro del ámbito del procesado de señal y las comunicaciones. En particular, se tratan problemas de identificación e igualación de sistemas no lineales, y problemas de separación ciega de fuentes no lineal ("blind source separation", BSS). Esta tesis se divide en tres partes. La primera parte consiste en un estudio de la literatura sobre los métodos kernel. En la segunda parte, se proponen una serie de técnicas nuevas basadas en regresión con kernels para resolver problemas de identificación e igualación de sistemas de Wiener y de Hammerstein, en casos supervisados y ciegos. Como contribución adicional se estudia el campo del filtrado adaptativo mediante kernels y se proponen dos algoritmos recursivos de mínimos cuadrados mediante kernels ("kernel recursive least-squares", KRLS). En la tercera parte se tratan problemas de decodificación ciega en que las fuentes son dispersas, como es el caso en comunicaciones digitales. La dispersidad de las fuentes se refleja en que las muestras observadas se agrupan, lo cual ha permitido diseñar técnicas de decodificación basadas en agrupamiento espectral. Las técnicas propuestas se han aplicado al problema de la decodificación ciega de canales MIMO rápidamente variantes en el tiempo, y a la separación ciega de fuentes post no lineal. / In the last decade, kernel methods have become established techniques to perform nonlinear signal processing. Thanks to their foundation in the solid mathematical framework of reproducing kernel Hilbert spaces (RKHS), kernel methods yield convex optimization problems. In addition, they are universal nonlinear approximators and require only moderate computational complexity. These properties make them an attractive alternative to traditional nonlinear techniques such as Volterra series, polynomial filters and neural networks.This work aims to study the application of kernel methods to resolve nonlinear problems in signal processing and communications. Specifically, the problems treated in this thesis consist of the identification and equalization of nonlinear systems, both in supervised and blind scenarios, kernel adaptive filtering and nonlinear blind source separation.In a first contribution, a framework for identification and equalization of nonlinear Wiener and Hammerstein systems is designed, based on kernel canonical correlation analysis (KCCA). As a result of this study, various other related techniques are proposed, including two kernel recursive least squares (KRLS) algorithms with fixed memory size, and a KCCA-based blind equalization technique for Wiener systems that uses oversampling. The second part of this thesis treats two nonlinear blind decoding problems of sparse data, posed under conditions that do not permit the application of traditional clustering techniques. For these problems, which include the blind decoding of fast time-varying MIMO channels, a set of algorithms based on spectral clustering is designed. The effectiveness of the proposed techniques is demonstrated through various simulations.