Single-carrier frequency-domain equalization with hybrid decision feedback equalizer for Hammerstein channels containing nonlinear transmit amplifier

We propose a nonlinear hybrid decision feedback equalizer (NHDFE) for single-carrier (SC) block transmission systems with nonlinear transmit high power amplifier (HPA), which significantly outperforms our previous nonlinear SC frequency-domain equalization (NFDE) design. To obtain the coefficients of the channel impulse response (CIR) as well as to estimate the nonlinear mapping and the inverse nonlinear mapping of the HPA, we adopt a complex-valued (CV) B-spline neural network approach. Specifically, we use a CV B-spline neural network to model the nonlinear HPA, and we develop an efficient alternating least squares scheme for estimating the parameters of the Hammerstein channel, including both the CIR coefficients and the parameters of the CV B-spline model. We also adopt another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can be estimated using the least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. The effectiveness of our NHDFE design is demonstrated in a simulation study, which shows that the NHDFE achieves a signal-to-noise ratio gain of 4dB over the NFDE at the bit error rate level of 10−4

Comparative performance of complex-valued B-spline and polynomial models applied to iterative frequency-domain decision feedback equalization of Hammerstein channels

Complex-valued (CV) B-spline neural network approach offers a highly effective means for identifying and inverting practical Hammerstein systems. Compared with its conventional CV polynomial-based counterpart, a CV B-spline neural network has superior performance in identifying and inverting CV Hammerstein systems, while imposing a similar complexity. This paper reviews the optimality of the CV B-spline neural network approach. Advantages of B-spline neural network approach as compared with the polynomial based modeling approach are extensively discussed, and the effectiveness of the CV neural network-based approach is demonstrated in a real-world application. More specifically, we evaluate the comparative performance of the CV B-spline and polynomial-based approaches for the nonlinear iterative frequency-domain decision feedback equalization (NIFDDFE) of single-carrier Hammerstein channels. Our results confirm the superior performance of the CV B-spline-based NIFDDFE over its CV polynomial-based counterpart

Formes d'ondes avancées et traitements itératifs pour les canaux non linéaires satellites

L'augmentation de l'efficacité spectrale des transmissions mono-porteuses sur un lien de diffusion par satellite est devenu un défi d'envergure afin de pallier la demande croissante en débits de transmission. Si des techniques émergentes de transmissions encouragent l'utilisation de modulations à ordre élevé telles que les modulations de phase et d'amplitude (APSK), certaines dégradations sont encourues lors du traitement à bord du satellite. En effet, en raison de l'utilisation d'amplificateurs de puissance ainsi que de filtres à mémoires, les modulations d'ordre élevé subissent des distorsions non-linéaires dues à la fluctuation de leur enveloppe, ce qui nécessite des traitements au sein de l'émetteur ou bien au sein du récepteur. Dans cette thèse, nous nous intéressons au traitement de l'interférence non-linéaire au sein du récepteur, avec une attention particulière aux égaliseurs itératifs qui améliorent les performances du système au prix d'une complexité élevée. A partir du modèle temporel des interférences non-linéaires induites par l'amplificateur de puissance, des algorithmes de réception optimaux et sous optimaux sont dérivés, et leurs performances comparées. Des égaliseurs à complexité réduite sont aussi étudiés dans le but d'atteindre un compromis performances-complexité satisfaisant. Ensuite, un modèle des non-linéarités est dérivé dans le domaine fréquentiel, et les égaliseurs correspondants sont présentés. Dans un second temps, nous analysons et dérivons des récepteurs itératifs pour l'interférence entre symboles non linéaire. L'objectif est d'optimiser les polynômes de distributions d'un code externe basé sur les codes de contrôle de parité à faible densité (LDPC) afin de coller au mieux à la sortie de l'égaliseur. Le récepteur ainsi optimisé atteint de meilleures performances comparé à un récepteur non optimisé pour le canal non-linéaire. Finalement, nous nous intéressons à une classe spécifique de techniques de transmissions mono-porteuse basée sur le multiplexage par division de fréquence (SC-OFDM) pour les liens satellites. L'avantage de ces formes d'ondes réside dans l'efficacité de leur égaliseur dans le domaine fréquentiel. Des formules analytiques de la densité spectrale de puissance et du rapport signal sur bruit et interférence sont dérivées et utilisées afin de prédire les performances du système. ABSTRACT : Increasing both the data rate and power efficiency of single carrier transmissions over broadcast satellite links has become a challenging issue to comply with the urging demand of higher transmission rates. If emerging transmission techniques encourage the use of high order modulations such as Amplitude and Phase Shift Keying (APSK) and Quadrature Amplitude Modulation (QAM), some channel impairments arise due to onboard satellite processing. Indeed, due to satellite transponder Power Amplifiers (PA) as well as transmission filters, high order modulations incur non linear distortions due to their high envelope fluctuations which require specific processing either at the transmitter or at the receiver. In this thesis, we investigate on non linear interference mitigation at the receiver with a special focus on iterative equalizers which dramatically enhance the performance at the cost of additional complexity. Based on the time domain model of the non linear interference induced by the PA, optimal and sub-optimal receiving algorithms are proposed and their performance compared. Low complexity implementations are also investigated for the sake of a better complexity-performance trade-off. Then, a non linear frequency domain model is derived and the corresponding frequency equalizers are investigated. In the second part, we analyse and design an iterative receiver for the non linear Inter Symbol Interference (ISI) channel. The objective is to optimize an outer Low Density Parity Check (LDPC) code distribution polynomials so as to best fit the inner equalizer Extrinsic information. The optimized receiver is shown to achieve better performance compared to a code only optimized for linear ISI channel. Finally, we investigate on a specific class of single carrier transmissions relying on Single Carrier Orthogonal Frequency Division Multiplexing (SCO-FDM) for satellite downlink. The advantage of such waveforms lies in their practical receiver implementation in the frequency domain. General analytical formulas of the power spectral density and signal to noise and interference ratio are derived and used to predict the bit error rate for frequency selective multiplexers

Adaptive Algorithms for Intelligent Acoustic Interfaces

Modern speech communications are evolving towards a new direction which involves users in a more perceptive way. That is the immersive experience, which may be considered as the “last-mile” problem of telecommunications. One of the main feature of immersive communications is the distant-talking, i.e. the hands-free (in the broad sense) speech communications without bodyworn or tethered microphones that takes place in a multisource environment where interfering signals may degrade the communication quality and the intelligibility of the desired speech source. In order to preserve speech quality intelligent acoustic interfaces may be used. An intelligent acoustic interface may comprise multiple microphones and loudspeakers and its peculiarity is to model the acoustic channel in order to adapt to user requirements and to environment conditions. This is the reason why intelligent acoustic interfaces are based on adaptive filtering algorithms. The acoustic path modelling entails a set of problems which have to be taken into account in designing an adaptive filtering algorithm. Such problems may be basically generated by a linear or a nonlinear process and can be tackled respectively by linear or nonlinear adaptive algorithms. In this work we consider such modelling problems and we propose novel effective adaptive algorithms that allow acoustic interfaces to be robust against any interfering signals, thus preserving the perceived quality of desired speech signals. As regards linear adaptive algorithms, a class of adaptive filters based on the sparse nature of the acoustic impulse response has been recently proposed. We adopt such class of adaptive filters, named proportionate adaptive filters, and derive a general framework from which it is possible to derive any linear adaptive algorithm. Using such framework we also propose some efficient proportionate adaptive algorithms, expressly designed to tackle problems of a linear nature. On the other side, in order to address problems deriving from a nonlinear process, we propose a novel filtering model which performs a nonlinear transformations by means of functional links. Using such nonlinear model, we propose functional link adaptive filters which provide an efficient solution to the modelling of a nonlinear acoustic channel. Finally, we introduce robust filtering architectures based on adaptive combinations of filters that allow acoustic interfaces to more effectively adapt to environment conditions, thus providing a powerful mean to immersive speech communications

Adaptive Algorithms for Intelligent Acoustic Interfaces

Modern speech communications are evolving towards a new direction which involves users in a more perceptive way. That is the immersive experience, which may be considered as the “last-mile” problem of telecommunications. One of the main feature of immersive communications is the distant-talking, i.e. the hands-free (in the broad sense) speech communications without bodyworn or tethered microphones that takes place in a multisource environment where interfering signals may degrade the communication quality and the intelligibility of the desired speech source. In order to preserve speech quality intelligent acoustic interfaces may be used. An intelligent acoustic interface may comprise multiple microphones and loudspeakers and its peculiarity is to model the acoustic channel in order to adapt to user requirements and to environment conditions. This is the reason why intelligent acoustic interfaces are based on adaptive filtering algorithms. The acoustic path modelling entails a set of problems which have to be taken into account in designing an adaptive filtering algorithm. Such problems may be basically generated by a linear or a nonlinear process and can be tackled respectively by linear or nonlinear adaptive algorithms. In this work we consider such modelling problems and we propose novel effective adaptive algorithms that allow acoustic interfaces to be robust against any interfering signals, thus preserving the perceived quality of desired speech signals. As regards linear adaptive algorithms, a class of adaptive filters based on the sparse nature of the acoustic impulse response has been recently proposed. We adopt such class of adaptive filters, named proportionate adaptive filters, and derive a general framework from which it is possible to derive any linear adaptive algorithm. Using such framework we also propose some efficient proportionate adaptive algorithms, expressly designed to tackle problems of a linear nature. On the other side, in order to address problems deriving from a nonlinear process, we propose a novel filtering model which performs a nonlinear transformations by means of functional links. Using such nonlinear model, we propose functional link adaptive filters which provide an efficient solution to the modelling of a nonlinear acoustic channel. Finally, we introduce robust filtering architectures based on adaptive combinations of filters that allow acoustic interfaces to more effectively adapt to environment conditions, thus providing a powerful mean to immersive speech communications

Flexible methods for blind separation of complex signals

One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved. For this scope in this thesis a flexible approach is introduced and the shape of the activation functions is changed during the learning process using the so-called “spline functions”. The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable. A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable. Unfortunately the linear environment is unrealistic in many practical applications. In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”. The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission. In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery: usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed. Several experimental results, tested by different objective indexes, show the effectiveness of the proposed approaches

Flexible methods for blind separation of complex signals

One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved. For this scope in this thesis a flexible approach is introduced and the shape of the activation functions is changed during the learning process using the so-called “spline functions”. The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable. A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable. Unfortunately the linear environment is unrealistic in many practical applications. In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”. The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission. In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery: usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed. Several experimental results, tested by different objective indexes, show the effectiveness of the proposed approaches

Oblique Sounding and HF Communication Techniques for Very Long Haul Ionospheric Links

El sistema de comunicació ràdio d’alta freqüència (HF, en anglès) és usat arreu del món per agències governamentals i no governamentals sempre que calgui una alternativa a les comunicacions via satèl•lit: vaixells a alta mar, avions fora de cobertura de xarxes ràdio amb visió directa, operacions militars, zones on la infraestructura ha estat destruïda per algun tipus de desastre o bé zones llunyanes sense cap altre tipus de comunicació. La ràdio HF representa una alternativa, o un sistema de backup al satèl•lit per a comunicacions de llarg abast i en redueix els costos, evita la vulnerabilitat i els problemes de sobirania. En aquesta tesi s’ha estudiat l’enllaç HF entre la base antàrtica espanyola Juan Carlos I, situada a l’illa Livingston a l’arxipèlag de les Shetland del Sud, i Espanya. L’objectiu d’aquest treball és estudiar els problemes que afecten la propagació; és a dir, la relació senyal a soroll i interferència, la dispersió multicamí i la dispersió per efecte Doppler, i dissenyar la capa física d’un enllaç HF de baixa velocitat, poca potència i llarg abast. Pel que fa aquest últim punt es fan un parell de propostes: espectre eixamplat per seqüència directa (DSSS, en anglès) i multiplexació per divisió en freqüència ortogonal (OFDM, en anglès). El repte que es planteja és el de la definició de les característiques dels símbols que millor encaixen en aquest canal per tal d’obtenir un benefici de la diversitat temporal i freqüencial que ofereix el canal. Des de l’any 2003 diverses campanyes han permès estudiar aquest canal HF, però no va ser fins la campanya 2009/2010 que s’obtingué un foto de les característiques, diürnes i nocturnes, de la ionosfera. En els articles que es presenten en aquesta tesi hem estès el rang freqüencial d’estudi respecte a investigacions prèvies i hem mostrat diferències de comportament entre el dia i la nit. Hem usat els resultats de la caracterització del canal per a dissenyar i comparar la bondat dels símbols DSSS i OFDM. Ambdues possibilitats han resultat ser candidates a implementar l’enllaç HF entre l’Antàrtida i Espanya. Tot i així, ambdues tècniques representen visions diferents de la implementació del mòdem: mentre que DSSS obté bons resultats a baixa velocitat en entorns amb baixa relació senyal a soroll, OFDM aconsegueix tasses de velocitat més elevades en canals més benignes.Los sistemas de radio de alta frecuencia (HF, en inglés) son usados por agencias gubernamentales y no gubernamentales en todo el mundo siempre que se necesite una alternativa a las comunicaciones por satélite: barcos en alta mar, aviones fuera del rango de cobertura de las redes radio de visión directa, operaciones militares, zonas donde la infraestructura ha sido destruida por algún desastre. Ésta ofrece una alternativa, o representa un sistema de backup, a las comunicaciones vía satélite, evitando los costes, la vulnerabilidad y los problemas de soberanía de las comunicaciones por satélite. En esta tesis se ha estudiado el enlace HF entre la base antártica española Juan Carlos I en la isla Livingston, en las Shetland del sur y España. El objetivo de este trabajo es el estudio de las limitaciones de la propagación ionosférica (como la relación señal a ruido e interferencia, la dispersión multicamino y la dispersión por efecto Doppler) y el diseño de la capa física de un enlace HF de baja velocidad, baja potencia y largo alcance. Se han estudiado un par de propuestas para este enlace, como son el espectro ensanchado por secuencia directa (DSSS, en inglés) y la multiplexación por división en frecuencia ortogonal (OFDM, en inglés). El reto ha sido definir las características que mejor se adecuan a este enlace para poder aprovechar la diversidad temporal y frecuencial que ofrece el canal HF. Desde el año 2003 diversas campañas de sondeo han permitido estudiar el canal HF pero no es hasta la campaña 2009/2010 que se consigue una fotografía de la actividad ionosférica tanto nocturna como diurna. En los artículos que se presentan en esta tesis hemos extendido los estudios previos a todo el rango de frecuencias HF y hemos mostrado las diferencias entre el día y la noche. Hemos usado estos resultados de caracterización del canal para diseñar y comparar símbolos DSSS y símbolos OFDM. Ambas posibilidades han resultado ser posibles candidatas para implementar un enlace HF de baja velocidad entre la Antártida y España. Sin embargo ambas técnicas representan dos aproximaciones distintas a la implementación del módem. Mientras que DSSS consigue un buen funcionamiento a baja velocidad en escenarios con baja relación señal a ruido, OFDM consigue tasas de transmisión más altas en escenarios más benignos.High Frequency (HF) radio is used by governmental and non nongovernmental agencies worldwide whenever an alternative to satellites for sky wave communication is needed: ships at sea, aircraft out of range of line-of-sight radio networks, military operations, disaster areas with communication infrastructure destroyed or distant regions lacking other communications. It offers an alternative to satellites, or a backup, for long-haul communications, thus avoiding the costs, vulnerabilities and sovereignty concerns of satellite communications. In this thesis the HF link between the Antarctic Spanish Station Juan Carlos I in Livingston Island, South Shetlands and Spain is studied. The aim of this study is to address the impairments that affect HF propagation (i.e., signal-to-noise plus interference ratio, multipath and Doppler shift and spread) and to design the physical layer of a low rate, low power and long-haul HF link. Some proposals regarding this last issue are addressed, i.e., direct sequence spread spectrum (DSSS) and orthogonal frequency division multiplexing (OFDM). The challenge is to define the symbol characteristics that best fit the link to benefit from time and frequency diversity that offers the HF channel. Since 2003 several transmission campaigns have allowed to study the HF channel but it is not until the 2009/2010 campaign that we have achieved a whole picture of both diurnal and nocturnal ionospheric activity. In the papers presented in this thesis we have extended the previous research to the whole range of HF frequencies and we have shown the differences on performance between day and night. We have used the results from channel characterization to design and compare the performance of DSSS and OFDM symbols. Both techniques have turned out to be possible candidates to implement a low rate HF link between Antarctica and Spain. However, both techniques stand for different approaches of the modem: DSSS achieves good performance at low data rate in low SNR scenarios, whereas OFDM achieves higher data rate in benign channel