Unsupervised Learning for Monaural Source Separation Using Maximization–Minimization Algorithm with Time–Frequency Deconvolution

This paper presents an unsupervised learning algorithm for sparse nonnegative matrix factor time–frequency deconvolution with optimized fractional β -divergence. The β -divergence is a group of cost functions parametrized by a single parameter β . The Itakura–Saito divergence, Kullback–Leibler divergence and Least Square distance are special cases that correspond to β=0, 1, 2 , respectively. This paper presents a generalized algorithm that uses a flexible range of β that includes fractional values. It describes a maximization–minimization (MM) algorithm leading to the development of a fast convergence multiplicative update algorithm with guaranteed convergence. The proposed model operates in the time–frequency domain and decomposes an information-bearing matrix into two-dimensional deconvolution of factor matrices that represent the spectral dictionary and temporal codes. The deconvolution process has been optimized to yield sparse temporal codes through maximizing the likelihood of the observations. The paper also presents a method to estimate the fractional β value. The method is demonstrated on separating audio mixtures recorded from a single channel. The paper shows that the extraction of the spectral dictionary and temporal codes is significantly more efficient by using the proposed algorithm and subsequently leads to better source separation performance. Experimental tests and comparisons with other factorization methods have been conducted to verify its efficacy

GNSS array-based acquisition: theory and implementation

This Dissertation addresses the signal acquisition problem using antenna arrays in the general framework of Global Navigation Satellite Systems (GNSS) receivers. The term GNSS classi es those navigation systems based on a constellation of satellites, which emit ranging signals useful for positioning. Although the American GPS is already available, which coexists with the renewed Russian Glonass, the forthcoming European contribution (Galileo) along with the Chinese Compass will be operative soon. Therefore, a variety of satellite constellations and signals will be available in the next years. GNSSs provide the necessary infrastructures for a myriad of applications and services that demand a robust and accurate positioning service. The positioning availability must be guaranteed all the time, specially in safety-critical and mission-critical services. Examining the threats against the service availability, it is important to take into account that all the present and the forthcoming GNSSs make use of Code Division Multiple Access (CDMA) techniques. The ranging signals are received with very low precorrelation signal-to-noise ratio (in the order of ���22 dB for a receiver operating at the Earth surface). Despite that the GNSS CDMA processing gain o ers limited protection against Radio Frequency interferences (RFI), an interference with a interference-to-signal power ratio that exceeds the processing gain can easily degrade receivers' performance or even deny completely the GNSS service, specially conventional receivers equipped with minimal or basic level of protection towards RFIs. As a consequence, RFIs (either intentional or unintentional) remain as the most important cause of performance degradation. A growing concern of this problem has appeared in recent times. Focusing our attention on the GNSS receiver, it is known that signal acquisition has the lowest sensitivity of the whole receiver operation, and, consequently, it becomes the performance bottleneck in the presence of interfering signals. A single-antenna receiver can make use of time and frequency diversity to mitigate interferences, even though the performance of these techniques is compromised in low SNR scenarios or in the presence of wideband interferences. On the other hand, antenna arrays receivers can bene t from spatial-domain processing, and thus mitigate the e ects of interfering signals. Spatial diversity has been traditionally applied to the signal tracking operation of GNSS receivers. However, initial tracking conditions depend on signal acquisition, and there are a number of scenarios in which the acquisition process can fail as stated before. Surprisingly, to the best of our knowledge, the application of antenna arrays to GNSS signal acquisition has not received much attention. This Thesis pursues a twofold objective: on the one hand, it proposes novel arraybased acquisition algorithms using a well-established statistical detection theory framework, and on the other hand demonstrates both their real-time implementation feasibility and their performance in realistic scenarios. The Dissertation starts with a brief introduction to GNSS receivers fundamentals, providing some details about the navigation signals structure and the receiver's architecture of both GPS and Galileo systems. It follows with an analysis of GNSS signal acquisition as a detection problem, using the Neyman-Pearson (NP) detection theory framework and the single-antenna acquisition signal model. The NP approach is used here to derive both the optimum detector (known as clairvoyant detector ) and the sov called Generalized Likelihood Ratio Test (GLRT) detector, which is the basis of almost all of the current state-of-the-art acquisition algorithms. Going further, a novel detector test statistic intended to jointly acquire a set of GNSS satellites is obtained, thus reducing both the acquisition time and the required computational resources. The eff ects of the front-end bandwidth in the acquisition are also taken into account. Then, the GLRT is extended to the array signal model to obtain an original detector which is able to mitigate temporally uncorrelated interferences even if the array is unstructured and moderately uncalibrated, thus becoming one of the main contributions of this Dissertation. The key statistical feature is the assumption of an arbitrary and unknown covariance noise matrix, which attempts to capture the statistical behavior of the interferences and other non-desirable signals, while exploiting the spatial dimension provided by antenna arrays. Closed form expressions for the detection and false alarm probabilities are provided. Performance and interference rejection capability are modeled and compared both to their theoretical bound. The proposed array-based acquisition algorithm is also compared to conventional acquisition techniques performed after blind null-steering beamformer approaches, such as the power minimization algorithm. Furthermore, the detector is analyzed under realistic conditions, accounting for the presence of errors in the covariance matrix estimation, residual Doppler and delay errors, and signal quantization e ects. Theoretical results are supported by Monte Carlo simulations. As another main contribution of this Dissertation, the second part of the work deals with the design and the implementation of a novel Field Programmable Gate Array (FPGA)-based GNSS real-time antenna-array receiver platform. The platform is intended to be used as a research tool tightly coupled with software de ned GNSS receivers. A complete signal reception chain including the antenna array and the multichannel phase-coherent RF front-end for the GPS L1/ Galileo E1 was designed, implemented and tested. The details of the digital processing section of the platform, such as the array signal statistics extraction modules, are also provided. The design trade-o s and the implementation complexities were carefully analyzed and taken into account. As a proof-of-concept, the problem of GNSS vulnerability to interferences was addressed using the presented platform. The array-based acquisition algorithms introduced in this Dissertation were implemented and tested under realistic conditions. The performance of the algorithms were compared to single antenna acquisition techniques, measured under strong in-band interference scenarios, including narrow/wide band interferers and communication signals. The platform was designed to demonstrate the implementation feasibility of novel array-based acquisition algorithms, leaving the rest of the receiver operations (mainly, tracking, navigation message decoding, code and phase observables, and basic Position, Velocity and Time (PVT) solution) to a Software De ned Radio (SDR) receiver running in a personal computer, processing in real-time the spatially- ltered signal sample stream coming from the platform using a Gigabit Ethernet bus data link. In the last part of this Dissertation, we close the loop by designing and implementing such software receiver. The proposed software receiver targets multi-constellation/multi-frequency architectures, pursuing the goals of e ciency, modularity, interoperability, and exibility demanded by user domains that require non-standard features, such as intermediate signals or data extraction and algorithms interchangeability. In this context, we introduce an open-source, real-time GNSS software de ned receiver (so-named GNSS-SDR) that contributes with several novel features such as the use of software design patterns and shared memory techniques to manage e ciently the data ow between receiver blocks, the use of hardware-accelerated instructions for time-consuming vector operations like carrier wipe-o and code correlation, and the availability to compile and run on multiple software platforms and hardware architectures. At this time of writing (April 2012), the receiver enjoys of a 2-dimensional Distance Root Mean Square (DRMS) error lower than 2 meters for a GPS L1 C/A scenario with 8 satellites in lock and a Horizontal Dilution Of Precision (HDOP) of 1.2.Esta tesis aborda el problema de la adquisición de la señal usando arrays de antenas en el marco general de los receptores de Sistemas Globales de Navegación por Satélite (GNSS). El término GNSS engloba aquellos sistemas de navegación basados en una constelación de satélites que emiten señales útiles para el posicionamiento. Aunque el GPS americano ya está disponible, coexistiendo con el renovado sistema ruso GLONASS, actualmente se está realizando un gran esfuerzo para que la contribución europea (Galileo), junto con el nuevo sistema chino Compass, estén operativos en breve. Por lo tanto, una gran variedad de constelaciones de satélites y señales estarán disponibles en los próximos años. Estos sistemas proporcionan las infraestructuras necesarias para una multitud de aplicaciones y servicios que demandan un servicio de posicionamiento confiable y preciso. La disponibilidad de posicionamiento se debe garantizar en todo momento, especialmente en los servicios críticos para la seguridad de las personas y los bienes. Cuando examinamos las amenazas de la disponibilidad del servicio que ofrecen los GNSSs, es importante tener en cuenta que todos los sistemas presentes y los sistemas futuros ya planificados hacen uso de técnicas de multiplexación por división de código (CDMA). Las señales transmitidas por los satélites son recibidas con una relación señal-ruido (SNR) muy baja, medida antes de la correlación (del orden de -22 dB para un receptor ubicado en la superficie de la tierra). A pesar de que la ganancia de procesado CDMA ofrece una protección inherente contra las interferencias de radiofrecuencia (RFI), esta protección es limitada. Una interferencia con una relación de potencia de interferencia a potencia de la señal que excede la ganancia de procesado puede degradar el rendimiento de los receptores o incluso negar por completo el servicio GNSS. Este riesgo es especialmente importante en receptores convencionales equipados con un nivel mínimo o básico de protección frente las RFIs. Como consecuencia, las RFIs (ya sean intencionadas o no intencionadas), se identifican como la causa más importante de la degradación del rendimiento en GNSS. El problema esta causando una preocupación creciente en los últimos tiempos, ya que cada vez hay más servicios que dependen de los GNSSs Si centramos la atención en el receptor GNSS, es conocido que la adquisición de la señal tiene la menor sensibilidad de todas las operaciones del receptor, y, en consecuencia, se convierte en el factor limitador en la presencia de señales interferentes. Un receptor de una sola antena puede hacer uso de la diversidad en tiempo y frecuencia para mitigar las interferencias, aunque el rendimiento de estas técnicas se ve comprometido en escenarios con baja SNR o en presencia de interferencias de banda ancha. Por otro lado, los receptores basados en múltiples antenas se pueden beneficiar del procesado espacial, y por lo tanto mitigar los efectos de las señales interferentes. La diversidad espacial se ha aplicado tradicionalmente a la operación de tracking de la señal en receptores GNSS. Sin embargo, las condiciones iniciales del tracking dependen del resultado de la adquisición de la señal, y como hemos visto antes, hay un número de situaciones en las que el proceso de adquisición puede fallar. En base a nuestro grado de conocimiento, la aplicación de los arrays de antenas a la adquisición de la señal GNSS no ha recibido mucha atención, sorprendentemente. El objetivo de esta tesis doctoral es doble: por un lado, proponer nuevos algoritmos para la adquisición basados en arrays de antenas, usando como marco la teoría de la detección de señal estadística, y por otro lado, demostrar la viabilidad de su implementación y ejecución en tiempo real, así como su medir su rendimiento en escenarios realistas. La tesis comienza con una breve introducción a los fundamentos de los receptores GNSS, proporcionando algunos detalles sobre la estructura de las señales de navegación y la arquitectura del receptor aplicada a los sistemas GPS y Galileo. Continua con el análisis de la adquisición GNSS como un problema de detección, aplicando la teoría del detector Neyman-Pearson (NP) y el modelo de señal de una única antena. El marco teórico del detector NP se utiliza aquí para derivar tanto el detector óptimo (conocido como detector clarividente) como la denominada Prueba Generalizada de la Razón de Verosimilitud (en inglés, Generalized Likelihood Ratio Test (GLRT)), que forma la base de prácticamente todos los algoritmos de adquisición del estado del arte actual. Yendo más lejos, proponemos un nuevo detector diseñado para adquirir simultáneamente un conjunto de satélites, por lo tanto, obtiene una reducción del tiempo de adquisición y de los recursos computacionales necesarios en el proceso, respecto a las técnicas convencionales. El efecto del ancho de banda del receptor también se ha tenido en cuenta en los análisis. A continuación, el detector GLRT se extiende al modelo de señal de array de antenas para obtener un detector nuevo que es capaz de mitigar interferencias no correladas temporalmente, incluso utilizando arrays no estructurados y moderadamente descalibrados, convirtiéndose así en una de las principales aportaciones de esta tesis. La clave del detector es asumir una matriz de covarianza de ruido arbitraria y desconocida en el modelo de señal, que trata de captar el comportamiento estadístico de las interferencias y otras señales no deseadas, mientras que utiliza la dimensión espacial proporcionada por los arrays de antenas. Se han derivado las expresiones que modelan las probabilidades teóricas de detección y falsa alarma. El rendimiento del detector y su capacidad de rechazo a interferencias se han modelado y comparado con su límite teórico. El algoritmo propuesto también ha sido comparado con técnicas de adquisición convencionales, ejecutadas utilizando la salida de conformadores de haz que utilizan algoritmos de filtrado de interferencias, como el algoritmo de minimización de la potencia. Además, el detector se ha analizado bajo condiciones realistas, representadas con la presencia de errores en la estimación de covarianzas, errores residuales en la estimación del Doppler y el retardo de señal, y los efectos de la cuantificación. Los resultados teóricos se apoyan en simulaciones de Monte Carlo. Como otra contribución principal de esta tesis, la segunda parte del trabajo trata sobre el diseño y la implementación de una nueva plataforma para receptores GNSS en tiempo real basados en array de antenas que utiliza la tecnología de matriz programable de puertas lógicas (en ingles Field Programmable Gate Array (FPGA)). La plataforma está destinada a ser utilizada como una herramienta de investigación estrechamente acoplada con receptores GNSS definidos por software. Se ha diseñado, implementado y verificado la cadena completa de recepción, incluyendo el array de antenas y el front-end multi-canal para las señales GPS L1 y Galileo E1. El documento explica en detalle el procesado de señal que se realiza, como por ejemplo, la implementación del módulo de extracción de estadísticas de la señal. Los compromisos de diseño y las complejidades derivadas han sido cuidadosamente analizadas y tenidas en cuenta. La plataforma ha sido utilizada como prueba de concepto para solucionar el problema presentado de la vulnerabilidad del GNSS a las interferencias. Los algoritmos de adquisición introducidos en esta tesis se han implementado y probado en condiciones realistas. El rendimiento de los algoritmos se comparó con las técnicas de adquisición basadas en una sola antena. Se han realizado pruebas en escenarios que contienen interferencias dentro de la banda GNSS, incluyendo interferencias de banda estrecha y banda ancha y señales de comunicación. La plataforma fue diseñada para demostrar la viabilidad de la implementación de nuevos algoritmos de adquisición basados en array de antenas, dejando el resto de las operaciones del receptor (principalmente, los módulos de tracking, decodificación del mensaje de navegación, los observables de código y fase, y la solución básica de Posición, Velocidad y Tiempo (PVT)) a un receptor basado en el concepto de Radio Definida por Software (SDR), el cual se ejecuta en un ordenador personal. El receptor procesa en tiempo real las muestras de la señal filltradas espacialmente, transmitidas usando el bus de datos Gigabit Ethernet. En la última parte de esta Tesis, cerramos ciclo diseñando e implementando completamente este receptor basado en software. El receptor propuesto está dirigido a las arquitecturas de multi-constalación GNSS y multi-frecuencia, persiguiendo los objetivos de eficiencia, modularidad, interoperabilidad y flexibilidad demandada por los usuarios que requieren características no estándar, tales como la extracción de señales intermedias o de datos y intercambio de algoritmos. En este contexto, se presenta un receptor de código abierto que puede trabajar en tiempo real, llamado GNSS-SDR, que contribuye con varias características nuevas. Entre ellas destacan el uso de patrones de diseño de software y técnicas de memoria compartida para administrar de manera eficiente el uso de datos entre los bloques del receptor, el uso de la aceleración por hardware para las operaciones vectoriales más costosas, como la eliminación de la frecuencia Doppler y la correlación de código, y la disponibilidad para compilar y ejecutar el receptor en múltiples plataformas de software y arquitecturas de hardware. A fecha de la escritura de esta Tesis (abril de 2012), el receptor obtiene un rendimiento basado en la medida de la raíz cuadrada del error cuadrático medio en la distancia bidimensional (en inglés, 2-dimensional Distance Root Mean Square (DRMS) error) menor de 2 metros para un escenario GPS L1 C/A con 8 satélites visibles y una dilución de la precisión horizontal (en inglés, Horizontal Dilution Of Precision (HDOP)) de 1.2

Mixture of beamformers for speech separation and extraction

In many audio applications, the signal of interest is corrupted by acoustic background noise, interference, and reverberation. The presence of these contaminations can significantly degrade the quality and intelligibility of the audio signal. This makes it important to develop signal processing methods that can separate the competing sources and extract a source of interest. The estimated signals may then be either directly listened to, transmitted, or further processed, giving rise to a wide range of applications such as hearing aids, noise-cancelling headphones, human-computer interaction, surveillance, and hands-free telephony. Many of the existing approaches to speech separation/extraction relied on beamforming techniques. These techniques approach the problem from a spatial point of view; a microphone array is used to form a spatial filter which can extract a signal from a specific direction and reduce the contamination of signals from other directions. However, when there are fewer microphones than sources (the underdetermined case), perfect attenuation of all interferers becomes impossible and only partial interference attenuation is possible. In this thesis, we present a framework which extends the use of beamforming techniques to underdetermined speech mixtures. We describe frequency domain non-linear mixture of beamformers that can extract a speech source from a known direction. Our approach models the data in each frequency bin via Gaussian mixture distributions, which can be learned using the expectation maximization algorithm. The model learning is performed using the observed mixture signals only, and no prior training is required. The signal estimator comprises of a set of minimum mean square error (MMSE), minimum variance distortionless response (MVDR), or minimum power distortionless response (MPDR) beamformers. In order to estimate the signal, all beamformers are concurrently applied to the observed signal, and the weighted sum of the beamformers’ outputs is used as the signal estimator, where the weights are the estimated posterior probabilities of the Gaussian mixture states. These weights are specific to each timefrequency point. The resulting non-linear beamformers do not need to know or estimate the number of sources, and can be applied to microphone arrays with two or more microphones with arbitrary array configuration. We test and evaluate the described methods on underdetermined speech mixtures. Experimental results for the non-linear beamformers in underdetermined mixtures with room reverberation confirm their capability to successfully extract speech sources

Mathematical optimization techniques for cognitive radar networks

This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from a bistatic model (i.e. two transmitters and a single receiver) and ending with a cognitive network (i.e. multiple transmitting and multiple receiving radars). The environment under investigation always features strong signal-dependent clutter and noise. All algorithms are based on an iterative waveform-filter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and cross-correlation properties. Finally, robust optimization techniques are introduced to account for the assumptions made by cognitive radars on certain second order statistics such as the covariance matrix of the clutter. More specifically, initial optimization techniques were proposed for the case of bistatic radars. By maximizing the signal to interference and noise ratio (SINR) under certain constraints on the transmitted signals, it was possible to iteratively optimize both the orthogonal transmission waveforms and the receiver filter. Subsequently, the above work was extended to a convex optimization framework for a waveform design technique for bistatic radars where both radars transmit and receive to detect targets. The method exploited prior knowledge of the environment to maximize the accumulated target return signal power while keeping the disturbance power to unity at both radar receivers. The thesis further proposes convex optimization based waveform designs for multiple input multiple output (MIMO) based cognitive radars. All radars within the system are able to both transmit and receive signals for detecting targets. The proposed model investigated two complementary optimization techniques. The first one aims at optimizing the signal to interference and noise ratio (SINR) of a specific radar while keeping the SINR of the remaining radars at desired levels. The second approach optimizes the SINR of all radars using a max-min optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signal-dependent model was tested against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered signal-dependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar cross-section and Doppler parameters of the clutters. Approximations based on Taylor series were invoked to make the optimization problem convex and {subsequently} determine robust waveforms with specific SINR outage constraints. Finally, this thesis introduces robust optimization techniques for through-the-wall radars. These are also cognitive but rely on different optimization techniques than the ones previously discussed. By noticing the similarities between the minimum variance distortionless response (MVDR) problem and the matched-illumination one, this thesis introduces robust optimization techniques that consider uncertainty on environment-related parameters. Various performance analyses demonstrate the effectiveness of all the above algorithms in providing a significant increase in SINR in an environment affected by very strong clutter and noise

Modelling, Simulation and Data Analysis in Acoustical Problems

Modelling and simulation in acoustics is currently gaining importance. In fact, with the development and improvement of innovative computational techniques and with the growing need for predictive models, an impressive boost has been observed in several research and application areas, such as noise control, indoor acoustics, and industrial applications. This led us to the proposal of a special issue about “Modelling, Simulation and Data Analysis in Acoustical Problems”, as we believe in the importance of these topics in modern acoustics’ studies. In total, 81 papers were submitted and 33 of them were published, with an acceptance rate of 37.5%. According to the number of papers submitted, it can be affirmed that this is a trending topic in the scientific and academic community and this special issue will try to provide a future reference for the research that will be developed in coming years