Performance analysis of MUSIC for spatially distributed sources

In this paper, the direction of arrival (DOA) localization of spatially distributed sources impinging on a sensor array is considered. The performance of the well known MUSIC estimator is studied in presence of model errors due to angular dispersion of sources. Taking into account the coherently distributed source model proposed in [1], we establish closed-form expressions of the DOA estimation error and mean square error (MSE) due to both the model errors and the effects of a finite number of snapshots. The analytical results are validated by numerical simulations and allow to analyze the performance of MUSIC for coherently distributed sources

Localisation de sources aéroacoustiques et imagerie à haute résolution

Localization of Coherently Distributed (CD) source presents a challenge in the array signal processing. Our work motivates the localization of aero-acoustic source based on its spatial extension. This challenge is practically ignored in the literature of acoustic imaging field where many applications consist in mapping noisy source to reduce its contribution. The thesis presents the three following contributions. First, we propose a Joint Angle, Distance, Spread and Shape Estimator called JADSSE. The estimation of the so-called spread shape distribution parameter proposed by JADSSE avoids the modeling error due to the required a priori knowledge on the source shape when using classical estimators. Second, we expand the Decoupled DSPE to the near field. This method decouples the Direction of Arrival (DoA) and the range estimation from the spread estimation. Meanwhile, this method prevents the spread estimation for unknown shape distribution. Therefore, we propose the DADSSE to successively estimate the DOA, the range and then the spread and the shape distribution of the source. Third, we generalize the CD model and the JADSSE to consider the bi-dimensional spread of the source. Next, we propose two source power estimation approaches accounting the spatial spread of the source. The proposed methods are tested using a set of experimental data of the Renault wind tunnel application. Results show the presence of new aero-acoustic sources especially the overlapped ones with weak powers. We provide a tool to better map and characterize the aero-acoustic source by estimating the position, spread, power and shape.La localisation de source Distribuée Cohérente (DC) présente un défi du traitement d'antenne. Les contributions de cette thèse s’articulent principalement autour de trois aspects. Premièrement, un estimateur conjoint de l'angle, la distance, la dispersion et la forme de la source appelée JADSSE est proposé pour le cas champ proche. L’estimation d’un paramètre de forme de distribution de la dispersion permet d’éviter des erreurs de modèles sur l’a priori de la forme de la distribution. Deuxièmement, on généralise l'estimateur Decoupled DSPE en champ proche. Cette approche permet de découpler l'estimation de la Direction D’Arrivée (DDA) et de la distance de l'estimation de la dispersion. Afin de permettre l’estimation de la dispersion sans connaître a priori les formes de distribution, on propose le DADSSE qui consiste à estimer successivement la DDA, la distance et ensuite la dispersion et la forme de la distribution de la source. Troisièmement, on généralise le modèle DC avec une dispersion spatiale bidimensionnelle de la source ainsi que l’estimateur JADSSE. Deux approches sont proposées pour l’estimation de la puissance prenant en compte le modèle d’étalement des sources. Les méthodes proposées sont testées sur les données expérimentales de la soufflerie de Renault. Les résultats mettent en évidence des sources aéro-acoustiques proches et de faibles puissances. L’ensemble de ces travaux permet de fournir un outil pour une meilleure cartographie et caractérisation des sources aéro-acoustiques grâce à l’estimation de la position, l'étalement, la puissance et la forme

Channel estimation and signal enhancement for DS-CDMA systems

This dissertation focuses on topics of Bayesian-based multiuser detection, space-time (S-T) transceiver design, and S-T channel parameter estimation for direct-sequence code-division multiple-access (DS-CDMA) systems. Using the Bayesian framework, various linear and simplified nonlinear multiuser detectors are proposed, and their performances are analyzed. The simplified non-linear Bayesian solutions can bridge the performance gap between sub-optimal linear multiuser detectors and the optimum multiuser detector. To further improve the system capacity and performance, S-T transceiver design approaches with complexity constraint are investigated. Novel S-T receivers of low-complexity that jointly use the temporal code-signature and the spatial signature are proposed. Our solutions, which lead to generalized near-far resistant S-T RAKE receivers, achieve better interference suppression than the existing S-T RAKE receivers. From transmitter side, we also proposed a transmit diversity (TD) technique in combination with differential detection for the DS-CDMA systems. It is shown that the proposed S-T TD scheme in combination with minimum variance distortionless response transceiver (STTD+MVDR) is near-far resistant and outperforms the conventional STTD and matched filter based (STTD+MF) transceiver scheme. Obtaining channel state information (CSI) is instrumental to optimum S-T transceiver design in wireless systems. Another major focus of this dissertation is to estimate the S-T channel parameters. We proposed an asymptotic, joint maximum likelihood (ML) method of estimating multipath channel parameters for DS-CDMA systems. An iterative estimator is proposed to further simplify the computation. Analytical and simulation results show that the iterative estimation scheme is near-far resistant for both time delays and DOAs. And it reaches the corresponding CRBs after a few iterations

Statistical Error Analysis of a DOA Estimator for a PCL System Using the Cramer-RAO Bound Theorem

Direction of Arrival (DOA) estimation of signals has been a popular research area in Signal Processing. DOA estimation also has a significant role in the object location process of Passive Coherent Location (PCL) systems. PCL systems have been in open literature since 1986 and their applications are not as clearly understood as the DOA estimation problem. However, they are the focus of many current research efforts and show much promise. The purpose of this research is to analyze the DOA estimation errors in a PCL system. The performance of DOA estimators is studied using the Cramer-Rao Bound (CRB) Theorem. The CRB provides a lower bound on the variance of unbiased DOA estimators. Since variance is a desirable property for measuring the accuracy of an estimator, the CRB gives a good indication about the performance of an estimator. Previous DOA estimators configured with array antennas used the array antenna manifold, or the properties of the array antenna structure, to estimate signal DOA. Conventional DOA estimators use arbitrary signal (AS) structures. Constant Modulus (CM) DOA estimators restrict the input signals to a family of constant envelope signals, and when there are multiple signals in the environment, CM DOA estimators are able to separate signals from each other using the CM signal property. CM estimators then estimate the DOA for each signal individually. This research compares the CRB for AS and CM DOA estimators for a selected system. The CRB is also computed for this system when single and multiple and moving objects are present. The CRBAS and CRBCM are found to be different for the multiple signal case and moving object cases

A survey on 5G massive MIMO Localization

Massive antenna arrays can be used to meet the requirements of 5G, by exploiting different spatial signatures of users. This same property can also be harnessed to determine the locations of those users. In order to perform massive MIMO localization, refined channel estimation routines and localization methods have been developed. This paper provides a brief overview of this emerging field

A Geometric Deep Learning Approach to Sound Source Localization and Tracking

La localización y el tracking de fuentes sonoras mediante agrupaciones de micrófonos es un problema que, pese a llevar décadas siendo estudiado, permanece abierto. En los últimos años, modelos basados en deep learning han superado el estado del arte que había sido establecido por las técnicas clásicas de procesado de señal, pero estos modelos todavía presentan problemas para trabajar en espacios con alta reverberación o para realizar el tracking de varias fuentes sonoras, especialmente cuando no es posible aplicar ningún criterio para clasificarlas u ordenarlas. En esta tesis, se proponen nuevos modelos que, basados en las ideas del Geometric Deep Learning, suponen un avance en el estado del arte para las situaciones mencionadas previamente.Los modelos propuestos utilizan como entrada mapas de potencia acústica calculados con el algoritmo SRP-PHAT, una técnica clásica de procesado de señal que permite estimar la energía acústica recibida desde cualquier dirección del espacio. Además, también proponemos una nueva técnica para suprimir analíticamente el efecto de una fuente en las funciones de correlación cruzada usadas para calcular los mapas SRP-PHAT. Basándonos en técnicas de banda estrecha, se demuestra que es posible proyectar las funciones de correlación cruzada de las señales capturadas por una agrupación de micrófonos a un espacio ortogonal a una dirección dada simplemente usando una combinación lineal de las funciones originales con retardos temporales. La técnica propuesta puede usarse para diseñar sistemas iterativos de localización de múltiples fuentes que, tras localizar la fuente con mayor energía en las funciones de correlación cruzada o en los mapas SRP-PHAT, la cancelen para poder encontrar otras fuentes que estuvieran enmascaradas por ella.Antes de poder entrenar modelos de deep learning necesitamos datos. Esto, en el caso de seguir un esquema de aprendizaje supervisado, supone un dataset de grabaciones de audio multicanal con la posición de las fuentes etiquetada con precisión. Pese a que existen algunos datasets con estas características, estos no son lo suficientemente extensos para entrenar una red neuronal y los entornos acústicos que incluyen no son suficientemente variados. Para solventar el problema de la falta de datos, presentamos una técnica para simular escenas acústicas con una o varias fuentes en movimiento y, para realizar estas simulaciones conforme son necesarias durante el entrenamiento de la red, presentamos la que es, que sepamos, la primera librería de software libre para la simulación de acústica de salas con aceleración por GPU. Tal y como queda demostrado en esta tesis, esta librería es más de dos órdenes de magnitud más rápida que otras librerías del estado del arte.La idea principal del Geometric Deep Learning es que los modelos deberían compartir las simetrías (i.e. las invarianzas y equivarianzas) de los datos y el problema que se quiere resolver. Para la estimación de la dirección de llegada de una única fuente, el uso de mapas SRP-PHAT como entrada de nuestros modelos hace que la equivarianza a las rotaciones sea obvia y, tras presentar una primera aproximación usando redes convolucionales tridimensionales, presentamos un modelo basado en convoluciones icosaédricas que son capaces de aproximar la equivarianza al grupo continuo de rotaciones esféricas por la equivarianza al grupo discreto de las 60 simetrías del icosaedro. En la tesis se demuestra que los mapas SRP-PHAT son una característica de entrada mucho más robusta que los espectrogramas que se usan típicamente en muchos modelos del estado del arte y que el uso de las convoluciones icosaédricas, combinado con una nueva función softargmax que obtiene una salida de regresión a partir del resultado de una red convolucional interpretándolo como una distribución de probabilidad y calculando su valor esperado, permite reducir enormemente el número de parámetros entrenables de los modelos sin reducir la precisión de sus estimaciones.Cuando queremos realizar el tracking de varias fuentes en movimiento y no podemos aplicar ningún criterio para ordenarlas o clasificarlas, el problema se vuelve invariante a las permutaciones de las estimaciones, por lo que no podemos compararlas directamente con las etiquetas de referencia dado que no podemos esperar que sigan el mismo orden. Este tipo de modelos se han entrenado típicamente usando estrategias de entrenamiento invariantes a las permutaciones, pero estas normalmente no penalizan los cambios de identidad por lo que los modelos entrenados con ellas no mantienen la identidad de cada fuente de forma consistente. Para resolver este problema, en esta tesis proponemos una nueva estrategia de entrenamiento, a la que llamamos sliding permutation invariant training (sPIT), que es capaz de optimizar todas las características que podemos esperar de un sistema de tracking de múltiples fuentes: la precisión de sus estimaciones de dirección de llegada, la exactitud de sus detecciones y la consistencia de las identidades asignadas a cada fuente.Finalmente, proponemos un nuevo tipo de red recursiva que usa conjuntos de vectores en lugar de vectores para representar su entrada y su estado y que es invariante a las permutaciones de los elementos del conjunto de entrada y equivariante a las del conjunto de estado. En esta tesis se muestra como este es el comportamiento que deberíamos esperar de un sistema de tracking que toma como entradas las estimaciones de un modelo de localización multifuente y se compara el rendimiento de estas redes recursivas invariantes a las permutaciones con redes recursivas GRU convencionales para aplicaciones de tracking de fuentes sonoras.The localization and tracking of sound sources using microphone arrays is a problem that, even if it has attracted attention from the signal processing research community for decades, remains open. In recent years, deep learning models have surpassed the state-of-the-art that had been established by classic signal processing techniques, but these models still struggle with handling rooms with strong reverberations or tracking multiple sources that dynamically appear and disappear, especially when we cannot apply any criteria to classify or order them. In this thesis, we follow the ideas of the Geometric Deep Learning framework to propose new models and techniques that mean an advance of the state-of-the-art in the aforementioned scenarios. As the input of our models, we use acoustic power maps computed using the SRP-PHAT algorithm, a classic signal processing technique that allows us to estimate the acoustic energy received from any direction of the space and, therefore, compute arbitrary-shaped power maps. In addition, we also propose a new technique to analytically cancel a source from the generalized cross-correlations used to compute the SRP-PHAT maps. Based on previous narrowband cancellation techniques, we prove that we can project the cross-correlation functions of the signals captured by a microphone array into a space orthogonal to a given direction by just computing a linear combination of time-shifted versions of the original cross-correlations. The proposed cancellation technique can be used to design iterative multi-source localization systems where, after having found the strongest source in the generalized cross-correlation functions or in the SRP-PHAT maps, we can cancel it and find new sources that were previously masked by thefirst source. Before being able to train deep learning models we need data, which, in the case of following a supervised learning approach, means a dataset of multichannel recordings with the position of the sources accurately labeled. Although there exist some datasets like this, they are not large enough to train a neural network and the acoustic environments they include are not diverse enough. To overcome this lack of real data, we present a technique to simulate acoustic scenes with one or several moving sound sources and, to be able to perform these simulations as they are needed during the training, we present what is, to the best of our knowledge, the first free and open source room acoustics simulation library with GPU acceleration. As we prove in this thesis, the presented library is more than two orders of magnitude faster than other state-of-the-art CPU libraries. The main idea of the Geometric Deep Learning philosophy is that the models should fit the symmetries (i.e. the invariances and equivariances) of the data and the problem we want to solve. For single-source direction of arrival estimation, the use of SRP-PHAT maps as inputs of our models makes the rotational equivariance of the problem undeniably clear and, after a first approach using 3D convolutional neural networks, we present a model using icosahedral convolutions that approximate the equivariance to the continuous group of spherical rotations by the discrete group of the 60 icosahedral symmetries. We prove that the SRP-PHAT maps are a much more robust input feature than the spectrograms typically used in many state-of-the-art models and that the use of the icosahedral convolutions, combined with a new soft-argmax function that obtains a regression output from the output of the convolutional neural network by interpreting it as a probability distribution and computing its expected value, allows us to dramatically reduce the number of trainable parameters of the models without losing accuracy in their estimations. When we want to track multiple moving sources and we cannot use any criteria to order or classify them, the problem becomes invariant to the permutations of the estimates, so we cannot directly compare them with the ground truth labels since we cannot expect them to be in the same order. This kind of models has typically been trained using permutation invariant training strategies, but these strategies usually do not penalize the identity switches and the models trained with them do not keep the identity of every source consistent during the tracking. To solve this issue, we propose a new training strategy, which we call sliding permutation invariant training, that is able to optimize all the features that we could expect from a multi-source tracking system: the precision of the direction of arrival estimates, the accuracy of the source detections, and the consistency of the assigned identities. Finally, we propose a new kind of recursive neural network that, instead of using vectors as their input and their state, uses sets of vectors and is invariant to the permutation of the elements of the input set and equivariant to the permutations of the elements of the state set. We show how this is the behavior that we should expect from a tracking model which takes as inputs the estimates of a multi-source localization model and compare these permutation-invariant recursive neural networks with the conventional gated recurrent units for sound source tracking applications.<br /