Asymptotic Performance for Delayed Exponential Process

International audienceThe damped and delayed sinusoidal (DDS) model can be defined as the sum of sinusoids whose waveforms can be damped and delayed. This model is suitable for compactly modeling short time events. This property is closely related to its ability to reduce the time-support of each sinusoidal component. In this correspondence, we derive exact and approximate asymptotic Cramér–Rao bounds (CRBs) for the DDS model. This analysis shows that this model has better, or at least similar, theoretical performance than the well-known exponentially damped sinusoidal (EDS) model. In particular, the performance in the DDS case is significantly improved compared to that of the EDS for closely spaced sinusoids thanks to the nonzero time delays. Consequently, we can exploit the advantageous properties of the DDS model and, in the same time, we can keep high theoretical model parameter estimation accuracy

Recursive Hybrid Cramér–Rao Bound for Discrete-Time Markovian Dynamic Systems

Abstract—In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. As a contribution to the hybrid estimation framework, we introduce a recursive hybrid Cramér–Rao lower bound for discrete-time Markovian dynamic systems depending on unknown deterministic parameters. Additionally, the regularity conditions required for its existence and its use are clarified

A Constrained Hybrid Cramér-Rao Bound for Parameter Estimation

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. Numerous works have shown the versatility of deterministic constrained Cramér-Rao bound for estimation performance analysis and design of a system of measurement. However in many systems both random and non-random parameters may occur simultaneously. In this communication, we propose a constrained hybrid lower bound which take into account of equality constraint on deterministic parameters. The usefulness of the proposed bound is illustrated with an application to radar Doppler estimation

Frequency synchronization in HSPA+/LTE communications : a general model and towards uniform implementation

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Diversity receiver design and channel statistic estimation in fading channels

The main goal of this thesis is to provide an in-depth study of two important techniques that are effective in improving the performance, data rate, or bandwidth-efficiency in wireless communication systems. The two techniques are, first, diversity combining equipped with quadrature amplitude modulation (QAM), and second, the estimation of fading channel statistical properties;To effectively combat the adverse effect of fading and to improve the error rate performance in wireless communications, one of the major approaches is to employ diversity combining techniques. In the first part of this thesis, we focus on the equal gain combining (EGC) and hybrid-selection equal gain combining (HS/EGC) for bandwidth-efficient wireless systems (i.e. QAM systems). For EGC QAM systems, we propose the receiver structure and the corresponding decision variables, and then study the effects of imperfect channel estimation (ICE) and quantify the loss of the signal-to-noise ratio (SNR) gain caused by ICE. For HS/EGC QAM system, we develop a general approach to derive unified error rate and outage probability formulas over various types of fading channels based on the proposed HS/EGC receiver. The main contribution of this work lies in that it provides effective hybrid diversity schemes and new analytical approaches to enable thorough analysis and effective design of bandwidth efficient wireless communication systems which suffer from ICE and operate in realistic multipath channels;Channel statistic information is proven to be critical in determining the systems design, achievable data rate, and achievable performance. In the second part of this thesis, we study the estimation of the fading channel Statistics and Probability; We propose several iterative algorithms to estimate the first- and second-order statistics of general fading or composite fading-shadowing channels and derive the Cramer-Rao bounds (CRBs) for all the cases. We demonstrate that these iterative methods are efficient in the sense that they achieve their corresponding CRBs. The main contribution of this work is that it bridges the gap between the broad utilization of fading channel statistical properties and the lack of systematic study that makes such statistical properties available

Caractérisation des performances minimales d'estimation pour des modèles d'observations non-standards

In the parametric estimation context, estimators performances can be characterized, inter alia, by the mean square error and the resolution limit. The first quantities the accuracy of estimated values and the second defines the ability of the estimator to allow a correct resolvability. This thesis deals first with the prediction the "optimal" MSE by using lower bounds in the hybrid estimation context (i.e. when the parameter vector contains both random and non-random parameters), second with the extension of Cramér-Rao bounds for non-standard estimation problems and finally to the characterization of estimators resolution. This manuscript is then divided into three parts :First, we fill some lacks of hybrid lower bound on the MSE by using two existing Bayesian lower bounds: the Weiss-Weinstein bound and a particular form of Ziv-Zakai family lower bounds. We show that these extended lower bounds are tighter than the existing hybrid lower bounds in order to predict the optimal MSE.Second, we extend Cramer-Rao lower bounds for uncommon estimation contexts. Precisely: (i) Where the non-random parameters are subject to equality constraints (linear or nonlinear). (ii) For discrete-time filtering problems when the evolution of states are defined by a Markov chain. (iii) When the observation model differs to the real data distribution.Finally, we study the resolution of the estimators when their probability distributions are known. This approach is an extension of the work of Oh and Kashyap and the work of Clark to multi-dimensional parameters estimation problems.Dans le contexte de l'estimation paramétrique, les performances d'un estimateur peuvent être caractérisées, entre autre, par son erreur quadratique moyenne (EQM) et sa résolution limite. La première quantifie la précision des valeurs estimées et la seconde définit la capacité de l'estimateur à séparer plusieurs paramètres. Cette thèse s'intéresse d'abord à la prédiction de l'EQM "optimale" à l'aide des bornes inférieures pour des problèmes d'estimation simultanée de paramètres aléatoires et non-aléatoires (estimation hybride), puis à l'extension des bornes de Cramér-Rao pour des modèles d'observation moins standards. Enfin, la caractérisation des estimateurs en termes de résolution limite est également étudiée. Ce manuscrit est donc divisé en trois parties :Premièrement, nous complétons les résultats de littérature sur les bornes hybrides en utilisant deux bornes bayésiennes : la borne de Weiss-Weinstein et une forme particulière de la famille de bornes de Ziv-Zakaï. Nous montrons que ces bornes "étendues" sont plus précises pour la prédiction de l'EQM optimale par rapport à celles existantes dans la littérature.Deuxièmement, nous proposons des bornes de type Cramér-Rao pour des contextes d'estimation moins usuels, c'est-à-dire : (i) Lorsque les paramètres non-aléatoires sont soumis à des contraintes d'égalité linéaires ou non-linéaires (estimation sous contraintes). (ii) Pour des problèmes de filtrage à temps discret où l'évolution des états (paramètres) est régit par une chaîne de Markov. (iii) Lorsque la loi des observations est différente de la distribution réelle des données.Enfin, nous étudions la résolution et la précision des estimateurs en proposant un critère basé directement sur la distribution des estimées. Cette approche est une extension des travaux de Oh et Kashyap et de Clark pour des problèmes d'estimation de paramètres multidimensionnels

Performance analysis of assisted-GNSS receivers

The goal of this thesis is to improve the understanding of the performance of Global Navigation Satellite System (GNSS) receivers that use assistance data provided by cellular networks. A typical example of such a receiver is a mobile phone including a Global Positioning System (GPS) receiver. Using assistance data such as an accurate estimate of the GPS system time is known to improve the availability and the time-tofirst- fix performance of a GNSS receiver. However, the performance depends on the architecture of the cellular network and may vary significantly across networks. This thesis presents three new contributions to the performance analysis of assisted-GNSS receivers in cellular networks. I first introduce a mathematical framework that can be used to calculate a theoretical lower bound of the time-to-first-fix (TTFF) in an assisted-GNSS receiver. Existing methods, for example the flow-graph method, generally focus on calculating the theoretical mean acquisition time of a pseudo-noise signal for one satellite only. I extend these methods to calculate the full probability distribution of the joint acquisition of several satellites, as well as the sequential acquisition of satellites, which is commonly performed in assisted receivers. The method is applied to real measurements made in a multipath fading channel. I next consider time assistance in unsynchronised cellular networks. It is often argued that unsynchronised networks can not provide fine-time aiding since they do not have a common clock, although few experimental results have been reported in the existing literature. I carried out experiments on a GSM network, a second-generation cellular network, in Cambridge, UK, in order to measure the time stability of the synchronisation signals. The results showed a large variability in the time stabilities across different base stations and I evaluated the performance of an ensemble filter that combines the measurements into a single, more accurate, estimate of the universal time. The main contribution is to show that the performance of such a filter is adequate to provide fine-time assistance to a satellite navigation receiver. Finally, I address the positioning performance of an assisted receiver in synchronised cellular networks. Cellular positioning has been often investigated in the literature, but few results on real networks have been presented. Many positioning methods are proprietary and little information about their performance in real networks haven been published publicly. A CDMA2000 cellular network in Calgary, Canada, was used to collect experimental data. The time stability and the synchronisation of the CDMA2000 pilot signals were excellent and were used to evaluate the performance of CDMA2000-based cellular positioning system. I then developed a method to combine the pseudo-range measurements from the GPS signals and the CDMA2000 base stations. I evaluated the performance of positioning in both outdoor and indoor environments, and I analysed the effects and the possible mitigation of non-line-of-sight signals. The main contribution is to show that additional satellite navigation signals can improve the accuracy of cellular positioning beyond what is theoretically expected from the improvement in the geometry.Cambridge Silicon Radi

Efficient complementary sequences-based architectures and their application to ranging measurements

Premio Extraordinario de Doctorado de la UAH en 2015En las últimas décadas, los sistemas de medición de distancias se han beneficiado de los avances en el área de las comunicaciones inalámbricas. En los sistemas basados en CDMA (Code-Division Multiple-Access), las propiedades de correlación de las secuencias empleadas juegan un papel fundamental en el desarrollo de dispositivos de medición de altas prestaciones. Debido a las sumas ideales de correlaciones aperiódicas, los conjuntos de secuencias complementarias, CSS (Complementary Sets of Sequences), son ampliamente utilizados en sistemas CDMA. En ellos, es deseable el uso de arquitecturas eficientes que permitan generar y correlar CSS del mayor número de secuencias y longitudes posibles. Por el término eficiente se hace referencia a aquellas arquitecturas que requieren menos operaciones por muestra de entrada que con una arquitectura directa. Esta tesis contribuye al desarrollo de arquitecturas eficientes de generación/correlación de CSS y derivadas, como son las secuencias LS (Loosely Synchronized) y GPC (Generalized Pairwise Complementary), que permitan aumentar el número de longitudes y/o de secuencias disponibles. Las contribuciones de la tesis pueden dividirse en dos bloques: En primer lugar, las arquitecturas eficientes de generación/correlación para CSS binarios, derivadas en trabajos previos, son generalizadas al alfabeto multinivel (secuencias con valores reales) mediante el uso de matrices de Hadamard multinivel. Este planteamiento tiene dos ventajas: por un lado el aumento del número de longitudes que pueden generarse/correlarse y la eliminación de las limitaciones de las arquitecturas previas en el número de secuencias en el conjunto. Por otro lado, bajo ciertas condiciones, los parámetros de las arquitecturas generalizadas pueden ajustarse para generar/correlar eficientemente CSS binarios de mayor número de longitudes que con las arquitecturas eficientes previas. En segundo lugar, las arquitecturas propuestas son usadas para el desarrollo de nuevos algoritmos de generación/correlación de secuencias derivadas de CSS que reducen el número de operaciones por muestra de entrada. Finalmente, se presenta la aplicación de las secuencias estudiadas en un nuevo sistema de posicionamiento local basado en Ultra-Wideband y en un sistema de posicionamiento local basado en ultrasonidos

Traitement du signal pour les communications numériques au travers de canaux radio-mobiles

This manuscript of ''Habilitation à diriger les Recherches'' (Habilitation to conduct researches) gives me the opportunity to take stock of the last 14 years on my associate professor activities and on my research works in the field of signal processing for digital communications, particularly for radio-mobile communications. The purpose of this signal processing is generally to obtain a robust transmission, despite the passage of digital information through a communication channel disrupted by the mobility between the transmitter and the receiver (Doppler effect), the phenomenon of echoes (multi-path propagation), the addition of noise or interference, or by limitations in bandwidth, in transmitted power or in signal-to-noise ratio. In order to recover properly the digital information, the receiver needs in general to have an accurate knowledge of the channel state. Much of my work has focused on receiver synchronization or more generally on the dynamic estimation of the channel parameters (delays, phases, amplitudes, Doppler shifts, ...). We have developed estimators and studied their performance in asymptotic variance, and have compared them to minimum lower bound (Cramer-rao or Bayesian Cramer Rao bounds). Some other studies have focused only on the recovering of information (''detection'' or ''equalization'' task) by the receiver after channel estimation, or proposed and analyzed emission / reception schemes, reliable for certain scenarios (transmit diversity scheme for flat fading channel, scheme with high energy efficiency, ...).Ce mémoire de HDR est l'occasion de dresser un bilan des 14 dernières années concernant mes activités d'enseignant-chercheur et mes travaux de recherche dans le domaine du traitement du signal pour les communications numériques, et plus particulièrement les communications radio-mobiles. L'objet de ce traitement du signal est globalement l'obtention d'une transmission robuste, malgré le passage de l'information numérique au travers d'un canal de communication perturbé par la mobilité entre l'émetteur et le récepteur (effet Doppler), le phénomène d'échos, l'addition de bruit ou d'interférence, ou encore par des limitations en bande-passante, en puissance transmise ou en rapport-signal à bruit. Afin de restituer au mieux l'information numérique, le récepteur a en général besoin de disposer d'une connaissance précise du canal. Une grande partie de mes travaux s'est intéressé à l'estimation dynamique des paramètres de ce canal (retards, phases, amplitudes, décalages Doppler, ...), et en particulier à la synchronisation du récepteur. Quelques autres travaux se sont intéressés seulement à la restitution de l'information (tâches de ''détection'' ou d' ''égalisation'') par le récepteur une fois le canal estimé, ou à des schémas d'émission / réception spécifiques. La synthèse des travaux commence par une introduction générale décrivant les ''canaux de communications'' et leurs problèmes potentiels, et positionne chacun de mes travaux en ces termes. Une première partie s'intéresse aux techniques de réception pour les signaux à spectre étalé des systèmes d'accès multiple à répartition par codes (CDMA). Ces systèmes large-bande offrent un fort pouvoir de résolution temporelle et des degrés de liberté, que nous avons exploités pour étudier l'égalisation et la synchronisation (de retard et de phase) en présence de trajets multiples et d'utilisateurs multiples. La première partie regroupe aussi d'autres schémas d'émission/réception, proposés pour leur robustesse dans différents scénarios (schéma à diversité pour canaux à évanouissement plats, schéma à forte efficacité énergétique, ...). La seconde partie est consacrée à l'estimation dynamique Bayésienne des paramètres du canal. On suppose ici qu'une partie des paramètres à estimer exhibe des variations temporelles aléatoires selon une certaine loi à priori. Nous proposons d'abord des estimateurs et des bornes minimales d'estimation pour des modèles de transmission relativement complexes, en raison de la distorsion temporelle due à la forte mobilité en modulation multi-porteuse (OFDM), ou de la présence de plusieurs paramètres à estimer conjointement, ou encore de non linéarités dans les modèles. Nous nous focalisons ensuite sur le problème d'estimation des amplitudes complexes des trajets d'un canal à évolution lente (à 1 ou plusieurs bonds). Nous proposons des estimateurs récursifs (dénommés CATL, pour ''Complex Amplitude Tracking Loop'') à structure imposée inspirée par les boucles à verrouillage de phase numériques, de performance asymptotiques proches des bornes minimales. Les formules analytiques approchées de performances asymptotiques et de réglages de ces estimateurs sont établies sous forme de simples fonctions des paramètres physiques (spectre Doppler, retards, niveau de bruit). Puis étant donné les liens établis entre ces estimateurs CATL et certains filtres de Kalman (construits pour des modèles d'état de type marche aléatoire intégrée), les formules approchées de performances asymptotiques et de réglage de ces filtres de Kalman sont aussi dérivées

Spectrally efficient systems for satellite communications

In questa Tesi verranno proposte tre diverse soluzioni il cui scopo è l'incremento dell'efficienza spettrale nei sistemi satellitari. Per prima cosa, considereremo uno scenario multi-utente a multiplazione di frequenza, che è uno degli scenari inclusi nello standard DVB-RCS. Useremo modulazioni a fase continua (CPM) concatenate serialmente ad un codificatore tramite un interleaver. La già elevata efficienza spettrale delle CPM può essere ulteriormente aumentata sfruttando la tecnica del "frequency packing". Un tale incremento però rende necessaria un'accurata sincronizzazione affinché il ricevitore funzioni correttamente. Pertanto verranno progettati e testati degli stimatori iterativi di fase e frequenza. In seguito, ci concentreremo su sistemi a divisione di codice basati sulle CPM. Verrà quindi proposta una nuova tecnica di espansione spettrale, progettata ad hoc per le CPM. Mostreremo come ottenere facilmente delle densità spettrali di potenza larghe, piatte e lisce, senza ricorrere a sequenze di spreading, e senza tutte le problematiche di progettazione a queste collegate. Inoltre, ricaveremo degli algoritmi di rivelazione multi-utente subottimi che saranno impiegati per mostrare come il sistema proposto possa superare le prestazioni di tutti gli altri sistemi in letteratura, sia in termini di probabilità d'errore che di efficienza spettrale. Infine, considerando lo scenario previsto dallo standard DVB-S2, proporremo di incrementarne l'efficienza spettrale attraverso la tecnica del "time and frequency packing". Questa tecnica causa l'insorgenza di interferenza intersimbolica e intercanale, che a loro volta provocano l'aumento del numero di simboli pilota necessari per una corretta sincronizzazione di fase e frequenza. Sarà pertanto introdotto un nuovo design dei piloti, e saranno derivati opportuni algoritmi di rivelazione ottimi e subottimi a ridotta complessità. Mostreremo come il sistema proposto possa superare le prestazioni dello standard DVB-S2 sia in termini di probabilità d'errore che di efficienza spettrale.In this Thesis we propose three different solutions aiming at increasing the spectral efficiency in satellite communications. First, we will consider a multi-user scenario with frequency multiplexing, that is one of the scenarios included in the DVB-RCS standard. We will adopt continuous phase modulations (CPMs) serially concatenated with an outer code through an interleaver. The high spectral efficiency of CPMs can be further increased exploiting the frequency packing technique. Such an improvement does not come for free, in fact an accurate synchronization has to be guaranteed to allow the detector to work properly. To this purpose, new iterative frequency and phase estimators will be derived and the synchronization accuracy tested. Then, we will focus on code division multiple access (CDMA) systems employing CPMs. A brand new spectral spreading technique, especially tailored to CPMs, will be presented. We will show how to easily obtain a large, flat, and smooth power spectral density, without resorting to spreading sequences and then getting rid of all the design problems that come with. Moreover, we will derive some suboptimal multi-user detectors that will be employed to show that the proposed system outperforms all the other considered systems, found in the literature, in terms of bit error rate and spectral efficiency. Finally, considering the DVB-S2 scenario, we will propose to increase the spectral efficiency through time and frequency packing. This technique will cause intersymbol and interchannel interferences to arise, requiring a significant increase in the number of pilots used to carry out frequency and phase synchronization. Therefore, new pilot designs will be introduced, and suited optimal and suboptimal reduced-complexity algorithms derived. We will show that the proposed systems may outperform the DVB-S2 standard in terms of bit error rate and spectral efficiency