Bayesian and Hybrid Cramér–Rao Bounds for the Carrier Recovery Under Dynamic Phase Uncertain Channels

International audience—In this paper, we study Bayesian and hybrid Cramér–Rao bounds (BCRB and HCRB) for the code-aided (CA), the data-aided (DA), and the non-data-aided (NDA) dynamical phase estimation of QAM modulated signals. We address the bounds derivation for both the offline scenario, for which the whole observation frame is used, and the online which only takes into account the current and the previous observations. For the CA scenario we show that the computation of the Bayesian information matrix (BIM) and of the hybrid information matrix (HIM) is NP hard. We then resort to the belief-propagation (BP) algorithm or to the Bahl–Cocke–Jelinek–Raviv (BCJR) algorithm to obtain some approximate values. Moreover, in order to avoid the calculus of the inverse of the BIM and of the HIM, we present some closed form expressions for the various CRBs, which greatly reduces the computation complexity. Finally, some simulations allow us to compare the possible improvements enabled by the offline and the CA scenarios. Index Terms—Bayesian Cramér–Rao bound (BCRB), code-aided (CA) bound, data-aided (DA) bound, dynam-ical phase estimation, hybrid Cramér–Rao bound (HCRB), non-data-aided (NDA), offline, online

On a Hybrid Preamble/Soft-Output Demapper Approach for Time Synchronization for IEEE 802.15.6 Narrowband WBAN

In this paper, we present a maximum likelihood (ML) based time synchronization algorithm for Wireless Body Area Networks (WBAN). The proposed technique takes advantage of soft information retrieved from the soft demapper for the time delay estimation. This algorithm has a low complexity and is adapted to the frame structure specified by the IEEE 802.15.6 standard for the narrowband systems. Simulation results have shown good performance which approach the theoretical mean square error limit bound represented by the Cramer Rao Bound (CRB)

Recursive joint Cramér‐Rao lower bound for parametric systems with two‐adjacent‐states dependent measurements

Joint Cramér-Rao lower bound (JCRLB) is very useful for the performance evaluation of joint state and parameter estimation (JSPE) of non-linear systems, in which the current measurement only depends on the current state. However, in reality, the non-linear systems with two-adjacent-states dependent (TASD) measurements, that is, the current measurement is dependent on the current state as well as the most recent previous state, are also common. First, the recursive JCRLB for the general form of such non-linear systems with unknown deterministic parameters is developed. Its relationships with the posterior CRLB for systems with TASD measurements and the hybrid CRLB for regular parametric systems are also provided. Then, the recursive JCRLBs for two special forms of parametric systems with TASD measurements, in which the measurement noises are autocorrelated or cross-correlated with the process noises at one time step apart, are presented, respectively. Illustrative examples in radar target tracking show the effectiveness of the JCRLB for the performance evaluation of parametric TASD systems

Max-log demapper architecture design for DVB-T2 rotated QAM constellations

International audience— Rotated and cyclic-Q delayed (RCQD) quadrature amplitude modulation (QAM) improve DVB-T2 system performance over highly time-frequency selective channels. However, when compared with conventional QAM demapper, the RCQD demapper requires a higher computational complexity. In this paper, a complexity-reduced max-log demapper is derived and implemented over a FPGA platform. The proposed demapper allows to find the maximum likelihood (ML) point with a search spanning only M signal constellation points and guarantees to obtain the same log-likelihood ratio (LLR) metrics as the optimum max-log soft decision demapper while spanning at most 2 M signal constellation points. The optimized hardware implementation introduces only a slight performance loss compared to the floating-point full complexity max-log performance. Index Terms — DVB-T2, Rotated and Cyclic Q Delayed (RCQD) Constellations, Log-Likelihood Ratio (LLR), Max-Log Demapper

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

A low-complexity 2D signal space diversity solution for future broadcasting systems

-DVB-T2 was the first industrial standard deploying rotated and cyclic Q delayed (RCQD)modulation to improve performance over fading channels. This enablesimportantgains compared toconventional quadrature amplitude modulations(QAM) under severe channel conditions.However, the corresponding demodulation complexitystill prevents its use forwider applications. This paper proposes several rotation angles for different QAM constellations anda corresponding low-complexity detection method. Results show that the proposed solution simplifies both the transmitter and the receiver with often betterperformancethan the proposed angles in DVB-T2. Compared with the lowest complexity demappers currently used in DVB-T2, the proposed solution achieves an additional reduction bymore than 60%. Index Terms- DVB-T2, Rotated and Cyclic Q Delayed (RCQD) Modulations, Signal Space Diversity (SSD), Fading Channel, Quadrature Amplitude Modulations (QAM), Max-Log, ComputationalComplexity

Localizability Optimization for Multi Robot Systems and Applications to Ultra-Wide Band Positioning

RÉSUMÉ: RÉSUMÉ Les Systèmes Multi-Robots (SMR) permettent d’effectuer des missions de manière efficace et robuste du fait de leur redondance. Cependant, les robots étant des véhicules autonomes, ils nécessitent un positionnement précis en temps réel. Les techniques de localisation qui utilisent des Mesures Relatives (MR) entre les robots, pouvant être des distances ou des angles, sont particulièrement adaptées puisqu’elles peuvent bénéficier d’algorithmes coopératifs au sein du SMR afin d’améliorer la précision pour l’ensemble des robots. Dans cette thèse, nous proposons des stratégies pour améliorer la localisabilité des SMR, qui est fonction de deux facteurs. Premièrement, la géométrie du SMR influence fondamentalement la qualité de son positionnement pour des MR bruitées. Deuxièmement, les erreurs de mesures dépendent fortement de la technologie utilisée. Dans nos expériences, nous nous focalisons sur la technologie UWB (Ultra-Wide Band), qui est populaire pour le positionnement des robots en environnement intérieur en raison de son coût modéré et sa haute précision. Par conséquent, une partie de notre travail est consacrée à la correction des erreurs de mesure UWB afin de fournir un système de navigation opérationnel. En particulier, nous proposons une méthode de calibration des biais systématiques et un algorithme d’atténuation des trajets multiples pour les mesures de distance en milieu intérieur. Ensuite, nous proposons des Fonctions de Coût de Localisabilité (FCL) pour caractériser la géométrie du SMR, et sa capacité à se localiser. Pour cela, nous utilisons la Borne Inférieure de Cramér-Rao (BICR) en vue de quantifier les incertitudes de positionnement. Par la suite, nous fournissons des schémas d’optimisation décentralisés pour les FCL sous l’hypothèse de MR gaussiennes ou log-normales. En effet, puisque le SMR peut se déplacer, certains de ses robots peuvent être déployés afin de minimiser la FCL. Cependant, l’optimisation de la localisabilité doit être décentralisée pour être adaptée à des SMRs à grande échelle. Nous proposons également des extensions des FCL à des scénarios où les robots embarquent plusieurs capteurs, où les mesures se dégradent avec la distance, ou encore où des informations préalables sur la localisation des robots sont disponibles, permettant d’utiliser la BICR bayésienne. Ce dernier résultat est appliqué au placement d’ancres statiques connaissant la distribution statistique des MR et au maintien de la localisabilité des robots qui se localisent par filtrage de Kalman. Les contributions théoriques de notre travail ont été validées à la fois par des simulations à grande échelle et des expériences utilisant des SMR terrestres. Ce manuscrit est rédigé par publication, il est constitué de quatre articles évalués par des pairs et d’un chapitre supplémentaire. ABSTRACT: ABSTRACT Multi-Robot Systems (MRS) are increasingly interesting to perform tasks eÿciently and robustly. However, since the robots are autonomous vehicles, they require accurate real-time positioning. Localization techniques that use relative measurements (RMs), i.e., distances or angles, between the robots are particularly suitable because they can take advantage of cooperative schemes within the MRS in order to enhance the precision of its positioning. In this thesis, we propose strategies to improve the localizability of the SMR, which is a function of two factors. First, the geometry of the MRS fundamentally influences the quality of its positioning under noisy RMs. Second, the measurement errors are strongly influenced by the technology chosen to gather the RMs. In our experiments, we focus on the Ultra-Wide Band (UWB) technology, which is popular for indoor robot positioning because of its mod-erate cost and high accuracy. Therefore, one part of our work is dedicated to correcting the UWB measurement errors in order to provide an operable navigation system. In particular, we propose a calibration method for systematic biases and a multi-path mitigation algorithm for indoor distance measurements. Then, we propose Localizability Cost Functions (LCF) to characterize the MRS’s geometry, using the Cramér-Rao Lower Bound (CRLB) as a proxy to quantify the positioning uncertainties. Subsequently, we provide decentralized optimization schemes for the LCF under an assumption of Gaussian or Log-Normal RMs. Indeed, since the MRS can move, some of its robots can be deployed in order to decrease the LCF. However, the optimization of the localizability must be decentralized for large-scale MRS. We also propose extensions of LCFs to scenarios where robots carry multiple sensors, where the RMs deteriorate with distance, and finally, where prior information on the robots’ localization is available, allowing the use of the Bayesian CRLB. The latter result is applied to static anchor placement knowing the statistical distribution of the MRS and localizability maintenance of robots using Kalman filtering. The theoretical contributions of our work have been validated both through large-scale simulations and experiments using ground MRS. This manuscript is written by publication, it contains four peer-reviewed articles and an additional chapter

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

Characterization, Verification and Control for Large Quantum Systems

Quantum information processing offers potential improvements to a wide range of computing endevaors, including cryptography, chemistry simulations and machine learning. The development of practical quantum information processing devices is impeded, however, by challenges arising from the apparent exponential dimension of the space one must consider in characterizing quantum systems, verifying their correct operation, and in designing useful control sequences. In this work, we address each in turn by providing useful algorithms that can be readily applied in experimental practice. In order to characterize the dynamics of quantum systems, we apply statistical methods based on Bayes' rule, thus enabling the use of strong prior information and parameter reduction. We first discuss an analytically-tractable special case, and then employ a numerical algorithm, sequential Monte Carlo, that uses simulation as a resource for characterization. We discuss several examples of SMC and show its application in nitrogen vacancy centers and neutron interferometry. We then discuss how characterization techniques such as SMC can be used to verify quantum systems by using credible region estimation, model selection, state-space modeling and hyperparameterization. Together, these techniques allow us to reason about the validity of assumptions used in analyzing quantum devices, and to bound the credible range of quantum dynamics. Next, we discuss the use of optimal control theory to design robust control for quantum systems. We show extensions to existing OCT algorithms that allow for including models of classical electronics as well as quantum dynamics, enabling higher-fidelity control to be designed for cutting-edge experimental devices. Moreover, we show how control can be implemented in parallel across node-based architectures, providing a valuable tool for implementing proposed fault-tolerant protocols. We close by showing how these algorithms can be augmented using quantum simulation resources to enable addressing characterization and control design challenges in even large quantum devices. In particular, we will introduce a novel genetic algorithm for quantum control design, MOQCA, that utilizes quantum coprocessors to design robust control sequences. Importantly, MOQCA is also memetic, in that improvement is performed between genetic steps. We then extend sequential Monte Carlo with quantum simulation resources to enable characterizing and verifying the dynamics of large quantum devices. By using novel insights in epistemic information locality, we are able to learn dynamics using strictly smaller simulators, leading to an algorithm we call quantum bootstrapping. We demonstrate by using a numerical example of learning the dynamics of a 50-qubit device using an 8-qubit simulator

D11.2 Consolidated results on the performance limits of wireless communications

Deliverable D11.2 del projecte europeu NEWCOM#The report presents the Intermediate Results of N# JRAs on Performance Limits of Wireless Communications and highlights the fundamental issues that have been investigated by the WP1.1. The report illustrates the Joint Research Activities (JRAs) already identified during the first year of the project which are currently ongoing. For each activity there is a description, an illustration of the adherence and relevance with the identified fundamental open issues, a short presentation of the preliminary results, and a roadmap for the joint research work in the next year. Appendices for each JRA give technical details on the scientific activity in each JRA.Peer ReviewedPreprin