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

MSE bounds for phase estimation in presence of recursive nuisance parameters

The mean squared error (MSE) is commonly used to measure and compare the performance of various phase estimation techniques in communications and signal processing systems. When the received signal contains recursive nuisance parameters, the MSE is extremely difficult to obtain and even the conventional modified Cramér-Rao bound (MCRB) can not be readily applied. In this paper, a recursive MSE bound and its simplified calculation method are proposed to solve the problem. As an application example, an adaptive hybrid antenna array and its associated angle-of-arrival (AoA) estimation technique are presented. The MSE of the AoA estimation is simulated and compared with the recursive MSE bound and MCRB. The results show that the proposed recursive MSE bound provides a tighter lower MSE bound than the recursive MCRB

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)

Borné de Cramér-Rao sous contraintes pour l’estimation simultanée de paramètres aléatoires et non aléatoires

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. On the other hand, numerous works have shown the versatility of deterministic constrained Cramér-Rao bound for estimation performance analysis and design of a system of measurement. In this communication, we propose a constrained hybrid lower bound which takes into account equality constraints on deterministic parameters. The proposed bound is then compared to previous bounds of the literature. Finally, the usefulness of the proposed bound is illustrated with an application to radar Doppler estimation

Contribution du Gipsa-lab au projet ANR LURGA " Localisation d'Urgence Reconfigurable par GALILEO "

Rapport technique du laboratoire Gipsa-lab mis en ligne en 2014, issu d'un document livrable pour le projet ANR LURGA datant de Janvier 2010.Le présent document est une re-édition d'une contribution du Gipsa-lab au projet ANR (pour " Agence Nationale de la Recherche ") LURGA (pour " Localisation d'Urgence Reconfigurable par Galiléo "). Il est constitué d'une partie " avant propos " qui rappelle très brièvement le but du projet LURGA ainsi que les partenaires et leur roles, puis du livrable T.3.2 " rapport de spécification des algorithmes de détection basés sur le filtrage particulaire (version finale) ", qui constitue l'essentiel de la contribution du laboratoire Gipsa-lab. Le but final du projet LURGA est d'améliorer les performances des algorithmes de localisation qui sont basés sur l'estimation des temps d'arrivée. En préliminaire au travail de localisation, la tâche de synchronisation est ainsi cruciale. Le rapport T.3.2 décrit ainsi les algorithmes de synchronisation permettent d'estimer le délai, la phase, et l'amplitude du signal reçu ou des bornes inférieures de performances associées à ce problème

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