Bounding rare event probabilities in computer experiments

We are interested in bounding probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo methods designed for rare events cannot be used. We then propose a strategy to deal with this difficulty based on importance sampling methods. This proposal relies on Kriging metamodeling and is able to achieve sharp upper confidence bounds on the rare event probabilities. The variability due to the Kriging metamodeling step is properly taken into account. The proposed methodology is applied to a toy example and compared to more standard Bayesian bounds. Finally, a challenging real case study is analyzed. It consists of finding an upper bound of the probability that the trajectory of an airborne load will collide with the aircraft that has released it.Comment: 21 pages, 6 figure

Maximin design on non hypercube domain and kernel interpolation

In the paradigm of computer experiments, the choice of an experimental design is an important issue. When no information is available about the black-box function to be approximated, an exploratory design have to be used. In this context, two dispersion criteria are usually considered: the minimax and the maximin ones. In the case of a hypercube domain, a standard strategy consists of taking the maximin design within the class of Latin hypercube designs. However, in a non hypercube context, it does not make sense to use the Latin hypercube strategy. Moreover, whatever the design is, the black-box function is typically approximated thanks to kernel interpolation. Here, we first provide a theoretical justification to the maximin criterion with respect to kernel interpolations. Then, we propose simulated annealing algorithms to determine maximin designs in any bounded connected domain. We prove the convergence of the different schemes.Comment: 3 figure

Performance of MMSE STBC MC-CDMA over Rayleigh and MIMO METRA channels

International audienceThe performance of MMSE Single-user Detection (SD) and Multi-user Detection (MD) STBC MC-CDMA systems are analysed and compared in the case of two transmit antennas and one or two receive antennas over Rayleigh fading channels and then over the stochastic MIMO METRA channel model. With two transmit and one receive antennas, MD achieves a gain of roughly 1 dB for non-full load systems while the same performance are obtained with MD and SD for full load systems. Besides, with two receive antennas, we present a sub-optimal and an optimal MMSE SD MIMO MC-CDMA schemes, this last one offering a very good performance/complexity trade-off. Finally, the very good behaviour of MMSE STBC MC-CDMA systems is confirmed over the realistic METRA MIMO channel

STBC MC-CDMA systems: Comparison of MMSE single user and multiple user detection schemes over Rayleigh and MIMO METRA channels

International audienceThe performance of MMSE single-user detection (SD) and multi-user detection (MD) STBC multi-carrier code division multiple access (MC-CDMA) systems are analysed and compared in the case of two transmit antennas and one or two receive antennas over Rayleigh fading channels and then over the stochastic multiple input multiple output (MIMO) METRA channel model. With two transmit and one receive antennas, MD achieves a gain of roughly 1 dB for non-full load systems while the same performance is obtained with MD and SD for full load systems. Besides, with two receive antennas, we present a sub-optimal and an optimal MMSE SD MIMO MC-CDMA schemes, this last one offering a very good performance. Finally, the very good behaviour of MMSE space-time block coding (STBC) MC-CDMA systems is confirmed over the realistic multi element transmit receive antennas (METRA) MIMO channel

Multicarrier CDMA: A very promissing multiple access scheme for future wideband wireless networks

International audienceIn this paper, multicarrier techniques are studied in the context of the future wideband wireless networks. After a brief presentation of the third generation mobile networks, MC-CDMA systems are considered for the downlink of the future high rate cellular networks. The performance of different mono-user and multi-user detection techniques are compared with the help of Monte Carlo simulations over a frequency selective Rayleigh channel. Thus, the efficiency of MC-CDMA as a very promising multiple access and robust modulation scheme is successfully demonstrated for the downlink of the future wideband mobile networks. Finally, the first results concerning the performance of Multicarrier CDMA technique combined with space-time block coding in order to build a Multiple Input Multiple Output/MC-CDMA system are presented over a Rayleigh channel

De la terre à la mer, les frères Barbedienne

Cet article analyse à une échelle micro-historique le passage de la terre à la mer d’une famille de paysans bretons. Durant les premières décennies du xixesiècle, cette famille s’enfonce progressivement dans la pauvreté. Cependant, sa situation géographique, en bordure de la baie de Saint-Brieuc, permet à trois garçons de trouver facilement une réponse provisoire et partielle à la précarité des revenus agricoles: l’embarquement saisonnier pour la grande pêche à Terre-Neuve. Assez rapidement toutefois, les circonstances et les nécessités les amènent à quitter définitivement la terre pour devenir pêcheurs puis marins. À partir de ce moment, formés par la grande pêche, ils participent aux différentes mutations de celle-ci: passage de Terre-Neuve à Islande, tentatives de diversification vers l’armement au commerce international. L’évolution ultime, dans la deuxième partie du siècle, amènera le plus jeune frère à participer à la lente migration des inscrits maritimes de Bretagne vers les grands ports de commerce alors en forte expansion. Les parcours des trois frères s’inscrivent donc dans l’évolution générale des pêcheries et du commerce breton au xixesiècle.This article analyzes, on a microhistoric scale, the passage of a Breton peasant family from the land to the sea. In the first decades of the 19th Century, this family progressively slipped deeper into poverty although their geographic location, right on the bay of Saint-Brieuc, made it possible for three boys to easily find a temporary, partial answer to the insecurity of agricultural revenue: seasonal departures to fish on Newfoundland’s coast. However, circumstance and need quickly led them to leave the land permanently in order to become first fishermen, then sailors. From this moment onward, trained in sea fishing, they participated in its different transformations: passage from Newfoundland to Iceland, and attempts at diversification towards international trade. The last evolution, in the second part of the century, led the youngest brother to participate in the slow migration of the naval enlisted men of Brittany towards commercial ports, at that time rapidly expanding. The experiences of the three brothers thus fit into the general evolution of fisheries and Breton commerce in the 19th Century

STBC MC-CDMA systems for indoor and outdoor scenarios

We compare the performance of Alamouti's space-time block coded MC-CDMA systems for indoor and outdoor realistic scenarios with zero forcing or minimum mean square error detection schemes. Two different configurations of the system are considered for the two scenarios. The different results obtained as well for indoor as for outdoor scenarios demonstrate that spatial diversity improves significantly the performance of MC-CDMA systems. Then, Alamouti's STBC MC-CDMA schemes derive full benefit from the frequency and spatial diversities and can be considered as a very realistic and promising candidate for the air interface downlink of the 4th generation mobile radio systems

Combination of Space-Time Block Coding with MC-CDMA Technique for MIMO systems with two, three and four transmit antennas

For future wideband wireless networks, space diversity schemes relying on multiple antennas at the receiver and/or at the transmitter are very attractive to combat fadings and improve the transmission performance. In this paper, Multi-Carrier Code Division Multiple Access (MC-CDMA) technique combined with several Space-Time Block Codes (STBC) is analyzed in the case of Nt transmit antennas and Nr receive antennas to provide a diversity order of NtNr for a 2 bps/Hz spectral efficiency. A general method to decode STBC from orthogonal designs associated with MC-CDMAis proposed. Two Single-user Detection techniques, Zero Forcing (ZF) and Minimum Mean Square Error (MMSE), are studied and compared in the downlink synchronous case over frequency selective Rayleigh channels

Codage temps-espace en blocs combiné avec un système multiporteuse à étalement de spectre de type MC-CDMA

Ce papier présente les performances de systèmes MIMO MC-CDMA à Nt antennes d'émission et Nr antennes de réception offrant une efficacité spectrale de 1 ou 2 bit/s/Hz. Les résultats sont obtenus pour différents schémas de codage temps-espace en blocs (STBC) dans le cas de la liaison descendante synchrone sur des canaux de Rayleigh sélectifs en fréquence pour les deux techniques de détection Zéro-Forcing (ZF) et Minimum Mean Square Error (MMSE). En outre, une méthode générale pour décoder les codes STBC orthogonaux associés aux signaux MC-CDMA est décrite. Par ailleurs, ces résultats démontrent l'intérêt d'un système STBC MC-CDMA reposant sur l'utilisation de codes temps-espace de rendement 1, et qu'il est en conséquence préférable d'utiliser la redondance au niveau du codage de canal et non au niveau du codage temps-espace