## Vol. 66, n° 7-8, July-August 2011

Content available on Springerlink

**Guest editors**

**Joe Wiart, Orange Labs, France
**

**Luk Arnault, Imperial College, UK**

**Walid Tabbara, Supélec, France**

## Foreword

## Statistics for management of complexity in electromagnetism

## Joined initiatives around uncertainty management, Generic methodologies, mathematical challenges, and numerical implementations

**Fabien Mangeant and EADS Innovation Works**

EADS, Suresnes, France

**Abstract** – Uncertainty in context-aware computing is mainly a consequence of the complexity of context acquisition mechanisms and context processing. The presence of uncertainty may harm the users’ confidence in the application, rendering it useless. This paper describes a three-phase strategy to manage uncertainty by identifying its possible sources, representing uncertain information, and determining how to proceed, once uncertain context is detected. We conducted an experiment to assess the impact and utility of uncertainty management in a location-aware museum guide that incorporated the approach proposed. The impact was measured by comparing the number of erroneous location estimations and the number of interactions performed by users. A survey was used to measure user friendliness, the utility of the application and user trust among 118 museum visitors who participated in the experiment. Results suggest that uncertainty management helps improve the accuracy of context estimates and the user’s perception on the reliability of the application.

**Keywords: ** Uncertainty management – Context-aware computing – User trust – Usability – Museum guides

## Uncertainty analysis of the specific absorption rate induced in a phantom using a stochastic spectral collocation method

**Ouanès Aiouaz ^{1}, David Lautru^{2}, Man-Fai Wong^{1}, Emmanuelle Conil^{1}, Azeddine Gati^{1}, Joe Wiart^{1} and Victor Fouad Hanna**

^{2 1}Orange Labs, Issy-les-Moulineaux, France

^{2}UPMC, Paris, France

**Abstract** – Uncertainty analysis of human exposure to radio waves is studied with a spectral approach of stochastic collocation methods. This approach allows determining in an efficient way the statistical moments of the output variable, the specific absorption rate, with respect to uncertain input parameters. Polynomial chaos expansions are used for the random output, and the spectral coefficients are determined by projection or regression. These techniques are used with an electromagnetic solver based on a finite difference time domain scheme. The convergence of the statistical moments is analyzed for two case studies. Global sensitivity is also analyzed for the uncertain position of a cellular phone in the close vicinity of a human head model.

**Keywords**: Uncertainty – Stochastic collocation methods – FDTD – Specific absorption rate (SAR) – Sensitivity

## A surrogate model to assess the whole body SAR induced by multiple plane waves at 2.4 GHz

**Thierry Kientega ^{1}, Emmanuelle Conil^{1}, Abdelhamid Hadjem^{1}, Elodie Richalot^{2}, Azzedine Gati^{1}, Man Fai Wong^{1}, Odile Picon^{2} and Joe Wiart^{1
}**

^{1}Orange Labs, Issy-les-Moulineaux, France

^{2}ESYCOM, Université Paris-Est Marne-la-Vallée, France

**Abstract** – The assessment of the exposure to electromagnetic waves is nowadays a key question. Dealing with the relationship between exposure and incident field, most of previous investigations have been performed with a single plane wave. Realistic exposure in the far field can be modeled as multiple plane waves with random direction of arrival, random amplitude, and random phase. This paper, based on numerical investigations, studies the whole body specific absorption rate (SAR) linked to the exposure induced by five random plane waves having uniformly distributed angles of arrival in the horizontal plane, log-normal distributed amplitudes, and uniformly distributed phases. A first result shows that this random heterogeneous exposure generates maximal variations of ±25% for the whole body specific absorption. An important observation is that the exposure to a single plane wave arriving face to the body, used for the guidelines, does not constitute the worst case. We propose a surrogate model to assess the distribution of the whole body SAR in the case of an exposure to multiple plane waves. For a sample of 30 values of whole body SAR induced by five plane waves at 2.4 GHz, this simple approach, considering the resulting SAR as the sum of the SAR induced by each isolated plane wave, leads to an estimated distribution of whole body SAR following the real distribution with a p value of 76% according to the Kolmogorov statistical test.

**Keywords: ** Radiofrequencies – Surrogate model – Specific Absorption Rate (SAR) – FDTD – Statistical tests – Multiple plane waves exposure

## Computation of the field radiated by a FM transmitter by means of ordinary kriging

**Francois Jouvie ^{1}, Dominique Lecointe^{1}, Philippe Briend^{2}, Francois Jacquin^{2} and Emmanuel Nicolas^{2
}**

^{1}Supélec, Gif-sur-Yvette, France

^{2}TDF, Montrouge, France

**Abstract** – The maintenance of frequency modulation (FM) broadcasting sites is one of the activities of TDF to guarantee the availability of broadcasting services for its clients. As it is not always possible to stop the broadcasting due to the large number of listeners, TDF has to guarantee the safety of workplaces with respect to the limits of exposure to electromagnetic fields inside the mast near the antenna. Exposure limits are defined in the European Directive for workers (see [1]). Today, TDF carries out measurements with broadband fieldmeter to identify areas above the action level in terms of electric field limit, but for precise measurements, three axes probing with selective measurements are carried out, frequency by frequency, inside the workplace. Hence, the magnitude of the electric field in the zone is obtained either by a broadband fieldmeter which is moved manually along a vertical axis or by a selective three axes probing with a lot of punctual measurements to have a spatial sampling of the field in the volume of interest. Regrettably, in practice, measurements take a long time because of the difficult situation of measurement points, the closeness of metallic structures and a lack of place inside the mast. Consequently, the number of sampling points is generally too limited to assess the exposure. The challenge is not only to assess the field level anywhere inside the volume of interest, without any additional measurements, but also to know the uncertainty associated to the assessed value. By comparing these results to the limit value, one can conclude on the safety of the volume. As a simple interpolation of the measured values does not yield the associated uncertainty, we examine in this paper how ordinary kriging can be an effective tool to take up this challenge. The paper is organized as follows: in Section 2, we recall the main theoretical results concerning the ordinary kriging and, particularly, the variogram. In Section 3, we explain why numerical simulation is used as a help in the implemented process and we present a description of the FM transmitter numerical model. In Section 4, we detail the computations of bidimensional variograms that concern the distribution of electric field in restricted planes of the spatial coordinates system. In Section 5, we detail the construction of three-dimensional variograms that are necessary for the computation of fields over volumes. Finally, some concluding remarks are given in Section 6.

**Keywords:** Ordinary kriging – Statistical methods in electromagnetism – Computation of radiated electromagnetic field

## An empirical statistical detection of non-ideal field distribution in a reverberation chamber confirmed by a simple numerical model based on image theory

**Emmanuel Amador ^{1}, Christophe Lemoine^{1} and Philippe Besnier^{1
}**

^{1}INSA, IETR, Rennes, France

**Abstract** – In this article, the effect of the size of the antennas on the distribution of the electric field observed in a reverberation chamber is analyzed. Our hypothesis is that the more the antenna is voluminous, the more the behavior of the chamber appears to be ideal through measurement analysis. A simple numerical model is presented and used to verify the phenomenon and give credence to the assumption.

**Keywords: ** Reverberation chamber – Rayleigh distribution – Weibull distribution – Statistical test – Modeling – Image theory

## Experimental determination of the higher electric field level inside an overmoded reverberation chamber using the generalized extreme value distribution

**Gérard Orjubin ^{1} and Man-Fai Wong^{2
}**

^{1}Université française d’Egypte, le Caire, Egypte

^{2}Orange Labs, Issy-les-Moulineaux, France

**Abstract** – Reverberation chamber (RC), in which a complex electromagnetic environment is created, is of great interest as a versatile test and measurement tool, and its performance is conveniently evaluated through the field statistics. Following a previous paper in which the generalized extreme value (GEV) distribution was proposed to model the maximum field inside an RC, this work presents an experimental validation of the GEV use for the overmoded RC. The electric field is measured with a small sensor for a large number of points inside the RC, and the GEV parameters are accurately estimated. Since the maximum field distribution for this overmoded RC is found to be of reverse Weibull type, the field distribution is right bounded by a higher level that can be determined.

**Keywords: ** Generalized extreme value distribution – High-intensity radiation field (HIRF) – Higher-order statistics – Maximum value – Reverberation chamber

## Minimum-value distribution of random electromagnetic fields for modeling deep fading in wireless communications

**Gabriele Gradoni ^{1} and Luk R. Arnaut^{2
}**

^{1}Universita Politecnica delle Marche, Ancona, Italy

^{2}Imperial College, London, UK

**Abstract** – In this work, we presented a theoretical investigation of the minimum-value distribution inside complex electromagnetic environments. In particular, a statistical model for characterizing the minimum value of the complex-value field or power inside a dynamic mode-tuned or mode-stirred reverberation chamber is presented and discussed. Such an EM environment serves as an emulator of multipath radiowave propagation for indoor/outdoor wireless communication channels. It is found that, for both overmoded and undermoded regimes, the generalized extreme value distribution leads to the reverse Fréchet and Weibull types for complex-value (Cartesian and total) fields and for the total energy (or intensity). These distributions are stable and follow from the convergent behavior of the lower tail for their corresponding parent distribution of the Cartesian field magnitude, namely a χ 2. On the other hand, received power exhibits a Pareto-type distribution because of the unbounded left tail of the negative exponential parent distribution.

**Keywords: ** Generalized extreme value – Reverberation chamber – Fading

## Estimation of the probability distributions for cable coupling using unscented transforms

**David W. P. Thomas ^{1}, Leonardo R. A. X. de Menezes^{2}, Christos Christopoulos^{1}, Frank Leferink^{3} and Hans J. G. Bergsma^{4
}**

^{1}The University of Nottingham, UK

^{2}Universidade de Brasilia, Brazil

^{3}Thales, Hengelo, The Netherlands

^{4}University of Twente, The Netherlands

**Abstract** – This work presents the use of unscented transforms (UT) for the description of statistical uncertainty in electromagnetic coupling between cables. UT greatly reduce the computational burden for the statistical analysis of nonlinear problems compared with more traditional approaches such as the Monte Carlo technique. Coupling between cables has a nonlinear parameter dependence and has a high variability due to the variability in the cable braid manufacture and the highly variable nature of cable layout. Therefore, cable coupling can only be defined within statistical limits. First, it is shown that by analyzing the resonances the important features of maximum coupling and the point of maximum coupling can be characterized. It is then demonstrated how UT can be used to efficiently identify the parameters which contribute significantly to the uncertainty in cable coupling and then to provide a measure of the probability distribution for the multivariate problem.

**Keywords: ** Unscented transforms – Statistical analysis – Cable coupling – EMC

## Statistical study of the influence of building architectural properties on scattered fields in urban environment

**Shermila Mostarshedi ^{1}, Elodie Richalot^{1}, Man-Fai Wong^{2}, Joe Wiart^{2} and Odile Picon^{1
}**

^{1}ESYCOM, Université Paris-Est Marne-la-Vallée, France

^{2}Orange Labs, Issy-les-Moulineaux, France

**Abstract** – Statistical studies on the reflection coefficient of concrete–glass building facades are conducted using a fast and an accurate method based on the Green’s functions. The variation of different architectural parameters, such as concrete permitting and distribution, size and type of windows, are studied. The influence of selected parameters on the total reflection coefficient of the building is quantified for different incidence and observation angles as well as in different diffraction zones.

**Keywords:** Wave propagation – Urban environment – Scattering – Statistical study – Green’s functions