A new, efficient and very accurate simulation approach based on a hybrid ray tracing technique is presented. The unique combination of a ray-density normalization (RDN) with Physical Optics (PO) and the Physical Theory of Diffraction (PTD) makes the algorithm almost universally applicable to arbitrary simulations of large and complex objects.

Starting from a transmitter, a specified number N of rays, serving as representatives of propagation paths, is launched over an adjustable angular range towards the object. These rays are traced according to the well-known Shooting and Bouncing Rays (SBR) technique, which allows for a practically unlimited number of reflections. Each time a ray hits a surface, the illuminated area corresponding to this ray is given by its ray-density. This area serves as the integration area for the PO calculation. Thus, the PO integral reduces to a sum of ray contributions. A similar procedure is applied to the calculation of PTD contributions.

As the algorithm has already been verified in [1], this paper gives an overview on simulation results obtained at highly complex objects and focusses on the implementation of PO for dielectric objects. A special problem with dielectrics is the splitting of the incident wave into a reflected and a transmitted one. This task has been solved by deciding randomly for each ray if it is to be reflected or transmitted. Thus, memory-consuming recursive algorithms are avoided and merely the ray-density must be adjusted. With this approach, good convergence of results is observed if the number of rays hitting the surface is large enough. As an example, Fig. 1 shows the relative field strength distribution in the aperture plane of a generic dielectric radome (ε_r = 1.5) as it is used e.g. as a nose radome for aircraft. The direction of the incident wave is "nose-on" and the frequency is 10 GHz. As can be seen from Fig. 1, the radome definitely influences the field strength distribution in the aperture plane, where the antenna, e.g. a planar array, is placed. The results of such simulations can be used for compensating the radome effects by an appropriate feeding of the array elements.

Further applications of the presented hybrid asymptotic algorithm include RCS predictions of arbitrary objects, especially aircraft and other flying objects. Besides, high-resolution range profiles can be created by performing simulations over a wider frequency range, which can be used for identifying flying objects by their scattered fields.

A very challenging topic is the modelling of resonant structures such as engine intakes, which require consideration of a large number of reflections as well as very complex interior structures. Although first simulations yield quite promising results, it is observed that an adequate treatment of arbitrary curved surfaces must be implemented in further work in order to improve the accuracy of results and the versatility of the algorithm.

Fig. 1: Relative field distribution in the aperture plane of a generic radome (in dB).

[1] F. Weinmann, "Ray Tracing with PO/PTD for RCS Modeling of Large Complex Objects," accepted for publication in IEEE Trans. Antennas Propagat.

The transient radiation from line and point sources embedded in planarly layered media is investigated in connection with the leaky modes. The proposed method involves the evaluation of the spatial-wavenumber inversion integral using complex-plane analysis, which results in the frequency-domain field represented by a discrete series of residues and a continuous branch-cut integral. By properly deforming integration paths in both the complex frequency plane and complex wavenumber plane and by including the improper modes (leaky modes) in the residue series it is shown that the branch-cut integral contribution vanishes. The resulting time-domain field is obtained as a temporal inversion of the residue series, which leads to rapidly convergent one-dimensional integrals. The method is simple, physically insightful, and easy to implement on a computer. It leads to an efficient computation of the transient fields due to line and point sources in a layered medium and is applicable to multilayered lossy dielectric media and planarly layered media with negative frequency-dependent permittivity and permeability (homogenized metamaterial structures).

The method requires the complete characterization of complex frequency-plane branch-point singularities and generalized cutoff frequencies associated with the discrete surface-wave modes of a laterally infinite, planarly layered background structure. The analysis of singularities in the complex frequency plane enables to understand the dynamics of poles and branch points in the complex wavenumber plane. It is shown that for a proper selection of the frequency path (above certain complex frequency-plane branch points), the improper modes originated in the second and fourth quadrants of the complex wavenumber plane eventually become proper modes as the frequency varies along this path. This observation is critical, which allows to add an additional segment on the improper Riemann sheet of the wavenumber plane to the branch-cut integration. This additional contour encloses in a counter-clockwise direction the improper modes which eventually become proper modes and is such that the new integration contour is never crossed as modes migrate from the improper sheet to the proper Riemann sheet. The resulting integral over the deformed contour in the complex wavenumber plane, which is an entire function of frequency in the upper-half frequency plane, is shown to vanish (using the method of steepest descents), and the residue summation, which includes proper and improper modes, represents a convergent sum.

The method is applicable for all times of interest, although for certain source-receiver locations an "early-time" period is identified, which encompasses the specular reflection from the nearest interface, and during which time the residue series requires a special treatment. The numerical results of the scattered transient potentials due to electric and magnetic line and point sources in planarly layered media are obtained by the proposed leaky-wave analysis technique and compared with the full-wave solution results, showing an excellent agreement for "early-time" and "late-time" periods.

The electromagnetic environment in urban areas is growing increasingly complex. Sources of electromagnetic exposure like TV, FM, GSM, Wifi and others are spreading continuously and in the case of Wifi their geographical locations cannot be catalogued exhaustively anymore. Furthermore, the complexity of any highly urbanized environment and the lack of information about the dielectric properties of buildings lead to complex configuration so that a precise deterministic modelling of the electromagnetic exposure at any a given location of interest is probably out-of-reach. On the other hand there is a growing demand to assess the human exposure induce by these wireless communications. In a project between France Télécom R & D, Ecole des Mines and Supélec the application of geostatistical methods in this context is being explored. Geostatistics provides the right framework for setting up such exposure maps and its spatial statistical model yields an estimate of exposure as well as an associated error (De Doncker et al., Electromagnetics, 26: 111-122). The project consists of three phases: geostatistical evaluation of data generated by the numerical model EMF (both in free space and with the addition of obstacles), statistical analysis of measurements performed in the area of the Quartier Latin in Paris and, finally, joint evaluation of an urban area both by statistical and deterministic numerical modelling. The paper reports about the first two phases of this ongoing project, in which the spatial variation is modelled using the variogram, followed by a spatial regression known as kriging. The paper will also present results about using a kriging algorithm that integrates numerical model output as external drift.

Polarization is seen as a potential source of diversity gain in urban areas for future radio communication networks or evolution of existing networks [Y. Zhou - "Probability of Error and Capacity of Multi-polarization Antenna Systems for Downlink Mobile Communications" - IEEE Trans. Veh. Technol - Jan 2006, vol. 55, #1, pp256-269].
This type of diversity is convenient to keep small antenna sizes both at the Transmitter and at the receiver [R.G. Vaughan, "Polarization diversity in mobile communications", IEEE Trans. Veh. Technol, vol 39, #3, pp177-186, 1990].

The proposed paper resumes a work carry out at 5GHz in urban areas, where the depolarisation effects have been characterised both by CW measurement and simulations.
On the one side, works reported in the literature tackle with the subject in a full statistical manner, related to large area (ex: city or rural scale) or confined (indoor buildings) measurements, without a precise physical analysis of experimental datasets.
On the other side, some studies are only based on speculative simulations. Furthermore, it seems that depolarization in the 5 GHz band, has not yet been largely investigated.

The particularity of our approach is to focus on a "middle scale area" case, that is a limited urban area composed of a few buildings and streets so that phenomenological study of wave interaction is achievable. The full polarimetric HH, HV, VH and VV parameters amplitude have been measured by using a H/V oriented printed dipole antenna mounted on a car roof and one emitter installed on one elevated building. The roads of measurements are selected so that various types of radio interaction are possible.
In addition, simulations of the XPD (cross-depolarisation discrimination) value is made by using a 3D ray-tracing tool, combined with UTD methods. The model is applied on a high resolution geo data map of the investigated area, where perfectly conducting and dielectric surfaces are considered.

By comparing simulated and experimental XPD curves on some particular portions of the route, the measured level of XPD is correlated directly with the 3D visualization of the simulated ray paths. It is shown that depolarisation mechanisms are directly linked to dominant interactions, such as oblique reflection on wall or a double reflections between the road and houses.

The proposed paper will illustrate and analyse these simulated and measured results. Methods will be suggested to enrich the simulated responses that seem to provide only part of the depolarisation effects. The influence of the geo map data details will be shown.

Nowadays, to model the forward propagation in sea environment the Parabolic Wave equation (PWE) is recognised to be an efficient tool and is used for example on board of certain ships. The resolution technique applied is the Discrete Mixed Fourier Transform (DMFT) method that determine accurately and fastly the wave propagation above realistic surface. This method, proposed by Kuttler and Dockery, allows to model the influence of the dielectric surface taking into account all the refraction effects. This paper presents improvements of the method by taking into account the surface roughness and devoted to high frequencies radar applications.

To model the influence on the surface roughness on the propagation, modified impedance including shadowing effects is proposed. It has a strong dependence with the local grazing angle. The shadowing effects can be modelled with the Wagner or Smith approaches [1]. From these formulations, the illuminated height distribution is derived and it is included in the classical modified Fresnel reflection coefficient [2][3], in which the shadowing effect is ignored [1]. This statistic approach has been validated by comparison with a Monte Carlo process for different roughness (or sea state) that consists in computing the propagation above series of sea surface realisations.

Nevertheless, the classical DMFT can be numerically unstable, in particular when the rough surface is modelled by equivalent effective impedance. To avoid this problem the forward and backward Difference DMFT [4] could be used according to the equivalent impedance conditions. In this paper another approach is proposed to model the propagation in sea environment, considering rough sea in PWE resolution approach. This model is based on the classical Split Step Fourier resolution of the PWE, where the boundary condition is included by the image theory at each step. The obtained method is very accurate and unconditionally stable at high frequencies.

[1] V. Fabbro, C. Bourlier, P. F. Combes, "Forward Propagation Modeling Above Gaussian Rough Surfaces by the Parabolic Wave Equation: Introduction of the Shadowing Effect", Progress In Electromagnetic Research, PIER 58, pp 243-269, 2006.
[2] C. Bourlier, N. Pinel and V. Fabbro, Illuminated height PDF of a random rough surface and its impact on the forward propagation above oceans at grazing angles, Submitted to Symposium EUCAP 2006.
[3] J. R. Kuttler and R. Janaswamy, Improved Fourier transform methods for solving the parabolic wave equation, Radio Science., vol. 37, No 2, 10.1029/2001RS002488, 2002.

Due to blockage by solid obstacles such as buildings and terrain features, as well as to shadowing by vegetation, signals from the GPS (Global Positioning System) satellites experiment fading and additional delays. Due to deep fades, loss of lock, and relatively slow reacquisition times, the number of satellites being tracked by multichannel GPS receivers may decrease. In addition, the pseudoranges between satellite and receivers, contaminated by the extra signal delays, will also be incorrect. The combination of these effects induces location errors and, in extreme cases, may prevent receivers from operating.

This contribution presents results from a computer simulation model developed to analyze the effects of urban areas on the position error of GPS receivers and on the availability of the service.

Initially, a set of maps of three path states (clear, shadowed and blocked) as functions of azimuth and elevation are generated by processing the 30-arc-second digital elevation model provided by the Globe project, building databases, and a vegetation model. Three densely urbanized areas (Irajá, Ipanema and Copacabana) of the City of Rio de Janeiro with different height distributions are selected for study. Each of the areas is characterized by a set of path state maps corresponding to a large number of receiver locations.

In each step of the simulation, the GPS satellite positions are updated and the azimuths and elevations of all the paths connecting a satellite and a receiver are calculated. Next, signal strengths and pseudoranges are assigned to all the paths with elevations above 10 degrees. The signal strength assignment is performed using random number generators appropriate to the corresponding path state, according to the Urban Three-state Fade Model. The number of satellites tracked by a receiver coincides with the number of corresponding signals that are stronger than a pre-established threshold. The pseudorange associated with each of these signals is equal to the sum of the geometric length of the corresponding path with another distance which depends on the path state. That is, to a random component related to signal delays in the clear state, another component is added to represent delays by trees in the shadowed state or due to diffraction by hard structures (buildings or mountains) in the blocked state. These pseudoranges are then used to estimate vertical and horizontal position errors. Additionally, once a channel of a receiver loses lock, the model assumes that a reacquisition procedure is initiated and only successfully completed after the signal remains above the threshold for a non-interrupted and pre-specified length of time. Several parameters of interest are then used to update histograms. A final processing at the end of the simulation run provides statistics for these parameters.

The results to be presented are the probabilities of different path-state mixtures, as well as the cumulative distribution functions for: (1) received signal levels; (2) number of available satellites; and (3) horizontal position error. The results will be discussed to highlight the effects of the selected urban environments on the above parameters.

This paper presents results from a series of experiments that were conducted to measure the effect of Tropospheric ducting on propagation over the ocean in the Q-band. The tests were performed in February and November of 2005 off the Mid-Atlantic coast of the United States near Ocean City, Maryland. Testing involved transmitting a tone from a research vessel (RV) and measuring the signal strength of the tone at several receivers positioned along the coast in high-rise hotels, ranging in height from 19 to 50 meters. Propagation loss, which was computed as a function of distance between the RV and the various receiver locations, was estimated by computing the FFT of the received signal and examining the amplitude of the appropriate frequency bins containing the tone energy. By calibrating the receivers appropriately, it was possible to map the FFT magnitudes of the tones to actual received power levels, which, when compared to the known transmit power, provided a straightforward means of estimating the propagation loss. This process was repeated as the RV moved along a relatively straight course beginning close to shore (about 4 km) and continuing out to about 65 km at its furthest point. Data were collected during a total of six days, three in February and three in November.

In addition to measuring signal strength, meteorological data were also collected along the path between the RV and receiver. These data were used to generate height profiles of refractivity, which enabled us to characterize the evaporation and surface ducting features present during the testing. The refractivity profiles were computed based on measurements of temperature, humidity, wind speed, and atmospheric pressure made onboard the RV as well as by an instrumented helicopter that flew between the RV and the shore-based receivers. The meteorological data were collected periodically during the course of the experiment. In the February tests, the evaporation duct heights were observed to vary between about 3 and 9 meters, and no significant surface or elevated ducts were present. During the November tests, significant evaporation and surface ducting were observed.

The paper presents plots of measured propagation loss versus over-water path length. In order to facilitate the interpretation of these results, reference curves are superimposed on these plots showing free space propagation loss as well as propagation loss due to the diffraction and refractivity effects caused by a standard atmosphere. The impact of ducting on propagation loss is readily observed by comparing the measured propagation loss with the reference curves. The measurements in this study demonstrate that atmospheric ducting had a significant effect on propagation. By way of illustration, when the path length is 50 km, the measured propagation loss is observed to be more than 60 dB less than the predicted loss due to a standard atmosphere without ducting. Greater differences are observed at larger path lengths. This study addresses the impact of ducting on propagation in a frequency band that is underrepresented in the published literature.

High-frequency techniques have been successfully applied to compute electromagnetic wave radiation in various engineering domains. In some cases, asymptotic methods such as geometrical optics are used in industry to evaluate various EM interactions. However, some difficulties like caustics or grazing incidence may arise with some complex situations. In this paper, we propose a new efficient method to treat grazing incidences and heavy curved surfaces (according to the wavelength). For this purpose, a new beam formulation, the Conformal Gaussian Beams (CGB)[1] is used.

Conformal Gaussian Beams are defined from elementary electric or magnetic currents with a Gaussian amplitude distribution and a linear phase on a regular curved surface. Without loss of generality, their general expression can be reduced to:

with

We first derive the asymptotic Plane-Wave Spectrum of a CGB by the saddle-point method using the Franz fields integrals and the Weyl expansion of the free-space Green function. Comparisons between the analytical formulation and numerical calculations have been made.

Next, using a far-field approximation, we also obtain the analytical far-field of a CGB. Comparisons with a numerical current integral show very good results as presented on the figure. è represents the direction from the local normal to the surface.

Far-field amplitude in dB of CGB,
with W₀=2ë, β_x=k*sin(45°), β_y=0 and R=500ë. The local curvature of the surface is 5ë.

This technique combined with Fresnel coefficients on the plane-wave spectrum of a CGB will lead to the reflected and transmitted fields by a dielectric multilayer interface. This is of great interest in electromagnetic computation of radome properties.

[1] A. Chabory, S. Bolioli, and J. Sokoloff, "Novel gabor-based Gaussian beam expansion for curved aperture radiation in dimension two", Progress In Electromagnetics Research, vol. PIER 58, pp.171-185, 2006.

There is a strong requirement to avoid using divers to undertake sub-sea activities. The preferred role is intervention by using autonomous robotic systems, both vehicles and manipulators. This will only be achievable if robust through seawater communications can be established. Presently in order to undertake such sub-sea activities it is necessary to use acoustic transmitter and receiver systems, which are only capable of operating with low data rates (<100kbits/s). Optical sensors can also be used but these rely on clear water and in many sea conditions propagation beyond 10m is not possible. Therefore it is advantageous, if an alternative technique could be used, as this could provide a complementary system to those using ultrasonic waves. This paper will describe the use of electromagnetic (em) waves for the first time to transmit data and images through seawater. By establishing high-speed data rates, the actions of the robot can be up quickly undertaken thus ensuring a safe working environment. The theoretical and experimental measurements will be also presented.

Once these techniques are perfected, and then it is possible to establish deep water systems to recover oil and gas at depths well below the dive limit of 200m. Even within the dive limit, the ability to remotely control sub-sea equipment will reduce the burden on the diver hence allowing longer missions to be undertaken with less physical effort being expended by the diver. Furthermore, as a major development in oceanography is the installation of deep water observatories to measure both seismic activity for plate tectonic movement and to monitor marine life. The use of the em wave system would reduce the complexity of the system and enable the AUV to remain in contact with the base observatory during its mission.

As well as high-speed data communications, em waves can also be used for a wide range of activities for which ultrasonic waves have previously been used. These include such techniques as range finding and anti-collision navigation of sub-sea vehicles. Additional systems for pollution monitoring can be developed based upon radio frequency and microwave transmission.