Panayiotis Frangos

A numerical solution to the Zakharov-Shabat inverse scattering problem

A novel numerical method to solve the inverse scattering problem associated with the Zakharov-Shabat coupled mode equations is developed. In this problem the coupling coefficient for two propagating modes is determined from reflection data. Both codirectional and contradirectional coupling can be accommodated as well as the presence of bound states. Analytical results based on an independent analytical method are derived in order to demonstrate the accuracy of the proposed method, which is applicable to a broad class of reflection data. >

The electromagnetic inverse scattering problem for layered dispersionless dielectrics

The problem of exactly reconstructing the one-dimensional refractive index profile of a dispersionless dielectric from reflection data is considered. The available data consist of reflection coefficient measurements at many wavenumbers due to a normally incident electromagnetic plane wave upon a dielectric half-space or equivalently the impulse response measurement of the half-space. A closed-form analytical technique is described and applied to several solutions. These solutions are compared with results from a numerical method that uses leapfrogging in space and time and other analytical methods. Finally, the robustness of this technique with respect to imprecise and bandlimited data is examined and compared with a previous result.

Scattering from fractally corrugated surfaces: an exact approach.

We consider the scattering of optical or electromagnetic waves from perfectly conducting rough surfaces modeled by a multiscale fractal function through the use of the extended boundary condition method. This exact method is developed here through the expansion of the surface field in terms of generalized Floquet modes, which results in a closed-form solution that can be evaluated numerically. The method is validated by comparison with the Kirchhoff (approximate) method in its regime of validity and by calculation of the energy balance parameter.

Scattering from fractally corrugated surfaces with use of the extended boundary condition method

A new method for scattering from fractally corrugated conducting surfaces is formulated with use of the extended boundary condition method. Here we expand the fields through generalized Floquet modes and obtain analytical closed-form expressions for the scattering amplitudes for both horizontal and vertical polarization of the incident optical and electromagnetic waves. The accuracy of the proposed method is checked in several ways, such as comparison with approximate methods previously presented in the literature (Rayleigh and Kirchhoff methods) and calculation of the energy-balance parameter. Finally, numerical scattering results from fractal surfaces are provided.

The reconstruction of stratified dielectric profiles using successive approximations

The problem of reconstructing the one-dimensional refractive index profiles from electromagnetic reflection data is considered for lossless, dispersionless dielectrics. The Balanis integral equation is solved by the method of successive kernel approximation. Both continuous and discontinuous profile examples demonstrate the accuracy of this method by comparing and contrasting the results with those of a leapfrogging numerical solution and associated analytical results. The convergence criterion for this method is specified.

A radio-coverage prediction model in wireless communication systems based on physical optics and the physical theory of diffraction [Wireless Corner]

In this paper, a two-dimensional (2D) simulation method for the calculation of radio coverage in urban-area sites is presented, based on the analytical methods of physical optics (PO) and the physical theory of diffraction (PTD). The method takes into account the electromagnetic field at the receiving antenna due to first- and higher-order propagation mechanisms. Emphasis is given on the computation of the scattered near or Fresnel-zone field using numerical techniques, since in a typical urban environment, the scattered near or Fresnel-zone field occupies a large percentage of the area under investigation. The high resolution radio-coverage plots are computed by complex vector addition of all of the received signals for several values of the channel parameters. Finally, a comparison of the radio-coverage results obtained through this method with the corresponding results based on different electromagnetic methods and measurements, previously published in the literature, is presented.

Increasing the Efficiency of Rake Receivers for Ultra-Wideband Applications

In diversity rich environments, such as in Ultra-Wideband (UWB) applications, the a priori determination of the number of strong diversity branches is difficult, because of the considerably large number of diversity paths, which are characterized by a variety of power delay profiles (PDPs). Several Rake implementations have been proposed in the past, in order to reduce the number of the estimated and combined paths. To this aim, we introduce two adaptive Rake receivers, which combine a subset of the resolvable paths considering simultaneously the quality of both the total combining output signal-to-noise ratio (SNR) and the individual SNR of each path, reducing the number of combined paths, while keeping the desirable performance. These schemes achieve better adaptation to channel conditions compared to other known receivers, without further increasing the complexity. Their performance is evaluated in different practical UWB channels, whose models are based on extensive propagation measurements. The proposed receivers compromise between the power consumption, complexity and performance gain for the additional paths, resulting in important savings in power and computational resources.

Scattering of Electromagnetic Waves From a Rectangular Plate Using an Enhanced Stationary Phase Method Approximation

A time-efficient high frequency analytical model for the calculation of the scattered field from a perfect electric conductor (PEC) plate is presented here, which is based on the physical optics (PO) approximation and the stationary phase method (SPM). Using the SPM analysis for the three-dimensional (3D) scattering problem under consideration, the scattered electric field is calculated analytically. It follows that the analytical formula proposed here yields an accurate and fast algorithm for the calculation of the scattered electromagnetic (EM) field, which can be used trustfully in a variety of radio propagation problems. The accuracy of the proposed analytical method is checked through a straightforward numerical integration over the PO currents, as well as through finite element boundary integral full-wave exact solution. Comparison results are given in the far field, Fresnel zone and the near field area.

Experimental confirmation of nonlinear inverse scattering algorithms

Two fundamentally different nonlinear inversion techniques are implemented here to investigate the reconstruction of a dispersionless refractive profile from experimental reflection data. The first nonlinear technique used is approximate and based on the Riccati differential equation, and the second technique is exact and based on the Balanis integral equation. Neither of these techniques has been experimentally tested to date. Previous inversions have been applied to other methods and for the most part have been restricted to synthetic data. In this microwave experiment, band-limited frequency-domain reflection data are collected and used for the reconstruction of the refractive profile of a Plexiglas slab.

SCATTERING OF ELECTROMAGNETIC WAVES FROM A RECTANGULAR PLATE USING AN EXTENDED STATIONARY PHASE METHOD BASED ON FRESNEL FUNCTIONS (SPM-F)

This paper presents an extension over a novel, three dimensional high frequency method for the calculation of the scattered electromagnetic (EM) fleld from a Perfect Electric Conductor (PEC) plate, which is based on the Physical Optics (PO) approximation and the Stationary Phase Method (SPM). This extension deflnes a new analytical method which is proved to be very e-cient in computer execution time and enhances the accuracy of its predecessor around the area of the main scattering lobe. This new analytical method accomplishes high accuracy through the use of higher order approximation terms, which imply the use of Fresnel functions (SPM- F method). By using higher order Fresnel approximation terms, no impact on the time e-ciency of the SPM method appears to