# Showing papers in "IEEE Transactions on Antennas and Propagation in 1994"

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TL;DR: This paper presents how to optimally thin an array using genetic algorithms, which determines which elements are turned off in a periodic array to yield the lowest maximum relative sidelobe level.

Abstract: Large arrays are difficult to thin in order to obtain low sidelobes. Traditional statistical methods of aperiodic array synthesis fall far short of optimum configurations. Traditional optimization methods are not well suited for optimizing a large number of parameters or discrete parameters. This paper presents how to optimally thin an array using genetic algorithms. The genetic algorithm determines which elements are turned off in a periodic array to yield the lowest maximum relative sidelobe level. Simulation results for 200 element linear arrays and 200 element planar arrays are shown. The arrays are thinned to obtain sidelobe levels of less than -20 dB. The linear arrays are also optimized over both scan angle and bandwidth. >

987 citations

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TL;DR: In this article, the authors discuss the use of the active element pattern for prediction of the scan performance of large phased array antennas and provide a new derivation of the basic active element patterns relations in terms of scattering parameters.

Abstract: This review article discusses the use of the active element pattern for prediction of the scan performance of large phased array antennas. The introduction and application of the concept of the active element pattern goes back at least 30 years but the subject is generally not covered in modern antenna engineering textbooks or handbooks, and many contemporary workers are unfamiliar with this simple but powerful idea. In addition, early references on this subject do not provide a rigorous discussion or derivation of the active element pattern, relying instead on a more qualitative interpretation. The purpose of this article is to make the technique of active element patterns more accessible to antenna engineers, and to provide a new derivation of the basic active element pattern relations in terms of scattering parameters. >

582 citations

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TL;DR: The paper presents the analysis of small antennas mounted on hand-held transceivers using the finite-difference time-domain (FDTD) method, which is used to predict the gain patterns and broadband input impedance behavior of monopole, planar inverted F, and loop antenna elements mounted on the handset.

Abstract: The design of antennas for hand-held communications devices depends on the implementation of simulation tools that can accurately model general topologies. The paper presents the analysis of small antennas mounted on hand-held transceivers using the finite-difference time-domain (FDTD) method. The key features of the FDTD implementation are discussed, with particular emphasis placed upon modeling of the source region. The technique is used to predict the gain patterns and broadband input impedance behavior of monopole, planar inverted F, and loop antenna elements mounted on the handset. Effects of the conducting handset chassis, the plastic casing around the device, and lumped elements integrated into the antenna design are illustrated. Experimental results are provided to verify the accuracy of the computational methodology. The concept of antenna diversity is discussed, and key assumptions and expressions are provided that characterize the multipath fading fields. Several computational examples demonstrate the diversity performance of two receiving antennas on a single handset. >

313 citations

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TL;DR: In this article, a method to model tropospheric radiowave propagation over land in the presence of range-dependent refractivity is presented, based on the split-step Fourier algorithm to solve the parabolic wave equation.

Abstract: A method to model tropospheric radiowave propagation over land in the presence of range-dependent refractivity is presented. The terrain parabolic equation model (TPEM), is based on the split-step Fourier algorithm to solve the parabolic wave equation, which has been shown to be numerically efficient. Comparisons between TPEM, other terrain models (SEKE, GTD, FDPEM), and experimental data show predominantly excellent agreement. TPEM is also compared to results from an experiment in the Arizona desert in which range-dependent refractive conditions were measured. Although horizontal polarization is used in the implementation of the model, vertical polarization is also discussed. >

295 citations

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TL;DR: The multiple signal classification (MUSIC) algorithm developed by Schmidt [1986] is applied for two-dimensional radar imaging and the performance of the MUSIC algorithm using spatial smoothing for decorrelation is demonstrated.

Abstract: The multiple signal classification (MUSIC) algorithm developed by Schmidt [1986] is applied for two-dimensional radar imaging. The performance of the MUSIC algorithm using spatial smoothing for decorrelation is demonstrated. Two-dimensional radar images are generated for a simulated target as well as a target measured in the compact range at the University of Pretoria, South Africa. >

274 citations

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TL;DR: In this article, a method for implementing the general Floquet boundary condition in the finite-difference time-domain algorithm (FDTD) is presented, where the Floquet type of phase shift boundary condition is incorporated into the time domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation at each time step.

Abstract: A method for implementing the general Floquet boundary condition in the finite-difference time-domain algorithm (FDTD) is presented. The Floquet type of phase shift boundary condition is incorporated into the time-domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation of the solution at each time step. With this approach, the characteristics of periodic structures comprised of arbitrarily shaped inhomogeneous geometries can be computed for an arbitrary angle of incidence. Theoretical results are compared for various planar frequency selective surfaces (FSS) and for one with a three-dimensional element, e.g., a thick, double, concentric square loop. >

234 citations

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TL;DR: Theoretical analysis, physical reasonings, and experimental verifications are presented for a frequency selective surface with circular ring elements in this article, where the dielectric loading effect is used to reduce ring size and element spacing to avoid the grating lobe problem.

Abstract: Theoretical analysis, physical reasonings, and experimental verifications are presented for a frequency selective surface with circular ring elements. Both double-screen and single-screen designs are generated for a tri-band system that reflects the X-band signal while transmitting through the S- and Ku-band signals. In these designs, the dielectric loading effect is used to reduce ring size and element spacing and thus avoid the grating lobe problem. The circular ring element is very insensitive to a large variation of the RF incident angle. >

187 citations

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TL;DR: In this article, a new concept of field computation is presented based on the postulate of the existence of linear equations of the discretized nodal values of the fields, different from the conventional equations, but leading to the same solutions.

Abstract: Numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations. The new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields, different from the conventional equations, but leading to the same solutions. The postulated equations are local and invariant to excitation. It is shown how the equations can be determined by a sequence of "measures". The measured equations are particularly useful at the mesh boundary, where the finite difference methods fail. The measured equations do not assume the physical condition of absorption, so they are also applicable to concave boundaries. Using the measured equations, one can terminate the finite difference mesh very close to the physical boundary and still obtain robust solutions. It will definitely make a great impact on the way one applies finite difference and finite element methods in many problems. Computational results using the measured equations of invariance in two and three dimensions are presented. >

185 citations

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TL;DR: In this paper, a resistively loaded bow-tie antenna is considered as a radiator for temporally short, broadbandwidth pulses, and the geometrical details of the antenna and the resistive loading along the antenna are chosen to optimize this antenna for pulse radiation.

Abstract: Resistively loaded bow-tie antennas are considered as radiators for temporally short, broad-bandwidth pulses. Analysis is by the finite-difference time-domain (FDTD) method. The geometrical details of the antenna and the resistive loading along the antenna are chosen to optimize this antenna for pulse radiation. Theoretical results for the reflected voltage in the coaxial feed line and the time-varying radiated electric field are compared throughout with experimental measurements. The optimized, resistive bow-tie antenna is shown to radiate a pulse that more closely resembles that of the excitation than is radiated by a metallic bow tie of comparable size. Issues involving the use of the FDTD method for modeling fully three-dimensional antennas are also discussed. These issues include the use of a simple feed model and the staircasing of the edges of the antenna. >

176 citations

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TL;DR: In this paper, a formulation based upon the method of moments (MoM) is presented for the computation of input impedance of dielectric resonator antennas, which consists of axially symmetric D resonators fed by thin wire elements.

Abstract: A formulation based upon the method of moments (MoM) is presented for the computation of input impedance of dielectric resonator antennas. The class of antennas modeled by this method consists of axially symmetric dielectric resonators fed by thin wire elements. The formulation is general in that the feed structure may be interior or exterior to the dielectric resonator. To demonstrate the utility of this technique, parametric studies are performed on a cylindrical dielectric resonator antenna (CDRA) operating at frequencies that excite the important HEM/sub 11/ resonator antenna mode. The integrity of this technique is established both experimentally and numerically. >

175 citations

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TL;DR: In this article, a multiband frequency selective surface (FSS) with perfectly conducting multiring patch elements is presented, and it is found that the narrow-ring approximation is valid for a ring width less than 0.025/spl lambda with /spl lambda/ being the wavelength of the FSS's resonant frequency.

Abstract: Theoretical discussions and experimental verifications are presented for a multiband frequency selective surface (FSS) with perfectly conducting multiring patch elements. It is found that the narrow-ring approximation is valid for a ring width less than 0.025/spl lambda/ with /spl lambda/ being the wavelength of the FSS's resonant frequency. A single screen double-ring element FSS is demonstrated for (1) a low-pass FSS that reflects the Ka-band signal while passing the S-, X-, and Ku-band signals, and (2) a tri-band system that reflects the X-band signal while transmitting through the S- and Ku-band signals. In addition, a double screen four-band FSS with non-similar double-ring elements is developed by cascading the above mentioned two single screens. The good agreement obtained between the measured and the computed results verified the computer codes and the approaches of the paper. >

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TL;DR: In this paper, a preprocessing technique that in conjunction with spatial smoothing circumvents the difficulty of direction-of-arrival estimation of coherent signals in the case of uniform circular arrays is presented.

Abstract: We present a preprocessing technique that in conjunction with spatial smoothing circumvents the difficulty of direction-of-arrival estimation of coherent signals in the case of uniform circular arrays. Special consideration is given to problems arising in practice, such as mutual coupling and array geometry imperfections. Simulation results illustrating the performance of this scheme in conjunction with the MUSIC method are included. >

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TL;DR: In this article, a double-square-loop (DSL) FSS with perfectly conducting double-squeeze-loop patch elements is proposed for the Cassini Project.

Abstract: Design and experimental verifications are presented for a four-band frequency selective surface (FSS) with perfectly conducting double-square-loop (DSL) patch elements. A single screen DSL element FSS is demonstrated for (1) a four-band FSS which reflects the X- and Ka-band signals while passing the Sand Ku-band signals, and (2) a low-pass (or Ka-add-on) FSS that reflects the Ka-band signal while passing the S-, X-, and Ku-band signals. Cascading the above low-pass FSS with a previously published single screen tri-band FSS, a double screen FSS is also successfully demonstrated for the Cassini four-band application. The good agreement obtained between the measured and the computed results verified both the single and double screen four-frequency FSS approaches for the Cassini Project. >

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TL;DR: In this article, a computational scheme is presented for accurately predicting the farfield amplitude and phase characteristics of Global Positioning System (GPS) antennas flush-mounted to a corrugated groundplane.

Abstract: In this paper a computational scheme is presented for accurately predicting the farfield amplitude and phase characteristics of Global Positioning System (GPS) antennas flush-mounted to a corrugated groundplane. The algorithm developed is particularly well-suited in beamshaping of (GPS) antennas in order to provide a high level of multipath rejection. The usefulness of the analytical model has been verified by the excellent agreement achieved between experimental data and predicted amplitude and phase patterns. >

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TL;DR: In this article, an experimental investigation was conducted to determine the nature of bistatic scattering from rough dielectric surfaces at 10 GHz, focusing on the dependence of coherent and incoherent scattered fields on surface roughness for the specular direction.

Abstract: An experimental investigation was conducted to determine the nature of bistatic scattering from rough dielectric surfaces at 10 GHz. This paper focusses specifically on the dependence of coherent and incoherent scattered fields on surface roughness for the specular direction. The measurements, which were conducted for a smooth surface with ks >

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TL;DR: In this paper, a simple FDTD model was developed for use with antennas that are fed from transmission lines, where the incident and reflected waveforms within the transmission line were of interest, and the latter was determined directly in the FDTD calculation.

Abstract: A simple FDTD model is developed for use with antennas that are fed from transmission lines. The model is especially designed for use with transient excitations, where the incident and reflected waveforms within the transmission line are of interest, and the latter is determined directly in the FDTD calculation. The model is verified for both transmission and reception of transient waveforms by comparison with measured results for a cylindrical monopole antenna with a plane reflector. >

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TL;DR: The paper presents a method for the computation of the monostatic radar cross section (RCS) of electrically large conducting objects modeled by nonuniform rational B-spline (NURBS) surfaces using the physical optic (PO) technique, which makes use of a small number of patches to model complex bodies.

Abstract: The paper presents a method for the computation of the monostatic radar cross section (RCS) of electrically large conducting objects modeled by nonuniform rational B-spline (NURBS) surfaces using the physical optic (PO) technique. The NURBS surfaces are expanded in terms of rational Bezier patches by applying the Cox-De Boor transform algorithm. This transformation is justified because Bezier patches are numerically more stable than NURBS surfaces. The PO integral is evaluated over the parametric space of the Bezier surfaces using asymptotic integration. The scattering field contribution of each Bezier patch is expressed in terms of its geometric parameters. Excellent agreement with PO predictions is obtained. The method is quite efficient because it makes use of a small number of patches to model complex bodies, so it requires very little memory and computing time. >

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TL;DR: In this article, a realistic 3D man model and an approximate linear dipole antenna were used to model the EM coupling effects of a human operator on antenna radiation characteristics, such as the antenna input impedance, radiation patterns, the radiation power (into free space), the power absorbed by the body, and the radiation efficiency, etc.

Abstract: EM coupling effects of a human operator on antenna radiation characteristics, such as the antenna input impedance, radiation patterns, the radiation power (into free space), the power absorbed by the body, the radiation efficiency, etc., of a portable communication dipole antenna were investigated in detail. A realistically shaped 3D man model and an approximate linear dipole antenna were used to model this problem. Coupled integral equations (CIE) and the method of moments (MoM) were employed to numerically solve this antenna-body coupling problem. Numerical examples are presented for the antenna located in front of the head (distance ranging from 5 to 1 cm) or adjacent to the abdomen (0.6 cm distance) at 830 MHz. It is found that, when coupled with the operator body, the antenna input impedance will have significant deviation from those in free space and different positions. Due to the operator body absorption effect, the maximum attenuation of the H-plane antenna gain may reach about 15 dB for the antenna at the head position and 25 dB for the abdomen position, toward the direction of the body side. Also, the antenna radiation efficiency is reduced to the range from 0.72 to 0.29 for the head position and 0.15 for the abdomen position, respectively. Moreover, the cross-polarization field is significant, especially in the E plane of /spl phi/=90/spl deg/. This is important for the antenna RF design and communication link budget consideration of portable radio systems. >

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TL;DR: In this paper, the amplitude of the electric field radiated by a retransmitting antenna can be easily calculated from ray theory in long tunnels, but for short tunnels, one of the most critical points is either the radiation towards free space of a mobile station emitting in the tunnel or, on the contrary, the penetration of an external wave inside the tunnel.

Abstract: Characterization of high frequency electromagnetic wave propagation in tunnels has important applications in the field of mobile communication. In long tunnels, the amplitude of the electric field radiated by a retransmitting antenna can be easily calculated from ray theory. However, for short tunnels, one of the most critical points is either the radiation towards free space of a mobile station emitting in the tunnel or, on the contrary, the penetration of an external wave inside the tunnel. This coupling between the inside and the outside is treated through the uniform theory of diffraction. By comparing theoretical and experimental results, it is shown that this theory leads to adequate prediction of the field variation and allows the authors to point out the influence of parameters, such as the position of the mobile in the tunnel and the influence of the angle of incidence, on the entrance plane of an incoming external wave. >

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TL;DR: In this article, the concept of the frequency-domain physical-optics approximation to the time domain was extended to determine some significant properties of large reflector antennas, such as the effects of time-delayed mutual coupling between points on the surface.

Abstract: The authors extend the concept of the frequency-domain physical-optics approximation to the time domain, and use it to determine some significant properties of large reflector antennas. When this method is used to determine the equivalent surface-current density on the reflector, the effects of time-delayed mutual coupling between points on the surface are ignored. Consequently, many of the numerical limitations found in other conventional time-domain techniques are avoided, e.g. boundary-truncation error, interpolation error, numerical dispersion error, numerical instability, error accumulation with time marching, etc. More significantly, this method requires relatively small amounts of computer memory and CPU time. Several applications to the transient analysis of pulsed radar systems are given. >

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TL;DR: In this paper, four FD-TD extensions for the modeling of pulse propagation in Debye or Lorentz dispersive media are analyzed through studying the stability and phase error properties of the coupled difference equations corresponding to Maxwell's equations and to the equations for the dispersion.

Abstract: Four FD-TD extensions for the modeling of pulse propagation in Debye or Lorentz dispersive media are analyzed through studying the stability and phase error properties of the coupled difference equations corresponding to Maxwell's equations and to the equations for the dispersion. For good overall accuracy the author shows that all schemes should be run at their Courant stability limit, and that the timestep should finely resolve the medium timescales. Particularly, for Debye schemes it should be at least /spl Delta/t=10/sup /spl minus/3//spl tau/, while for Lorentz schemes it should be /spl Delta/t=10/sup /spl minus/2//spl tau/, where /spl tau/ is a typical medium relaxation time. A numerical experiment with a Debye medium confirms this. The author has determined that two of the discretizations for Debye media are totally equivalent. In the Lorentz medium case the author establishes that the method that uses the polarization differential equation to model dispersion is stable for all wavenumbers, and that the method using the local-in-time constitutive relation is weakly unstable for modes with wavenumber k such that k/spl Delta/x>/spl pi//2. >

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TL;DR: In this paper, the moment method is used to solve the integral equations describing the capacitively fed rectangular microstrip antenna element, which consists of a ground plane, a radiating patch, and a small patch located between ground plane and radiating patches.

Abstract: The moment method is used to solve the integral equations describing the capacitively fed rectangular microstrip antenna element. This element consists of a ground plane, a radiating patch, and a small patch located between ground plane and radiating patch. The small patch is fed by a coaxial probe. It excites the radiating patch through capacitive coupling. After checking the accuracy by comparing calculated and measured results, the effect of the capacitor patch is analyzed theoretically. A procedure is given to determine capacitor patches which yield elements matched to the coaxial feed. It is shown how a matched configuration can be found for a given capacitor patch height. >

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TL;DR: In this paper, a new formulation for the design of Chebyshev arrays is presented which makes no direct use of Chebyhev polynomials and is expressed in terms of cosine/cosine-hyperbolic functions based on which all analysis and design steps are carried out.

Abstract: A new formulation for the design of Chebyshev arrays is presented which makes no direct use of Chebyshev polynomials. The array factor is expressed in terms of cosine/cosine-hyperbolic functions based on which all analysis and design steps are carried out. Zeros of the array factor are used to obtain a system of equations for excitation currents. Solving this system of equations, current magnitudes are determined in terms of the current of one element chosen as the independent variable. A general formulation for an even or odd but otherwise arbitrary number of elements is presented. The minimum number of elements required to achieve the desired beamwidth and side lobe level is obtained in a single step without resorting to an iterative process. The optimum spacing between elements for broadside and end fire arrays is also addressed. Numerical results for example cases are provided. >

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TL;DR: In this paper, a new analysis technique for infinite phased array antennas was developed and demonstrated, which consists of the finite element method (FEM) in combination with integral equation radiation conditions and a novel periodic boundary condition for 3D FEM grids.

Abstract: A new analysis technique for infinite phased array antennas was developed and demonstrated. It consists of the finite element method (FEM) in combination with integral equation radiation conditions and a novel periodic boundary condition for 3-D FEM grids. Accurate modeling of rectangular, circular and circular-coaxial feeds is accomplished by enforcing continuity between the FEM solution and several waveguide modes across an aperture in the array's ground plane. The radiation condition above the array is enforced by a periodic integral equation in the form of a Floquet mode summation, thus reducing the solution to that of a single array unit cell. The periodic boundary condition at unit cell side walls is enforced through a matrix transformation. That mathematically "folds" opposing side walls onto each other with a phase shift appropriate to the array lattice and scan angle. The unit cell electric field is expanded in vector finite elements. Galerkin's method is used to cast the problem as a matrix equation, which is solved by the conjugate gradient method. A general-purpose computer code was developed and validated for cases of open-ended waveguides, microstrip patches, clad monopoles and printed flared notches, showing that the analysis method is accurate and versatile. >

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TL;DR: In this paper, a novel approach to reduce the matrix size associated with the method of moments (MoM) solution of the problem of electromagnetic scattering from arbitrary shaped closed bodies is presented.

Abstract: A novel approach to reducing the matrix size associated with the method of moments (MoM) solution of the problem of electromagnetic scattering from arbitrary shaped closed bodies is presented. The key step in this approach is to represent the scattered field in terms of a series of beams produced by multipole sources located in a complex space. On the scatterer boundary, the fields generated by these multipole sources resemble the Gabor basis functions. By utilizing the properties of the Gabor series, guidelines for selecting the orders as well as locations of the multipole sources are developed. It is shown that the present approach not only reduces the number of unknowns, but also generates a generalized impedance matrix with a banded structure and a low condition number. The accuracy of the proposed method is verified by comparing the numerical results with those derived by using the method of moments. >

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TL;DR: In this article, two models of mobile radio wave propagation over buildings are presented, the flat edge model and the multiple edge diffraction model, where buildings are assumed to be of constant height and spacing.

Abstract: Two models of mobile radio wave propagation over buildings are presented. The first, the flat edge model, provides a simple yet accurate representation when buildings are assumed to be of constant height and spacing. The second model combines the first with a rapid new method of calculating multiple edge diffraction to allow deterministic predictions with arbitrary buildings and spacings. This allows predictions to be made with real building data, and the effect of building variations on location variability of the received signal to be assessed. Both models are compared with measurements made in suburban areas in the 900 and 1800 MHz bands and excellent agreement is obtained. >

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TL;DR: In this article, it is shown that the spatial step should vary as /spl Delta/x/spl sim/g[e/sub /spl phi/t/sub c/]/sup 1/s/ in order to maintain a prescribed phase error level e/sub/spl phI throughout the computation time t/subc/, where s is the spatial order of accuracy of the scheme and g is a geometric factor.

Abstract: For FD-TD methods(used to solve Maxwell's equations) we determine the spatial resolution of the discretized domain in terms of the total computation time and the desired phase error. It is shown that the spatial step should vary as /spl Delta/x/spl sim/g[e/sub /spl phi/t/sub c/]/sup 1/s/ in order to maintain a prescribed phase error level e/sub /spl phi throughout the computation time t/sub c/, where s (=2 or 4) is the spatial order of accuracy of the scheme and g is a geometric factor. Significantly, we show that the rule of thumb of using 10-20 points per wavelength to determine the spatial cell size for the standard scheme is not optimal. Our results are verified by numerical simulations in two dimensions with the Yee (1966) scheme and a new fourth-order accurate FD-TD scheme. >

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TL;DR: In this paper, a diversity antenna comprising a short whip antenna top loaded with a small cylinder and a new built-in antenna has been developed for very small portable telephones in the 800-MHz band.

Abstract: A diversity antenna comprising a short whip antenna top loaded with a small cylinder and a new built-in antenna has been developed for very small portable telephones in the 800-MHz band. Wire-grid analyses and whip antenna experiments yielded good radiation characteristic results when the equivalent electrical length of the whip antenna equalled a half wavelength. The built-in antenna features extreme compactness, its size being one-third that of a conventional planar inverted-F antenna. The characteristics were investigated experimentally, and an antenna of 3.5 cc volume with a gain of -1 dBd and a bandwidth of 30 MHz was designed at 879 MHz. Finally, the diversity characteristics were subjected to field measurements and a diversity correlation of 0.26 was obtained. >

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TL;DR: In this article, plane wave reflection and transmission characteristics for typical concrete block walls are examined theoretically and experimentally to determine the frequency dependence of the specularly and non-specularly transmitted and reflected fields.

Abstract: Buildings such as warehouses, supermarkets and retail department stores typically have walls constructed from concrete (cinder) blocks. The web and void design of the individual blocks and their arrangement within a wall creates a periodic structure, which exhibits frequency dependent transmission and reflections characteristics in the UHF bands proposed for future Personal Communication Systems (PCS). For higher frequencies, higher order Floquet modes excited at the periodic structure can propagate away from the wall, suggesting that significant power can be carried away from the wall in non-specular directions. Indoor propagation prediction models must consider the non-specular paths exited by walls with a periodic nature in order to account for all of the scattered power. In this work, plane wave reflection and transmission characteristics for typical concrete block walls are examined theoretically and experimentally to determine the frequency dependence of the specularly and non-specularly transmitted and reflected fields. >

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TL;DR: Induced current distributions on conducting bodies of arbitrary shape modelled by NURBS surfaces are obtained by using a moment method approach to solve an electric field integral equation (EFIE) by applying the Cox-de Boor transformation algorithm.

Abstract: Induced current distributions on conducting bodies of arbitrary shape modelled by NURBS (non uniform rational B-splines) surfaces are obtained by using a moment method approach to solve an electric field integral equation (EFIE). The NURBS surfaces are expanded in terms of Bezier patches by applying the Cox-de Boor transformation algorithm. This transformation is justified because Bezier patches are numerically more stable than NURBS surfaces. New basis functions have been developed which extend over pairs of Bezier patches. These basis functions can be considered as a generalization of "rooftop" functions. The method is applied to obtain RCS values of several objects modelled with NURBS surfaces. Good agreement with results from other methods is observed. The method is efficient and versatile because it uses geometrical modelling tools that are quite powerful. >