# Showing papers in "IEEE Transactions on Antennas and Propagation in 1997"

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TL;DR: Using these techniques, the FMM and MLFMA can solve the problem of electromagnetic scattering by large complex three-dimensional objects such as an aircraft on a small computer.

Abstract: The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer.

1,562 citations

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TL;DR: In this paper, the theoretical modeling and practical design of millimeter wave reflectarrays using microstrip patch elements of variable size is discussed and a full-wave treatment of plane wave reflection from a uniform infinite array of microstrip patches is described and used to generate the required patch-design data and to calculate the radiation patterns of the reflectarray.

Abstract: This paper discusses the theoretical modeling and practical design of millimeter wave reflectarrays using microstrip patch elements of variable size. A full-wave treatment of plane wave reflection from a uniform infinite array of microstrip patches is described and used to generate the required patch-design data and to calculate the radiation patterns of the reflectarray. The critical parameters of millimeter wave reflectarray design, such as aperture efficiency, phase errors, losses, and bandwidth are also discussed. Several reflectarray feeding techniques are described, and measurements from four reflectarray design examples at 28 and 77 GHz are presented.

1,142 citations

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TL;DR: The basic genetic algorithm is described and its history in the electromagnetics literature is recounted, the application of advanced genetic operators to the field of electromagNETics is described, and designs are presented for a number of different applications.

Abstract: Genetic algorithms are on the rise in electromagnetics as design tools and problem solvers because of their versatility and ability to optimize in complex multimodal search spaces. This paper describes the basic genetic algorithm and recounts its history in the electromagnetics literature. Also, the application of advanced genetic operators to the field of electromagnetics is described, and design results are presented for a number of different applications.

837 citations

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TL;DR: In this paper, a compact representation of the electric and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification is given.

Abstract: A compact representation is given of the electric- and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification. Furthermore, mixed-potential integral equations are derived within the framework of this transmission-line formalism for arbitrarily shaped, conducting or penetrable objects embedded in the multilayered medium. The development emphasizes laterally unbounded environments, but an extension to the case of a medium enclosed by a rectangular shield is also included.

774 citations

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TL;DR: In this paper, the resonant frequencies and radiation Q-factors of the lowest order "magnetic-dipole" modes are derived on the basis of a first-order theory.

Abstract: Theoretical and experimental investigations on rectangular dielectric resonator antennas having a value of /spl epsiv//sub r/, in the range of 10 to 100 are reported. The resonant frequencies and radiation Q-factors of the lowest order "magnetic-dipole" modes are derived on the basis of a first-order theory. The accuracy of the model in predicting the resonant frequency and radiation Q-factor is verified by comparison with results of a rigorous theory and experiments. Various feeds for the antennas such as probe, microstrip slot, and microstrip line are described. Measured radiation patterns are shown and the effect of feed and mode degeneracy on the cross-polarisation levels is discussed.

703 citations

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TL;DR: It is shown that fully interpolatory higher order vector basis functions of the Nedelec type are defined in a unified and consistent manner for the most common element shapes and sample numerical results confirm the faster convergence of the higher order functions.

Abstract: Low-order vector basis functions compatible with the Nedelec (1980) representations are widely used for electromagnetic field problems. Higher-order functions are receiving wider application, but their development is hampered by the complex procedures used to generate them and lack of a consistent notation for both elements and bases. In this paper, fully interpolatory higher order vector basis functions of the Nedelec type are defined in a unified and consistent manner for the most common element shapes. It is shown that these functions can be obtained as the product of zeroth-order Nedelec representations and interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties of the vector functions are discussed, and expressions for the vector functions of arbitrary polynomial order are presented. Sample numerical results confirm the faster convergence of the higher order functions.

648 citations

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TL;DR: A simple and flexible genetic algorithm for pattern synthesis of antenna array with arbitrary geometric configuration that directly represents the array excitation weighting vectors as complex number chromosomes and uses decimal linear crossover without a crossover site.

Abstract: A simple and flexible genetic algorithm (GA) for pattern synthesis of antenna array with arbitrary geometric configuration is presented. Unlike conventional GA using binary coding and binary crossover, this approach directly represents the array excitation weighting vectors as complex number chromosomes and uses decimal linear crossover without a crossover site. Compared with conventional GAs, this approach has a few advantages: giving a clearer and simpler representation of the problem, simplifying chromosome construction, and totally avoiding binary encoding and decoding so as to simplify software programming and to reduce CPU time. This method also allows us to impose constraints on phases and magnitudes of complex excitation coefficients for preferable implementation in practice using digital phase shifters and digital attenuators. Successful applications show that the approach can be used as a general tool for pattern synthesis of arbitrary arrays.

455 citations

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TL;DR: In this paper, the authors proposed a planar dual-band inverted-F antenna for cellular handsets, which operates at the 0.9-GHz and 1.8-GHz bands.

Abstract: Cellular telephone handsets are now being designed to have dual-mode capabilities. In particular, there is a requirement for internal antennas for GSM and DCS1800 systems. This paper describes a novel planar dual-band inverted-F antenna for cellular handsets, which operates at the 0.9-GHz and 1.8-GHz bands. The dual-band antenna has almost the same size as a conventional inverted-F antenna operating at 0.9 GHz and has an isolation between bands of better than 17 dB. The bandwidths of the antenna are close to those required for the above systems. Good dual-band action is also obtained for other frequency ratios in the range of 1.3-2.4. Studies also show that the dual-band antenna can operate with one or two feeds. A finite-difference time-domain analysis has been shown to give calculated results close to those measured.

447 citations

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TL;DR: In this paper, various time-domain finite-element methods for the simulation of transient electromagnetic wave phenomena are discussed, including nodal and edge/facet element basis functions, along with the numerical stability properties of the different methods.

Abstract: Various time-domain finite-element methods for the simulation of transient electromagnetic wave phenomena are discussed. Detailed descriptions of test/trial spaces, explicit and implicit formulations, nodal and edge/facet element basis functions are given, along with the numerical stability properties of the different methods. The advantages and disadvantages of mass lumping are examined. Finally, the various formulations are compared on the basis of their numerical dispersion performance.

419 citations

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TL;DR: In this article, the design and testing of an aperture-coupled circularly polarized antenna for Global Positioning System (GPS) applications is described, which operates at both the L1 and L2 frequencies of 1575 and 1227 MHz.

Abstract: This paper describes the design and testing of an aperture-coupled circularly polarized antenna for Global Positioning System (GPS) applications. The antenna operates at both the L1 and L2 frequencies of 1575 and 1227 MHz, which is required for differential GPS systems in order to provide maximum positioning accuracy. Electrical performance, low-profile, and cost were equally important requirements for this antenna. The design procedure is discussed, and measured results are presented. Results from a manufacturing sensitivity analysis are also included.

396 citations

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TL;DR: In this article, a capacitively loaded planar inverted-F antenna (PIFA) was proposed and studied, and it was found that the capacitive load reduced the resonance length of the PIFA from /spl lambda/4 to less than /spl ε/S.

Abstract: A capacitively loaded planar inverted-F antenna (PIFA) is proposed and studied. It is found that the capacitive load reduces the resonance length of the PIFA from /spl lambda//4 to less than /spl lambda//S. A design with a bandwidth of 178 MHz centered at 1.8 GHz is provided to demonstrate that compact antennas for mobile telephone handsets can be constructed using this approach. The finite-difference time-domain (FDTD) method is used in the study and experimental verification is also provided.

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TL;DR: Various methods for efficiently solving electromagnetic problems can be roughly classified into surface and volume problems, while fast methods are either differential or integral equation based.

Abstract: Various methods for efficiently solving electromagnetic problems are presented. Electromagnetic scattering problems can be roughly classified into surface and volume problems, while fast methods are either differential or integral equation based. The resultant systems of linear equations are either solved directly or iteratively. A review of various differential equation solvers, their complexities, and memory requirements is given. The issues of grid dispersion and hybridization with integral equation solvers are discussed. Several fast integral equation solvers for surface and volume scatterers are presented. These solvers have reduced computational complexities and memory requirements.

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TL;DR: An iterative reconstruction algorithm based on the Levenberg-Marquardt method is tested with synthetic data and two methods for choosing the regularization parameter, an empirical method and generalized cross validation method, are examined.

Abstract: This paper refers to quantitative reconstruction of the dielectric and conductive property distributions of biological objects by means of active microwave imaging. An iterative reconstruction algorithm based on the Levenberg-Marquardt method is tested with synthetic data. The influence of the receiver geometry is investigated and two methods for choosing the regularization parameter, an empirical method and generalized cross validation (GCV) method, are examined.

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TL;DR: In this paper, the problem of error estimation in the numerical solution of integral equations that arise in electromagnetics is addressed, and the results of all of the impedance matrices that result from discretizing the integral equations are shown to be bounded when the elements are computed appropriately.

Abstract: The problem of error estimation in the numerical solution of integral equations that arise in electromagnetics is addressed. The direct method (Green's theorem or field approach) and the indirect method (layer ansatz or source approach) lead to well-known integral equations both of the first kind [electric field integral equations (EFIE)] and the second kind [magnetic field integral equations (MFIE)]. These equations are analyzed systematically in terms of the mapping properties of the integral operators. It is shown how the assumption that field quantities have finite energy leads naturally to describing the mapping properties in appropriate Sobolev spaces. These function spaces are demystified through simple examples which also are used to demonstrate the importance of knowing in which space the given data lives and in which space the solution should be sought. It is further shown how the method of moments (or Galerkin method) is formulated in these function spaces and how residual error can be used to estimate actual error in these spaces. The condition number of all of the impedance matrices that result from discretizing the integral equations, including first kind equations, is shown to be bounded when the elements are computed appropriately. Finally, the consequences of carrying out all computations in the space of square integrable functions, a particularly friendly Sobolev space, are explained.

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TL;DR: In this article, a procedure for predicting the combined effect of rain attenuation and several other propagation impairments (at frequencies between 4 and 35 GHz) along Earth-satellite paths is presented.

Abstract: The rapid growth of satellite services using higher frequency bands such as the Ka-band has highlighted a need for estimating the combined effect of different propagation impairments. Many projected Ka-band services will use very small terminals and, for some, rain effects may only form a relatively small part of the total propagation link margin. It is therefore necessary to identify and predict the overall impact of every significant attenuating effect along any given path. A procedure for predicting the combined effect of rain attenuation and several other propagation impairments (at frequencies between 4 and 35 GHz) along Earth-satellite paths is presented. Where an accurate model exist for some phenomena, these have been incorporated into the prediction procedure. New models were developed, however, for rain attenuation, cloud attenuation, and low-angle fading to provide more overall accuracy, particularly at very low elevation angles (<10/spl deg/). In the absence of a detailed knowledge of the occurrence probabilities of different impairments, an empirical approach is taken in estimating their combined effects. An evaluation of the procedure is made using slant-path attenuation data that have been collected with simultaneous beacon and radiometer measurements which allow a near complete account of different impairments. Results indicate that the rain attenuation element of the model provides the best average accuracy globally between 10 and 30 GHz and that the combined procedure gives prediction accuracies comparable to uncertainties associated with the year-to-year variability of path attenuation.

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TL;DR: An efficient algorithm has been developed that provides the mesh refinement by the factor of two in each direction that can be used in two-dimensional and three-dimensional problems and provides for subgridding in both space and time.

Abstract: In many computational problems solved using the finite-difference time-domain (FDTD) technique, there is a need to model selected volumes with higher resolution than the whole computational space. An efficient algorithm has been developed for this purpose that provides the mesh refinement by the factor of two in each direction. The algorithm can be used in two-dimensional (2-D) and three-dimensional (3-D) problems and provides for subgridding in both space and time. Performance of the 3-D algorithm was tested in waveguides and resonators. A high accuracy and efficiency were observed in all test cases with insignificant (of an order of -60 dB) reflections from mesh interfaces. Practical applications of the algorithm in the analyses of a resonator with a dielectric rod and of a cellular phone behavior in the vicinity of the operator head are also reported.

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TL;DR: In this paper, a theory for a complete far-field transmit-receive system characterization of short-pulse antennas is derived in the time domain, which is characterized by a set of cascaded operators which transform the source waveform and power into similar quantities at the receiving antenna terminals.

Abstract: A theory for a complete far-field transmit-receive system characterization of short-pulse antennas is derived in the time domain. The transmit-receive antenna system is characterized by a set of cascaded operators, which transform the source waveform and power into similar quantities at the receiving antenna terminals. Two such sets are defined. The first one is phrased in terms of the wave-type "time-dependent effective-height" operator, while the second one is defined in terms of the energy-type "gain operator". Both definitions fit within a complete transmit-receive system description, the latter being equivalent to the frequency-domain Friis equation. However, these operators are derived entirely in the context of the time-domain field equation. The starting point in the time-domain analysis of the effective height is the slant stack transform (SST) of the time-dependent current distribution in a manner equivalent to the spatial Fourier transform used in the frequency domain. The vector autocorrelation of the transmitting effective height is then used to define the time-dependent gain operator under impulsive source excitation. Time-domain reciprocity leads to the definitions of antenna parameters under receiving conditions and the corresponding equivalent circuit. The parameters defined in this way fit within a consistent transmit-receive convolution operator, operating on the autocorrelation of the input signal. This independent time-domain representation is thus similar to the frequency-domain representation. However, unlike the conventional frequency-domain circuit parameters, which relate voltage and current amplitudes, the time-domain circuit representation is based on incident and reflected wave-type constituents. In addition, the use of appropriate norms facilitates the transformation of our operators to stand-alone figures of merits. The general concepts developed are demonstrated for a short dipole antenna.

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TL;DR: The theoretical far-field patterns and Gaussian-beam coupling efficiencies for a double-slot antenna placed off aids on extended hemispherical silicon and quartz lenses are investigated in this paper.

Abstract: The theoretical far-field patterns and Gaussian-beam coupling efficiencies are investigated for a double-slot antenna placed off aids on extended hemispherical silicon and quartz lenses. Measured off-axis radiation patterns at 250 GHz agree well with the theory. Results are presented that show important parameters versus off-axis displacement: scan angle, directivity, Gaussicity, and reflection loss. Directivity contour plots are also presented and show that near-diffraction limited performance can be achieved at off-axis positions at nonelliptical extension lengths. Some design rules are discussed for imaging arrays on dielectric lens antennas.

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TL;DR: In this article, a vector sensor is composed of six spatially co-located nonisotropic polarization-sensitive antennas, measuring all six electromagnetic field components of the incident wave field, and closed-form parameter estimates are obtained through a vector cross-product operation on each decoupled signal-subspace eigenvector of the data correlation matrix.

Abstract: This paper introduces a novel eigenstructure-based algorithm uni-vector-sensor ESPRIT that yields closed-form direction-of-arrival (DOA) estimates and polarization estimates using one electromagnetic vector sensor. A vector sensor is composed of six spatially co-located nonisotropic polarization-sensitive antennas, measuring all six electromagnetic field components of the incident wave field. Uni-vector-sensor ESPRIT is based on a matrix-pencil pair of temporally displaced data sets collected from a single electromagnetic vector sensor. The closed-form parameter estimates are obtained through a vector cross-product operation on each decoupled signal-subspace eigenvector of the data correlation matrix. This method exploits the electromagnetic sources' polarization diversity in addition to their spatial diversity, requires no a priori knowledge of signal frequencies, suffers no frequency-DOA ambiguity, pairs automatically the x-axis direction cosines with the y-axis direction cosines, eliminates array interelement calibration, can resolve up to five completely polarized uncorrelated monochromatic sources from near field or far field. It impressively out-performs an array of spatially displaced identically polarized antennas of comparable array-manifold size and computational load.

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TL;DR: In this paper, a microstrip antenna on a micromachined 635-/spl mu/m thick substrate was used to synthesize a localized low dielectric-constant environment.

Abstract: Micromachining techniques using closely spaced holes have been used underneath a microstrip antenna on a high dielectric-constant substrate (/spl epsiv//sub r/=10.8) to synthesize a localized low dielectric-constant environment (/spl epsiv//sub r/=2.3). The measured radiation efficiency of a microstrip antenna on a micromachined 635-/spl mu/m thick /spl epsiv//sub r/=10.8 Duroid 6010 substrate increased from 48/spl plusmn/3% to 73/spl plusmn/3% at 12.8-13.0 GHz (including 3.3-cm feed line losses). We believe that this technique can be applied to millimeter-wave antennas (microstrip, dipoles, slots, etc.) on silicon and GaAs substrates to result in relatively wideband (3-6%) monolithic microwave integrated circuits (MMIC) active antenna modules for phased-arrays and collision-avoidance systems.

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TL;DR: In this article, the authors extended the finite-difference time-domain (FDTD) solution of Maxwell's equations to nonlinear optics and achieved robustness by directly solving the optical E and H fields in space and time.

Abstract: This paper summarizes algorithms which extend the finite-difference time-domain (FDTD) solution of Maxwell's equations to nonlinear optics. The use of the FDTD in this field is novel. Previous modeling approaches were aimed at modeling optical-wave propagation in electrically long structures such as fibers and directional couplers, wherein the primary flow of energy is along a single principal direction. However, the FDTD is aimed at modeling compact structures having energy flow in arbitrary directions. Relative to previous methods, the FDTD achieves robustness by directly solving, for fundamental quantities, the optical E and H fields in space and time rather than performing asymptotic analyses or assuming paraxial propagation and nonphysical envelope functions. As a result, it is almost completely general. It permits accurate modeling of a broad variety of dispersive and nonlinear media used in emerging technologies such as micron-sized lasers and optical switches.

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TL;DR: In this paper, a 2D unitary ESPRIT algorithm is used to decorrelate coherent waves in a planar array placed on a mobile in an urban cellular environment.

Abstract: The in-depth knowledge of the mobile radio channel is particularly important for radio communication modeling and advanced technology system design. We propose an accurate method to determine jointly the azimuth and elevation angle and the delay of waves incoming at the receiver. The method is applied to measurements of the complex impulse response of the mobile radio channel, performed on a planar array placed on a mobile in an urban cellular environment. The directions-of-arrival (DOA) were obtained by the means of a direction finding algorithm-two-dimensional (2-D) unitary ESPRIT. Two-dimensional spatial smoothing as an extension of ordinary spatial smoothing is utilized to decorrelate coherent waves. The application of 2-D unitary ESPRIT increases the angular resolution over conventional Fourier analysis or the scattering function by an order of magnitude and overcomes difficulties due to secondary lobes. The time delay is determined from wideband channel sounder measurements. The results confirm some assumptions on propagation mechanisms: (1) the wave-guiding property of streets (canyon effect), which is especially pronounced for long-delayed paths; (2) the variation of the number of incoming waves with their excess delay-the larger the excess delay, the lower the number of paths comprising an echo in the power delay profile; (3) if a single path remains, the privileged DOA is the direction of the street; (4) the exponential part of the power delay profile due to scatterers all around the receiver; and (5) the elevation dependence or the impinging power. In the tested receiver locations, paths with elevations between 0/spl deg/ and 40/spl deg/ dominate, containing about 90% of the received power.

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TL;DR: In this paper, a particular formulation of the method of moments which relies on a triangular-patch geometrical model of the exterior surface of the scattering body and operates according to a "marching-on-in-time" scheme is presented.

Abstract: Numerical techniques based on a time-domain recursive solution of the electric field integral equation (EFIE) may exhibit instability phenomena induced by the joint space-time discretization. The above problem is addressed with specific reference to the evaluation of electromagnetic scattering from perfectly conducting bodies of arbitrary shape. We analyze a particular formulation of the method of moments which relies on a triangular-patch geometrical model of the exterior surface of the scattering body and operates according to a "marching-on-in-time" scheme, whereby the surface current distribution at a given time step is recursively evaluated as a function of the current distribution at previous steps. A heuristic stability condition is devised which allows us to define a proper time step, as well as a geometrical discretization criterion, ensuring convergence of the numerical procedure and, therefore, eliminating insurgence of late-time oscillations. The stability condition is discussed and validated by means of a few working examples.

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TL;DR: In this paper, a local grid method for finite-difference time-domain (FDTD) calculation is proposed, which allows dielectric and/or conducting materials to traverse the boundary of the main-grid-local-grid boundary surfaces.

Abstract: Often, a finite-difference time-domain (FDTD) calculation requires a relatively higher mesh resolution in only small subvolumes of the total mesh space. By locally applying finer grids (local grids) to these volumes, the necessary resolution can be obtained. Computation time and memory requirements may be far less than for an FDTD space with the smaller mesh resolution throughout. In many situations, it is important that these local-grids function when materials traverse the main-grid-local-grid (MG-LG) boundary surfaces, since the volumes that require local grids may not be isolated in a homogeneous medium. A local-grid method, which allows dielectric and/or conducting materials to traverse the boundaries, is developed. Three different FDTD problems that utilize the local-grid method are used as validation tests. Results are compared with uniform mesh FDTD solutions.

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Duke University

^{1}TL;DR: A method of using genetic algorithms to optimize the element spacing and lengths of Yagi-Uda antennas is presented and the results are compared to published results from other optimization techniques and to well-designed equally spaced arrays.

Abstract: A method of using genetic algorithms to optimize the element spacing and lengths of Yagi-Uda antennas is presented. A method of moments code, NEC2, performs the task of evaluating each of the antenna designs generated by the genetic algorithm (GA) during the optimization process. To illustrate the capabilities of the method, the length and spacing of several Yagi-Uda antennas are optimized for various performance characteristics. The results are compared to published results from other optimization techniques and to well-designed equally spaced arrays.

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TL;DR: This paper discusses the application of a three-layer radial-basis function neural network (RBFNN), which can learn multiple source-direction findings of a six-element array and shows that the RBFNN substantially reduced the CPU time for the DOA estimation computations.

Abstract: The problem of direction of arrival (DOA) estimation of mobile users using linear antenna arrays is addressed. To reduce the computational complexity of superresolution algorithms, e.g. multiple signal classification (MUSIC), the DOA problem is approached as a mapping which can be modeled using a suitable artificial neural network trained with input output pairs. This paper discusses the application of a three-layer radial-basis function neural network (RBFNN), which can learn multiple source-direction findings of a six-element array. The network weights are modified using the normalized cumulative delta rule. The performance of this network is compared to that of the MUSIC algorithm for both uncorrelated and correlated signals. It is also shown that the RBFNN substantially reduced the CPU time for the DOA estimation computations.

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TL;DR: In this article, a general formulation for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media is presented, and two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations.

Abstract: A general formulation is presented for finite-difference time-domain (FDTD) modeling of wave propagation in arbitrary frequency-dispersive media. Two algorithmic approaches are outlined for incorporating dispersion into the FDTD time-stepping equations. The first employs a frequency-dependent complex permittivity (denoted Form-1), and the second employs a frequency-dependent complex conductivity (denoted Form-2). A Pade representation is used in Z-transform space to represent the frequency-dependent permittivity (Form-1) or conductivity (Form-2). This is a generalization over several previous methods employing either Debye, Lorentz, or Drude models. The coefficients of the Pade model may be obtained through an optimization process, leading directly to a finite-difference representation of the dispersion relation, without introducing discretization error. Stability criteria for the dispersive FDTD algorithms are given. We show that several previously developed dispersive FDTD algorithms can be cast as special cases of our more general framework. Simulation results are presented for a one-dimensional (1-D) air/muscle example considered previously in the literature and a three-dimensional (3-D) radiation problem in dispersive, lossy soil using measured soil data.

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TL;DR: In this article, a new fourth-order finite-difference time domain (FDTD) scheme was developed that exhibits extremely low-phase errors at low-grid resolutions compared to the conventional FDTD scheme.

Abstract: A new fourth-order finite-difference time-domain (FDTD) scheme has been developed that exhibits extremely low-phase errors at low-grid resolutions compared to the conventional FDTD scheme. Moreover, this new scheme is capable of combining with the standard Yee (1966) scheme to produce a stable hybrid algorithm. The problem of wave propagation through a building is simulated using this new hybrid algorithm to demonstrate the large savings in computing resources it could afford. With this new development, the FDTD method can now be used to successfully model structures that are thousands of wavelengths large, using the present day computer technology.

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TL;DR: In this paper, it was found through a vector integral-equation analysis and the reciprocity theorem that the gain of a microstrip antenna can be greatly enhanced with a photonic band gap material layer either as the substrate or the superstrate.

Abstract: It is found through a vector integral-equation analysis and the reciprocity theorem that the gain of a microstrip antenna can be greatly enhanced with a photonic band-gap material layer either as the substrate or the superstrate. The beam angle is found to coincide with that of a leaky-wave mode of a planar-grating structure. This observation suggests that high gain is due to the excitation of strong leaky-wave fields.

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TL;DR: The fast multipole method fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional (2-D) rough surface and is shown to be more efficient than another O(N log N) algorithm, the multilevel fast multipoles algorithm (MLFMA), for surfaces of small height.

Abstract: The fast multipole method fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional (2-D) rough surface. The resulting algorithm computes a matrix-vector multiply in O(N log N) operations. This algorithm is shown to be more efficient than another O(N log N) algorithm, the multilevel fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2-D random rough surfaces using a workstation. For the rougher surface, backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient. For the smoother surface, the Monte Carlo results compare well with the results of the approximate Kirchhoff theory.