J.W. Schuster

Comparison of GTD and FDTD predictions for UHF radio wave propagation in a simple outdoor urban environment

The continuing growth of wireless communication systems has led to an interest in the development of site-specific propagation models. In designing microcell systems there is a often a desire to have a good understanding of the propagation characteristics within the cell. Site-specific models offer a fast and inexpensive means of obtaining this information without the need for on-site measurements. The finite difference time domain (FDTD) method was initially developed by Yee in 1966. The method is commonly applied to three-dimensional scattering and radiation problems. But with the exception of analyzing the propagation within a single room, even the largest computers do not have nearly enough memory to model full three-dimensional indoor or outdoor propagation problems. However, in many cases a two-dimensional approximation to the geometry can be used, and two-dimensional FDTD has previously been applied to indoor propagation. This paper considers the application of 2D FDTD to a simple outdoor environment and develops a simple approach for introducing the correct spherical wave spreading. Comparisons to FDTD predictions could be used to evaluate and refine the GTD based methods.

Scattering from coated targets using a frequency-dependent, surface impedance boundary condition in FDTD

One method for reducing the radar cross section of objects such as aircraft and missiles is the application of a lossy coating. Computing scattering from targets coated with dielectric/magnetic materials is challenging due to the reduced wavelengths of an incident field inside the coating. These smaller wavelengths require finer sampling of the fields. A technique for implementing this calculation without greatly increased memory requirements or computation times has previously been developed using a finite-difference time-domain (FDTD) code which has been tested in one, two, and three dimensions. The method requires knowledge of the frequency behaviour of the complex permittivity and permeability, and the thickness of the dielectric coating and is applicable to thin coatings when one or more reflections from the conducting surface are significant. The impedance at the surface of the coating is computed based on the given information and then approximated using a summation of causal functions. The approximated impedance is Z-transformed and added to the FDTD code in special update equations for the fields at the surface of the coating. No computations are required inside the coatings so the FDTD grid can be sized based on the free-space wavelength. The result obtained is valid over the entire frequency range of interest, assuming that the approximated surface impedance is a good match over the entire range. Comparisons with measurements of a scale model coated missile show good agreement and almost no increase in resource requirements over a standard FDTD calculation for an uncoated metal target.

An accurate FDTD algorithm for dispersive media using a piecewise constant recursive convolution technique

The recursive convolution (RC) approach is one of several that have been developed to extend the basic finite difference time domain (FDTD) algorithm to permit modeling of broadband pulse propagation in frequency-dependent dielectric and magnetic media. This paper has shown that a second order accurate scheme can be obtained with the recursive convolution approach without abandoning the assumption of piecewise constant fields over each time step. This new formulation yields an algorithm with the same memory requirements and computational speed as the original RC method of Luebbers et al. (1990). Comparisons with the dispersion errors of piecewise linear recursive convolution and the auxiliary equation methods of Young et al. (1995) and Joseph et al. (1991) show the formulation in this paper to be at least as accurate as these other methods.

Application of moving window FDTD to prediction of path loss over irregular terrain

The full wave electromagnetic calculation method that is most efficiently applied to electrically large problems is the Finite Difference Time Domain (FDTD) method. FDTD offers several advantages over the commonly used ray and PE methods. It is full wave, so that the approximations and assumptions needed for application of PE and ray methods do not limit its accuracy. It call include all of the pertinent information available for the propagation path, including terrain profile, terrain permittivity and conductivity, vegetation features, and atmospheric conditions. The FDTD mesh, assuming a uniform atmosphere, need be only long enough (the dimension along the propagation path) to contain the dispersed pulse, and high enough to include the terrain profile and a few Fresnel zones above the highest elevation.

Full wave propagation model based on moving window FDTD

A new approach to wave oriented radio propagation modeling based on extended finite difference time domain (FDTD) methods has been developed. The new approach takes advantage of the fact that when a pulsed radio wave propagates over a long distance the significant pulse energy exists only over a small part of the propagation path at any instant of time. This allows the use of a relatively small FDTD computational mesh that exists only over a portion of the propagation path, moving along with the pulse energy. At the leading edge of the FDTD mesh inside the moving window the appropriate terrain and atmospheric material parameters are added to the mesh. At the trailing edge the terrain, foliage and atmosphere that has been left behind by the pulse is removed. Absorbing boundaries are used appropriately at the boundaries of the mesh. The potential savings over using a full FDTD mesh over the entire length of the propagation path are enormous. The proposed method promises to be the first full wave method applicable to radio propagation prediction calculations over long propagation paths. The moving window FDTD method has been applied to propagation over different types of irregular terrain. Comparisons with path loss measurements and ray-based methods show good accuracy and illustrate the advantages of a full wave method. Applications to foliage covered terrain have also been demonstrated.

Application of moving window FDTD to predicting path loss over forest covered irregular terrain

A new wave oriented approach to modeling radiowave propagation based on an extended finite difference time domain (FDTD) method has been developed. The new approach takes advantage of the fact that when a pulsed radio wave propagates over a long distance, the significant pulse energy exists only over a small part of the propagation path at any instant of time. This allows the use of a relatively small FDTD computational mesh that exists only over a portion of the propagation path and moves along with the pulse. At the leading edge of the FDTD mesh, inside the moving window, the appropriate terrain and foliage parameters are added to the mesh. At the trailing edge, the terrain and foliage that have been left behind by the pulse are removed. The moving window FDTD (MWFDTD) method has previously been applied to propagation over different types of irregular terrain. This paper extends this approach to forest covered terrain by treating the foliage as a lossy dielectric layer. Comparisons with path loss measurements show good accuracy and illustrate the advantages of a full wave method.

Application of moving window FDTD to modeling the effects of atmospheric variations and foliage on radio wave propagation over terrain

A new approach to wave oriented radio propagation modeling based on extended finite difference time domain (FDTD) method has been developed. In order to model radio wave propagation using standard FDTD, the entire propagation path would need to be included in the FDTD grid. This would require prohibitive amount of computer memory and time. The new approach takes advantage of the fact that when a pulsed radio wave propagates over a long distance the significant pulse energy exists only over a small part of the propagation path at any instant of time. This allows the use of a relatively small FDTD computational mesh that exists only over a portion of the propagation path and move along with the pulse. At the leading edge of the FDTD mesh inside the moving window the appropriate terrain, foliage, and atmospheric parameters are added to the mesh. At the trailing edge the terrain and foliage that have been left behind by the pulse are removed. Since this method solves Maxwells equation directly, all physics relevant to radio wave propagation is included in this model In addition, since it is based on the FDTD method, this model can take advantage of the extensive research that has been done on the FDTD algorithm, such as the higher-order finite differencing and multiresolution time domain (MRTD). The moving window FDTD (MWFDTD) method has previously been applied to propagation over different types of irregular terrain. This paper extends this approach to forest covered terrain by treating the foliage as a lossy dielectric layer. In addition, using MWFDTD, atmospheric refractive effects can also be included simultaneously with irregular terrain effects and foliage. We apply our method to radio wave propagation in atmospheric ducts. Comparisons with path loss measurements show good accuracy and illustrate the advantages of a full wave method. While this method is slower than other propagation models, it is potentially much more accurate. Therefore, MWFDTD can be used to validate other faster propagation models, and can provide predictions in cases where a high degree of accuracy is desired.

Application of the recursive convolution technique to modeling lumped circuit elements in FDTD simulations

This paper presents a simple approach for extending the basic Yee FDTD algorithm to allow for modeling combinations of resistors, capacitors and inductors as lumped elements. This approach uses the recursive convolution (RC) technique previously applied in FDTD for simulating pulse propagation in frequency dependent dielectric media. In the application presented, the potential across the lumped load is updated by a recursive evaluation of the convolution of the current with the inverse Fourier transform of the impedance. This approach can be used whenever the impedance can be approximated over the frequency range of interest with functions which have inverse Fourier transforms containing the exponential time dependence required by the RC method. A parallel LCR satisfies this requirement, and any number of parallel LCR circuits in series can be modeled as a lumped load located at a single FDTD cell location. The formulation in this paper also permits a voltage or current source to be included within the lumped element.

Comparison of site-specific radio propagation path loss predictions to measurements in an urban area

With high frequency portable communication systems becoming more common, the need for fast and accurate predictions of high frequency radio propagation in urban environments has rapidly increased. Until recently such predictions were usually based on empirical methods, especially if a relatively large number of predictions were required. But advances in both computational methods and computer speeds now allow for fast, site-specific predictions of radio propagation even in a complex urban area. We are primarily concerned with narrow band signal attenuation, but the methods presented are also applicable to signal delay and delay spread predictions. Measurements were made at frequencies of 900 and 1900 MHz.

FDTD for three-dimensional propagation in a magnetized ferrite

In the standard Yee FDTD algorithm, the constitutive parameters /spl epsi/, /spl mu/ and /spl sigma/ are assumed to be constant with respect to frequency for all media located in the computational space. Modifications to the Yee algorithm are required to allow for modeling of propagation in dispersive media. Luebbers and Hunsberger (1992) demonstrated that, because of the exponential nature of the time domain susceptibility functions of Debye and Lorentz materials, the convolution relating the time domain electric field and the electric flux density can be performed efficiently using recursion. Their approach has therefore come to be known as the recursive convolution method. The recursive convolution approach was applied in Melon et al. (1994) to lossless ferrites for a two dimensional problem with the biasing field parallel to the z axis. This approach requires four convolutions per magnetic field component. In the formulation presented here an arbitrary direction for the biasing field is allowed and a maximum of three complex numbers per cell is required. Update equations for both total and scattered field forms have been derived.