Computer modeling of multipath propagation: Review of ray‐tracing techniques

Abstract

The field of ray tracing and related differential equations are reviewed in reference to multipath propagation. Past efforts are limited in that analytical approaches require simple refractive index profiles and computer ray tracing usually does not include the crucial boundary condition that rays have to hit the receiver with adequate accuracy. We describe a three‐dimensional computer program that finds all the important rays converging on the receiver within 2 × 10−6 m. We obtain the angles of launch and arrival, the ray trajectories, and the divergence or convergence factor of each ray intensity. A complex vector differential equation is also solved for the electric field polarization components from which we calculate the attenuation and depolarization. We include antenna amplitude and phase copolar and cross‐polar patterns. The potentiality of the computer program is illustrated for two refractive index profiles and varying receiver height assuming zero earth curvature. The first profile has a transition in refractive index at an elevated layer of about 300 m. Angles of arrival approaching ± 1° off boresight and time delays up to 19 ns are possible. The second profile has a transition in the refractive index gradient at a low‐altitude layer of 70 m. As the receiver height is changed from 40 to 80 m, rays appear, disappear, and coalesce. When rays coalesce, they also converge, and this leads to enhanced fields. We find that the depolarization is strongly dependent on the ground‐reflected rays for circular polarization and on the antenna patterns for all polarizations. Interference due to other rays is consequential. The divergence factor and the phases of the antennas are also important parameters.

Determination of radar coverage diagrams in complex environments using closed form ray tracing

“…In the special case of a homogeneous atmosphere, beam power density at a distance D from the transmitter is inversely proportional to D2 (i.e., uniform spherical wave). However, an inhomogeneous atmosphere may cause divergence or convergence of beams, and thus power density cannot be determined as such [Shkarofsky and Nickerson, 1982].…”

“…The second requirement is more difficult to achieve, especially in radar coverage diagrams, if direct information from ray traces is used. This is because the homing accuracy of ray tracing equations in an inhomogeneous atmosphere can only be improved by iteration [Shkarofsky and Nickerson, 1982]. In radar coverage diagram calculation, this is practically unachievable due to the huge number of rays calculated.…”

Evaluation of EM‐wave propagation in fully three‐dimensional atmospheric refractive index distributions

“…While significant understanding in many areas of science and engineering has arisen from such mathematical treatments, there still remain many important scientific problems, like the problem we consider in this paper, propagation of GPS (Global Positioning System) signals in fully three‐dimensional atmospheres, for which the methodologies 1 through 4 are either inadequate or exceedingly costly. For example, methods based on the parabolic approximation [ Coles et al , 1995; Martin and Flatté , 1988; Reilly , 1991; Rubio et al , 1999; Shkarofsky and Nickerson , 1982] turn out to be extremely expensive for large fully three‐dimensional atmospheric configurations, and, thus, studies based on such methodologies assume two‐dimensional atmospheres, i.e., atmospheres for which the refractive index is constant in the cross‐range direction [ Levy , 2000]. Similar considerations apply to the multiple phase screen (MPS) method [ Karayel and Hinson , 1997; Sokolovskiy , 2001; Ao et al , 2003] that is used often in GPS applications.…”

Hybrid Computational Techniques: Electromagnetic Propagation Analysis in Complex Indoor Environments

“…method of moment (MoM) or finite difference time domain (FDTD) [6]. The second group are those methods based on geometrical approximations, such as ray launching (RL) and ray tracing (RT) [7]. The advantage of these methods is the precision of the results, but the drawback is that the simulation computational time can be unaffordable if the analyzed scenario is complex and with large dimensions.…”