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

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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 × 10−6m. 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.