Radio wave propagation path loss in the irregular terrain environments

Abstract

Equation (1) can be factored as:u(x + Llx, z) = e ikf1x ( -l + Q )u(x, z) (3) {~+ik(1-Q) } {~+ik(1+Q)} U = 0 (2) description of the theory can be referred to [1]. The horizontal polarization is considered in the following discussion. For the two-dimensional scalar wave equation, assume x is horizontal direction, z is vertical direction:This means the PE can easily be marched in range, the solution at range X + Llx is obtained from that in range x, provided the field is known on an initial plane and adequate boundary conditions on the scattering objects. It is easy to obtain standard parabolic equation (SPE) from forward expression: 1 a 2 2 where Q = ---+ m . The first and second k 2 az 2 terms in (2) describe the forward and backward propagating fields, respectively. The forward expression au = -ik(1-Q) has the formal solution: ax a 2u . au a 2u 2 2 -+21k-+-+k (m -1)u=O (1) ax 2 ax az 2 where u(x, z) = e-ikxE (x, z ) is time dependence for horizontal polarization, a reduced function along the preferred propagation direction (the x-coordinate), k = 2n / A is the free-space wave number, m is the modified refractive index, modified to take account of the curvature of the Earth: m(x, z) = n(x, z) + z / r , where r is the Earth's radius, n is the atmosphere refractive index. It is important to emphasize that all of the effects of atmospheric refraction are incorporated inton.Abstract-This paper proposes an efficient, full-wave computation technique to investigate the radio wave propagation with irregular terrain environment, this methodology is based on the parabolic wave equation (PE). A split-step transform algorithm is used to solve the PE; a staircase terrain modeling is used to approximate complex terrain. It is used to calculate the reflection and interference mechanism in the standard atmosphere and successfully applied to model the field in the presence of knife edge and smoothness hill terrain. The results are validated by the comparisons with hybrid methods in AREPS.

The Influence of PE Initial Field Construction Method on Radio Wave Propagation Loss and Tropospheric Duct Inversion

“…The forward propagation part is retained, and the wide-angle parabolic equation constructed by Greene approximation is as follows [16]:…”