NUMERICAL MODELING OF TROPOSPHERIC RADIO WAVE PROPAGATION USING WAVELETS

The problem of anomalous propagation in troposphere has been studied for many
years. Various models are available in literature. Among them, the parabolic wave
equation (PWE) method is considered most reliable. The standard PWE with
appropriate boundary conditions is solved using various numerical schemes like Splitstep Fourier method and Finite Element/Difference method. However, these
techniques are either less accurate and/or computationally more expensive.
In this work, two novel wavelet based numerical algorithms are presented for
tropospheric radio wave propagation modeling. First, a Wavelet Galerkin Method
(WGM) is developed using Daubechies scaling function as basis functions. The
discretization process converts PWE to an Ordinary Differential Equation (ODE)
which is then solved with Crank-Nicolson (CN) method. Fictitious domain approach
is used to incorporate the impedance boundary conditions. It is found that the
complexity and computational cost of WGM is almost same as of conventional Finite
Element (FE) method and, like FE method, it also requires small range steps for high
frequencies. Second, a split-step wavelet method (SSWM) is developed.