Propagation path loss in mixed-path environment using narrow angle and wide-angle Parabolic equations

A model to predict the propagation path loss through the urban foliated semi-confined environment using parabolic equations (PE) is proposed. For this case the propagation in 15° to the paraxial direction and the implicit finite differences scheme of the Crank-Nicolson type is used. To wide-angle relative to the paraxial direction propagation (up to 90°), it used mixed Fourier transform and considers the impedance boundary conditions. A campaign of measurements taken in three mixed-path environment was carried out to validate the model. The frequency used was 900 MHz to Benfica and Marituba, and 1.8 GHz for Barcarena. Numerical examples demonstrate the computational efficiency of the proposed method.