Vol. 44

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

A Decomposition Method for Computing Radiowave Propagation Loss Using Three-Dimensional Parabolic Equation

By Guizhen Lu, Ruidong Wang, Zhi Cao, and Kehua Jiang
Progress In Electromagnetics Research M, Vol. 44, 183-189, 2015


The parabolic equation(PE) method is widely used in radiowave propagation predictions. It has the advantages of high efficiency and stability, but it will lead to greater predicting errors in some situations, because the effects of transverse terrain gradients are not modeled. This problem can be solved by extending the 2D PE to the three-dimensional (3D) PE. However, the computing efficiency will degrade because of large scale matrix operations. In this paper, a new method is presented, in which the 3D PE is decomposed into two 2D PEs. It increases the computational efficiency and accuracy effectively. To verify the capability of the proposed method in radiowave propagation prediction, an experiment platform was set up. The computational results using this new method are compared with the experimental and Method of Moment(MoM) numerical computational results. Good agreements are achieved in the comparison.


Guizhen Lu, Ruidong Wang, Zhi Cao, and Kehua Jiang, "A Decomposition Method for Computing Radiowave Propagation Loss Using Three-Dimensional Parabolic Equation," Progress In Electromagnetics Research M, Vol. 44, 183-189, 2015.


    1. Recmmendation ITU-R P.1546-2, "Method for point to area prediction for terratrial services in the frequency range 30MHz to 3000 MHz," International Telecommunication Union Geneva, 2005.

    2. Leontovich, M. A. and V. A. Fock, "Solution of propagation of electromagnetic waves along the Earths surface by the method of parabolic equations," J. Phys. USSR, Vol. 10, 13-23, 1946.

    3. Tappert, F., "The parabolic equation method," Wave Propagation in Underwater Acoustics, J. B. Keller and J. S. Papadakis (eds.), 224-287, Springer-Verlag, New York, 1977.

    4. Kuttler, J. R. and G. D. Dockery, "Theoretical description of the PE/Fourier split-step method of representing electromagnetic propagation in the troposphere," Radio Science, Vol. 26, No. 2, 381-393, 1991.

    5. Dockery, G. D. and J. R. Kuttler, "An improved impedance-boundary algorithm for Fourier split-step solution of parabolic wave equation," IEEE Trans. AP, Vol. 44, No. 12, 1592-1599, 1996.

    6. Levy, M. F., "Transparent boundary conditions for parabolic equation solutions of radiowave propagation problems," IEEE Trans. AP, Vol. 45, No. 9, 66-72, 1997.

    7. Ozgun, O., "Two-way Fourier split step algorithm over variable terrain with narrow and wide angle propagators," Antennas and Propagation Society International Symposium 2010 IEEE, 2010.

    8. Apaydm, G. and L. Sevgi, "Groundwave propagation at short ranges and accurate source modeling," IEEE Mag. AP, Vol. 55, No. 3, 245-262, 2013.

    9. Barrios, A. E., "Parabolic equation modeling in horizontally inhomogeneous environments," IEEE Trans. AP, Vol. 40, No. 7, 791-797, July 1992.

    11. Zelley, C. A., "Radiowave propagation over irregular terrain using the 3D parabolic eaquation," IEEE Trans. AP, Vol. 47, No. 10, 1586-1596, 1999.

    12. Saini, L. and U. Casiragh, "A 3D Fourier split-step technique for modelling microwave propagation in urban areas," Proc. 4th Eur. Conf. Radio Relay Syst., 210-214, October 1993.

    13. Iqbal, A. and V. Jeoti, "A split step wavelet method for radiowave propagation modelling in tropospheric ducts," Radioengineering, Vol. 23, No. 4, 987-996, 2014.

    14. Ozgun, O., "Recursive two-way parabolic equation approach for modeling terrain effects in tropospheric propagation," IEEE Trans. AP, Vol. 57, No. 9, 2706-2714, 2009.

    15. Apaydin, G. and O. Ozgun, "Two-way split-step fourier and finite element based parabolic equation propagation tools: comparisons and calibration," IEEE Trans. AP, Vol. 58, No. 4, 1302-1313, 2010.