Improved ITU Model for Rainfall Attenuation Prediction of in Terrestrial Links

  • Angel D. Pinto-Mangones
  • Juan M. Torres-Tovio
  • Nelson A. Pérez-GarcíaEmail author
  • Luiz A. R. da Silva Mello
  • Alejandro F. Ruiz-Garcés
  • Joffre León-Acurio
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1066)


Rain attenuation is one of the main detrimental effects on the performance of wireless telecommunications systems operating in frequencies above 10 GHz. Mitigation of its impacts requires, among other things, the use of rain attenuation models adequate to local climatic characteristics in which the communications systems will be implemented. In this paper, a modified version of the ITU-R Recommendation ITU-R.P.530-17 prediction method is proposed. The model maintains the concept of the distance correction factor used in the ITU-R model, but considers the full rainfall rate distribution. To derive the model, a nonlinear regression adjustment is performed based on results from measurements carried out in temperate and tropical climate. Subsequently, a fine-tuning of the model parameters is carried out using the computational intelligence technique, Particle Swarm Optimization (PSO). The accuracy of the proposed model, evaluated by the root mean square error (RMSE), is higher than that of several tested models for unavailability percentages of time in the range from 0.001% to 0.1%.


Rain attenuation Terrestrial links Full rainfall rate distribution Nonlinear regression Particle swarm optimization 


  1. 1.
    Perez-Garcia, N.A., Torres-Tovio, J.M., Pinto-Mangones, A.D., Ramirez, E.J.: Planificación y Dimensionamiento de Sistemas de Comunicación Vía Satélite. Sello Editorial Corporación Universidad del Sinú, Montería (2018). ISBN 978-958-8553-52-8Google Scholar
  2. 2.
    International Telecommunication Union (ITU): ITU-R Recommendation P.530-17. Propagation data and prediction methods required for the design of terrestrial line-of-sight systems, Geneva, Switzerland (2017)Google Scholar
  3. 3.
    Perez-Garcia, N., Pinto-Mangones, A.D., Torres-Tovio, J.M., Perez-Di Santis, T.: Planificación y Dimensionamiento de Sistemas Celulares y de Radio Acceso, vol. 1. Sello Editorial Corporación Universitaria del Sinú, Montería (2017). ISBN 978-958-8553-41-2Google Scholar
  4. 4.
    Silva Mello, L.A.R., Pontes, M.S., Souza, R.M., Perez-Garcia, N.A.: Prediction of rain attenuation in terrestrial links using full rainfall rate distribution. Electron. Lett. 43(25), 1442–1443 (2007). ISSN 0013-5194CrossRefGoogle Scholar
  5. 5.
    Silva Mello, L.A.R., Pontes, M.S.: Unified method for the prediction of rain attenuation in satellite and terrestrial links. J. Microwaves Optoelectron. Electromagnet. Appl. 11(1), 1–14 (2012). ISSN 2179-1074CrossRefGoogle Scholar
  6. 6.
    Crane, R.K.: Prediction of attenuation by rain. IEEE Trans. Commun. 28(9), 1717–1733 (1980). ISSN 0090-6778CrossRefGoogle Scholar
  7. 7.
    Koryu-Ishii, T.: Handbook of Microwave Technology, vol. 2. Academic Press, San Diego (1995). ApplicationsGoogle Scholar
  8. 8.
    Abdulrahman, A.Y., Rahman, T.A., Rahim, K.A., Islam, M.R., Abdulrahman, M.K.A.: Rain attenuation predictions on terrestrial radio links: differential equations approach. Trans. Emerg. Telecommun. Technol. 23(3), 293–301 (2012). ISSN 2161-3915CrossRefGoogle Scholar
  9. 9.
    Ghiani, R., Luini, L., Fanti, A.: A physically based rain attenuation model for terrestrial links. Radio Sci. 52(8), 972–980 (2017). ISSN 1944-799XCrossRefGoogle Scholar
  10. 10.
    Bonnans, J.F., Gilbert, J.C., Lemaréchal, C., Sagastizábal, C.A.: Numerical Optimization Theoretical and Practical Aspects, 2nd edn. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  11. 11.
    Cheng, S., Lu, H., Lei, X., Shi, Y.: A quarter century of particle swarm optimization. Complex & Intelligent Systems 4(3), 227–239 (2018). ISSN 2199-4536CrossRefGoogle Scholar
  12. 12.
    Sun, J., Lai, C.H., Wu, X.J.: Particle Swarm Optimisation: Classical and Quantum Perspectives. CRC Press, Boca Raton (2012)zbMATHGoogle Scholar
  13. 13.
    International Telecommunication Union (ITU): Databank DBGS3. Accessed 24 January 2019
  14. 14.
    Abdulrahman, A.Y., Falade, A., Olufeagba, B.J., Mohammed, O.O., Rahman, T.A.: Statistical evaluation of measured rain attenuation in tropical climate and comparison with prediction models. J. Microwaves Optoelectron. Electromagnet. Appl. 15(2), 123–134 (2016). ISSN 2179-1074CrossRefGoogle Scholar
  15. 15.
    Ulaganthen, K., Rahman, T.A., Islam, M.R.: Complementary cumulative distribution function for rain rate and rain attenuation for tropical region Malaysia. Int. J. Manag. Appl. Sci. 3(1), 54–57 (2017). Special Issue-1, ISSN 2394-7926Google Scholar
  16. 16.
    International Telecommunication Union (ITU): ITU-R Recommendation P.838-3. Specific attenuation model for rain for use in prediction methods, Geneva, Switzerland (2005)Google Scholar
  17. 17.
    Luini, L., Capsoni, C.: MultiEXCELL: a new rainfall model for the analysis of the millimetre wave propagation through the atmosphere. In: 3rd European Conference on Antennas and Propagation, March 2009, Berlin, Germany, pp. 1946–1950 (2009). ISBN 978-1-4244-4753-4Google Scholar
  18. 18.
    Dennis Jr., J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1996)CrossRefGoogle Scholar
  19. 19.
    Lange, K.: Optimization, 2nd edn. Springer, New York (2013)CrossRefGoogle Scholar
  20. 20.
    Armijo, L.: Minimization of functions having Lipschitz-continuous first partial derivatives. Pac. J. Math. 16(1), 1–3 (1966). ISSN 0030-8730MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Lange, K.: Numerical Analysis for Statisticians, 2nd edn. Springer, New York (2010)CrossRefGoogle Scholar
  22. 22.
    Wen, G.K., Mamat, M., Mohd, I.B., Dasril, Y.: A novel of step size selection procedures for steepest descent method. Applied Mathematical Sciences 6(51), 2507–2518 (2012). ISSN 1314-7552MathSciNetzbMATHGoogle Scholar
  23. 23.
    Rujano-Molina, L.M., Perez-Garcia, N.A., Nariño, T.: Distribuciones acumulativas de la tasa de lluvias con tiempo de integración de 1-minuto en Venezuela. Ingenieria Al Dia 3(1), 24–44 (2017). ISSN 2389-7309Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Angel D. Pinto-Mangones
    • 1
  • Juan M. Torres-Tovio
    • 1
  • Nelson A. Pérez-García
    • 2
    Email author
  • Luiz A. R. da Silva Mello
    • 3
  • Alejandro F. Ruiz-Garcés
    • 1
  • Joffre León-Acurio
    • 4
  1. 1.Universidad del SinúMontería, CórdobaColombia
  2. 2.Universidad de Los AndesMéridaVenezuela
  3. 3.Pontifícia Universidade do Rio de JaneiroRio de JaneiroBrazil
  4. 4.Universidad Técnica de BabahoyoBabahoyoEcuador

Personalised recommendations