A New Non-stationary Channel Model Based on Drifted Brownian Random Paths

Conference paper


This paper utilizes Brownian motion (BM) processes with drift to model mobile radio channels under non-stationary conditions. It is assumed that the mobile station (MS) starts moving in a semi-random way, but subject to follow a given direction. This moving scenario is modelled by a BM process with drift (BMD). The starting point of the movement is a fixed point in the two-dimensional (2D) propagation area, while its destination is a random point along a predetermined drift. To model the propagation area, we propose a non-centred one-ring scattering model in which the local scatterers are uniformly distributed on a ring that is not necessarily centred on the MS. The semi-random movement of the MS results in local angles-of-arrival (AOAs) and local angles-of-motion (AOMs), which are stochastic processes instead of random variables. We present the first-order density of the AOA and AOM processes in closed form. Subsequently, the local power spectral density (PSD) and autocorrelation function (ACF) of the complex channel gain are provided. The analytical results are simulated, illustrated, and physically explained. It turns out that the targeted Brownian path model results in a statistically non-stationary channel model. The interdisciplinary idea of the paper opens a new perspective on the modelling of non-stationary channels under realistic propagation conditions.


Brownian motion processes Channel modelling Local autocorrelation function Local power spectral density Non-centred one-ring scattering model Non-stationary channels Targeted motions 


  1. 1.
    A. Abdi, M. Kaveh, A space-time correlation model for multielement antenna systems in mobile fading channels. IEEE J. Sel. Areas Commun. 20(3), 550–560 (2002)CrossRefGoogle Scholar
  2. 2.
    M. Pätzold, B.O. Hogstad, A space-time channel simulator for MIMO channels based on the geometrical one-ring scattering model, in Proceedings of the 60th IEEE Semiannual Vehicular Technology Conference, VTC 2004-Fall, vol. 1 (Los Angeles, 2004), pp. 144–149Google Scholar
  3. 3.
    D.S. Shiu, G.J. Foschini, M.J. Gans, J.M. Kahn, Fading correlation and its effect on the capacity of multielement antenna systems. IEEE Trans. Commun. 48(3), 502–513 (2000)CrossRefGoogle Scholar
  4. 4.
    A. Borhani, M. Pätzold, A unified disk scattering model and its angle-of-departure and time-of-arrival statistics. IEEE Trans. Veh. Technol. 62(2), 473–485 (2013)CrossRefGoogle Scholar
  5. 5.
    K.T. Wong, Y.I. Wu, M. Abdulla, Landmobile radiowave multipaths’ DOA-distribution: assessing geometric models by the open literature’s empirical datasets. IEEE Trans. Antennas Propag. 58(2), 946–958 (2010)CrossRefGoogle Scholar
  6. 6.
    A. Gehring, M. Steinbauer, I. Gaspard, M. Grigat, Empirical channel stationarity in urban environments, in Proceedings of the 4th European Personal Mobile Communications Conference, Vienna, 2001Google Scholar
  7. 7.
    A. Ispas, G. Ascheid, C. Schneider, R. Thom, Analysis of local quasi-stationarity regions in an urban macrocell scenario, in Proceedings of the 71th IEEE Vehicular Technology Conference, VTC 2010-Spring. Taipei, 2010Google Scholar
  8. 8.
    D. Umansky, M. Pätzold, Stationarity test for wireless communication channels, in Proceedings of the IEEE Global Communications Conference, IEEE GLOBECOM 2009. HonoluluGoogle Scholar
  9. 9.
    A. Paier, J. Karedal, N. Czink, H. Hofstetter, C. Dumard, T. Zemen, F. Tufvesson, A.F. Molisch, C.F. Mecklenbräucker, Characterization of vehicle-to-vehicle radio channels from measurement at 5.2 GHz. Wirel. Pers. Commun. 50(1), 19–32 (2009)Google Scholar
  10. 10.
    A. Chelli, M. Pätzold, A non-stationary MIMO vehicle-to-vehicle channel model based on the geometrical T-junction model, in Proceedings of the International Conference on Wireless Communications and Signal Processing, WCSP 2009. Nanjing, 2009Google Scholar
  11. 11.
    A. Ghazal, C. Wang, H. Hass, R. Mesleh, D. Yuan, X. Ge, A non-stationary MIMO channel model for high-speed train communication systems, in Proceedings of the 75th IEEE Vehicular Technology Conference, VTC 2012-Spring. Yokohama, 2012Google Scholar
  12. 12.
    J. Karedal, F. Tufvesson, N. Czink, A. Paier, C. Dumard, T. Zemen, C.F. Mecklenbräuker, A.F. Molisch, A geometry-based stochastic MIMO model for vehicle-to-vehicle communications. IEEE Trans. Wirel. Commun. 8(7), 3646–3657 (2009)CrossRefGoogle Scholar
  13. 13.
    G. Matz, On non-WSSUS wireless fading channels. IEEE Trans. Wirel. Commun. 4(5), 2465–2478 (2005)Google Scholar
  14. 14.
    A. Borhani, M. Pätzold, A non-stationary one-ring scattering model. In: Proceedings of the IEEE Wireless Communications and Networking, Conference (WCNC’13). Shanghai, 2013Google Scholar
  15. 15.
    P. Pearle, B. Collett, K. Bart, D. Bilderback, D. Newman, S. Samuels, What Brown saw and you can too. Am. J. Phys. 78(12), 1278–1289 (2010)CrossRefGoogle Scholar
  16. 16.
    A. Borhani, M. Pätzold, Modelling of non-stationary mobile radio channels incorporating the Brownian mobility model with drift, in Proceedings of the World Congress on Engineering and Computer Science, WCECS 2013. Lecture Notes in Engineering and Computer Science, San Francisco, 23–25 Oct, pp. 695–700Google Scholar
  17. 17.
    B.H. Fleury, D. Dahlhaus, Investigations on the time variations of the wide-band radio channel for random receiver movements, in Proceedings of the IEEE International Symposium on Spread Spectrum Techniques and Applications (ISSSTA ‘94), vol. 2. Oulu, pp. 631–636Google Scholar
  18. 18.
    T. Camp, J. Boleng, V. Davies, A survey of mobility models for ad hoc network research. Wirel. Commun. Mobile Comput. 2(5), 483–502 (2002)CrossRefGoogle Scholar
  19. 19.
    A. Einstein, Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen. Ann. Phys. 17, 549–560 (1905)CrossRefzbMATHGoogle Scholar
  20. 20.
    P. Langevin, Sur la théorie du mouvement brownien. C. R. Acad. Sci. Paris 146, 530–533 (1908)zbMATHGoogle Scholar
  21. 21.
    D.S. Lemons, A. Gythiel, On the theory of Brownian motion. Am. J. Phys. 65(11), 530–533 (1979)Google Scholar
  22. 22.
    R.C. Earnshaw, E.M. Riley, Brownian Motion: Theory, Modelling and Applications (Nova Science Pub Inc, New York, 2011)Google Scholar
  23. 23.
    M. Pätzold, Mobile Fading Channels, 2nd edn. (Wiley, Chichester, 2011)CrossRefGoogle Scholar
  24. 24.
    W.C. Jakes (ed.), Microwave Mobile Communications (IEEE Press, Piscataway, 1994)Google Scholar
  25. 25.
    A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd edn. (McGraw-Hill, New York, 1991)Google Scholar
  26. 26.
    F. Hlawatsch, F. Auger, Time-Frequency Analysis: Concepts and Methods (Wiley, London, 2008)CrossRefGoogle Scholar
  27. 27.
    I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products, 7th edn. (Elsevier Academic Press, Amsterdam, 2007)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Faculty of Engineering and ScienceUniversity of AgderGrimstadNorway

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