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

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Transactions on Engineering Technologies

Abstract

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.

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Notes

  1. 1.

    A translation of [20] into English has been provided in [21].

  2. 2.

    We have chosen the ring's center as the starting point of the movement to enable the verification of our numerical results (see Sect. 7) with the ones from the one-ring scattering model. However, the analytical results provided in the paper are not limited to such a special case.

  3. 3.

    The frequency shift caused by the Doppler effect is given by \( f = f_{\hbox{max} } \cos (\alpha ) \), where \( f_{\hbox{max} } = f_{0} v/c_{0} \) is the maximum Doppler frequency, \( f_{0} \) denotes the carrier frequency, \( c_{0} \) stands for the speed of light, and \( \alpha \) equals the difference between the AOA and the AOM [24].

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Authors and Affiliations

  1. Faculty of Engineering and Science, University of Agder, 4898, Grimstad, Norway

    Alireza Borhani & Matthias Pätzold

Authors
  1. Alireza Borhani
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  2. Matthias Pätzold
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Correspondence to Alireza Borhani .

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Editors and Affiliations

  1. Computer & Communication, Catholic University of DaeGu, DaeGu, Korea, Republic of (South Korea)

    Haeng Kon Kim

  2. IAENG Secretariat, International Association of Engineers, Hong Kong, Hong Kong SAR

    Sio-Iong Ao

  3. College of Engineering, California State Polytechnic University, Pomona, California, USA

    Mahyar A. Amouzegar

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Borhani, A., Pätzold, M. (2014). A New Non-stationary Channel Model Based on Drifted Brownian Random Paths. In: Kim, H., Ao, SI., Amouzegar, M. (eds) Transactions on Engineering Technologies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9115-1_33

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  • DOI: https://doi.org/10.1007/978-94-017-9115-1_33

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  • Online ISBN: 978-94-017-9115-1

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