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A Novel MIMO Channel Model for Vehicle-to-Vehicle Communication System on Narrow Curved-Road Environment

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Abstract

This paper presents a generalized statistical multiple-input multiple-output (MIMO) fading channel model for a vehicle-to-vehicle (V2V) non-line of sight mobile communication system on narrow curved-road environments. The MIMO channel model captures the propagation effect that occurs when vehicles move towards a junction with a side road and corner scatterings. In this paper, both single- and double-bounced scattering mechanisms are considered and it is assumed that the scatterers are uniformly distributed in the form of narrow arcs outside the annular road. Our geometry-based channel model takes the exact relationship between the angle-of-arrival and the angle-of-departure into account. Thereafter, the statistical properties of the model are studied under the assumption of non-isotropic scattering. Analytical expressions of different parameters, such as the space–time-frequency cross-correlation function, Doppler power spectral density, and MIMO channel capacity are provided. Furthermore, the influence of model parameters on the performance of V2V communication system has been analyzed. The study provides a design layout of MIMO V2V communication systems with a wide-band spatial channel model enabling the performance analysis of new high-data-rate transmission schemes for narrow curved-road propagations.

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Acknowledgements

We acknowledge Professor Fumiyuki Adachi, Department of Electrical and Electronic Engineering, Tohoku University, Japan, for his help on this paper. The research was supported by the Scientific & Technological Support Project of Jiangsu University (No. 14KJA510001), the National Nature Science Foundation of China (No. 61471153) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province.

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Authors and Affiliations

  1. Department of Communications, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Denghong Tang & Jie Zhou

  2. Department of Automatic Engineering, Hangzhou Dianzi University, Hangzhou, 310000, China

    Genfu Shao

  3. Department of Electrical and Electronic Engineering, Niigata University, Niigata, 950-2181, Japan

    Hisakazu Kikuchi

Authors
  1. Denghong Tang
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  2. Genfu Shao
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  3. Jie Zhou
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  4. Hisakazu Kikuchi
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Corresponding author

Correspondence to Jie Zhou.

Appendix

Appendix

In this appendix, we provide the final results for the space cross-correlation function, the space–time cross-correlation functions, the temporal auto-correlation function, the frequency cross-correlation function, respectively.

$$\begin{aligned} r_{{pq,p^{{\prime }} q^{{\prime }} }} \left( {\delta_{T} ,\delta_{R} } \right) & = r_{{pq,p^{{\prime }} q^{{\prime }} }} \left( {\delta_{T} ,\delta_{R} ,0,0} \right) = \eta_{SBT} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {g^{T} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} d\alpha^{T} \\ & \quad + \eta_{SBR} \int\limits_{{\alpha_{\hbox{min} }^{R} }}^{{\alpha_{\hbox{max} }^{R} }} {g^{R} p_{{\alpha^{R} }} \left( {\alpha^{R} } \right)} d\alpha^{R} \\ & \quad + \eta_{DB} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {\int\limits_{{\beta_{\hbox{min} }^{R} }}^{{\beta_{\hbox{max} }^{R} }} {g^{TR} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} } p_{{\beta^{R} }} \left( {\beta^{R} } \right)d\beta^{R} d\alpha^{T} \\ \end{aligned}$$
(34)
$$\begin{aligned} r_{T} \left( {\delta_{T} ,\tau } \right) & = r_{{pq,p^{{\prime }} q^{{\prime }} }} \left( {\delta_{T} ,0,0,\tau } \right) = \eta_{SBT} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {e^{{j\frac{2\pi }{\lambda }\left[ {\left( {p - p^{{\prime }} } \right)\delta_{T} \cos \left( {\alpha^{T} - \gamma_{T} } \right)} \right]}} e^{{j\left( {f_{m}^{T} + f_{m}^{R} } \right)\tau }} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} d\alpha^{T} \\ & \quad + \eta_{SBR} \int\limits_{{\alpha_{\hbox{min} }^{R} }}^{{\alpha_{\hbox{max} }^{R} }} {e^{{j\frac{2\pi }{\lambda }\left[ {\left( {p - p^{{\prime }} } \right)\delta_{T} \cos \left( {\alpha^{R} - \gamma_{T} } \right)} \right]}} e^{{j\left( {f_{n}^{T} + f_{n}^{R} } \right)\tau }} p_{{\alpha^{R} }} \left( {\alpha^{R} } \right)} d\alpha^{R} \\ & \quad + \eta_{DB} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {\int\limits_{{\beta_{\hbox{min} }^{R} }}^{{\beta_{\hbox{max} }^{R} }} {e^{{j\frac{2\pi }{\lambda }\left[ {\left( {p - p^{{\prime }} } \right)\delta_{T} \cos \left( {\alpha^{T} - \gamma_{T} } \right)} \right]}} e^{{j\left( {f_{m}^{T} + f_{n}^{R} } \right)\tau }} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} } p_{{\beta^{R} }} \left( {\beta^{R} } \right)d\beta^{R} d\alpha^{T} \\ \end{aligned}$$
(35)
$$\begin{aligned} r_{R} \left( {\delta_{R} ,\tau } \right) & = r_{{pq,p^{{\prime }} q^{{\prime }} }} \left( {0,\delta_{R} ,0,\tau } \right) = \eta_{SBT} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {e^{{j\frac{2\pi }{\lambda }\left[ {\left( {q - q^{{\prime }} } \right)\delta_{R} \cos \left( {\beta^{T} - \gamma_{R} } \right)} \right]}} e^{{j\left( {f_{m}^{T} + f_{m}^{R} } \right)\tau }} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} d\alpha^{T} \\ & \quad + \eta_{SBR} \int\limits_{{\alpha_{\hbox{min} }^{R} }}^{{\alpha_{\hbox{max} }^{R} }} {e^{{j\frac{2\pi }{\lambda }\left[ {\left( {q - q^{{\prime }} } \right)\delta_{R} \cos \left( {\beta^{R} - \gamma_{R} } \right)} \right]}} e^{{j\left( {f_{n}^{T} + f_{n}^{R} } \right)\tau }} p_{{\alpha^{R} }} \left( {\alpha^{R} } \right)} d\alpha^{R} \\ & \quad + \eta_{DB} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {\int\limits_{{\beta_{\hbox{min} }^{R} }}^{{\beta_{\hbox{max} }^{R} }} {e^{{j\frac{2\pi }{\lambda }\left[ {\left( {q - q^{{\prime }} } \right)\delta_{R} \cos \left( {\beta^{R} - \gamma_{R} } \right)} \right]}} e^{{j\left( {f_{m}^{T} + f_{n}^{R} } \right)\tau }} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} } p_{{\beta^{R} }} \left( {\beta^{R} } \right)d\beta^{R} d\alpha^{T} \\ \end{aligned}$$
(36)
$$\begin{aligned} r_{pq} \left( \tau \right) & = r_{{pq,p^{{\prime }} q^{{\prime }} }} \left( {0,0,0,\tau } \right) = \eta_{SBT} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {e^{{j\left( {f_{m}^{T} + f_{m}^{R} } \right)\tau }} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} d\alpha^{T} \\ & \quad + \eta_{SBR} \int\limits_{{\alpha_{\hbox{min} }^{R} }}^{{\alpha_{\hbox{max} }^{R} }} {e^{{j\left( {f_{n}^{T} + f_{n}^{R} } \right)\tau }} p_{{\alpha^{R} }} \left( {\alpha^{R} } \right)} d\alpha^{R} \\ & \quad + \eta_{DB} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {\int\limits_{{\beta_{\hbox{min} }^{R} }}^{{\beta_{\hbox{max} }^{R} }} {e^{{j\left( {f_{m}^{T} + f_{n}^{R} } \right)\tau }} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} } p_{{\beta^{R} }} \left( {\beta^{R} } \right)d\beta^{R} d\alpha^{T} \\ \end{aligned}$$
(37)
$$\begin{aligned} r_{{\tau^{{\prime }} }} \left( {\nu^{{\prime }} } \right) & = r_{{pq,p^{{\prime }} q^{{\prime }} }} \left( {0,0,\nu^{{\prime }} ,0} \right) = \eta_{SBT} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {e^{{ - 2\pi j\nu^{{\prime }} \tau_{pmq}^{{\prime }} }} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} d\alpha^{T} \\ & \quad + \eta_{SBR} \int\limits_{{\alpha_{\hbox{min} }^{R} }}^{{\alpha_{\hbox{max} }^{R} }} {e^{{ - 2\pi j\nu^{{\prime }} \tau_{pnq}^{{\prime }} }} p_{{\alpha^{R} }} \left( {\alpha^{R} } \right)} d\alpha^{R} \\ & \quad + \eta_{DB} \int\limits_{{\alpha_{\hbox{min} }^{T} }}^{{\alpha_{\hbox{max} }^{T} }} {\int\limits_{{\beta_{\hbox{min} }^{R} }}^{{\beta_{\hbox{max} }^{R} }} {e^{{ - 2\pi j\nu^{{\prime }} \tau \tau_{pmnq}^{{\prime }} }} p_{{\alpha^{T} }} \left( {\alpha^{T} } \right)} } p_{{\beta^{R} }} \left( {\beta^{R} } \right)d\beta^{R} d\alpha^{T} \\ \end{aligned}$$
(38)

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Tang, D., Shao, G., Zhou, J. et al. A Novel MIMO Channel Model for Vehicle-to-Vehicle Communication System on Narrow Curved-Road Environment. Wireless Pers Commun 98, 3409–3430 (2018). https://doi.org/10.1007/s11277-017-5021-6

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