Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Extended Sum-of-Sinusoids-Based Simulation for Rician Fading Channels in Vehicular Ad Hoc Networks

  • Published:
International Journal of Wireless Information Networks Aims and scope Submit manuscript

Abstract

In this paper, we propose an extended reference model and two novel Sum-of-Sinusoids (SoS) models (statistical and deterministic simulation models) propagation models considering the Rician K-factor and vehicle speed ratio in Vehicular Ad Hoc Networks (VANETs). Our models consider comprehensive scene of wave propagation in VANETs, including infrastructure-to-vehicle (I2V) channels with a LOS or NLOS environment, inter-vehicle communication (IVC) channels with a LOS or NLOS environment. The analysis of the statistical properties of the proposed models show that the statistics of the new models match those of the reference model at a large range of normalized time delays. The proposed models show improved approximations to the desired auto-correlation and faster convergence with the increase of Rician K-factor and vehicle speed ratio.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. M. Boban, O. K. Tonguz, and J. Barros, Unicast communication in Vehicular Ad Hoc Networks: a reality check, IEEE Communications Letters, Vol. 13, No. 12, pp. 995–997, 2009.

    Article  Google Scholar 

  2. A. F. Molisch, F. Tufvesson, J. Karedal, and C. F. Mecklenbrauker, A survey on vehicle-to-vehicle propagation channels, IEEE Transactions on Wireless Communications, Vol. 16, No. 6, pp. 12–22, 2009.

    Article  Google Scholar 

  3. Z. Shen and J. P.Thomas, Security and QoS self-optimization in mobile ad hoc networks, IEEE Transactions on Mobile Computing, Vol. 7, No. 9, pp. 1138–1151, 2008.

    Article  Google Scholar 

  4. T. Taleb, E. Sakhaee, A. Jamalipour, K. Hashimoto, N. Kato, and Y. Nemoto, A stable routing protocol to support ITS services in VANET networks, IEEE Transactions on Vehicular Technology, Vol. 56, No. 6, pp. 3337–3347, 2007.

    Article  Google Scholar 

  5. W. J. Wang, F. Xie, and M. Chatterjee, Small-scale and large-scale routing in vehicular ad hoc networks, IEEE Transactions on Vehicular Technology, Vol. 58, No. 9, pp. 5200–5213, 2009.

    Article  Google Scholar 

  6. H. Saleet, O. Basir, R. Langar, and R. Boutaba, Region-based location-service-management protocol for VANETs, IEEE Transactions on Vehicular Technology, Vol. 59, No. 2, pp. 917–931, 2010.

    Article  Google Scholar 

  7. R. H. Clarke, A statistical theory of mobile-radio reception, Bell Systems Technical Journal, Vol. 47, No. 6, pp. 957–1000, 1968.

  8. M. J. Gans, A power-spectral theory of propagation in the mobile-radio environment, IEEE Transactions on Vehicular Technology, Vol. 21, pp. 27–38, 1972.

    Article  Google Scholar 

  9. P. Dent, G. E. Bottomley, and T. Croft, Jakes fading model revisited, IEEE Electronics Letters, Vol. 29, pp. 1162–1163, 1993.

    Article  Google Scholar 

  10. M. F. Pop and N. C. Beaulieu, Limitations of sum-of-sinusoids fading channel simulators, IEEE Transactions on Communications, Vol. 49, pp. 699–708, 2001.

    Article  Google Scholar 

  11. C. Xiao, Y. R. Zheng, and N. C. Beaulieu, Novel sum-of-sinusoids simulation models for Rayleigh and Rician fading channels, IEEE Transactions on Wireless Communications, Vol. 5, No. 12, pp. 3667–3679, 2006.

    Article  Google Scholar 

  12. A. S. Akki and F. Haber, A statistical model for mobile-to-mobile land communication channel, IEEE Transactions on Vehicular Technology, Vol. 35, No. 1, pp. 2–7, 1986.

    Article  Google Scholar 

  13. F. Vatalaro and A. Forcella, Doppler spectrum in mobile-to-mobile communications in the presence of three-dimensional multipath scattering, IEEE Transactions on Vehicular Technology, Vol. 46, No. 1, pp. 213–219, 1997.

    Article  Google Scholar 

  14. R. Wang and D. Cox, Channel modeling for ad hoc mobile wireless networks, in Proceedings of IEEE Vehicular Technology Conference, May, 2002, Vol. 1, pp. 21–25.

  15. D. J. Young and N. C. Beaulieu, The generation of correlated Rayleigh random variates by inverse discrete Fourier transform, IEEE Transactions on Communications, Vol. 48, no. 7, pp. 1114–1127, 2000.

    Article  Google Scholar 

  16. C. S. Patel, S. L. Stuber, and T. G. Pratt, Simulation of Rayleigh faded mobile-to-mobile communication channels, IEEE Vehicular Technology Conference, Vol. 1, pp. 163–167, 2003.

    Google Scholar 

  17. C. S. Patel, G. L. Stuber, and T. G. Pratt, Simulation of Rayleigh-faded mobile-to-mobile communication channels, IEEE Transactions on Communications, Vol. 53, No. 11, pp. 1876–1884, 2005.

    Article  Google Scholar 

  18. L. C. Wang, W. C. Liu, and Y. H. Cheng, Statisitical analysis of a mobile-to-mobile Rician fading channel model, IEEE Transactions on Vehicular Technology, Vol. 58, No. 1, pp. 32–38, 2009.

    Article  Google Scholar 

  19. A. G. Zajic, and G. L. Stuber, A new simulation model for mobile-to-mobile rayleigh fading channels, IEEE Wireless Communication Networking Conference, (WCNC’06), Apr. 2006.

Download references

Acknowledgments

This work were supported by the National Natural Science Foundation of China (No. 60762005), the Natural Science Foundation of Jiangxi Province for Youth (No. 2010GQS0153 and No. 2009GQS0070) and the Graduate Student Innovation Foundation of Jiangxi Province (No. YC10A032).

Author information

Authors and Affiliations

  1. School of Information Engineering, Nanchang University, Nanchang, 330031, China

    Yuhao Wang & Xing Xing

  2. Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, T2N 1N4, Canada

    Siyue Chen

Authors
  1. Yuhao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xing Xing
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Siyue Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuhao Wang.

Appendix I

Appendix I

1.1 Proof of Correlation Auto-Function of the In-Phase Component of the Statistical SoS Model

Proof

we first prove the (19)

$${R_{Z_{ck}Z_{ck}}(\tau)}=E[Z_{ck}(t)Z_{ck}(t+\tau)]=\frac{1}{1+K}\left\{\frac{4}{N_{0}M}E\left[\sum_{n,m=1}^{N_{0},M}{\hbox{cos}{(2\pi f_{1}t\hbox{cos}{\alpha_{nk}}+\phi_{nmk})}}{\hbox{cos}{(2\pi f_{2}t\hbox{cos}{\beta_{mk}})}}\, \cdot\,\sum_{p,q=1}^{N_{0},M}{\hbox{cos}(2\pi f_{1}(t+\tau)\hbox{cos}{\alpha_{pk}}+\phi_{pqk})}\hbox{cos}{(2\pi f_{2} (t+\tau) \hbox{cos}{\beta_{qk}})}\right]+K E\left[{\hbox{cos}{(2\pi f_{0}t+\phi_{0})}}\,\cdot\,\hbox{cos}{(2\pi f_{0}(t+\tau)+\phi_{0})}\right]+2{\sqrt{\frac{K}{N_{0}M}}} E\left[\sum_{n,m=1}^{N_{0},M}\hbox{cos}{(2\pi f_{1} t\hbox{cos}{\alpha_{nk}}+\phi_{nmk})}\hbox{cos}{(2\pi f_{2} t \hbox{cos}{\beta_{mk}})}\,\cdot\,\hbox{cos}{(2\pi f_{0}(t+\tau)+\phi_{0})}\right]+E\left[\hbox{cos}{(2\pi f_{0}t+\phi_{0})}\,\cdot\,2{\sqrt{\frac{K}{N_{0}M}}}\sum_{n,m=1}^{N_{0},M}\hbox{cos}{(2\pi f_{1}(t+\tau)\hbox{cos}{\alpha_{nk}}+\phi_{nmk})}\hbox{cos}{(2\pi f_{2}(t+\tau)\hbox{cos}{\beta_{mk}})}\right]\right\}=\frac{1}{1+K}\left\{\frac{1}{N_{0}M}E\left[\sum_{n,m=1}^{N_{0},M}\hbox{cos}{(2\pi f_{1}\tau\hbox{cos}{\alpha_{nk}})}\hbox{cos}{(2\pi f_{2}\tau\hbox{cos}{\beta_{mk}})}\right]\right\}+\frac{K}{2(1+K)}\hbox{cos}{(2\pi f_{0}\tau)}=\frac{1}{1+K}\left\{\frac{1}{N_{0}}\sum_{n=1}^{N_{0}}\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}\hbox{cos}{\left[2\pi f_{1}\tau\hbox{cos}{\left(\frac{2\pi n}{4N_{0}}+\frac{2\pi k}{4PN_{0}}+\frac{\theta-\pi}{4N_{0}}\right)}\right]}d\theta\,\cdot\,\frac{1}{M}\sum_{m=1}^{M}\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}\hbox{cos}{\left[2\pi f_{2}\tau\hbox{cos}{\left(\frac{2\pi m}{2M}+\frac{2\pi k}{2PM}+\frac{\psi-\pi}{2M}\right)}\right]}d\psi\right\}+\frac{K}{2(1+K)}\hbox{cos}{(2\pi f_{0}\tau)}=\frac{1}{1+K}\left\{\frac{1}{N_{0}}\sum_{n=1}^{N_{0}}\frac{1}{2\pi}\int\limits_{\frac{2\pi (n-1)}{4N_{0}}+\frac{2\pi k}{4PN_{0}}}^{\frac{2\pi n}{4N_{0}}+\frac{2\pi k}{4PN_{0}}}\hbox{cos}{(2\pi f_{1}\tau\hbox{cos}{\gamma_{n}})}\cdot4 N_{0}d\gamma_{n}\,\cdot\, \frac{1}{M}\sum_{n=1}^{M}\frac{1}{2\pi}\int\limits_{\frac{2\pi (m-1)}{2M}+\frac{2\pi k}{2PM}}^{\frac{2\pi M}{2M}+\frac{2\pi k}{2PM}}\hbox{cos}{(2\pi f_{2}\tau\hbox{cos}{\gamma_{m}})}\,\cdot\,2 Md\gamma_{m}\right\}+\frac{K}{2(1+K)}\hbox{cos}{(2\pi f_{0}\tau)}=\frac{1}{1+K}\left\{\frac{1}{N_{0}}\cdot\frac{1}{2\pi}\int\limits_{\frac{2\pi k}{4PN_{0}}}^{\frac{\pi}{2}+\frac{2\pi k}{4PN_{0}}}\hbox{cos}{(2\pi f_{1}\tau\hbox{cos}{\gamma_{n}})}\,\cdot\,4 N_{0}d\gamma_{n}\,\cdot\,\frac{1}{M}\cdot\frac{1}{2\pi}\int\limits_{\frac{2\pi k}{2PM}}^{\pi+\frac{2\pi k}{2PM}}\hbox{cos}{(2\pi f_{2}\tau\hbox{cos}{\gamma_{m}})}\,\cdot\,2 Md\gamma_{m}\right\}+\frac{K}{2(1+K)}\hbox{cos}{(2\pi f_{0}\tau)}=\frac{1}{1+K}\left[\frac{2}{\pi}\int\limits_{0}^{\frac{\pi}{2}}\hbox{cos}{(2\pi f_{1}\tau\hbox{cos}{\gamma_{1}})}d\gamma_{1}\cdot\frac{1}{\pi}\int\limits_{0}^{\pi}\hbox{cos}{(2\pi f_{2}\tau\hbox{cos} {\gamma_{2}})}d\gamma_{2}\right]\frac{K}{2(1+K)}\hbox{cos}{(2\pi f_{0}\tau)}=\frac{2J_{0}(2\pi f_{1}\tau)J_{0}(2\pi f_{2}\tau)+K\hbox{cos}{(2\pi f_{0}\tau)}}{2(1+K)}$$

This completes the proof of (27). Similarly, one can prove the (28) and (29), details are omitted for brevity.

1.2 Proof of Variance of Auto-Correlation of the Complex Envelope

Proof

We start with the first equality of (22) and derive

$$ {Var\{\hat{R}_{Z_{ck}Z_{ck}}(\tau)\}}=E\left[\left|\hat{R}_{Z_{ck}Z_{ck}}(\tau)-\frac{2J_{0}(2\pi f_{1}\tau)J_{0}(2\pi f_{2}\tau)+K\hbox{cos}{(2\pi f_{0}\tau)}}{2(1+K)}\right|^{2}\right]=E\left[|\hat{R}_{Z_{ck}Z_{ck}}(\tau)|^{2}\right]-\frac{J_{0}^{2}(2\pi f_{1}\tau)J_{0}^{2}(2\pi f_{2}\tau)}{(1+K)^{2}}-\left[\frac{K\hbox{cos}{2\pi f_{0}\tau}}{2(1+K)}\right]^{2}=E\left\{\frac{1}{(1+K)^{2}}\cdot\frac{1}{N_{0}^{2}M^{2}}\left[\sum_{n,m=1}^{N_{0},M}\hbox{cos}{(2\pi f_{1}\tau\hbox{cos}{\alpha_{nk}})}\hbox{cos}{(2\pi f_{2}\tau\hbox{cos}{\beta_{mk}})}\,\cdot\,\sum_{p,q=1}^{N_{0},M}\hbox{cos}{(2\pi f_{1}\tau\hbox{cos}{\alpha_{pk}})}\hbox{cos}{(2\pi f_{2}\tau\hbox{cos}{\beta_{qk}})}\right]\right\}-\frac{J_{0}^{2}(2\pi f_{1}\tau)J_{0}^{2}(2\pi f_{2}\tau)}{(1+K)^{2}}=\frac{1}{(1+K)^{2}}\cdot\frac{1}{N_{0}^{2}M^{2}}\left\{E\left[\sum_{n,m=1}^{N_{0},M}\hbox{cos}^{2}{(2\pi f_{1}\tau\hbox{cos}{\alpha_{nk}})}\hbox{cos}^{2}{(2\pi f_{2}\tau\hbox{cos}{\beta_{mk}})}\right]\,\cdot\,\sum_{n,m=1}^{N_{0},M}\sum_{p,q=1}^{N_{0},M}E\left[\hbox{cos}{(2\pi f_{1}\tau\hbox{cos}{\alpha_{nk}})}\hbox{cos}{(2\pi f_{2}\tau\hbox{cos}{\beta_{mk}})}\right] E\left[\hbox{cos}{(2\pi f_{1}\tau\hbox{cos}{\alpha_{pk}})}\quad (n\neq p \;\;\text{or}\;\;m\neq q)\,\cdot\,\hbox{cos}{(2\pi f_{2}\tau\hbox{cos}{\beta_{qk}})}\right]\right\}-\frac{J_{0}^{2}(2\pi f_{1}\tau)J_{0}^{2}(2\pi f_{2}\tau)}{(1+K)^{2}}=\frac{1}{(1+K)^{2}}\,\cdot\,\frac{1}{N_{0}^{2}M^{2}}\left\{N_{0}M\cdot\frac{1+J_{0}(4\pi f_{1}\tau)J_{0}(4\pi f_{2}\tau)}{4}+N_{0}^{2}M^{2}\left[J_{0}^{2}(2\pi f_{1}\tau)J_{0}^{2}(2\pi f_{2}\tau)-f_{c}(2\pi f_{1}\tau,2\pi f_{2}\tau)\right]\right\}-\frac{J_{0}^{2}(2\pi f_{1}\tau)J_{0}^{2}(2\pi f_{2}\tau)}{(1+K)^{2}}=\left[\frac{1+J_{0}(4\pi f_{1}\tau)J_{0}(4\pi f_{2}\tau)}{4N_{0}M}-f_{c}(2\pi f_{1}\tau, 2\pi f_{2}\tau)\right]/(1+K)^{2}$$

Similarly, we can validate the second equality of (30) and (31). Thus, we have

$$ {Var\{\hat{R}_{Z_{k}Z_{k}}(\tau)\}}=E\left[\left|\hat{R}_{Z_{k}Z_{k}}(\tau)-\frac{2J_{0}(2\pi f_{1}\tau)J_{0}(2\pi f_{2}\tau)+K\exp{(j2\pi f_{0}\tau)}}{1+K}\right|^{2}\right]=E\left[\left|2\hat{R}_{Z_{ck}Z_{ck}}(\tau)+j2\hat{R}_{Z_{ck}Z_{sk}}(\tau)-\frac{2J_{0}(2\pi f_{1}\tau)J_{0}(2\pi f_{2}\tau)}{(1+K)}-\frac{K\exp{j2\pi f_{0}\tau}}{(1+K)}\right|\right]^{2}=[\frac{1+J_{0}(4\pi f_{1}\tau)J_{0}(4\pi f_{2}\tau)}{N_{0}M}-4f_{c}(2\pi f_{1}\tau, 2\pi f_{2}\tau)]/(1+K)^{2}$$

This completes the proof.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, Y., Xing, X. & Chen, S. Extended Sum-of-Sinusoids-Based Simulation for Rician Fading Channels in Vehicular Ad Hoc Networks. Int J Wireless Inf Networks 19, 147–157 (2012). https://doi.org/10.1007/s10776-011-0167-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10776-011-0167-8

Keywords

Search

Navigation