Authors A.O. Pasiuk, E.S. Semenov, S.V. Galich, E.E. Arepyeva
Month, Year 05, 2017 @en
Index UDC 621.391.6
Abstract In the modeling of wireless communication systems, it is necessary to take into account a large number of different parameters, including aspects of the physical transmission medium. When transmitting signals through a wireless environment, the signal is affected by a variety of factors, such as signal attenuation, reflection from moving and stationary objects, signal power dissipation, Doppler effect in case of a receiver and / or transmitter movement, etc. In order to take into account all these factors in modeling, it is necessary to imagine how they affect the signal in a real environment. Therefore, the construction of models of wireless multipath channels (regardless of the transmission technology) is an actual task for the study. In this paper we consider the models of multipath channels with fading, distributed according to the Rayleigh law, on the basis of the Jakes model and the method of filtering a Gaussian random variable with correct statistical properties. These models are implemented in the Jupyter Notebook environment in the Python programming language. The expediency of using a model based on the Gaussian filtering for the generation of complex channel coefficients for wireless Rayleigh channels with fading is shown.. The developed models make it possible to obtain samples of complex channel coefficients with correct statistical properties (average, autocorrelation, cross-correlation of real and imaginary parts of complex channel coefficients), taking into account the set of input parameters: sampling frequency, maximum Doppler shift, simulation time, channel power delay profile.

Download PDF

Keywords Rayleigh fading; multipath propagation; Jakes spectrum; wireless channel modeling; com-plex channel gain.
References 1. Technical specification 3GPP TS 36.101 version 13.6.1 Release 13. LTE; Evolved Universal Terrestrial Radio Access (E-UTRA); User Equipment (UE) radio transmission and reception. ETSI.
2. Sagari S., Trappe W., Greenstein L. Equivalent Tapped Delay Line Channel Responses with Reduced Taps, Vehicular Technology Conference (VTC Fall), 2013, No. 78, pp. 1-5.
3. Parsons J.D. The Mobile radio propagation channel, Second Edition. John Wiley & Sons Ltd. 2000, 436 p.
4. Svyaz' s podvizhnymi ob"ektami v diapazone SVCh [Communication with mobile objects in the range microwave], ed. by U.K. Dzheyksa: translated from English, ed. By M.S. Yarlykova, M.V. Chernyakova. Moscow: Svyaz', 1979, 520 p.
5. Bello P.A. Characterization of randomly time-variant linear channels, IEEE Trans. on Commun, 1963, Vol. 11, No. 4, pp. 360-393.
6. Turin G.L. Introduction to spread-spectrum antimultipath techniques and their application to urban digital radio, IEEE Proc., 1980, Vol. 68, No. 3, pp. 328-353.
7. Hoeher P. A statistical discrete-time model for the WSSUS multipath channel, Vehicular Technology, IEEE Transactions on, 1992, Vol. 41, No. 4, pp. 461-468.
8. Prokis Dzh. Tsifrovaya svyaz' [Digital communication]: translated from English, ed. by
D.D. Klovskogo. Moscow: Radio i svyaz', 2000, 800 p.
9. Gans M.J. A power-spectral theory of propagation in the mobile-radio environment, IEEE transactions on vehicular technology, 1972, No. 1, pp. 27-38.
10. Clarke R.H. A statistical theory of mobile-radio reception, Bell System Technical Journal, 1968, No. 47, pp. 957-1000.
11. Pop M.F., Beaulieu N.C. Limitations of sum-of-sinusoids fading channel simulators, IEEE Transactions on Communications, 2001, No. 49, pp. 699-708.
12. Zheng Y., Xiao C. Simulation models with correct statistical properties for Rayleigh fading channels, IEEE Transactions on Communications, 2003, No. 6, pp. 920-928.
13. Silva V.A., Abrao T. Statistically correct simulation models for the generation of multiple un-correlated Rayleigh fading waveforms, Eighth IEEE International Symposium on Spread Spec-trum Techniques and Applications - Programme and Book of Abstracts, pp. 472-476.
14. Smith J.I. A computer generated multipath fading simulation for mobile radio, IEEE Transac-tions on Vehicular Technology, 1975, No. 3, pp. 39-40.
15. Mfeze M., Tonye E. Comparative Approach of Doppler Spectra for Fading Channel Modelling by the Filtered White Gaussian Noise Method, International Journal of Computer Science and Telecommunications, 2015, Vol. 6, No. 11, pp. 1-12.
16. Yong Soo Cho, Jaekwon Kim, Won Young Yang, Chung G. Kang. MIMO-OFDM wireless communications with MATLAB. Wiley-IEEE Press. 2010, 544 p.
17. Project Jupyter. Available at: (Accessed 06 Marhc 2017).
18. Documentation – Available at: (Accessed 06 Marhc 2017).
19. Overview – NumPy v1.12 Manual. Available at: (Accessed 06 Marhc 2017).
20. Clarke R.H. A Statistical Theory of Mobile-Radio Reception, Bell System Technical Journal, 1968, Vol. 47, No. 6, pp. 957-1000.

Comments are closed.