This paper studies the influence of shadowing on the statistical properties of the channel capacity. The problem is addressed by using a Suzuki process as an appropriate statistical channel model for land mobile terrestrial channels. Using this model, exact solutions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity are derived. The results are studied for different levels of shadowing, corresponding to different terrestrial environments. It is observed that the shadowing effect has a significant influence on the variance and the maximum value of the PDF and LCR of the channel capacity, but it has almost no impact on the mean capacity of the channel. The correctness of the theoretical results is confirmed by simulation using a stochastic channel simulator based on the sum-of-sinusoids principle.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Holter, B. (2001). On the capacity of the MIMO channel—a tutorial introduction. In Proc. IEEE Norwegian Symposium on Signal Processing, Trondheim, Norway, Oct. 2001, pp. 167–172.
Hogstad, B. O., & Pätzold, M. (2007). Exact closed-form expressions for the distribution, level-crossing rate, and average duration of fades of the capacity of MIMO channels. In Proc. 65th IEEE Veh. Technol. Conf., VTC 2007-Spring. Dublin, Ireland, Apr. 2007, pp. 455–460.
Giorgetti A., Smith P.J., Shafi M. and Chiana M. (2003). MIMO capacity, level crossing rates and fades: The impacts of spatial/temporal channel correlation. Journal of Communications and Networks 5(2): 104–115
Hogstad, B. O., & Pätzold, M. (2004). Capacity studies of MIMO models based on the geometrical one-ring scattering model. In Proc. 15th IEEE Int. Symp. on Personal, Indoor and Mobile Radio Communications, PIMRC 2004, Vol. 3. Barcelona, Spain, Sep. 2004, pp. 1613–1617.
Young W.R. (1968). Characteristics of small-area signal fading on mobile circuits in the 150 MHz band. IEEE Transactions on Vehicular Technology 17: 24–30
Nylund H.W. (1952). Comparison of mobile radio transmission at 150, 450, 900 and 3700 MHz. Bell System Technical Journal, 31: 1068–1085
Okumura Y., Ohmori E., Kawano T. and Fukuda K. (1968). Field strength and its variability in VHF and UHF land mobile radio services. Review of the Electrical Communications Laboratories 16: 825–873
Jakes, W. C. (Ed.). (1993). Microwave mobile communicaitons. IEEE Press, Piscataway, NJ
Gudmundson M. (1991). Correlation model for shadow fading in mobile radio systems. Electronics Letters 27(23): 2145–2146
Black D.M. and Reudink D.O. (1972). Some characteristics of mobile radio propagation at 836 MHz in the Philadelphia area. IEEE Transactions on Vehicular Technology 21: 45–51
Reudink D.O. (1972). Comparison of radio transmission at X-band frequencies in suburban and urban areas. IEEE Transactions on Antennas and Propagation 20: 470–473
Ibrahim M.F. and Parsons J.D. (1983). Signal strength prediction in built-up areas. Proceedings of the IEEE 130(5): 377–384
Pätzold M., Killat U. and Laue F. (1998). An extended Suzuki model for land mobile satellite channels and its statistical properties. IEEE Transactions on Vehicular Technology 47(2): 617–630
Suzuki, H. (1977). A statistical model for urban radio propagation. IEEE Transactions on Communications, COM-25(7), 673–680.
Smith P.J., Garth L.M. and Loyka S. (2003). Exact capacity distributions for MIMO systems with small numbers of antennas. IEEE Communications Letters 7(10): 481–483
Ge, H., Wong, K. D., Barton, M., & Liberti, J. C. (2002). Statistical characterization of multiple-input multiple-output (MIMO) channel capacity. In Proc. IEEE Wireless Communications and Networking Conference, WCNC 2002, Vol. 2. Florida, USA, Mar. 2002, pp. 789–793.
Pätzold, M., & Yang, K. (2006). An exact solution for the level-crossing rate of shadow fading processes modelled by using the sum-of-sinusoids principle. In Proc. 9th Int. Symp. on Wireless Personal Multimedia Communications, WPMC 2006. San Diego, USA, Sep. 2006, pp. 188–193.
Papoulis A. and Pillai S. U. (2002). Probability, random variables and stochastic processes. (4th ed.). McGraw-Hill, New York
Foschini G.H. and Gans M.J. (1998). On limits of wireless communications in a fading environment when using multiple antennas. Wireless Personal Communications 6: 311–335
Pätzold M. (2002). Mobile fading channels. Wiley, Chichester
Pätzold, M., & Hogstad, B. O. (2006). Two new methods for the generation of multiple uncorrelated Rayleigh fading waveforms. In Proc. 63rd IEEE Semiannual Vehicular Technology Conference, IEEE VTC 2006-Spring, Vol. 6. Melbourne, Australia, May 2006, pp. 2782–2786.
The material in this paper is based on “The Impact of Shadowing on the Capacity of Mobile Fading Channels”, by Gulzaib Rafiq and Matthias Pätzold which appeared in the proceedings of 4th IEEE International Symposium on Wireless Communication Systems, ISWCS 2007, Trondheim, Norway, October 2007. © 2007 IEEE.
About this article
Cite this article
Rafiq, G., Pätzold, M. A Study of the Influence of Shadowing on the Statistical Properties of the Capacity of Mobile Radio Channels. Wireless Pers Commun 50, 5–18 (2009). https://doi.org/10.1007/s11277-008-9545-7
- Land mobile terrestrial channels
- Channel capacity
- Shadowing effects
- Lognormal process
- Suzuki process
- Level-crossing rate
- Average duration of fades