Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지

Capacity Bounds in Random Wireless Networks

  • Babaei, Alireza (Department of Electrical and Computer Engineering, Auburn University) ;
  • Agrawal, Prathima (Department of Electrical and Computer Engineering, Auburn University) ;
  • Jabbari, Bijan (Department of Electrical and Computer Engineering, George Mason University)
  • Received : 2010.11.26
  • Accepted : 2011.08.22
  • Published : 2012.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

We consider a receiving node, located at the origin, and a Poisson point process (PPP) that models the locations of the desired transmitter as well as the interferers. Interference is known to be non-Gaussian in this scenario. The capacity bounds for additive non-Gaussian channels depend not only on the power of interference (i.e., up to second order statistics) but also on its entropy power which is influenced by higher order statistics as well. Therefore, a complete statistical characterization of interference is required to obtain the capacity bounds. While the statistics of sum of signal and interference is known in closed form, the statistics of interference highly depends on the location of the desired transmitter. In this paper, we show that there is a tradeoff between entropy power of interference on the one hand and signal and interference power on the other hand which have conflicting effects on the channel capacity. We obtain closed form results for the cumulants of the interference, when the desired transmitter node is an arbitrary neighbor of the receiver. We show that to find the cumulants, joint statistics of distances in the PPP will be required which we obtain in closed form. Using the cumulants, we approximate the interference entropy power and obtain bounds on the capacity of the channel between an arbitrary transmitter and the receiver. Our results provide insight and shed light on the capacity of links in a Poisson network. In particular, we show that, in a Poisson network, the closest hop is not necessarily the highest capacity link.

Keywords

References

  1. E. S. Sousa, "Performance of a spread spectrum packet radio network link in a Poisson field of interferers," IEEE Trans. Inf. Theory, vol. 38, no. 6, pp.1743-1754, Nov. 1992. https://doi.org/10.1109/18.165447
  2. M. Souryal, B. Vojcic, and R. Pickholtz, "Ad hoc, multihop CDMA networks with route diversity in a Rayleigh fading channel," in Proc. IEEE MILCOM, 2001, pp. 1003-1007.
  3. A. Babaei and B. Jabbari, "Interference modeling and avoidance in spectrum underlay cognitive wireless networks," in Proc. IEEE ICC, Cape Town, South Africa, May 2010, pp. 1-5.
  4. J. Venkataraman and M. Haenggi, "Optimizing the throughput in random wireless ad hoc networks," in Proc. 42nd Annual Allerton Conf. Commun. Control Comput., Oct. 2004.
  5. P. Jacquet, "Shannon capacity in Poisson wireless network model," Problems of Inf. Theory, vol. 45, no. 3, pp. 193-203, 2009.
  6. X. Yang and A. P. Petropulu, "Co-channel interference modelling and analysis in a Poisson field of interferers in wireless communications," IEEE Trans. Signal Process., vol. 51, pp. 64-76, Jan. 2003. https://doi.org/10.1109/TSP.2002.806591
  7. P. Gupta and P. R. Kumar, "The capacity of wireless networks," IEEE Trans. Inf. Theory, vol. 46, no. 2, pp.388-404, Mar. 2000. https://doi.org/10.1109/18.825799
  8. J. Fiorina and D. Domenicali, "The non validity of the Gaussian approximation for multi-user interference in ultra wide band impulse radio: From an inconvenience to an advantage," IEEE Trans. Wireless Commun., vol. 8, no. 11, pp. 5483-5488, Nov. 2009. https://doi.org/10.1109/TWC.2009.070283
  9. A. Babaei, P. Agrawal, and B. Jabbari, "Satistical shaping of interference to maximize capacity in cognitive random wireless networks," in Proc. IEEE MILCOM, San Jose, USA, 2010, pp. 123-127.
  10. A. Hasan and J. G. Andrews, "The Guard Zone in Wireless Ad hoc Networks," IEEE Trans. Wireless Commun., vol. 6, no. 3, pp. 897-906, Mar. 2007. https://doi.org/10.1109/TWC.2007.04793
  11. K. Gulati, B. L. Evans, J. G. Andrews, and K. R. Tinsely, "Statistics of cochannel interference in a field of Poisson and Poisson-Poisson clustered interferers," IEEE Trans. Signal Process., vol. 58, no. 12, Dec. 2010.
  12. A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes. 4th ed., McGraw-Hill, 2002.
  13. Wolfram alpha: Computational knowledge engine. [Online]. Available: http://www.wolframalpha.com
  14. A. Babaei and B. Jabbari, "Distance distribution of bivariate Poisson network nodes," IEEE Commun. Lett., vol. 14, no. 9, pp. 848-850, Sept. 2010. https://doi.org/10.1109/LCOMM.2010.080610.100668
  15. M. Haengi, "On distances in uniformly random networks," IEEE Trans. Inf. Theory, vol. 51, no. 10, pp. 3584-3586, Oct. 2005. https://doi.org/10.1109/TIT.2005.855610
  16. M. G. Kendall and A. Stuart, The Advanced Theory of Statistics. vol. 1, 3rd ed., Griffin, London, 1979.
  17. X. Liu and M. Haenggi, "Throughput analysis of fading sensor networks with regular and random topologies," EURASIP J. Wireless Commun. Netw., pp. 554-564, Sept. 2005.
  18. R. Mathar and J. Mattfeldt, "On the distribution of cumulated interference power in Rayleigh fading channels," Wireless Netw., vol. 1, no. 1, pp. 31-36, 1995. https://doi.org/10.1007/BF01196256
  19. A. Dembo, T. Cover, and J. A. Thomas, "Information theoretic inequalities," IEEE Tran. Inf. Theory, vol. 37, no. 6, pp. 1501-1518, Nov. 1991. https://doi.org/10.1109/18.104312
  20. A. Hyvarinen, J. Karhunen, and E. Oja, Independent Component Analysis. John Wiley, 2001.
  21. J. F. C. Kingman, Poisson Processes. Oxford University Press, 1993.
  22. R. A. Askey and R. Roy, Beta function. NIST Handbook of Mathematical Functions, Cambridge University Press, 2010.
  23. S. Ihara, "On the capacity of channels with additive non-Gaussian noise," Inf. Control, vol. 37, pp. 34-39, 1978. https://doi.org/10.1016/S0019-9958(78)90413-8
  24. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. Dover, 1972.