Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Minimum Energy-per-Bit Wireless Multi-Hop Networks with Spatial Reuse

  • Bae, Chang-Hun (Electrical Engineering and Computer Science Department at the University of Michigan) ;
  • Stark, Wayne E. (Electrical Engineering and Computer Science Department at the University of Michigan)
  • Received : 2009.10.01
  • Published : 2010.04.30
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Abstract

In this paper, a tradeoff between the total energy consumption-per-bit and the end-to-end rate under spatial reuse in wireless multi-hop network is developed and analyzed. The end-to-end rate of the network is the number of information bits transmitted (end-to-end) per channel use by any node in the network that is forwarding the data. In order to increase the bandwidth efficiency, spatial reuse is considered whereby simultaneous relay transmissions are allowed provided there is a minimum separation between such transmitters. The total energy consumption-per-bit includes the energy transmitted and the energy consumed by the receiver to process (demodulate and decoder) the received signal. The total energy consumption-per-bit is normalized by the distance between a source-destination pair in order to be consistent with a direct (single-hop) communication network. Lower bounds on this energy-bandwidth tradeoff are analyzed using convex optimization methods. For a given location of relays, it is shown that the total energy consumption-per-bit is minimized by optimally selecting the end-to-end rate. It is also demonstrated that spatial reuse can improve the bandwidth efficiency for a given total energy consumption-per-bit. However, at the rate that minimizes the total energy consumption-per-bit, spatial reuse does not provide lower energy consumption-per-bit compared to the case without spatial reuse. This is because spatial reuse requires more receiver energy consumption at a given end-to-end rate. Such degraded energy efficiency can be compensated by varying the minimum separation of hops between simultaneous transmitters. In the case of equi-spaced relays, analytical results for the energy-bandwidth tradeoff are provided and it is shown that the minimum energy consumption-per-bit decreases linearly with the end-to-end distance.

Keywords

References

  1. L.-L. Xie and P. R. Kumar. "A network information theory for wireless communication: Scaling laws and optimal operation." IEEE Trans. In! Theory. vol. 50, no. 5, pp. 748-767, May 2004. https://doi.org/10.1109/TIT.2004.826631
  2. S. Verdu, "On channel capacity per unit cost," IEEE Trans. Inf. Theory, vol. 36, no. 5, pp.1019-1030, Sept. 1990. https://doi.org/10.1109/18.57201
  3. V. Rodoplu and T. H. Meng, "Bits-per-joule capacity of energy-limited wireless networks," IEEE Trans. Wireless Commun., vol. 6, no. 3, pp. 857-865, Mar. 2007. https://doi.org/10.1109/TWC.2007.05459
  4. J. Gomez-Vilardebo and A. I. Perez-Neira, "Bounds on maximum rate-per-energy for orthogonal AWGN multiple relay channels," IEEE Trans. Wireless Commun., vol. 7, no. 11, pp. 4238-4247, Nov. 2008. https://doi.org/10.1109/T-WC.2008.070486
  5. A. El Gamal, M. Mohseni, and S. Zabedi, "Bounds on capacity and minimum energy-per-bit for AWGN relay channels," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1545-1561, Apr. 2006. https://doi.org/10.1109/TIT.2006.871579
  6. M. Sikora, J. N. Laneman, M. Haenggi, D. J. Costello, and T. E. Fuja, "Bandwidth and power efficient routing in linear wireless networks," Joint Special Issue of IEEE Trans. Inf. Theory and IEEE Trans. Networking, vol. 52, pp. 2624-2633, June 2006.
  7. A. J. Goldsmith and S. B. Wicker, "Design challenges for energy-constrained ad hoc wireless networks," IEEE Wireless Commun. Mag., vol. 9,no.4,pp. 8-27,Aug. 2002. https://doi.org/10.1109/MWC.2002.1028874
  8. T. Shu, M. Krunz, and S. Vrudhula, "Joint optimization of transmission power-time and bit energy efficiency in CDMA wireless sensor networks," IEEE Trans. Wireless Commun., vol. 5, no. 3, pp. 3109-3118, Nov. 2006.
  9. S. Cui, R. Madan, A. J. Goldsmith, and S. Lall, "Cross-layer energy and delay optimization in small-scale sensor networks," IEEE Trans. Wireless Commun., vol. 6, no. 10, pp. 3688-3699, Oct. 2007 https://doi.org/10.1109/TWC.2007.060072
  10. A. Agustin and J. Vidal, "Amplify-and-forward cooperation under interference-limited spatial reuse of the relay slot," IEEE Trans. Wireless Commun., vol. 7, no. 5, pp. 1952-1962, May 2008. https://doi.org/10.1109/TWC.2008.070973
  11. O. Gurewitz, A. de Baynast, and E. K. Knightly, "Coopertative strategies and achievable rates for tree networks with optimal spatial reuse," IEEE Trans. Inf. Theory, vol. 53, no. 10, pp. 3596-3614, Oct. 2007. https://doi.org/10.1109/TIT.2007.905000
  12. C. Bae and W. E. Stark, "End-to-end energy-bandwidth tradeoff in multi-hop wireless networks," IEEE Trans. Inf. Theory, vol. 55, no. 9, pp. 4051-4066, Sept. 2009. https://doi.org/10.1109/TIT.2009.2025556
  13. R. Corless, G. Gonnet, D. Hare, D. Jeffrey, and D. Knuth, "On the Lambert-W function," Advances in Computational Mathematics, vol. 5, no. 1, pp.329-359, 1996. https://doi.org/10.1007/BF02124750
  14. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge Univ. Press, Cambridge, U.K., 2004
  15. J. G. Proakis, Digital Communications, McGraw-Hill Higher Education, 4th ed., 2000