Skip to main content

Advertisement

Log in

A Stochastic Geometry Approach to the Energy Load of Relaying in Large-Scale Wireless Networks

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

Multi-hop relaying divides a long radio link into multiple short radio links and thus may reduce the overall energy consumption in wireless networks. But using relaying imposes additional energy load at intermediate relays, the characterization of which is of fundamental interest. In this paper, we propose a novel stochastic geometric model to investigate the energy load of relaying in a random large-scale wireless network. We introduce a notion of relay selection window, defined as the range in which a helping relay is searched for a typical source-destination pair. Under the proposed model, we derive closed form expressions to characterize the dependency of the energy load of relaying on relay selection window and several other key network parameters. The results may have practical implications in the design of wireless networks.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Li, G. Y., Xu, Z., Xiong, C., Yang, C., Zhang, S., Chen, Y., et al. (2011). Energy-efficient wireless communications: Tutorial, survey, and open issues. IEEE Wireless Communications, 18(6), 28–35.

    Article  Google Scholar 

  2. Andrews, J. G., Buzzi, S., Choi, W., Hanly, S., Lozano, A., Soong, A., et al. (2014). What will 5G be? IEEE Journal on Selected Areas in Communications, 32(6), 1065–1082.

    Article  Google Scholar 

  3. Pabst, R., Walke, B. H., Schultz, D. C., Herhold, P., Yanikomeroglu, H., Mukherjee, S., et al. (2004). Relay-based deployment concepts for wireless and mobile broadband radio. IEEE Communications Magazine, 42(9), 80–89.

    Article  Google Scholar 

  4. Wei, N., Lin, X., & Zhang, Z. (2016). Optimal relay probing in millimeter wave cellular systems with device-to-device relaying. IEEE Transactions on Vehicular Technology, 99, 1.

    Google Scholar 

  5. Le, L., & Hossain, E. (2007). Multihop cellular networks: Potential gains, research challenges, and a resource allocation framework. IEEE Communications Magazine, 45(9), 66–73.

    Article  Google Scholar 

  6. Gozalvez, J., & Coll-Perales, B. (2013). Experimental evaluation of multihop cellular networks using mobile relays. IEEE Communications Magazine, 51(7), 122–129.

    Article  Google Scholar 

  7. Drucker, E. H. (1988) Development and application of a cellular repeater. In Proceedings of IEEE VTC (pp. 321–325).

  8. Laneman, J. N., Tse, D. N., & Wornell, G. W. (2004). Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Transactions on Information Theory, 50(12), 3062–3080.

    Article  MathSciNet  MATH  Google Scholar 

  9. Kramer, G., Gastpar, M., & Gupta, P. (2005). Cooperative strategies and capacity theorems for relay networks. IEEE Transactions on Information Theory, 51(9), 3037–3063.

    Article  MathSciNet  MATH  Google Scholar 

  10. Shan, H., Zhuang, W., & Wang, Z. (2009). Distributed cooperative MAC for multihop wireless networks. IEEE Communications Magazine, 47(2), 126–133.

    Article  Google Scholar 

  11. Bletsas, A., Khisti, A., Reed, D. P., & Lippman, A. (2006). A simple cooperative diversity method based on network path selection. IEEE Journal on Selected Areas in Communications, 24(3), 659–672.

    Article  Google Scholar 

  12. Zhou, Y., Liu, J., Zheng, L., Zhai, C., & Chen, H. (2011). Link-utility-based cooperative MAC protocol for wireless multi-hop networks. IEEE Transactions on Wireless Communications, 10(3), 995–1005.

    Article  Google Scholar 

  13. Zhai, C., Liu, J., Zheng, L., & Xu, H. (2009). Lifetime maximization via a new cooperative MAC protocol in wireless sensor networks. In Proceedings of IEEE GLOBECOM (pp. 1–6).

  14. Marchenko, N., Yanmaz, E., Adam, H. & Bettstetter, C. (2009). “Selecting a spatially efficient cooperative relay. In Proceedings of IEEE GLOBECOM (pp. 1–7).

  15. Yang, Y., Hu, H., Xu, J., & Mao, G. (2009). Relay technologies for WiMAX and LTE-advanced mobile systems. IEEE Communications Magazine, 47(10), 100–105.

    Article  Google Scholar 

  16. Lin, X., Andrews, J. G., Ghosh, A., & Ratasuk, R. (2014). An overview of 3GPP device-to-device proximity services. IEEE Communications Magazine, 52(4), 40–48.

    Article  Google Scholar 

  17. Sun, C., & Yang, C. (2012). Energy efficiency analysis of one-way and two-way relay systems. EURASIP Journal on Wireless Communications and Networking, 2012(1), 1–18.

    Article  Google Scholar 

  18. Ahmed, M. H. U., Razzaque, M. A., & Hong, C. S. (2013). DEC-MAC: Delay-and energy-aware cooperative medium access control protocol for wireless sensor networks. Annals of Telecommunications, 68(9–10), 485–501.

    Article  Google Scholar 

  19. Huang, R., Feng, C., & Zhang, T. (2013). On the design of energy efficient transmission in cooperative networks with bidirectional asymmetric traffic. Wireless Personal Communications, 72(3), 1707–1722.

    Article  Google Scholar 

  20. Fang, H., Lin, X., & Lok, T. M. (2012). Power allocation for multiuser cooperative communication networks under relay-selection degree bounds. IEEE Transactions on Vehicular Technology, 61(7), 2991–3001.

    Article  Google Scholar 

  21. Alves, H., Brante, G., Souza, R. D., & Rebelatto, J. L. (2012). Energy efficiency and throughput performance of power and rate allocation on incremental decode-and-forward relaying. Wireless Networks, 18(5), 495–505.

    Article  Google Scholar 

  22. Nomikos, N., Skoutas, D. N., Vouyioukas, D., Verikoukis, C., & Skianis, C. (2014). Capacity maximization through energy-aware multi-mode relaying. Wireless Personal Communications, 74(1), 83–99.

    Article  Google Scholar 

  23. Baccelli, F., & Blaszczyszyn, B. (2009). Stochastic geometry and wireless networks—Part I: Theory. Hanover, MA: Now Publishers Inc.

    MATH  Google Scholar 

  24. Gilbert, E. N. (1961). Random plane networks. Journal of the Society for Industrial and Applied Mathematics, 9(4), 533–543.

    Article  MathSciNet  MATH  Google Scholar 

  25. Takagi, H., & Kleinrock, L. (1984). Optimal transmission ranges for randomly distributed packet radio terminals. IEEE Transactions on Communications, 32(3), 246–257.

    Article  Google Scholar 

  26. Kleinrock, L., & Silvester, J. (1987). Spatial reuse in multihop packet radio networks. Proceedings of the IEEE, 75(1), 156–167.

    Article  Google Scholar 

  27. Zorzi, M., & Pupolin, S. (1995). Optimum transmission ranges in multihop packet radio networks in the presence of fading. IEEE Transactions on Communications, 43(7), 2201–2205.

    Article  Google Scholar 

  28. Baccelli, F., Klein, M., Lebourges, M., & Zuyev, S. (1997). Stochastic geometry and architecture of communication networks. Telecommunication Systems, 7(1–3), 209–227.

    Article  Google Scholar 

  29. Ilow, J., & Hatzinakos, D. (1998). Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers. IEEE Transactions on Signal Processing, 46(6), 1601–1611.

    Article  Google Scholar 

  30. Sousa, E. S. (1992). Performance of a spread spectrum packet radio network link in a Poisson field of interferers. IEEE Transactions on Information Theory, 38(6), 1743–1754.

    Article  MATH  Google Scholar 

  31. Jindal, N., Weber, S., & Andrews, J. G. (2008). Fractional power control for decentralized wireless networks. IEEE Transactions on Wireless Communications, 7(12), 5482–5492.

    Article  Google Scholar 

  32. Govindasamy, S., Bliss, D. W., & Staelin, D. H. (2007). Spectral efficiency in single-hop ad-hoc wireless networks with interference using adaptive antenna arrays. IEEE Journal on Selected Areas in Communications, 25(7), 1358–1369.

    Article  Google Scholar 

  33. Hunter, A. M., Andrews, J. G., & Weber, S. (2008). Transmission capacity of ad hoc networks with spatial diversity. IEEE Transactions on Wireless Communications, 7(12), 5058–5071.

    Article  Google Scholar 

  34. Baccelli, F., Blaszczyszyn, B., & Muhlethaler, P. (2006). An Aloha protocol for multihop mobile wireless networks. IEEE Transactions on Information Theory, 52(2), 421–436.

    Article  MathSciNet  MATH  Google Scholar 

  35. Nguyen, H. Q., Baccelli, F., Kofman, D. (2007). A stochastic geometry analysis of dense IEEE 802.11 networks. In Proceedings of IEEE INFOCOM (pp. 1199–1207).

  36. Brown, T. X. (2000). Cellular performance bounds via shotgun cellular systems. IEEE Journal on Selected Areas in Communications, 18(11), 2443–2455.

    Article  Google Scholar 

  37. Andrews, J. G., Baccelli, F., & Ganti, R. (2011). A tractable approach to coverage and rate in cellular networks. IEEE Transactions on Communications, 59(11), 3122–3134.

    Article  Google Scholar 

  38. Lin, X., Ganti, R., Fleming, P., & Andrews, J. (2013). Towards understanding the fundamentals of mobility in cellular networks. IEEE Transactions on Wireless Communications, 12(4), 1686–1698.

    Article  Google Scholar 

  39. Novlan, T. D., Dhillon, H. S., & Andrews, J. G. (2013). Analytical modeling of uplink cellular networks. IEEE Transactions on Wireless Communications, 12(6), 2669–2679.

    Article  Google Scholar 

  40. Madhusudhanan, P., Restrepo, J. G., Liu, Y. E., Brown, T. X., & Baker, K. R. (2012). Stochastic ordering based carrier-to-interference ratio analysis for the shotgun cellular systems. IEEE Wireless Communications Letters, 1(6), 565–568.

    Article  Google Scholar 

  41. Yu, S. M., Kim, S.-L. (2013). Downlink capacity and base station density in cellular networks. In Proceedings of International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt) (pp. 119–124).

  42. Lin, X., Ratasuk, R., Ghosh, A., & Andrews, J. G. (2014). Modeling, analysis and optimization of multicast device-to-device transmissions. IEEE Transactions on Wireless Communications, 13(8), 4346–4359.

    Article  Google Scholar 

  43. Akoum, S., & Heath, R. W. (2013). Interference coordination: Random clustering and adaptive limited feedback. IEEE Transactions on Signal Processing, 61(7), 1822–1834.

    Article  MathSciNet  Google Scholar 

  44. Zhai, C., Zhang, W., & Mao, G. (2012). Uncoordinated cooperative communications with spatially random relays. IEEE Transactions on Wireless Communications, 11(9), 3126–3135.

    Article  Google Scholar 

  45. Srinivasa, S., & Haenggi, M. (2014). Combining stochastic geometry and statistical mechanics for the analysis and design of mesh networks. Ad Hoc Networks, 13, 110–122.

    Article  Google Scholar 

  46. Lu, W., & Di Renzo, M. (2015). Stochastic geometry modeling and system-level analysis and optimization of relay-aided downlink cellular networks. IEEE Transactions on Communications, 63(11), 4063–4085.

    Article  Google Scholar 

  47. Lin, X., & Andrews, J. G. (2015). Connectivity of millimeter wave networks with multi-hop relaying. IEEE Wireless Communications Letters, 4(2), 209–212.

    Article  Google Scholar 

  48. Baek, S. J., & de Veciana, G. (2007). Spatial energy balancing through proactive multipath routing in wireless multihop networks. IEEE/ACM Transactions on Networking, 15(1), 93–104.

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank the anonymous reviewers for their valuable comments and suggestions, which helped improve the quality of the paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ning Wei.

Additional information

This research was supported in part by National Natural Science Foundation of China (Grant No. 61101092, 61571003), National Science and Technology Major Project of China (Grant No. 2012ZX03001003-003), Fundamental Research Funds for the Central Universities (Grant No. ZYGX2015J014) and National High-tech R&D Program of China (863 Program Grant No. 2014AA01A706).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, N., Liao, F. & Zhang, Z. A Stochastic Geometry Approach to the Energy Load of Relaying in Large-Scale Wireless Networks. Wireless Pers Commun 95, 1249–1263 (2017). https://doi.org/10.1007/s11277-016-3827-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-016-3827-2

Keywords

Navigation