Skip to main content


We’d like to understand how you use our websites in order to improve them. Register your interest.

Distributed Time Synchronization in Wireless Sensor Networks with Coupled Discrete-Time Oscillators


In wireless sensor networks, distributed timing synchronization based on pulse-coupled oscillators at the physical layer is currently being investigated as an interesting alternative to packet synchronization. In this paper, the convergence properties of such a system are studied through algebraic graph theory, by modeling the nodes as discrete-time clocks. A general scenario where clocks may have different free-oscillation frequencies is considered, and both time-invariant and time-variant network topologies (or fading channels) are discussed. Furthermore, it is shown that the system of oscillators can be studied as a set of coupled discrete-time PLLs. Based on this observation, a generalized system design is discussed, and it is proved that known results in the context of conventional PLLs for carrier acquisition have a counterpart in distributed systems. Finally, practical details of the implementation of the distributed synchronization algorithm over a bandlimited noisy channel are covered.



  1. 1.

    Sivrikaya F, Yener B: Time synchronization in sensor networks: a survey. IEEE Network 2004,18(4):45-50. 10.1109/MNET.2004.1316761

  2. 2.

    Hong Y-W, Scaglione A: A scalable synchronization protocol for large scale sensor networks and its applications. IEEE Journal on Selected Areas in Communications 2005,23(5):1085-1099.

  3. 3.

    Mirollo RE, Strogatz SH: Synchronization of pulse-coupled biological oscillators. SIAM Journal on Applied Mathematics 1990,50(6):1645-1662. 10.1137/0150098

  4. 4.

    Lucarelli D, Wang I-J: Decentralized synchronization protocols with nearest neighbor communication. Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems (SenSys '04), November 2004, Baltimore, Md, USA 62-68.

  5. 5.

    Godsil C, Royle G: Algebraic Graph Theory. Springer, New York, NY, USA; 2001.

  6. 6.

    Werner-Allen G, Tewari G, Patel A, Welsh M, Nagpal R: Firefly-inspired sensor network synchronicity with realistic radio effects. Proceedings of the 3rd International Conference on Embedded Networked Sensor Systems (SenSys '05), November 2005, San Diego, Calif, USA 142-153.

  7. 7.

    Hu A-S, Servetto SD: On the scalability of cooperative time synchronization in pulse-connected networks. IEEE Transactions on Information Theory 2006,52(6):2725-2748.

  8. 8.

    Hong Y-W, Scaglione A: Distributed change detection in large scale sensor networks through the synchronization of pulse-coupled oscillators. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 3: 869-872.

  9. 9.

    Barbarossa S, Celano F: Self-organizing sensor networks designed as a population of mutually coupled oscillators. Proceedings of the 6th IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC '05), June 2005, New York, NY, USA 475-479.

  10. 10.

    Wakamiya N, Murata M: Scalable and robust scheme for data fusion in sensor networks. Proceedings of the 1st International Workshop on Biologically Inspired Approaches to Advanced Information Technology (Bio-ADIT '04), January 2004, Lausanne, Switzerland 412-427.

  11. 11.

    Tong F, Akaiwa Y: Theoretical analysis of interbase-station synchronization systems. IEEE Transactions on Communications 1998,46(5):590-594. 10.1109/26.668726

  12. 12.

    Sourour E, Nakagawa M: Mutual decentralized synchronization for intervehicle communications. IEEE Transactions on Vehicular Technology 1999,48(6):2015-2027. 10.1109/25.806794

  13. 13.

    Olfati-Saber R, Murray RM: Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 2004,49(9):1520-1533. 10.1109/TAC.2004.834113

  14. 14.

    Moreau L: Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control 2005,50(2):169-182.

  15. 15.

    Lindsey WC, Ghazvinian F, Hagmann WC, Dessouky K: Network synchronization. Proceedings of the IEEE 1985,73(10):1445-1467.

  16. 16.

    Rappaport TS: Wireless Communications: Principles and Practice. Prentice-Hall, Upper Saddle River, NJ, USA; 2001.

  17. 17.

    Xiao L, Boyd S, Kim S-J: Distributed average consensus with least-mean-square deviation. Journal of Parallel and Distributed Computing 2007,67(1):33-46. 10.1016/j.jpdc.2006.08.010

  18. 18.

    Horn RA, Johnson CR: Matrix Analysis. Cambridge University Press, Cambridge, UK; 1985.

  19. 19.

    Zhang X-D, Luo R: Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices. Czechoslovak Mathematical Journal 2002,52(3):537-544. 10.1023/A:1021771612003

  20. 20.

    Veeravalli VV: Decentralized quickest change detection. IEEE Transactions on Information Theory 2001,47(4):1657-1665. 10.1109/18.923755

  21. 21.

    Norris JR: Markov Chains. Cambridge University Press, Cambridge, UK; 1998.

  22. 22.

    Elaydi SN: An Introduction to Difference Equations. Springer, New York, NY, USA; 1999.

  23. 23.

    Scutari G, Barbarossa S, Pescosolido L: Optimal decentralized estimation through self-synchronizing networks in the presence of propagation delays. Proceedings of the 7th IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC '06), July 2006, Cannes, France 1-5.

  24. 24.

    Meyr H, Moeneclaey M, Fechtel SA: Digital Communication Receivers. John Wiley & Sons, New York, NY, USA; 1998.

  25. 25.

    Gardner FM: Phaselock Techniques. John Wiley & Sons, New York, NY, USA; 1966.

  26. 26.

    Simeone O, Spagnolini U, Bar-Ness Y: "Small-world" effect of shadowing in pulse-couple distributed time synchronization. IEEE Communications Letters 2007,11(3):282-284.

Download references

Author information



Corresponding author

Correspondence to O. Simeone.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Simeone, O., Spagnolini, U. Distributed Time Synchronization in Wireless Sensor Networks with Coupled Discrete-Time Oscillators. J Wireless Com Network 2007, 057054 (2007).

Download citation


  • Wireless Sensor Network
  • Generalize System
  • Network Topology
  • Fading Channel
  • Convergence Property