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A new complexity metric for FH/SS sequences using fuzzy entropy

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Abstract

This paper presents a new complexity metric to evaluate the unpredictability of a frequency-hopping/spread-spectrum (FH/SS) sequence based on fuzzy entropy (FuzzyEn). According to the property of the FS/SS sequence, the definition of a fuzzy membership function for a complexity metric is presented and a basic theorem for FuzzyEn complexity is proved. Simulation and analytical results show that the proposed FuzzyEn works and can effectively discern the changing complexities of the FH/SS sequences, which are compared with a complexity metric based on approximate entropy (ApEn). The FuzzyEn scheme has obvious advantages in robustness to resolution parameters and sensitivity to vector dimensions.

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References

  1. Kumar P V. Frequency hopping code sequence designs having large linear span. IEEE Trans Inf Theory, 1988, 34: 146–151

    Article  Google Scholar 

  2. Park S B, Lee K E, Choi Y K. Some good frequency hopping sequences with arbitrary number of slots. In: Proc IEEE MILCOM, Washington DC, USA, 2001. 1325–1329

  3. Heidari-Bateni G, McGillem C D. A chaotic direct-sequence spread-spectrum communication system. IEEE Trans Commun, 1994, 42: 1524–1527

    Article  Google Scholar 

  4. Wang H X, Yu J B. A new cipher quasi-chaotic frequency hopping sequence for FH/CDMA communications. In: Proceedings of IEEE International Conference on Communications, Circuits and Systems and West Sino Expositions, Xi’an, China, 2002. 497–501

  5. Li Z, Chang Y L, Jin L J. A novel family of frequency hopping sequences for multi-hop Bluetooth networks. IEEE Trans Consum Electron, 2003, 49: 1084–1089

    Article  Google Scholar 

  6. Li Z, Chang Y L, Jin L J, et al. Analysis of FHMA performance on block cipher based frequency hopping sequences. IEEE Commun lett, 2004, 8: 434–436

    Article  Google Scholar 

  7. Li Z, Cai J P, Chang Y L. Determining the complexity of FH/SS sequence by approximate entropy. IEEE Trans Commun, 2009, 57: 812–820

    Article  Google Scholar 

  8. Rizomiliotis P, Kalouptsidis N. Results on the nonlinear span of binary sequences. IEEE Trans Inf Theory, 2005, 51: 1555–1563

    Article  MathSciNet  Google Scholar 

  9. Xiao G Z, Wei S M, Lam K Y, et al. A fast algorithm for determining the linear complexity of a sequence with period pn over GF(q). IEEE Trans Inf Theory, 2000, 46: 2203–2206

    Article  MATH  MathSciNet  Google Scholar 

  10. Kolokotronis N, Kalouptsidis N. On the linear complexity of nonlinear filtered PN-sequences. IEEE Trans Inf Theory, 2003, 49: 3047–3059

    Article  MathSciNet  Google Scholar 

  11. Griffin F, Shparlinski I E. On the linear complexity profile of the power generator. IEEE Trans Inf Theory, 2000, 46: 2159–2162

    Article  MATH  MathSciNet  Google Scholar 

  12. Gutierrez J, Shparlinski I E, Winterhof A. On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators. IEEE Trans Inf Theory, 2003, 49: 60–64

    Article  MATH  MathSciNet  Google Scholar 

  13. Kurosawa K, Sato F, Sakata T, et al. A relationship between linear complexity and k-error linear complexity. IEEE Trans Inf Theory, 2000, 46: 694–698

    Article  MATH  MathSciNet  Google Scholar 

  14. Lauder A G B, Paterson K G. Computing the error linear complexity spectrum of a binary sequence of period 2n. IEEE Trans Inf Theory, 2003, 49: 273–280

    Article  MATH  MathSciNet  Google Scholar 

  15. Li Z, Chang Y L, Jin L J. A novel family of frequency hopping sequences for multi-hop Bluetooth networks. IEEE Trans Consum Electron, 2003, 49: 1084–1089

    Article  Google Scholar 

  16. Li Z, Chang Y L, Jin L J, et al. Analysis of FHMA performance on block cipher based frequency hopping sequences. IEEE Commun Lett, 2004, 8: 434–436

    Article  Google Scholar 

  17. Liang M. The performance analysis of chaotic frequency-hopping sequences. J Electron Inf Technol, 2005, 27: 1741–1744

    Google Scholar 

  18. Ling C, Sun S G. Chaotic frequency hopping sequences. IEEE Trans Commun, 1998, 46: 1433–1437

    Article  Google Scholar 

  19. Li Z, Cai J P, Chang Y L. Determining the complexity of FH/SS sequence by approximate entropy. IEEE Trans Commun, 2009, 57: 812–820

    Article  Google Scholar 

  20. Pincus S M. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci USA, 1991, 88: 2297–2301

    Article  MATH  MathSciNet  Google Scholar 

  21. Lempel A, Ziv J. On the complexity of finite sequences. IEEE Trans Inf Theory, 1976, 22: 75–81

    Article  MATH  MathSciNet  Google Scholar 

  22. Hu B Q. Fundamentals of Fuzzy Theory (in Chinese). Wuhan: Wuhan University Press, 2004. 1–5, 103–116

    Google Scholar 

  23. Chen W T, Wang Z Z, Xie H B, et al. Characterization of surface EMG signal based on fuzzy entropy. IEEE Trans Neur Syst Reh Eng, 2007, 15: 266–272

    Article  Google Scholar 

  24. Ling C, Sun S G. Chaotic frequency hopping sequences. IEEE Trans Commun, 1998, 46: 1433–1437

    Article  Google Scholar 

  25. Xiao J H, Hu G, Qu Z L. Synchronization of spatiotemporal chaos and its application to multichannel spread spectrum communication. Phys Rev Lett, 1996, 77: 4162–4165

    Article  Google Scholar 

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Authors and Affiliations

  1. The State Key Laboratory of Integrated Service Networks (ISN), Xidian University, Xi’an, 710071, China

    XiaoJun Chen, JiangBo Si, Zan Li & BaoMing Bai

  2. The School of Microelectronics, Xidian University, Xi’an, 710071, China

    JuePing Cai

Authors
  1. XiaoJun Chen
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  2. JiangBo Si
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  3. Zan Li
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  4. JuePing Cai
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  5. BaoMing Bai
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Correspondence to Zan Li.

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Chen, X., Si, J., Li, Z. et al. A new complexity metric for FH/SS sequences using fuzzy entropy. Sci. China Inf. Sci. 54, 1491–1499 (2011). https://doi.org/10.1007/s11432-011-4203-1

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  • DOI: https://doi.org/10.1007/s11432-011-4203-1

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