Abstract
Frequency hopping sequences have been found wide applications in various modern frequency hopping spread spectrum communications and radar systems. With potential applications to these areas such as ultra wide bandwidth time hopping code division multiple access radio systems, multi-user and sonar systems, the design of quasi-synchronous time/frequency hopping code division multiple access systems by employing low hit zone hopping sequences has attracted wide attentions. In this paper, we present three construction methods for the low Hamming correlation zone frequency hopping sequences. The parameters of these sets of frequency hopping sequences with low hit zone are new and flexible. The constructed sequences are almost optimal and optimal respectively with respect to the Peng–Fan–Lee bounds. The simplicity of this technique makes it attractive for practical use.
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Lempel A., Greenberger H.: Families of sequences with optimal hamming correlation properties. IEEE Trans. Inform. Theory 20(1), 2149–2154 (1974)
Han Y.K., Yang K.: On the Sidel’nilov sequences as frequency hopping sequences. IEEE Trans. Inform. Theory 55(9), 4279–4285 (2009)
Ding C.S., Moisio M.J., Yuan J.: Algebraic constructions of optimal frequency hopping sequences. IEEE Trans. Inform. Theory 53(7), 2606–2610 (2007)
Ding C.S., Yin J.X.: Sets of optimal frequency hopping sequences. IEEE Trans. Inform. Theory 54(8), 3741–3745 (2004)
Ge G.N., Miao Y., Yao Z.X.: Optimal frequency hopping sequences: auto and cross correlation properties. IEEE Trans. Inform. Theory 55(2), 867–879 (2009)
Chu W.S., Colbourn C.J.: Optimal frequency hopping sequences via cyclotomy. IEEE Trans. Inform. Theory 51(3), 1139–1141 (2005)
De Gaudenzi R., Elia C., Viola R.: Bandlimited quasi-synchronous CDMA: a novel satellite access technique for mobile and personal communication systems. IEEE J. Sel. Areas Commun. 10(2), 328–343 (1992)
Long B., Zhang P., Hu J.: A generalized QS−CDMA system and the design of new spreading codes. IEEE Trans. Veh. Technol. 47, 1268–1275 (1998)
Kim Y.-S., Jang J.-W., No J.-S., Chung H.: New design of low correlation zone sequence sets. IEEE Trans. Inform. Theory 52(10), 4607–4616 (2006)
Win M.Z., Scholtz R.A.: Ultra-wide bandwidth time hopping spread spectrum impulse radio for wireless multiple-access communication. IEEE Trans. Commun. 48(4), 679–691 (2000)
Peng D.Y., Fan P.Z.: Lower bounds on Hamming auto and cross correlations of frequency hopping sequences. IEEE Trans. Inform. Theory 50(9), 2149–2154 (2004)
Peng D.Y., Fan P.Z., Lee M.H.: Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone. Sci. China Ser. F Inform. Sci. 49(2), 208–218 (2006)
Wang X.N., Fan P.Z.: A class of frequency hopping sequences with no hit zone. In: Proceedings of the Fourth International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT’2003), Chengdu, China, pp. 896–898. 27–29 Aug 2003.
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Communicated by S. Gao.
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Ma, W., Sun, S. New designs of frequency hopping sequences with low hit zone. Des. Codes Cryptogr. 60, 145–153 (2011). https://doi.org/10.1007/s10623-010-9422-8
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DOI: https://doi.org/10.1007/s10623-010-9422-8
Keywords
- Code division multiple access
- Frequency hopping sequence
- The Peng–Fan–Lee bounds
- Low Hamming correlation zone frequency hopping sequence