American Institute of Mathematical Sciences

Advanced
August  2013, 7(3): 293-310. doi: 10.3934/amc.2013.7.293

New classes of optimal frequency hopping sequences with low hit zone

Xianhua Niu 1, , Daiyuan Peng 2, and  Zhengchun Zhou 3,

1. 

School of Mathematics and Computer Engineering, The Key Laboratory of Network Intelligent Information Processing, Xihua University, Chengdu, Sichuan 610039, China
2. 

School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
3. 

School of Mathematics, Southwest Jiaotong University, Chengdu, 610031

Received  July 2012 Revised  February 2013 Published  July 2013

In this paper, a new design of frequency hopping sequences (FHSs) sets with low hit zone (LHZ) is presented based on interleaving technique. The key idea of the new design is to use short FHSs with good Hamming correlation together with certain appropriate shift sequences to construct a set of long FHSs with LHZ. By the new design, new sets of FHSs meeting the Peng-Fan-Lee bound are obtained. It is shown that all the sequences in the proposed FHS sets are shift distinct. The proposed FHS sets are suitable for quasi-synchronous frequency hopping code division multiple access systems to eliminate multiple-access interference.
Keywords: Hamming correlation, low hit zone, Frequency hopping sequences, interleaving technique..
Mathematics Subject Classification: Primary: 94A05, 94B6.
Citation: Xianhua Niu, Daiyuan Peng, Zhengchun Zhou. New classes of optimal frequency hopping sequences with low hit zone. Advances in Mathematics of Communications, 2013, 7 (3) : 293-310. doi: 10.3934/amc.2013.7.293
References:
[1]

W. Chu and C. J. Colbourn, Optimal frequency-hopping sequences via cyclotomy, IEEE Trans. Inf. Theory, 51 (2005), 1139-1141. doi: 10.1109/TIT.2004.842708.

[2]

J. H. Chung, Y. K. Han and K. Yang, New classes of optimal frequency-hopping sequences by interleaving technique, IEEE Trans. Inf. Theory, 55 (2009), 5783-5791. doi: 10.1109/TIT.2009.2032742.

[3]

J. H. Chung and K. Yang, Optimal frequency-hopping sequences with new parameters, IEEE Trans. Inf. Theory, 56 (2010), 1685-1693. doi: 10.1109/TIT.2010.2040888.

[4]

C. Ding, R. Fuji-Hara, Y. Fujiwara, et al., Sets of frequency hopping sequences: Bounds and optimal constructions, IEEE Trans. Inf. Theory, 55 (2009), 3297-3304. doi: 10.1109/TIT.2009.2021366.

[5]

C. Ding, T. Helleseth and H. Martinsen, New families of binary sequences with optimal three-level autocorrelation, IEEE Trans. Inf. Theory, 47 (2001), 428-433. doi: 10.1109/18.904555.

[6]

C. Ding, M. J. Moisio and J. Yuan, Algebraic constructions of optimal frequency hopping sequences, IEEE Trans. Inf. Theory, 53 (2007), 2606-2610. doi: 10.1109/TIT.2007.899545.

[7]

C. Ding and J. Yin, Sets of optimal frequency-hopping sequences, IEEE Trans. Inf. Theory, 54 (2008), 3741-3745. doi: 10.1109/TIT.2008.926410.

[8]

P. Z. Fan and M. Darnell, "Sequence Design for Communications Applications,'' RSP-John Wiley Sons Inc., London, 1996.

[9]

P. Z. Fan, M. H. Lee and D. Y. Peng, New family of hopping sequences for time/frequency hopping CDMA systems, IEEE Trans. Wir. Commun., 4 (2005), 2836-2842.

[10]

R. Fuji-Hara, Y. Miao and M. Mishima, Optimal frequency hopping sequences: A combinatorial approach, IEEE Trans. Inf. Theory, 50 (2004), 2408-2420. doi: 10.1109/TIT.2004.834783.

[11]

G. Ge, R. Fuji-Hara and Y. Miao, Further combinatorial constructions for optimal frequency hopping sequences, J. Combin. Theory Ser. A, 113 (2006), 1699-1718. doi: 10.1016/j.jcta.2006.03.019.

[12]

G. Ge, Y. Miao and Z. Yao, Optimal frequency hopping sequences: auto- and crosscorrelation properties, IEEE Trans. Inf. Theory, 55 (2009), 867-879. doi: 10.1109/TIT.2008.2009856.

[13]

G. Gong, Theory and applications of q-ary interleaved sequences, IEEE Trans. Inf. Theory, 41 (1995), 400-411. doi: 10.1109/18.370141.

[14]

G. Gong, New designs for signal sets with low cross correlation, balance property and large linear span: GF(p) case, IEEE Trans. Inf. Theory, 48 (2002), 2847-2867. doi: 10.1109/TIT.2002.804044.

[15]

S. Hong, C. Seol and K. Cheun, Performance of soft decision decoded synchronous FHSS multiple access networks using MFSK modulation under rayleigh fading, IEEE Trans. Commun., 59 (2011), 1066-1077.

[16]

H. D. Jia, D. Yuan, D. Y. Peng, et al., On a general class of quadratic hopping sequences, Sci. China Ser. F, 12 (2008), 2101-2114. doi: 10.1007/s11432-008-0136-8.

[17]

N. R. Lanka, S. A. Patnaik and R. A. Harjani, Frequency-hopped quadrature frequency synthesizer in 0.13-$\mu$m technology, IEEE J. Solid-State Circuits, 46 (2011), 1-12.

[18]

A. Lempel and H. Greenberger, Families of sequence with optimal Hamming correlation properties, IEEE Trans. Inf. Theory, 20 (1974), 90-94.

[19]

W. P. Ma and S. H. Sun, New designs of frequency hopping sequences with low hit zone, Des. Codes Crypt., 60 (2010), 145-153. doi: 10.1007/s10623-010-9422-8.

[20]

X. H. Niu, D. Y. Peng and Z. C. Zhou, New classes of optimal LHZ FHS with new parameters, in "The Sixth International Workshop on Signal Design and Its Applications in Communications (IWSDA'11),'' Guilin, China, (2011), 10-14.

[21]

D. Y. Peng and P. Z. Fan, Lower bounds on the Hamming auto- and cross correlations of frequency hopping sequences, IEEE Trans. Inf. Theory, 50 (2004), 2149-2154. doi: 10.1109/TIT.2004.833362.

[22]

D. Y. Peng, P. Z. Fan and M. H. Lee, Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone, Sci. China Ser. F, 49 (2006), 1-11. doi: 10.1007/s11432-006-0208-6.

[23]

H. Shao and N. Beaulieu, Direct sequence and time-hopping sequence designs for narrow band interference mitigation in impulse radio UWB systems, IEEE Trans. Commun., 59 (2011), 1957-1965.

[24]

M. K. Simon, J. K. Omura, R. A. Scholtz and B. K. Levitt, "Spread Spectrum Communications Handbook,'' McGraw-Hill, New York, 1994.

[25]

P. Udaya and M. U. Siddiqi, Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings, IEEE Trans. Inf. Theory, 44 (1998), 1492-1503. doi: 10.1109/18.681324.

[26]

P. Udaya and X. Tang, Low correlation zone sequences from interleaved construction, IEICE Trans. Fund., 93-A (2010), 2220-2226.

[27]

X. N. Wang and P. Z. Fan, A class of frequency hopping sequences with no hit zone, in "Proc. 4th International Conference on Parallel and Distributed Computing, Applications and Technologies,'' (2003), 896-898.

[28]

W. X. Ye and P. Z. Fan, Two classes of frequency hopping sequences with no-hit zone, in "Proc. 7th Int. Symp. on Communication Theory and Applications,'' Ambleside, UK, (2003), 304-306.

[29]

W. X. Ye and P. Z. Fan, Construction of frequency hopping sequences with no hit zone, J. Electronics (China), 24 (2007), 305-308. doi: 10.1007/s11767-005-0202-y.

[30]

W. X. Ye, P. Z. Fan and E. M. Gabidulin, Construction of non-repeating frequency-hopping sequences with no-hit zone, Electronics Letters, 42 (2006), 681-682. doi: 10.1049/el:20060775.

[31]

Q. Zeng, H. S. Li, Z. H. Zhang, et al., A frequency-hopping based communication infrastructure for wireless metering in smart grid, in "45th Annual Conference on Information Sciences and Systems (CISS),'' (2011), 23-25.

[32]

Z. C. Zhou, Z. Pan and X. H. Tang, New families of optimal zero correlation zone sequences based on interleaved technique and perfect sequences, IEICE Trans. Fund., 91 (2008), 3691-3697.

[33]

Z. C. Zhou, X. H. Tang and G. Gong, A new class of sequences with zero or low correlation zone based on interleaving technique, IEEE Trans. Inf. Theory, 54 (2008), 4267-4273. doi: 10.1109/TIT.2008.928256.

show all references

References:
[1]

W. Chu and C. J. Colbourn, Optimal frequency-hopping sequences via cyclotomy, IEEE Trans. Inf. Theory, 51 (2005), 1139-1141. doi: 10.1109/TIT.2004.842708.

[2]

J. H. Chung, Y. K. Han and K. Yang, New classes of optimal frequency-hopping sequences by interleaving technique, IEEE Trans. Inf. Theory, 55 (2009), 5783-5791. doi: 10.1109/TIT.2009.2032742.

[3]

J. H. Chung and K. Yang, Optimal frequency-hopping sequences with new parameters, IEEE Trans. Inf. Theory, 56 (2010), 1685-1693. doi: 10.1109/TIT.2010.2040888.

[4]

C. Ding, R. Fuji-Hara, Y. Fujiwara, et al., Sets of frequency hopping sequences: Bounds and optimal constructions, IEEE Trans. Inf. Theory, 55 (2009), 3297-3304. doi: 10.1109/TIT.2009.2021366.

[5]

C. Ding, T. Helleseth and H. Martinsen, New families of binary sequences with optimal three-level autocorrelation, IEEE Trans. Inf. Theory, 47 (2001), 428-433. doi: 10.1109/18.904555.

[6]

C. Ding, M. J. Moisio and J. Yuan, Algebraic constructions of optimal frequency hopping sequences, IEEE Trans. Inf. Theory, 53 (2007), 2606-2610. doi: 10.1109/TIT.2007.899545.

[7]

C. Ding and J. Yin, Sets of optimal frequency-hopping sequences, IEEE Trans. Inf. Theory, 54 (2008), 3741-3745. doi: 10.1109/TIT.2008.926410.

[8]

P. Z. Fan and M. Darnell, "Sequence Design for Communications Applications,'' RSP-John Wiley Sons Inc., London, 1996.

[9]

P. Z. Fan, M. H. Lee and D. Y. Peng, New family of hopping sequences for time/frequency hopping CDMA systems, IEEE Trans. Wir. Commun., 4 (2005), 2836-2842.

[10]

R. Fuji-Hara, Y. Miao and M. Mishima, Optimal frequency hopping sequences: A combinatorial approach, IEEE Trans. Inf. Theory, 50 (2004), 2408-2420. doi: 10.1109/TIT.2004.834783.

[11]

G. Ge, R. Fuji-Hara and Y. Miao, Further combinatorial constructions for optimal frequency hopping sequences, J. Combin. Theory Ser. A, 113 (2006), 1699-1718. doi: 10.1016/j.jcta.2006.03.019.

[12]

G. Ge, Y. Miao and Z. Yao, Optimal frequency hopping sequences: auto- and crosscorrelation properties, IEEE Trans. Inf. Theory, 55 (2009), 867-879. doi: 10.1109/TIT.2008.2009856.

[13]

G. Gong, Theory and applications of q-ary interleaved sequences, IEEE Trans. Inf. Theory, 41 (1995), 400-411. doi: 10.1109/18.370141.

[14]

G. Gong, New designs for signal sets with low cross correlation, balance property and large linear span: GF(p) case, IEEE Trans. Inf. Theory, 48 (2002), 2847-2867. doi: 10.1109/TIT.2002.804044.

[15]

S. Hong, C. Seol and K. Cheun, Performance of soft decision decoded synchronous FHSS multiple access networks using MFSK modulation under rayleigh fading, IEEE Trans. Commun., 59 (2011), 1066-1077.

[16]

H. D. Jia, D. Yuan, D. Y. Peng, et al., On a general class of quadratic hopping sequences, Sci. China Ser. F, 12 (2008), 2101-2114. doi: 10.1007/s11432-008-0136-8.

[17]

N. R. Lanka, S. A. Patnaik and R. A. Harjani, Frequency-hopped quadrature frequency synthesizer in 0.13-$\mu$m technology, IEEE J. Solid-State Circuits, 46 (2011), 1-12.

[18]

A. Lempel and H. Greenberger, Families of sequence with optimal Hamming correlation properties, IEEE Trans. Inf. Theory, 20 (1974), 90-94.

[19]

W. P. Ma and S. H. Sun, New designs of frequency hopping sequences with low hit zone, Des. Codes Crypt., 60 (2010), 145-153. doi: 10.1007/s10623-010-9422-8.

[20]

X. H. Niu, D. Y. Peng and Z. C. Zhou, New classes of optimal LHZ FHS with new parameters, in "The Sixth International Workshop on Signal Design and Its Applications in Communications (IWSDA'11),'' Guilin, China, (2011), 10-14.

[21]

D. Y. Peng and P. Z. Fan, Lower bounds on the Hamming auto- and cross correlations of frequency hopping sequences, IEEE Trans. Inf. Theory, 50 (2004), 2149-2154. doi: 10.1109/TIT.2004.833362.

[22]

D. Y. Peng, P. Z. Fan and M. H. Lee, Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone, Sci. China Ser. F, 49 (2006), 1-11. doi: 10.1007/s11432-006-0208-6.

[23]

H. Shao and N. Beaulieu, Direct sequence and time-hopping sequence designs for narrow band interference mitigation in impulse radio UWB systems, IEEE Trans. Commun., 59 (2011), 1957-1965.

[24]

M. K. Simon, J. K. Omura, R. A. Scholtz and B. K. Levitt, "Spread Spectrum Communications Handbook,'' McGraw-Hill, New York, 1994.

[25]

P. Udaya and M. U. Siddiqi, Optimal large linear complexity frequency hopping patterns derived from polynomial residue class rings, IEEE Trans. Inf. Theory, 44 (1998), 1492-1503. doi: 10.1109/18.681324.

[26]

P. Udaya and X. Tang, Low correlation zone sequences from interleaved construction, IEICE Trans. Fund., 93-A (2010), 2220-2226.

[27]

X. N. Wang and P. Z. Fan, A class of frequency hopping sequences with no hit zone, in "Proc. 4th International Conference on Parallel and Distributed Computing, Applications and Technologies,'' (2003), 896-898.

[28]

W. X. Ye and P. Z. Fan, Two classes of frequency hopping sequences with no-hit zone, in "Proc. 7th Int. Symp. on Communication Theory and Applications,'' Ambleside, UK, (2003), 304-306.

[29]

W. X. Ye and P. Z. Fan, Construction of frequency hopping sequences with no hit zone, J. Electronics (China), 24 (2007), 305-308. doi: 10.1007/s11767-005-0202-y.

[30]

W. X. Ye, P. Z. Fan and E. M. Gabidulin, Construction of non-repeating frequency-hopping sequences with no-hit zone, Electronics Letters, 42 (2006), 681-682. doi: 10.1049/el:20060775.

[31]

Q. Zeng, H. S. Li, Z. H. Zhang, et al., A frequency-hopping based communication infrastructure for wireless metering in smart grid, in "45th Annual Conference on Information Sciences and Systems (CISS),'' (2011), 23-25.

[32]

Z. C. Zhou, Z. Pan and X. H. Tang, New families of optimal zero correlation zone sequences based on interleaved technique and perfect sequences, IEICE Trans. Fund., 91 (2008), 3691-3697.

[33]

Z. C. Zhou, X. H. Tang and G. Gong, A new class of sequences with zero or low correlation zone based on interleaving technique, IEEE Trans. Inf. Theory, 54 (2008), 4267-4273. doi: 10.1109/TIT.2008.928256.

[1]

Limengnan Zhou, Daiyuan Peng, Hongyu Han, Hongbin Liang, Zheng Ma. Construction of optimal low-hit-zone frequency hopping sequence sets under periodic partial Hamming correlation. Advances in Mathematics of Communications, 2018, 12 (1) : 67-79. doi: 10.3934/amc.2018004
[2]

Xing Liu, Daiyuan Peng. Frequency hopping sequences with optimal aperiodic Hamming correlation by interleaving techniques. Advances in Mathematics of Communications, 2017, 11 (1) : 151-159. doi: 10.3934/amc.2017009
[3]

Hongyu Han, Sheng Zhang. New classes of strictly optimal low hit zone frequency hopping sequence sets. Advances in Mathematics of Communications, 2020, 14 (4) : 579-589. doi: 10.3934/amc.2020031
[4]

Xiujie Zhang, Xianhua Niu, Xin Tan. Constructions of optimal low hit zone frequency hopping sequence sets with large family size. Advances in Mathematics of Communications, 2022  doi: 10.3934/amc.2021071
[5]

Wenjuan Yin, Can Xiang, Fang-Wei Fu. Two constructions of low-hit-zone frequency-hopping sequence sets. Advances in Mathematics of Communications, 2022, 16 (2) : 249-267. doi: 10.3934/amc.2020110
[6]

Xing Liu, Daiyuan Peng. Sets of frequency hopping sequences under aperiodic Hamming correlation: Upper bound and optimal constructions. Advances in Mathematics of Communications, 2014, 8 (3) : 359-373. doi: 10.3934/amc.2014.8.359
[7]

Aixian Zhang, Zhengchun Zhou, Keqin Feng. A lower bound on the average Hamming correlation of frequency-hopping sequence sets. Advances in Mathematics of Communications, 2015, 9 (1) : 55-62. doi: 10.3934/amc.2015.9.55
[8]

Nian Li, Xiaohu Tang, Tor Helleseth. A class of quaternary sequences with low correlation. Advances in Mathematics of Communications, 2015, 9 (2) : 199-210. doi: 10.3934/amc.2015.9.199
[9]

Fang Liu, Daiyuan Peng, Zhengchun Zhou, Xiaohu Tang. New constructions of optimal frequency hopping sequences with new parameters. Advances in Mathematics of Communications, 2013, 7 (1) : 91-101. doi: 10.3934/amc.2013.7.91
[10]

Shanding Xu, Xiwang Cao, Jiafu Mi, Chunming Tang. More cyclotomic constructions of optimal frequency-hopping sequences. Advances in Mathematics of Communications, 2019, 13 (3) : 373-391. doi: 10.3934/amc.2019024
[11]

Wei-Wen Hu. Integer-valued Alexis sequences with large zero correlation zone. Advances in Mathematics of Communications, 2017, 11 (3) : 445-452. doi: 10.3934/amc.2017037
[12]

Chunlei Xie, Yujuan Sun. Construction and assignment of orthogonal sequences and zero correlation zone sequences for applications in CDMA systems. Advances in Mathematics of Communications, 2020, 14 (1) : 1-9. doi: 10.3934/amc.2020001
[13]

Lenny Fukshansky, Ahmad A. Shaar. A new family of one-coincidence sets of sequences with dispersed elements for frequency hopping cdma systems. Advances in Mathematics of Communications, 2018, 12 (1) : 181-188. doi: 10.3934/amc.2018012
[14]

Ming Su, Arne Winterhof. Hamming correlation of higher order. Advances in Mathematics of Communications, 2018, 12 (3) : 505-513. doi: 10.3934/amc.2018029
[15]

Fanxin Zeng, Xiaoping Zeng, Zhenyu Zhang, Guixin Xuan. Quaternary periodic complementary/Z-complementary sequence sets based on interleaving technique and Gray mapping. Advances in Mathematics of Communications, 2012, 6 (2) : 237-247. doi: 10.3934/amc.2012.6.237
[16]

Yu Zheng, Li Peng, Teturo Kamae. Characterization of noncorrelated pattern sequences and correlation dimensions. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 5085-5103. doi: 10.3934/dcds.2018223
[17]

Jingjun Bao. New families of strictly optimal frequency hopping sequence sets. Advances in Mathematics of Communications, 2018, 12 (2) : 387-413. doi: 10.3934/amc.2018024
[18]

Xianhong Xie, Yi Ouyang, Honggang Hu, Ming Mao. Construction of three classes of strictly optimal frequency-hopping sequence sets. Advances in Mathematics of Communications, 2022  doi: 10.3934/amc.2022024
[19]

Ferruh Özbudak, Eda Tekin. Correlation distribution of a sequence family generalizing some sequences of Trachtenberg. Advances in Mathematics of Communications, 2021, 15 (4) : 647-662. doi: 10.3934/amc.2020087
[20]

Wenli Ren, Feng Wang. A new class of optimal wide-gap one-coincidence frequency-hopping sequence sets. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2020131

2020 Impact Factor: 0.935

Tools

Metrics

  • PDF downloads (83)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy