A new family of one-coincidence sets of sequences with dispersed elements for frequency hopping cdma systems

Fukshansky, Lenny; Shaar, A.A.

doi:10.3934/amc.2018012

Cited by 4 publications

(7 citation statements)

References 3 publications

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“…Example 1. Select any FH sequence set (28,23,29,1) denoted as X 0 = {X 0,0 , ..., X 0,21 , X 0,22 } over F 29 , such that 23,18,8,17,6,13,27,26,24,20,12,25,22,16,4,9,19,10,21,14).…”

Section: New Sets Of Optimal Wg Fh Sequencementioning

confidence: 99%

“…Many methods to design WG FH sequences have so far been presented in the literature. For example, removing intermediate frequency bands method [11], dual frequency bands method [12], random translation substitution method and random uniform transfer substitution method [13,14], designs of intelligent WG FH sequences [15,16], designs of WG FH sequences based on prime number [17], constructions based on chaos theory [18,19], constructions over the finite fields [20][21][22][23], and so on. In addition, in order to evaluate the performances of WG FH sequences, the WG FH sequence theoretic bounds, including the bounds [20,21] when the maximum periodic HC is equal to 1 and the bounds [25,26] when the maximum periodic HC is greater than 0, have been also put forwarded.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, in order to evaluate the performances of WG FH sequences, the WG FH sequence theoretic bounds, including the bounds [20,21] when the maximum periodic HC is equal to 1 and the bounds [25,26] when the maximum periodic HC is greater than 0, have been also put forwarded. Although there have existed many known designs of WG FH sequences, but until now, there have been very few WG FH sequences with optimal HCs according to the corresponding theoretic bounds in the literature [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Sets of Wide-Gap Frequency-Hopping Sequence With Optimal Maximum Hamming Correlation

Wang

Yang

et al. 2022

IEEE Access

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In application, frequency-hopping (FH) communication system often suffers various interferences, such as single frequency narrow-band interference, partial band blocking interference and tracking interference, and so on. For all that, by using optimal Wide-Gap (WG) FH sequences, FH communication system can significantly improve the anti-interference performances. In this paper, the relations between WG FH sequence theoretic bounds published in the journal IEEE Access (Peihua Li et al., 2019) are first made clear, and then five types of generalized methods are presented to design new classes of WG FH sequence sets. It is shown that all designed WG FH sequence sets are optimal according to the bound derived by Peihua Li et al. And by selecting appropriate original sequence sets, many of the optimal WG FH sequence sets can be obtained by our methods. Most importantly, these WG FH sequence sets have new parameters that are not covered in the literature.

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“…Example 1. Select any FH sequence set (28,23,29,1) denoted as X 0 = {X 0,0 , ..., X 0,21 , X 0,22 } over F 29 , such that 23,18,8,17,6,13,27,26,24,20,12,25,22,16,4,9,19,10,21,14).…”

Section: New Sets Of Optimal Wg Fh Sequencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sets of Wide-Gap Frequency-Hopping Sequence With Optimal Maximum Hamming Correlation

Wang

Yang

et al. 2022

IEEE Access

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“…Corollary 3: Choose a (q − 1, q; q) OC sequence set C 1 in [21] where q > m(X ). We can obtain an optimal [21], [25] where p > m(X ) + 1. We can obtain an optimal (pN , pv, λ; pM ; Z ) LHZ FHS set over [22] where n, d are positive integers with 2 n, n > m(X ) and d ≤ √ 4n+1−1 2…”

Section: Construction 1: Construction Of Cyclically Distinct Lhz Fhs Sets With Length Nnmentioning

confidence: 99%

New Extension Interleaved Constructions of Optimal Frequency Hopping Sequence Sets With Low Hit Zone

2019

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In this paper, a designated interleaved structure of constructing optimal frequency-hopping sequence (FHS) sets with low hit zone (LHZ) is presented based on the Cartesian product. By the general structure, we obtain infinitely many optimal LHZ FHS sets with new and flexible parameters by combining the optimal LHZ FHS sets with one-coincidence sequence sets. Moreover, our constructions remove the constraint requiring that the extension factor is co-prime with the length of the original FHSs. In this paper, most of the extension constructions suffer from this constraint. As a result, our constructions allow great flexibility of choosing parameters of the LHZ FHS sets for a given quasi-synchronization frequency-hopping spread spectrum system.INDEX TERMS Frequency hopping sequences, low hit zone, optimal Hamming correlation, extension construction. I. INTRODUCTIONIn frequency-hopping multiple access (FHMA) communication systems, the signal of each user hop over the entire transmission bandwidth in a pseudo random fashion. FHMA communication systems are widely adopted in practice [1], [2]. For example, many popular systems, such as military communications [3], ultra wideband communications [4], 5G communication systems [5], HetNets [6], and Bluetooth [7], use FHMA methods. In such systems each user is represented by a sequence of hopping frequencies [8]. Simultaneous transmission by any two users over the same frequency band results in collisions of signals, and hence, it is very desirable that such collisions over the same frequency band are minimized. Thus, the design of a frequency hopping sequence (FHS) set with good property is an important problem.Different from conventional FHS design, the design of FHSs with low hit zone (LHZ) aims at making Hamming correlation equal to a very low value within a correlation zone [9]. The significance of LHZ FHS set is that, even there The associate editor coordinating the review of this manuscript and approving it for publication was Zilong Liu.XIAN-HUA NIU received the B.S. degree in communication engineering and the Ph.D. degree in information security from

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“…Ren et al [23] used an interleaving technology to extend an OC-FHS set of prime length to that of composite length. Based on prime sequence sets, Fukshansky and Shaar [9] proposed another class of OC-FHS sets, called HMC sequence sets. Later on, Lee et al [16] presented another construction of OC-FHS sets by a primitive element of the prime field.…”

Section: Introductionmentioning

confidence: 99%

A new class of optimal wide-gap one-coincidence frequency-hopping sequence sets

Ren¹,

Wang²

2023

AMC

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In this paper, we propose a new class of optimal one-coincidence FHS (OC-FHS) sets with respect to the Peng-Fan bounds, including prime sequence sets and HMC sequence sets as special cases. Thereafter, through investigating their properties, we determine all of the FHS distances in the OC-FHS set. Finally, for a given positive integer, we also propose a new class of wide-gap one-coincidence FHS (WG-OC-FHS) sets where the FHS gap is larger than the given positive integer. Moreover, such a WG-OC-FHS set is optimal with respect to the WG-Lempel-Greenberger bound and the WG-Peng-Fan bounds simultaneously.

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A new family of one-coincidence sets of sequences with dispersed elements for frequency hopping cdma systems

Cited by 4 publications

References 3 publications

Sets of Wide-Gap Frequency-Hopping Sequence With Optimal Maximum Hamming Correlation

Sets of Wide-Gap Frequency-Hopping Sequence With Optimal Maximum Hamming Correlation

New Extension Interleaved Constructions of Optimal Frequency Hopping Sequence Sets With Low Hit Zone

A new class of optimal wide-gap one-coincidence frequency-hopping sequence sets

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