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In order to solve the problems of low dimensional chaotic mapping, limited chaotic behavior, and discontinuous chaotic interval, a new construction method of chaotic frequency-hopping sequence was proposed. First, a new Logistics-Sine-Cosine chaotic map was generated by Cosine transformation method combined with Logistic and Sine mapping. Then, the intermediate multi-bit extraction method was used to quantify the sequence generated by the mapping as a frequency-hopping sequence. Finally, experiments show that the chaotic frequency-hopping sequence can effectively improve the randomness and complexity of the sequence under the premise of maintaining good balance and Hamming correlation, and can strengthen the anti-prediction and anti-interference in the communication process.

Frequency-hopping sequences (FHSs) with low Hamming correlation are essential for synchronization and multiple-access communication systems. In this paper, we propose a novel construction of FHSs using generalized cyclotomy. Our results reveal that the constructed FHSs exhibit a one-coincidence property, meaning that the smallest correlation between different FHSs, aside from the trivial case, is minimized. Additionally, the new sets of FHSs achieve an optimal size in relation to a known theoretical bound. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new constructions of one-coincidence frequency-hopping sequence (OC-FHS) sets over integer rings. These OC-FHSs are designed to minimize interference in frequency-hopping multiple access (FHMA) systems, which are widely used in various communication applications. By leveraging the properties of primitive elements in integer ring Z p n , we develop OC-FHS sets with lengths m p n − 1 for m dividing (p − 1) , along with constructions with composite lengths based on linear functions. The proposed OC-FHS sets include parameters not previously addressed in the literature and encompass some known cases as special cases. [ABSTRACT FROM AUTHOR]

Frequency hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems. In this paper, four new constructions for FHSs are presented, including a direct construction of FHSs by using cyclotomic cosets and three extension constructions of FHSs by using units of rings and multiplicative groups of finite fields. By these constructions, a number of series of new FHSs are then produced. These FHSs are optimal with respect to the Lempel-Greenberger bound. [ABSTRACT FROM AUTHOR]

Frequency hopping sequences with low hit zone is significant for application in quasi synchronous multiple-access systems. In this paper, we obtained two constructions of optimal frequency hopping sequence sets with low hit zone based on interleaving techniques. The presented low hit zone frequency hopping sequence sets are with new and flexible parameters and large family size which can meet the needs of the practical applications. Moreover, all the sequences in the proposed sets are cyclically inequivalent. Some low hit zone frequency hopping sequence sets constructed in literatures are included in our family. The proposed frequency hopping sequence sets with low hit zone are contributed for quasi-synchronous frequency hopping multiple access system to reduce or eliminate multiple-access interference. [ABSTRACT FROM AUTHOR]

In complex environments of wireless communication, to improve the communication anti-interference performance, quasi-synchronous frequency-hopping (FH) communication system requires low-hit-zone (LHZ) FH sequence sets with optimal Hamming correlation (HC) properties and flexible parameters. In this paper, based upon cyclotomy theory, two classes of LHZ FH sequence sets with flexible parameters not included in the literatures are designed, and the periodic HC properties of which are analyzed. It turns out that the designed LHZ FH sequence sets are optimal on the maximum periodic HC. And thus the new constructions can be used to provide optimal FH sequence sets for quasi-synchronous FH communication system.

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. [ABSTRACT FROM AUTHOR]

The research of cyclotomy theory can be traced to Gauss and it has been applied to many fields such as cryptography, coding theory, and combinatorics. According to $v$ prime numbers or compound words, the incision on the residue-like ring ${\mathbb Z}_{v}$ can be separated to classic incision or general incision. In this work, a kind of extended generalized cyclotomic classes is introduced. Based on this tangent method, a class of frequency hopping sequence set with the best average Hamming correlation is proposed.

In this paper, we present two constructions of low-hit-zone frequen-cy-hopping sequence (LHZ FHS) sets. The constructions in this paper generalize the previous constructions based on m m -sequences and d d -form functions with difference-balanced property, and generate several classes of optimal LHZ FHS sets and LHZ FHS sets with optimal periodic partial Hamming correlation (PPHC). [ABSTRACT FROM AUTHOR]

In frequency hopping (FH) communication systems, frequency hopping sequences (FHSs) are crucial in determining the system’s anti-jamming performance. If FHSs can ensure a wide-gap between two adjacent frequency points to avoid the frequency points with high interference probability, it will significantly improve the FH communication system’s anti-interference ability. Moreover, if each frequency point appears at the same number of times in a sequence period, the system’s anti-electromagnetic interference will be enhanced. Therefore, it is desirable to employ FHSs with low Hamming autocorrelation, wide frequency-hopping gap, and good uniformity in practical applications. However, to the best of our knowledge, no such infinite classes of FHSs have been reported in the literature to date. This paper aims to present two constructions of uniform wide-gap frequency-hopping sequences (WGFHSs) by concatenating two or three adequately designed sequences. For the first time, we obtain two infinite classes of WGFHSs, which are optimal with respect to the well-known Lempel-Greenberger bound. [ABSTRACT FROM AUTHOR]

For a quasi-synchronous frequency/time hopping (FH/TH) code-division multiple-access (CDMA) system which involves many users, the low-hit-zone (LHZ) FH/TH sequence set with large family size is necessary. In this paper, an upper bound on the family size of LHZ FH/TH sequence sets is derived. The new bound includes the Singleton bound on FH sequence sets as a special case. Further, three constructions of LHZ FH/TH sequence sets are presented, which have optimal/near optimal family size and also optimal maximum Hamming correlation (MHC) with respect to the new bound. They have very large family size compared with the known LHZ FH/TH sequence sets in the literature.

Copyright of Journal of Zhengzhou University (Natural Science Edition) is the property of Journal of Zhengzhou University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we investigate the Hamming correlation properties of column sequences from the (q - 1) × q d - 1 q - 1 array structure of M-ary Sidelnikov sequences of period q d - 1 for M | q - 1 and d ≥ 2 . We prove that the proposed set Γ (d) of some column sequences has the maximum non-trivial Hamming correlation upper bounded by the minimum of q - 1 M d - 1 and M - 1 M (2 d - 1) q + 1 + q - 1 M . When M = q - 1 , we show that Γ (d) is optimal with respect to the Singleton bound. The set Γ (d) can be extended to a much larger set Δ (d) by involving all the constant additions of the members of Γ (d) , which is also optimal with respect to the Singleton bound when M = q - 1 . [ABSTRACT FROM AUTHOR]

This paper is focused on the optimal design and performance analysis of a novel class of no-hit-zone frequency-hopping sequences (NHZ-FHSs) in quasi-synchronous FH multiple-access (QS-FHMA) systems. Although traditional NHZ-FHSs can offer interference-free FHMA performance when the signal arrival delay ($\tau $) does not exceed the width of NHZ ($Z_{\mathrm{ nh}}$), i.e., $|\tau |\leq Z_{\mathrm{ nh}}$ , the same performance cannot be guaranteed for $|\tau |>Z_{\mathrm{ nh}}$ in which traditional NHZ-FHZs may have large Hamming correlation (which denotes the total number of frequency hits of sequences) and consequently poor error probability performance. Since the strict quasi-synchronization (i.e., $|\tau |\leq Z_{\mathrm{ nh}}$) may be hard to maintain at all times in practical FHMA networks (e.g., infrastructureless ad hoc networks), it is also important to minimize the Hamming correlation for time-shifts outside of the NHZ. Such FHSs are called strong NHZ-FHSs (SNHZ-FHSs) in this paper. We derive a lower bound on the maximum Hamming correlation outside of the NHZ and then present a design algorithm for the optimal SNHZ-FHS set meeting our proposed lower bound with equality. We analyze the bit-error-rate (BER) performance of the FHMA system employing the proposed SNHZ-FHS sets using the average Hamming correlation function. The theoretical analysis and simulation results show that the proposed optimal SNHZ-FHS sets are feasible for practical FHMA networks with relaxed timing requirement and enhanced BER performance. [ABSTRACT FROM AUTHOR]

Frequency hopping (FH) sequences play an important role in FH spread spectrum communication systems. In this paper, a new theoretical bound on the FH sequences with respect to the size of the frequency slot set, the sequence length, the family size, and the maximum periodic Hamming correlation is established. The new bound is tighter than the Singleton bounds on the FH sequences derived by Ding et al. (IEEE Trans Inf Theory 55:3297–3304, 2009) and Yang et al. (IEEE Trans Inf Theory 57:7605–7613, 2011) (first by Sarwate in: Glisic and Leppanen (eds) Code division multiple access communications, Springer, Boston, 1995). In addition, the new bound employes the M o ¨ bius function. Then, more optimal FH sequence sets are obtained from Reed–Solomon codes. By utilizing the properties of cyclic codes, a new class of optimal FH sequence sets is obtained whose parameters meet the new bound. Further, two new constructions of FH sequence sets are presented. More new FH sequence sets are obtained by choosing proper base sequence sets. Meanwhile, the FH sequence sets constructed are optimal with respect to the new bound. [ABSTRACT FROM AUTHOR]

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In a frequency-hopping (FH) system, to avoid that the received signal would be prone to be interfered, the equipped FH sequence of each user should have wide FH gap, i.e., the adjacent two frequencies should have some gap. In this letter, we extend the Lempel–Greenberger bound and Peng-Fan bounds for wide-gap frequency-hopping sequences (WGFHSs). The proposed bounds are tight in the sense that they can be achieved by the parameters of some WGFHSs. [ABSTRACT FROM AUTHOR]

In a quasi-synchronous frequency-hopping multiple-access system, relative time delay between different users within a zone around the origin can be allowed. Therefore, frequency-hopping sequence (FHS) sets with low-hit-zone (LHZ) have attracted great interest of many related scholars. Moreover, on account of the limited synchronous time or hardware complexity, the periodic partial Hamming correlation (PPHC) plays a major role in determining the synchronization performance. In this paper, we first present three new generalized methods to construct LHZ-FHS sets via Cartesian product. Meanwhile, we pay our attention to the maximum periodic Hamming correlation (PHC) of the constructed LHZ-FHS sets in the first generalized method, and to the maximum PPHC of the constructed LHZ-FHS sets in the rest generalized methods. In addition, we also introduce five new classes of optimal LHZ-FHS sets based on these three generalized methods. [ABSTRACT FROM AUTHOR]

By using a type of permutation polynomials which were different from power permutations,the two classes of frequency-hopping sequence sets with low linear complexity was transformed into the ones with high linear complexity.The exact values of linear complexity of these sequences were given by applying the theoretical proof.The results show that the two new classes of frequency-hopping sequences sets not only have optimal Hamming correlation,but also have larger linear span and can resist the Berlekamp-Massey attack compared with the two primary classes of frequency-hopping sequence sets.

Frequency hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems. In this paper, we present combinatorial constructions for FHS sets, including direct constructions by using cyclotomic classes, recursive constructions based on cyclic difference matrices, merging blocks, and discrete logarithm. By these constructions, a number of series of new FHS sets are then produced. These FHS sets are optimal with respect to the Peng–Fan bounds. [ABSTRACT FROM PUBLISHER]

Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties are desirable in many synchronization and multiple-access systems. An FHS set is said to be strictly optimal if it has optimal partial Hamming correlation for any correlation window. In this paper, we derive upper bounds on the family sizes of FHS sets with respect to partial Hamming correlation from some classical bounds on error-correcting codes. We then present strictly optimal FHS sets having optimal family sizes with respect to one of the new bounds. In particular, our construction gives new parameters not covered in the literature. [ABSTRACT FROM AUTHOR]

The average Hamming correlation is an important indicator of frequency-hopping sequences (FHSs) which measures the average performance of FHSs employed in practical frequency-hopping multiple access (FHMA) communication systems. In this paper, a lower bound on average Hamming autoand cross correlations of an FHS set is derived. It generalizes and improves the lower bound proposed recently by Peng, Niu and Tang. A simple necessary and sufficient condition for an FHS set to meet the new bound is given. Based on this condition, two classes of FHS sets whose average Hamming correlations reach the proposed bound are introduced. [ABSTRACT FROM AUTHOR]

Frequency-hopping spread spectrum and direct-sequence spread spectrum are two main spread coding technologies in communication systems. Frequency-hopping sequences are needed in FH-CDMA systems. In this paper, a construction of optimal sets of frequency-hopping sequences using cyclotomy and the Chinese remainder theorem is introduced. It generalizes some earlier constructions, and produces new optimal sets of frequency-hopping sequences. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A mapping from \BBZN to \BBZM can be directly applied for the design of a sequence of period N with alphabet size M, where \BBZN denotes the ring of integers modulo N. The nonlinearity of such a mapping is closely related to the autocorrelation of the corresponding sequence. When M is a divisor of N, the sequence corresponding to a perfect nonlinear mapping has perfect autocorrelation, but it is not balanced. In this paper, we study balanced near-perfect nonlinear (NPN) mappings applicable for the design of sequence sets with low correlation. We first construct a new class of balanced NPN mappings from \BBZp^{2-p} to \BBZp for an odd prime p. We then present a general method to construct a frequency-hopping sequence (FHS) set from a nonlinear mapping. By applying it to the new class, we obtain a new optimal FHS set of period p^2-p with respect to the Peng–Fan bound, whose FHSs are balanced and optimal with respect to the Lempel–Greenberger bound. Moreover, we construct a low-correlation sequence set with size p, period p^2-p, and maximum correlation magnitude p from the new class of balanced NPN mappings, which is asymptotically optimal with respect to the Welch bound. [ABSTRACT FROM AUTHOR]

In this paper, an upper bound for a hybrid incomplete exponential sum over finite fields is derived. This bound is then used to obtain lower and upper bounds for aperiodic Hamming correlation of frequency-hopping sequences based on power functions. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an interleaving construction of new sets of frequency hopping sequences from the known ones. By choosing suitable known optimal frequency hopping sequences and sets of frequency hopping sequences and then recursively applying the proposed construction, optimal frequency hopping sequences and sets of frequency hopping sequences with new parameters can be obtained. [ABSTRACT FROM PUBLISHER]

In this paper, the partial Hamming correlation properties of frequency-hopping sequences (FHSs) are discussed. The Peng–Fan bounds on sets of FHSs are generalized to the case of partial correlation. Both individual FHSs with optimal partial autocorrelation and sets of FHSs with optimal partial correlation are presented. The former has more new parameters compared with the known individual FHSs with optimal partial autocorrelation, while the later is obtained in the literature for the first time. [ABSTRACT FROM PUBLISHER]

In this paper, two generic constructions of optimal frequency-hopping sequence (FHS) sets employing d-form functions with difference-balanced property are presented. They generalize the previous constructions of optimal FHS sets using m-sequences and produce new optimal FHS sets that cannot be produced by the earlier constructions. By choosing appropriate d-form functions with difference-balanced property, both constructions lead to FHSs with large linear complexity. In addition, one of the proposed constructions gives new optimal parameters of FHS sets. [ABSTRACT FROM AUTHOR]

For an integer k\geq 1, let qi,~1\leq i\leq k, be prime powers such that qi=Mif+1 for some integers Mi and f. In this paper, the k-fold cyclotomy of \BBFq1\times \cdots \times \BBFqk as a nontrivial generalization of the conventional cyclotomy (k=1 case) and its application to frequency-hopping sequences (FHSs) are presented, where \BBFq is the finite field with q elements. First, the definitions of k-fold cyclotomic classes and k-fold cyclotomic numbers are given. And then, their basic properties including k-fold diagonal sums are derived. Based on them, new optimal FHS sets of length N and frequency set size M or M+1 with respect to the Peng-Fan bound are constructed for a product N of distinct odd primes and a divisor M of N-1. Furthermore, new optimal FHSs of length N and frequency set size M with respect to the Lempel–Greenberger bound are constructed when N has at least one prime factor which is 3 modulo 4 and (N-1)/M is an even integer. Our constructions give several new optimal parameters not covered in the literature, which are summarized in Table I . [ABSTRACT FROM AUTHOR]