Frequency Hopping Sequence Sets Research Articles

New Algebraic and Combinatorial Constructions for Optimal Frequency Hopping Sequence Sets

New Algebraic and Combinatorial Constructions for Optimal Frequency Hopping Sequence Sets

New Constructions of One-Coincidence Sequence Sets over Integer Rings

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 Zpn, we develop OC-FHS sets with lengths mpn−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.

Construction of low-hit-zone frequency-hopping sequence sets with strictly optimal partial Hamming correlation based on Chinese Remainder Theorem

Construction of low-hit-zone frequency-hopping sequence sets with strictly optimal partial Hamming correlation based on Chinese Remainder Theorem

Construction of secure adaptive frequency hopping sequence sets based on AES algorithm

AbstractCommunication security has become particularly crucial with the rapid development of the Internet of Things (IoT). Frequency hopping spread spectrum (FHSS) technology, a prevalent method in wireless communication, has a wide range of applications in the Internet of Things. Enhancing the security of frequency hopping sequences is an essential means to improve the security of frequency hopping communication in the Internet of Things, as the performance of frequency hopping sequences plays a crucial role in frequency hopping systems. This paper proposes constructing secure adaptive frequency hopping sequence sets based on the advanced encryption standard (AES) algorithm. As a block cipher algorithm with superior security, the AES algorithm can provide a fundamental guarantee for the security of the proposed frequency hopping sequences. The mapping methods from ciphertext sequences to frequency hopping sequences proposed in this paper can achieve the construction of frequency hopping sequences of any frequency set size to meet the requirements of adaptive frequency hopping. In addition, we also model and analyse the problem of overlapping spectrum band of the IoT groups in the industrial, scientific, and medical (ISM) band, aiming to achieve better packet transmission performance by adjusting the frequency set size.

Low-hit-zone frequency hopping sequence sets under aperiodic Hamming correlation

AbstractThe study of aperiodic Hamming correlation (APC) of frequency hopping sequences (FHSs) is a hard problem that has not been paid enough attention in the literature. For low-hit-zone (LHZ) FHSs, the study of APC becomes more difficult. We call them LHZ FHSs under APC (LHZ-APC FHSs). LHZ-APC FHSs are studied for the first time in this paper. First, we establish a bound on the family sizes of LHZ-APC FHS sets. Then we present a method for constructions of LHZ-APC FHS sets based on conventional FHS sets under periodic Hamming correlation (conventional PC FHS sets). By choosing different conventional PC FHS sets, we obtain three classes of LHZ-APC FHS sets whose family sizes are optimal or near optimal according to this new bound. Further, we modify the construction method and get more new LHZ-APC FHS sets with optimal family sizes.

Constructions of optimal low hit zone frequency hopping sequence sets with large family size

<p style='text-indent:20px;'>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.</p>

Construction of three classes of strictly optimal frequency-hopping sequence sets

<p style='text-indent:20px;'>In this paper, we construct three classes of strictly optimal frequency-hopping sequence (FHS) sets with respect to partial Hamming correlation and family size. The first and second classes are based on the trace map, the third class is based on a generic construction.</p>

Construction of Two Kinds of Optimal Wide-Gap Frequency-Hopping Sequence Sets

Construction of Two Kinds of Optimal Wide-Gap Frequency-Hopping Sequence Sets

Construction of Near-Optimal Frequency Hopping Sequence Set with Low-Hit-Zone

The low-hit-zone (LHZ) frequency hopping sequence (FHS) sets are widely applicable in quasi-synchronous frequency hopping multiple-access (QS-FHMA) systems. In order to reduce mutual interference (MI) in the zone around the signal origin between different users, we recommend the LHZ FHS set instead of the conventional FHS set. In this letter, we propose a design of LHZ FHS sets via interleaving techniques. The obtained sequences can be confirmed that they are near-optimal in relation to the Peng-Fan-Lee bound.

Construction of Optimal Frequency Hopping Sequence Set with Low-Hit-Zone.

In quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems, low-hit-zone (LHZ) frequency-hopping sequence (FHS) sets have been well-applied to reduce mutual interference (MI). In this paper, we propose three constructions of LHZ FHS sets with new parameters via interleaving techniques. The obtained sequences can be verified that they are optimal with respect to the Peng-Fan-Lee bound.

Optimal Constructions of Low-Hit-Zone Frequency-Hopping Sequence Sets via Cyclotomy

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.

Optimal and near-optimal frequency-hopping sequences based on Gaussian period

<abstract><p>Frequency-hopping sequences (FHSs) have a decisive influence on the whole frequency-hopping communication system. The Hamming correlation function plays an important role in evaluating the performance of FHSs. Constructing FHS sets that meet the theoretical bounds is crucial for the research and development of frequency-hopping communication systems. In this paper, three new classes of optimal FHSs based on trace functions are constructed. Two of them are optimal FHSs and the corresponding periodic Hamming autocorrelation value is calculated by using the known Gaussian period. It is shown that the new FHSs are optimal according to the Lempel-Greenberger bound. The third class of FHSs is the near-optimal FHSs.</p></abstract>

Constructions of low-hit-zone frequency hopping sequence sets from cyclic codes

Constructions of low-hit-zone frequency hopping sequence sets from cyclic codes

Optimal Quasi-Orthogonal FH Sequences With Adaptive Array Receiver for Massive Connectivity in Asynchronous Multi-Cluster Networks

This paper is concerned with the enabling of massive connectivity in a multi-cluster network. In order to tackle significant amount of interference imposed by inter- and intra-cluster users, we consider a frequency-hopping (FH) system where an improved quasi-orthogonal hopping pattern, called optimal strong no-hit-zone FH sequence (SNHZ-FHS) set, is adopted in each cluster. We propose a flexible construction of SNHZ-FHS sets and derive their Hamming correlation values at different access delays. Since the maximum number of supportable users under traditional FH networks is strictly limited by the number of frequency slots, we investigate the design of a novel class of adaptive array beam-forming (BF) receiver in which SNHZ-FHS patterns (i.e., SNHZ-FH/BF) are reused over asynchronous multi-cluster uplink channels. Extensive numerical comparisons show that our proposed SNHZ-FH/BF system provides an effective means for attaining higher user capacity as well as remarkable capability of interference suppression.

Low-Hit-Zone Frequency-Hopping Sequence Sets with Wide-Gap and Optimal Hamming Correlation Properties

Low-Hit-Zone Frequency-Hopping Sequence Sets with Wide-Gap and Optimal Hamming Correlation Properties

New Constructions for Near-Optimal Sets of Frequency-Hopping Sequences via the Gaussian Periods in Finite Fields

Frequency-hopping sequences (FHSs) have been widely applied in frequency-hopping code-division multiple-access (FH-CDMA) systems, since they can be used for transmitting messages efficiently along with switching frequencies at set intervals by each sender. The performance of the FHSs has a great impact on the performance of FH-CDMA systems. The optimality achieving exactly the Peng-Fan bounds is an important performance measure. However, optimal sets of FHSs do not always exist for all lengths and alphabet sizes. Thus, it is meaningful to seek and design more near-optimal FHS sets whose parameters are near to achieving the Peng-Fan bounds. Let <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> be a power of a prime. In this paper, we present some classes of near-optimal sets of FHSs, whose parameters are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\left({\frac {3(q+1)}{2},\frac {2(q-1)}{3},3;q}\right)$ </tex-math></inline-formula> with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q\equiv 1 \pmod {12}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\left({\frac {q+1}{k},{k(q-1)},2;q}\right)$ </tex-math></inline-formula> with even <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\frac {q+1}{k}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\left({2(q^{2}+1),\frac {q^{2}-1}{2},2(q+1);q}\right)$ </tex-math></inline-formula> with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q \equiv 3 \pmod {4}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(19,18,4;7)$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(7,9,3;4)$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(91,45,7;16)$ </tex-math></inline-formula> respectively. Most importantly, these classes of near-optimal sets of FHSs have new parameters which are not covered in the foregoing literature.

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

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 betweenWG 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.

Optimal no‐hit‐zone frequency hopping sequence sets with wide gap

Using no-hit-zone frequency-hopping (FH) sequences with wide gap (WG NHZ FH sequences), the quasi-synchronous (QS) FH communication systems not only have good capability of preventing muti-path interference but also have strong capabilities of resisting the enemy's intentional interferences in the complicated electromagnetic interference conditions. This paper designs a new class of optimal WG NHZ FH sequence set which was not presented previously. It significantly meet the needs of high reliable QS FH communication under complicated electromagnetic interference conditions.

Construction of Multiple Optimal Polyphase Zero Correlation Zone Sequence Sets With Inter-Set Zero Cross-Correlation Zone

Based on DFT matrices and no-hit-zone (NHZ) frequency hopping sequence sets, a construction of multiple optimal polyphase zero correlation zone sequence sets with inter-set zero cross-correlation zone (ZCCZ) is proposed. The parameters of each subset are optimal, and arbitrary two sequences from different subsets have the same inter-set ZCCZ. Furthermore, new NHZ frequency hopping sequence sets are proposed, which can be used in the construction of multiple polyphase ZCZ sequence sets with inter-set ZCCZ. The resultant sequence sets presented in this letter can be applied to multi-cell QS-CDMA systems.

NHZ frequency hopping sequence sets under aperiodic Hamming correlation: Tighter bound and optimal constructions

NHZ frequency hopping sequence sets under aperiodic Hamming correlation: Tighter bound and optimal constructions