Hamming Correlation Research Articles

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

Low‐complexity algorithms for generating frequency hopping sequences with good aperiodic hamming correlation property

AbstractIn this letter, novel methods for quickly generating frequency hopping (FH) sequences with good out‐of‐phase peak aperiodic Hamming auto‐correlation (PAHAC) property are proposed. Compared with brute‐force search algorithm, the proposed algorithms have an obvious advantage on their time complexity. Results show that the algorithms can generate FH sequences with optimal/quasi‐optimal PAHAC performance in all tested cases.

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.

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>

Optimal wide-gap-zone frequency hopping sequences

In this paper, we generalize the concept of wide-gap frequency hopping sequences (WG-FHSs) to wide-gap-zone frequency hopping sequences (WGZ-FHSs) by placing restrictions on the parameters. Then we derive a lower bound on the maximum periodic Hamming correlation of WGZ-FHSs. Further, we give a construction for optimal WGZ-FHS sets with respect to the new bound.

New Bounds on the Partial Hamming Correlation of Wide-Gap Frequency-Hopping Sequences with Frequency Shift

New Bounds on the Partial Hamming Correlation of Wide-Gap Frequency-Hopping Sequences with Frequency Shift

New Bounds of No-Hit-Zone Frequency-Hopping Sequences with Frequency Shift

In quasi-synchronous FH multiple-access (QS-FHMA) systems, no-hit-zone frequency-hopping sequences (NHZ-FHSs) can offer interference-free FHMA performance. But, outside the no-hit-zone (NHZ), the Hamming correlation of traditional NHZ-FHZs maybe so large that the performance becomes not good. And in high-speed mobile environment, Doppler shift phenomenon will appear. In order to ensure the performance of FHMA, it is necessary to study the NHZ-FHSs in the presence of transmission delay and frequency offset. In this paper, We derive a lower bound on the maximum time-frequency two-dimensional Hamming correlation outside of the NHZ of NHZ-FHSs. The Zeng-Zhou-Liu-Liu bound is a particular situation of the new bound for frequency shift is zero.

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>

New bounds of wide‐gap frequency‐hopping sequences with frequency shift

With the rapid development of radar, the phenomenon of Doppler frequency shift is not rare. Frequency shift needs to be considered in order to accurately calculate the mutual interference between signals. Meanwhile, to reduce interference to the received signal, each user's frequency hopping sequence shall have wide frequency hopping gap. The authors introduce the time-frequency two-dimensional Hamming correlation function and extend the bounds for wide-gap frequency-hopping sequences. The Li–Fan–Yang–Wang bounds are the special cases of our bounds for frequency shift is zero.

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.

Optimal Low-Hit-Zone Frequency-Hopping Sequence Sets With Wide-Gap for FHMA Systems Under Follower Jamming

This letter is concerned with tackling both of the multi-access interference (MAI) and the follower jamming (FJ) in frequency-hopping multiple-access (FHMA) systems via novel FH sequence (FHS) design. We consider low-hit-zone (LHZ) FHS which provides lower MAIs in quasi-synchronous FHMA systems but suffers from FJ attack. We introduce an improved LHZ-FHS with wide-gap (i.e., WG-LHZ-FHS) for the neighboring carrier frequencies so as to combat the MAI and the FJ. We first present a general method to generate new WG-FHS sets and then construct the first known WG-LHZ-FHS sets with optimal periodic Hamming correlation (PHC) properties. Besides, the error-rate performance of the constructed WG-LHZ-FHS set imposed in an FHMA system under FJ is investigated. The numerical analysis and the system simulation results indicate that the proposed WG-LHZ-FHS set provides the better error-rate performance to combat the FJ as well as satisfactory capability of MAI suppression due to its combined merits of WG and LHZ.

Strong no‐hit‐zone frequency sequence set with wide gap

For the communication systems, no-hit-zone (NHZ) frequency hopping sequences have good anti-interference performance. However, the system's time delay may be out of the NHZ. In this situation, the maximum Hamming correlation is needed to be taken into consideration. When the maximum Hamming correlation of an optimal NHZ-FHS set is minimal, the NHZ-FHSs will be called strong NHZ-FHSs. It is also hoped that FHSs have a wide gap property to resist the enemy's intentional interferences. In this letter, a tighter bound for optimal NHZ-FHSs' maximum Hamming correlation is proposed and an optimal strong NHZ-FHS set is constructed with widegap.

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

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.

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

Low-Hit-Zone Wide Gap Frequency Hopping Sequence Sets With Optimal Average Hamming Correlation

In frequency hopping (FH) sequence design, the wide gap is an important performance indicator. In this paper, the average Hamming correlation of wide gap FH sequence (WG-FH sequence) sets with low hit zone, which has not yet been reported previously, is studied. A lower bound on the average Hamming auto-correlation and the average Hamming cross-correlation of low-hit-zone FH sequence sets is firstly derived. The new lower bound includes the bound for conventional FH sequence sets derived by Peng et al. as a special case. Then a construction of WG-FH sequence sets with multiple low hit zones is presented, which are optimal by the new bound for these low hit zones. Finally, another class of optimal WG-FH sequence sets with multiple low hit zones is presented, which have larger wide gap.

Frequency-Hopping Sequences With Optimal Average Hamming Correlation and Their Applications in Energy and Spectrum Harvesting Technologies Area

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.

Multi-Level Sequence-Based Frequency-Hopping in Multi-Cell Networks

In heterogeneous multi-cell networks (HetNets), inter-and intra-cell interference are critical issues impairing the performance. In this paper, the frequency-hopping (FH) technique based on an attractive FH sequence (FHS) set with two-level Hamming correlations is exploited in such networks. Motivating from the idea of no-and low-hit-zone FHS sets, a construction algorithm of the new FHS set is proposed by utilizing the interleaving technique. Then, the performance metric of such FHS set in terms of Hamming correlation properties are derived, which are verified by an example. Compared with classic FHS sets (patterns), the proposed FHS set offers a zero Hamming cross-correlation for intra-cell users, and a low Hamming cross-correlation for inter-cell users (i.e., multi-level quality-of-services). The intra-and inter-interference in multi-cell HetNets can be significantly reduced by the proposed sequence-based FH technique.

Two constructions of low-hit-zone frequency-hopping sequence sets

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ m $\end{document}</tex-math></inline-formula>-sequences and <inline-formula><tex-math id="M2">\begin{document}$ d $\end{document}</tex-math></inline-formula>-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).</p>