Class Of Frequency Hopping Sequences Research Articles

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>

Two classes of optimal frequency-hopping sequences with new parameters

Direct-sequence spread spectrum and frequency-hopping (FH) spread spectrum are two main spread-coding technologies. Frequency-hopping sequences (FHSs) achieving the well-known Lempel–Greenberger bound play an important part in FH code-division multiple-access systems. Our objective is to construct more FHSs with new parameters attaining the above bound. In this paper, two classes of FHSs are proposed by means of two partitions of $${{\mathbb {Z}}_{v}}$$ , where v is an odd positive integer. It is shown that all the constructed FHSs are optimal with respect to the Lempel–Greenberger bound. By choosing appropriate injective functions, infinitely many optimal FHSs can be recursively obtained. Above all, these FHSs have new parameters which are not covered in the former literature.

A Class of Frequency-Hopping Sequences with Prime-Power Length Based upon Generalized Cyclotomy

A Class of Frequency-Hopping Sequences with Prime-Power Length Based upon Generalized Cyclotomy

New Classes of Frequency-Hopping Sequences With Optimal Partial Correlation

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.

New Bound on Frequency Hopping Sequence Sets and Its Optimal Constructions

In this paper, we derive a new bound on maximum nontrivial Hamming correlation of frequency hopping (FH) sequences from the Singleton bound in error correcting code literature, and we discuss the relation between the new bound and the known ones on FH sequences. Further, we construct two classes of FH sequences from punctured Reed–Solomon codes and one class of FH sequences from polynomial functions, which meet the new bound.

On the Linear Complexity of Chung-Yang Sequences over GF(q)

In this letter, we determine the linear complexity and minimum polynomial of the frequency hopping sequences over GF(q) introduced by Chung and Yang, where q is an odd prime. The results of this letter show that these sequences are quite good from the linear complexity viewpoint. By modifying these sequences, another class of frequency hopping sequences are obtained. The modified sequences also have low Hamming autocorrelation and large linear complexity.

On a general class of quadratic hopping sequences

Based upon quadratic polynomials over the finite field, a new class of frequency hopping sequences with large family size suitable for applications in time/frequency hopping CDMA systems, multi-user radar and sonar systems is proposed and investigated. It is shown that the new time/frequency hopping sequences have at most one hit in their autocorrelation functions and at most two hits in their crosscorrelation functions except for a special case, and their family size is much larger than the conventional quadratic hopping sequences. The percentage of full collisions for the new quadratic hopping sequences is discussed. In addition, the average number of hits for the new quadratic hopping sequences, quadratic congruence sequences, extended quadratic congruence sequences and the general linear hopping sequences are also derived.