Optimal Partial Hamming Correlation Research Articles

New classes of strictly optimal low hit zone frequency hopping sequence sets

<p style='text-indent:20px;'>Low hit zone frequency hopping sequences (LHZ FHSs) with favorable partial Hamming correlation properties are desirable in quasi-synchronous frequency hopping multiple-access systems. An LHZ FHS set is considered to be strictly optimal when it has optimal partial Hamming correlation for all correlation windows. In this study, an interleaved construction of new sets of strictly optimal LHZ FHSs is proposed. Strictly optimal LHZ FHS sets with new and flexible parameters are obtained by selecting suitable known optimal FHSs and appropriate shift sequences.

Decimated m-sequences families with optimal partial Hamming correlation

In quasi-synchronous frequency-hopping multiple-access systems where relative delays are restricted within a certain zone, low hit zone frequency-hopping sequences (LHZ FHSs) with favorable partial Hamming correlation properties are desirable. In this paper, we present a new class of LHZ FHS sets with optimal partial Hamming correlation based on t-decimation of m-sequence.

A New Method to Construct Strictly Optimal Frequency Hopping Sequences With New Parameters

In order to evaluate the goodness of frequency hopping (FH) sequence design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FH sequence, so the study of the partial Hamming correlation of FH sequence is particularly important. If an FH sequence or an FH sequence set has an optimal partial Hamming correlation with respect to the partial Hamming correlation bound for all length of correlation window, then the FH sequence or the FH sequence set is said to be strictly optimal. In this paper, we first prove that there is no strictly optimal FH sequence set of family size $M$ and sequence length $N$ over a frequency slot set of size $q$ with respect to the partial Hamming correlation bound derived by Niu et al. when $N>{q^{2}}/{M}$ and $q\geq 2$ , and that by Cai et al. when $N>{q^{2}}/{M}$ and $q\geq {2N}/({N-2})$ . Furthermore, we define a special partition-type difference packing (DP) called $[N,\nabla,H_{a}^{l}]$ PDP and give several classes of $[N,\nabla,H_{a}^{l}]$ PDPs. Then, we present a new construction of strictly optimal FH sequences. By choosing different PDPs, the FH sequences constructed can give new and flexible parameters. By utilizing this construction method recursively, we can obtain new $[N,\nabla,H_{a}^{l}]$ PDPs, which lead to infinitely many classes of strictly optimal FH sequences with new parameters. Moreover, based upon an $[N,\nabla,H_{a}^{l}]$ PDP, we present a construction of strictly optimal FH sequence sets. By preceding construction method and recursive construction, we can also obtain infinite classes of strictly optimal FH sequence sets which can give new and flexible parameters.

New families of strictly optimal frequency hopping sequence sets

Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHS sets with optimal partial Hamming correlation. We present several direct constructions for balanced nested cyclic difference packings (BNCDPs) and balanced nested cyclic relative difference packings (BNCRDPs) by using trace functions and discrete logarithm. We also show three recursive constructions for FHS sets with partial Hamming correlation, which are based on cyclic difference matrices and discrete logarithm. Combing these BNCDPs, BNCRDPs and three recursive constructions, we obtain infinitely many new strictly optimal FHS sets with respect to the Peng-Fan bounds.

Construction of low-hit-zone frequency hopping sequences with optimal partial Hamming correlation by interleaving techniques

In quasi-synchronous frequency hopping code division multiple-access systems, frequency hopping sequences (FHSs) with low-hit-zone (LHZ) are commonly employed to minimize multiple-access interferen...

Frequency Hopping Sequences With Optimal Partial Hamming Correlation

Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHSs and FHS sets with optimal partial Hamming correlation. We first establish a correspondence between FHS sets with optimal partial Hamming correlation and multiple partition-type balanced nested cyclic difference packings with a special property. By virtue of this correspondence, some FHSs and FHS sets with optimal partial Hamming correlation are constructed from various combinatorial structures, such as cyclic difference packings and cyclic relative difference families. As a consequence, our constructions yield new FHSs and FHS sets with optimal partial Hamming correlation.

Strictly Optimal Frequency-Hopping Sequence Sets With Optimal Family Sizes

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.

A New Construction of Frequency-Hopping Sequences With Optimal Partial Hamming Correlation

Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, lower bounds on the partial Hamming correlation of FHSs and FHS sets are proposed. They slightly improve the known bounds by Eun et al. and Zhou et al. A construction of FHSs and FHS sets having optimal partial Hamming correlation with respect to the improved bounds is also presented based on the theory of generalized cyclotomy. Our construction yields optimal FHSs and FHS sets with new and flexible parameters not covered in this paper.

Set of Frequency-Hopping Sequence with Optimal Hamming Correlation

In wireless communication systems, frequency hopping (FH) spread spectrum and direct sequence spread spectrum are two main spread coding technologies. In this paper,by the Cartesian product, we construct one class of one-coincidence frequency-hopping sequence set. It is shown that this set has optimal balance property, optimal average periodic Hamming correlation properties and optimal average periodic partial Hamming correlation properties according to the bounds.

Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties

In order to evaluate the goodness of frequency hopping sequence (FHS) design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FHS, so the study of the partial Hamming correlation of FHS is particularly important. In this paper, a class of low-hit-zone (LHZ) FHS sets with good partial Hamming correlation properties which has not yet been reported previously is constructed based on interleaving techniques. It is shown that new FHS sets are optimal with respect to the partial Hamming correlation bound of FHSs with LHZ.

Frequency/time hopping sequence sets with optimal partial Hamming correlation properties

Frequency hopping/time hopping(FH/TH) sequences have found wide applications in various modern FH/TH spread spectrum communications, such as digital cellular mobile communication, short-range wireless communication, personal communication, and multi-user radar, sonar systems. In order to evaluate the goodness of FH/TH sequences design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FH/TH sequence, so the study of the partial Hamming correlation of FH/TH sequence is particularly important. In this paper, a new class of FH/TH sequence sets with good partial Hamming correlation properties is proposed and investigated. The construction of new FH/TH sequence sets is based upon the generalized m-sequence and generalized Gordon-Mills-Welch sequence over a polynomial residue class ring. It is shown that new FH/TH sequence sets are optimal with respect to the partial Hamming correlation bound.