New Extension Constructions of Optimal Frequency-Hopping Sequence Sets

Abstract

In this paper, a general framework of constructing optimal frequency hopping sequence (FHS) sets is presented based on the designated direct product. Under the framework, we obtain infinitely many new optimal FHS sets by combining a family of sequences that are newly constructed in this paper with some known optimal FHS sets. Our constructions of optimal FHS sets are also based on extension method. However, our constructions remove the constraint requiring that the extension factor is co-prime with the length of original FHSs and get new parameters. In literature, most of the extension constructions suffer from this constraint. As a result, our constructions allow a great flexibility of choosing parameters of FHS sets for a given frequency-hopping spread spectrum system.

A Construction of Optimal Frequency Hopping Sequence Set via Combination of Multiplicative and Additive Groups of Finite Fields

“…Proof. By applying the (k, lpf(k) − 1; k) OC sequence set given in [2,1,8], the (p − 1, p; p) OC sequence set given in [2,1,8] and the (k(p − 1), min{lpf(k) − 1, p}; kp) OC sequence set given in [2,8], respectively to Theorem 4, we obtain the desired FHS sets in Table 1.…”

“…Recursive constructions have been proposed in [2,10,16,1,8] to generate new families of optimal FHS sets under certain conditions. The framework of recursive constructions in [8] can be used to get FHS set with new parameters, which increase the length and alphabet size of the original FHS set, but preserve its family size and maximum Hamming correlation. In this section, by applying the FHS set S in Theorem 3 to a recursive construction, we obtain some new classes of FHS sets.…”

“…The recursive constructions extend the FHS set S in the above section by choosing different one-coincide sequence sets. There are some known constructions of OC sequence sets [12,4,15,11,8]. Based on the framework of the recursive construction in [8], we can obtain FHS sets with new parameters by combing the FHS set in Theorem 3 with OC sequence sets.…”

“…It is of particular interest to construct FHS sets which meet Peng-Fan bound. There are several algebraic method, combinatorial and recursive constructions in the literature [7,14,3,5,20,18,19,2,10,16,1,8,17].…”

A new class of optimal wide-gap one-coincidence frequency-hopping sequence sets

“…Later on, Lee et al [16] presented another construction of OC-FHS sets by a primitive element of the prime field. In addition, Niu et al [20] obtained an OC-FHS set with more flexible parameters by a designed direct product.…”