New families of optimal frequency hopping sequence sets

Frequency hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems. In this paper, we present some new algebraic and combinatorial constructions for FHS sets, including an algebraic construction via the linear mapping, two direct constructions by using cyclotomic classes and recursive constructions based on cyclic difference matrices. By these constructions, a number of series of new FHS sets are then produced. These FHS sets are optimal with respect to the Peng-Fan bounds.