Frequency hopping patterns based on finite geometry

This paper concentrates on the algebraic construction of a family of frequency hopping sequences patterns that are suitable for frequency hopping code-division multiple-access spread spectrum communication (FH-CDMA). The design philosophy of the construction is based on the finite geometry. The following family of frequency hopping patterns with good autocorrelation and crosscorrelation properties could be constructed this philosophy. For a given parameter k, where k is a positive integer, the period of the frequency hopping patterns is 2/sup 2k/-1 chips. The frequency alphabet is represented by 2/sup 2k/-1 frequencies. The crosscorrelation magnitudes being bounded by a value k-1. The out-of-phase autocorrelation magnitudes being zero for every phase shift. The cardinality of this family is at most 2/sup k/ patterns. Each frequency slot is used once within the sequence period and every pattern consists of the full frequency alphabet. Consequently, the designed sequences are nonrepeating hopping patterns suitable for initial synchronization. In general, the patterns are strongly nonlinear due to their construction.