A generalized hyperbolic frequency hopping sequences

We present the problem of constructing frequency hopping (FH) sequences. The new family of FH sequences we have constructed is called generalized hyperbolic FH sequences. The previous hyperbolic FH sequences, derived by S.V. Maric and E.I. Titlebaum (see IEEE Trans. Commun., vol.40, no.9, p.1442-7, 1992), and extended hyperbolic hopping, derived by M.S. Iacobucci and M.G.D. Benedetom (see IEEE Int. Conf. on Commun., p.817-20, 2002), which are analyzed by P.Z. Fan et al. (see IEEE Trans. Wireless Commun., TW03-502), are reviewed. From the results shown, we conclude that the proposed hyperbolic FH sequences have the family size of (p-1)³, wider than the (p-1) derived by Maric and Titlebaum and the (p-1)² presented by Iacobucci and Benedetom. Moreover, we get the same optimum Hamming autocorrelation and Hamming cross-correlation values as constructed by Maric and Titlebaum.