A class of frequency hop codes with nearly ideal characteristics for use in multiple-access spread-spectrum communications and radar and sonar systems

In the paper we address the problem of constructing frequency hop codes for use in multiuser communication systems such as multiple-access spread-spectrum communications and multiuser radar and sonar systems. Previous frequency hopping techniques are reviewed. The construction of a new family of frequency hop codes called hyperbolic frequency hop codes is given. Exactly p-1 codes of length p-1 exist for every prime, p. Additionally the fullness of the codes is proven. We review the concepts of multiple-access spread-spectrum communication systems and multiuser radar and sonar systems and it is shown that the hyperbolic frequency hop codes possess nearly ideal characteristics for use in both types of system. Specifically, in multiple-access communications the codes achieve minimum error probability, while in radar and sonar systems the codes have at most two hits in their autoand cross-ambiguity function. Examples of address assignment for multiple-access communications systems and radar and sonar autoand cross-ambiguity functions are also given.