Frequency- and time-hop coded signals for use in radar and sonar systems and multiple access communications systems

In the paper we review the use of multi-user radar and sonar as well as spread spectrum multiple access communications. In order to solve most of these problems we study the various families of frequency hop codes and discuss their mutual auto- and cross-ambiguity functions showing the trade-offs in design. The hyperbolic congruence code family is shown to be the optimum compromise between auto- and cross-ambiguity function properties. A bound on the size of ambiguity sidelobes, is shown and the additional trade-offs between good sidelobe behavior and good mainlobe behavior is discussed. New families of time-hop codes such as optical orthogonal codes are derived from the frequency-hop families