Multiuser sonar properties for Costas array frequency hop coded signals

The cross-ambiguity properties of Costas-array frequency-hop coded signals for use in wideband multiuser sonar systems are established. In order to prevent system crosstalk, cross-ambiguity function for the signals should be minimized. The conditions under which Costas arrays achieve the minimum value of their cross-ambiguity functions are provided. The upper bound on the maximum number of hits in the cross-ambiguity function for Welch-Costas arrays is given, and it is shown that the maximum number of hits depends on the form of the prime over which the arrays are constructed.