Time-frequency properties of extended quadratic congruential frequency hop signals

Frequency-hop pulse train signals used in applications such as coherent multiuser or multibeam echo location must be selected on the basis of good time-frequency characteristics in both auto- and cross-ambiguity domains. Toward this end, a class of frequency-hop signals is developed on the basis of an extension of the theory of quadratic congruences. An uniform upper bound is placed on the entire cross-ambiguity function surface, and bounds are placed on the amplitude of spurious peaks in the auto-ambiguity function. These bounds depend on time-bandwidth product and code length exclusively. Examples of typical auto- and cross-ambiguity functions are shown to illustrate the time-frequency properties of the signals.