Congruential frequency hop signals for multi-user environments: A comparative analysis

Frequency-hop pulse train signals used in applications such as coherent multiuser or multibeam echolocation must be selected on the basis of good time-frequency characteristics in both auto- and cross-ambiguity domains. A comparative analysis is presented for several classes of such signals, all algebraically constructed via congruences on a finite field. For each class, 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 functions. These bounds depend on time-bandwidth product and code length exclusively, which allows for a meaningful comparison across classes. Typical aspects of time-frequency behavior are shown to illustrate the associated detection and resolution properties.