The hit array: a synthesis tool for multiple access frequency hop signals

The hit array formalism was developed for the analysis of general frequency hop waveforms, in the context of coherent active radar and sonar echolocation systems, or multiple access spread spectrum communications. This formalism is shown to be useful for synthesis as well. Necessary and sufficient conditions are derived for a given hit array to be realizable, i.e., to correspond to a valid frequency hopping pattern. A general backtracking-type algorithm is presented to reconstruct the pattern(s) associated with this hit array. This makes it possible to synthesize a set of frequency hop waveforms directly from any given (realizable) hit array, and thus, because of the correspondence between hit array and ambiguity function, from any physically meaningful ambiguity function. In particular, for limited a priori range and Doppler shifts, this is the first efficient algorithm for direct synthesis from ideal ambiguity function specifications. Several reconstruction examples are shown for illustration purposes.<>