The hit array: an analysis formalism for multiple access frequencyhop coding

A formalism is presented for the analysis of general frequency hop waveforms, such as those suitable for use in coherent active radar and sonar echolocation systems as well as multiple-access spread-spectrum communications. This formalism is based on the concept of coincidence, or `hit', between two frequency hopping patterns. The collection of all possible hits, together with their locations, is recorded in time-frequency space, which produces the high array associated with the two patterns considered. If the code length is sufficiently small with respect to the time-bandwidth product chosen, the hit array can be viewed as a digital representation of the corresponding ambiguity function. Salient properties of the hit array formalism are derived, including simple relationships between hit arrays resulting from basic symmetry-preserving transformations. These properties make it possible to predict the performance of a given set of frequency hop waveforms directly from the associated set of frequency hopping patterns