The Hit Array: An Analysis Formalism for Multiple Access Frequency Hop Coding

Abstract

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 hit 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. © 1991 IEEE