Construction and Properties of Costas Arrays.

摘要

A Costas array is an nXn permutation matrix which, when regarded as a frequency hopping pattern (n frequencies vs. n time intervals) has an optimum ambiguity function, i.e., at most one coincidence for each shift in both time and frequency. Several systematic infinite families of constructions for Costas arrays have been found, all involving primitive roots in finite fields. A summary of the known constructions is presented for all n equal to or less than 360. The smallest case for which no construction has yet been found is n = 32. The total number of distinct Costas arrays has been enumerated for n equal to or less than 12, and all the individual Costas arrays are illustrated for n equal to or less than 8. These arrays are useful as frequency hopping patterns for radar and sonar signals, and as patterns for achieving two-dimensional alignment and synchronization. (Author)