Constructions and properties of Costas arrays
Abstract
In a frequencyhopping radar or sonar system, the signal consists of one or more frequencies being chosen from a set of available frequencies. Such a signal is conveniently represented by an n x n permutation matrix. Costas (1975) has conducted a search for permutation matrices for which a certain condition involving the ideal ambiguity function of the matrix is satisfied. Subsequently, permutation matrices which satisfy this condition have been called either constellations or Costas arrays. The present investigation provides a survey of current knowledge about Costas arrays. Systematic methods of construction are discussed, taking into account the Welch construction, the Lempel construction, the Golomb construction, and a table of known constructions. Costas arrays with special properties are considered, giving attention to periodic constructions, nonattacking queens, shearing, honeycomb arrays, and symmetric arrays.
 Publication:

IEEE Proceedings
 Pub Date:
 September 1984
 Bibcode:
 1984IEEEP..72.1143G
 Keywords:

 Frequency Hopping;
 Matrices (Mathematics);
 Radar Transmission;
 Sonar;
 Synthetic Arrays;
 Transmission Efficiency;
 Ambiguity;
 Antenna Design;
 Autocorrelation;
 Design Analysis;
 Permutations;
 Spectral Correlation;
 Electronics and Electrical Engineering