Constructions and Properties of Costas Arrays,
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES COMMUNICATIONS SCIENCES INST
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A Costas array is an n x n array of dots and blanks with exactly one dot in each row and column, and with distinct vector differences between all pairs of dots. As a frequency-hop pattern for radar or sonar, a Costas array has an optimum ambiguity function, since any translation of the array parallel to the coordinate axes produces at most one out-of-phase coincidence. We conjecture that n x n Costas arrays exist for every positive integer n. Using various constructions due to L. Welch, A. Lempel, and the authors, Costas arrays are shown to exist when n p - 1, n q - 2, n q - 3, and sometimes when n q - 4 and n q - 5, where p is a prime number, and q is a power of a prime number.
- Theoretical Mathematics