A new method to construct double periodic arrays with optimal correlation

Abstract

Double-periodic arrays with good correlation are useful for applications in multiple target Costas and sonar, optical communications, and more recently digital watermarking. There are only a few double-periodic constructions with perfect correlation. In previous work we presented a method to construct families of double-periodic arrays with perfect correlation from the Welch Costas construction using the Chinese Remainder. In this work we introduce a similar method to construct new families of double-periodic arrays without using the Chinese Remainder. We apply this new method to the Quadratic sonar and the Welch Costas arrays to produce new families of doubleperiodic arrays with perfect correlation properties. We also apply the method to the family of Quadratic sonars to produce new families of double-periodic arrays with close to perfect correlation. Finally we discuss the family size optimality of the constructions.

Algebraic Symmetries of Generic $(m+1)$-Dimensional Periodic Costas Arrays

“…The original two dimensional Costas arrays were introduced in [3], [5] and their periodicity properties have been studied in [6], [9], and more recently in [10]. Good correlation, and full periodicity properties such as those of some Costas arrays are very important for applications in digital watermarking [14], [15], and optical communications [7], [13].…”