A new method to construct double periodic arrays with optimal correlation

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 double-periodic 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.