Double periodic arrays with applications

Abstract

Algebraic constructions of families of double periodic arrays with good autoand cross-correlation have been used for applications in frequency hopping radar and sonar, Optical Code Division Multiple Access, design of experiments, and more recently in Digital Watermarking. We need the family size of these constructions to be as large as possible to increase multiple user or multiple target detection capacity. In this work we introduce the concept of Group Permutable Constant Weight Codes and we extend the Johnson Bound, to bound the cardinality of families of binary and non-binary Group Permutable Constant Weight Codes. These bounds are used to prove the optimality of some of our new constructions of Double Periodic Arrays. We also present three methods to construct families of Double Periodic Arrays. A method to increase the weight of double periodic arrays (Method A). With this method we deal with the need of double periodic arrays with the weight as large as possible while maintaining a good correlation value. We present a new method to increase the size of families of double periodic arrays (Method B).There are only a few families of double periodic arrays with perfect correlation properties. In many cases the new constructions generated with Method B result in new families of double periodic arrays with perfect correlation properties and in all cases at least the original correlation properties are preserved. Finally we present a combination of Method A and Method B to produce new families of double periodic constructions with increased family size and weight (Method C). When Method C is applied to a double periodic array we obtain new Fuja type families of double periodic arrays with unequal correlation constrains. More specifically, we obtain new families of double periodic arrays with cross-correlation much lower than auto-correlation ( c < a).