Design of infinite chaotic polyphase sequences with perfect correlation properties

In this paper we consider chaotic discrete-time systems which generate polyphase sequences. First we give the definition of infinite polyphase sequences with perfect correlation properties. Then a simple design rule for chaotic generators is derived which guarantees that the generated sequences are perfect. Following this rule we construct families of generators of infinite polyphase sequences. Finally, as an important characteristic for several applications, an explicit expression for the variance of a finite-length correlation estimator is derived