Aperiodic auto-correlation of polyphase sequences with a small peak-factor
The aperiodic auto-correlation function (ACF) of polyphase sequences that behave well in terms of the peak-factor is investigated. General considerations concerning arbitrary polyphase sequences are followed by the analysis of binary Rudin-Shapiro sequences and the so-called Zygmund sequences. In the first case, the asymptotic limit of the inverse merit-factor is considered to make clear that sequences with a very small peak-factor can exhibit poor aperiodic ACF properties. Then an investigation of the aperiodic ACF of Zygmund sequences is presented. The phase function of these sequences does not depend on the sequence length, and thus they are simple to design regarding the partial auto-correlation function.