Even-odd transformation with application to multiuser CW radars

An even odd transformation is a linear phase transformation which translates a set of sequences into another set, all of whose absolute even (also called periodic) and odd correlation functions become the respective absolute odd and even correlation functions of the original set. This transformation enables the choice of periodic or odd-periodic sequence sets to simplify the implementation of a multiuser CW radar without sacrificing its pulse compression performance. As an application example, the odd-perfect counterparts of the famous Zadoff-Chu sequence sets are derived. Of particular interest is a pair of odd perfect sequences with optimal odd cross-correlation levels, whose phase alphabet size is only half of that of the well-known P3 code for even lengths.