A New Construction Framework for Polyphase Complete Complementary Codes With Various Lengths

Complete complementary codes (CCC) with equal sequence lengths have found numerous applications in wireless communications owing to their ideal correlation properties. In modern multi-user multi-rate communication systems, CCCs with various sequence lengths for different complementary codes are desirable. In this paper, we propose a new construction of polyphase CCC with various lengths by using unimodular paraunitary (PU) matrices. Our key idea is to decompose a large square PU matrix into direct sum of matrices with smaller sizes (which is equivalent to block diagonalization of matrices) in order to construct CCC with various lengths. We show that our proposed constructions not only generalize several previously known methods but also lead us to new CCCs with both equal and various lengths.