Generalized Pairwise Complex Complementary Codes

Abstract

Complete complementary codes (CCs) have received much attention due to their ideal correlation properties. However, the small family size of CCs poses a tough challenge to their widespread application. To address this issue, we design a generalized pairwise complex complementary (GPCC) code set, which promises to expand twice as many codes if compared with an orthogonal code set. The GPCC code set consists of an in-phase branch (I-branch) and a quadrature branch (Q-branch). The correlation functions for both branches show the zero correlation zones (ZCZs). Moreover, beyond the ZCZs, the correlation functions for the I-branch and the Q-branch are complementary. Therefore, the ideal correlation property over the whole zone can be achieved. By cyclically shifting (CS) of a prime GPCC code, the codebook's size can be roughly expanded by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> times, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> refers to the code length. The proposed GPCC code set can be served as the address code pool for the multi-carrier code division multiple access (MC-CDMA), and the simulation results show that it achieves attractive bit error rate (BER) performance.