Z-Complementary Code Sets With Flexible Lengths From Generalized Boolean Functions

Shing-Wei Wu,Alphan Sahin,Chao-Yu Chen,Zhen-Ming Huang

doi:10.1109/access.2020.3047955

Abstract

In this paper, new direct constructions of Z-complementary code sets (ZCCSs) from generalized Boolean functions are proposed. In the literature, most ZCCS constructions based on generalized Boolean functions lead to sequences of power-of-two length. In this study, we show that our proposed methods result in ZCCSs of both power-of-two length and non-power-of-two length. Since the monomials of degrees more than 2 are employed in the proposed constructions, more ZCCSs can be obtained. The constructed ZCCSs admit the theoretical upper bound on the size for a ZCCS when the sequence length is a power of two. Also, the corresponding peak-to-average-power ratio (PAPR) is theoretically upper-bounded when a sequence in the set is used in OFDM. The proposed constructions extend the applications of ZCCSs in practical communication systems, e.g., multicarrier CDMA (MC-CDMA) system, by offering flexible sequence lengths, various set sizes, and bounded PAPR. For example, only one percent of sequences in the constructed ZCCS of size 16 and of length 128 have PAPRs larger than 8 whereas the theoretical upper bound is 16.

Highlights

Golay complementary pairs (GCPs) were first proposed by M
The definition of the GCP is extended to the Golay complementary set (GCS) by Tseng and Liu [2], where the sum of the aperiodic autocorrelations of all constituent sequences is zero except for the zero shift
We show that the obtained Z-complementary code sets (ZCCSs) can admit the theoretical upper bound on the set size and the peak-to-average-power ratio (PAPR) of the corresponding OFDM symbol with each sequence in the sets is bounded

Summary

INTRODUCTION

Golay complementary pairs (GCPs) were first proposed by M. The definition of the GCP is extended to the Golay complementary set (GCS) by Tseng and Liu [2], where the sum of the aperiodic autocorrelations of all constituent sequences is zero except for the zero shift. Later in [3], the complete complementary code (CCC) was proposed which includes a set of GCSs where the sum of cross-correlations of all sequences in two GCSs is zero for all shifts. The ZCCS includes the CCC as a special case with a larger set size and can relax the constraint on zero-sum of aperiodic cross-correlation for all lags It can support more users in MC-CDMA. The low PAPR property of the ZCCS was investigated in [28], [33], [40] As another contribution, we provide a construction of ZCCSs of non-power-of-two length.

PRELIMINARIES AND DEFINITIONS

GENERALIZED BOOLEAN FUNCTIONS

ZCCSs OF POWER-OF-TWO LENGTH

CONCLUSION