A Construction of Type-II ZCCS for the MC-CDMA System with Low PMEPR
Rajen Kumar, Sushant Kumar Jha, Prashant Kumar Srivastava, Sudhan Majhi
TL;DR
This work introduces a type-II ZCCS construction with arbitrary sequence lengths by taking the Kronecker product of a $(K,K,N)$-CCC with $r$ mutually orthogonal uni-modular sequences of length $P$, yielding a type-II $(rK,K,NP-P+1,NP)$-ZCCS. Barker sequences and unimodular scaling are leveraged to reduce column PMEPR, achieving an upper bound below $2$, and enabling new lengths for type-II ZCPs and ZCS with improved PMEPR relative to existing type-II constructions. The framework is applied to a QS MC-CDMA uplink system, where the ZCCS properties suppress MPI/MAI within the ZCZ, and simulations indicate superior BER performance and greater delay tolerance compared to type-I ZCCS. The paper also places the construction in context with existing type-II ZCPs and type-I versus type-II ZCCS, highlighting broader code counts, larger ZCZ widths, and practical advantages for multiuser, quasi-synchronous environments. Overall, the approach extends ZCCS design to longer, more flexible code sets with favorable PMEPR and performance characteristics for MC-CDMA applications.
Abstract
In this letter, we propose a novel construction of type-II $Z$-complementary code set (ZCCS) having arbitrary sequence length using the Kronecker product between a complete complementary code (CCC) and mutually orthogonal uni-modular sequences. In this construction, Barker sequences are used to reduce row sequence peak-to-mean envelope power ratio (PMEPR) for some specific lengths sequence and column sequence PMEPR for some specific sizes of codes. The column sequence PMEPR of the proposed type-II ZCCS is upper bounded by a number smaller than $2$. The proposed construction also contributes new lengths of type-II $Z$-complementary pair (ZCP) and type-II $Z$-complementary set (ZCS). Furthermore, the PMEPR of these new type-II ZCPs is also lower than existing type-II ZCPs.