Constructions of Optimal and Near-Optimal Quasi-Complementary Sequence Sets from Singer Difference Sets

Abstract

Compared with the perfect complementary sequence sets, quasicomplementary sequence sets (QCSSs) can support more users to work in multicarrier CDMA communications. A near-optimal periodic QCSS is constructed in this paper by using an optimal quaternary sequence set and an almost difference set. With the change of the values of parameters in the almost difference set, the near-optimal QCSS can become asymptotically optimal and the number of users supported by the subcarrier channels in CDMA system has an exponential growth.

A Generalized Construction of Multiple Complete Complementary Codes and Asymptotically Optimal Aperiodic Quasi-Complementary Sequence Sets

“…In [19], Liu et al stated the construction of aperiodic QCSSs, achieving the bounds proposed in [17], as a open problem. Since then a lot of research have been going on, both for periodic and aperiodic cases, for the construction of QCSSs with various parameters and correlation properties.…”

“…Since then a lot of research have been going on, both for periodic and aperiodic cases, for the construction of QCSSs with various parameters and correlation properties. However, most of the works, including [19], are related to periodic QCSS. Constructions of asymptotically optimal and nearoptimal periodic QCSS based on difference sets and almost difference sets were reported in [20] and [21], respectively.…”

“…To illustrate the permutation π on Z N let us have the following example. 1,2,3,4,5,6,7,8,9,10,11,12,13,14] and π(Z 15 ) = [0, 8,4,6,2,10,3,14,1,12,5,13,9,11,7].…”

“…In search of sequence sets which can support a large number of users in MC-CDMA systems, Liu et al [16] initially proposed low correlation zone complementary sequence set (LCZ-CSS). Further Liu et al [7] generalised the concept and proposed quasi complementary sequence sets (QCSSs) in 2013, which also includes Z-complementary sequence sets (ZCSSs) [8]- [14]. A (K, M, N, δ max )-QCSS is a set of K M × N sequence sets, where M denotes the flock size, and N denotes the sequence length.…”

A Tighter Correlation Lower Bound for Quasi-Complementary Sequence Sets

“…Recently, correlation lower bounds for LCZ complementary sequences are given in [19]. In addition, optimal and near-optimal QCSSs (with respect to a periodic correlation lower bound), each of which is constructed by modulating a Singer difference set with an optimal quadriphase sequence set, are presented in [20]. To date however, there has been no similar effort on tightening the aperiodic correlation lower bound of QCSSs given in (1).…”