A new construction of shift sequences is proposed under the condition of P|L, and then the inter-group complementary (IGC) sequence sets are constructed based on the shift sequence. By adjusting the parameter q, two or three IGC sequence sets can be obtained. Compared with previous methods, the proposed construction can provide more sequence sets for both synchronous and asynchronous code-division multiple access communication systems.

This letter presents new methods for transforming perfect ternary sequences into perfect 8-QAM+ sequences. Firstly, based on perfect ternary sequences with even period, two mappings which can map two ternary variables to an 8-QAM+ symbol are employed for constructing new perfect 8-QAM+ sequences. In this case, the proposed construction is a generalization of the existing one. Then based on perfect ternary sequence with odd period, perfect 8-QAM sequences are generated. Compared with perfect 8-QAM+ sequences, the resultant sequences have no energy loss.

This letter presents two constructions of Gaussian integer Z-periodic complementary sequences (ZPCSs), which can be used in multi-carriers code division multiple access (MC-CDMA) systems to remove interference and increase transmission rate. Construction I employs periodic complementary sequences (PCSs) as the original sequences to construct ZPCSs, the parameters of which can achieve the theoretical bound if the original PCS set is optimal. Construction II proposes a construction for yielding Gaussian integer orthogonal matrices, then the methods of zero padding and modulation are implemented on the Gaussian integer orthogonal matrix. The result Gaussian integer ZPCS sets are optimal and with flexible choices of parameters.

In this correspondence, two types of multiple binary zero correlation zone (ZCZ) sequence sets with inter-set zero cross-correlation zone (ZCCZ) are constructed. Based on orthogonal matrices with order N×N, multiple binary ZCZ sequence sets with inter-set even and odd ZCCZ lengthes are constructed, each set is an optimal ZCZ sequence set with parameters (2N2, N, N+1)-ZCZ, among these ZCZ sequence sets, sequences possess ideal cross-correlation property within a zone of length 2Z or 2Z+1. These resultant multiple ZCZ sequence sets can be used in quasi-synchronous CDMA systems to remove the inter-cell interference (ICI).

In this letter, a construction of asymmetric Gaussian integer zero correlation zone (ZCZ) sequence sets is presented based on interleaving and filtering. The proposed approach can provide optimal or almost optimal single Gaussian integer ZCZ sequence sets. In addition, arbitrary two sequences from different sets have inter-set zero cross-correlation zone (ZCCZ). The resultant sequence sets can be used in the multi-cell QS-CDMA system to reduce the inter-cell interference and increase the transmission data.

Based on a perfect Gaussian integer sequence, shift and combination operations are performed to construct Gaussian integer sequences with zero correlation zone (ZCZ). The resultant sequence sets are optimal or almost optimal with respect to the Tang-Fan-Matsufuji bound. Furthermore, the ZCZ Gaussian integer sequence sets can be provided for quasi-synchronous code-division multiple-access systems to increase transmission data rate and reduce interference.

This letter is devoted to constructing new Type-II Z-complementary pairs (ZCPs). A ZCP of length N with ZCZ width Z is referred to in short by the designation (N, Z)-ZCP. Inspired by existing works of ZCPs, systematic constructions of (2N+3, N+2)-ZCPs and (4N+4, 7/2N+4)-ZCPs are proposed by appropriately inserting elements into concatenated GCPs. The odd-length binary Z-complementary pairs (OB-ZCPs) are Z-optimal. Furthermore, the proposed construction can generate even-length binary Z-complementary pairs (EB-ZCPs) with ZCZ ratio (i.e. ZCZ width over the sequence length) of 7/8. It turns out that the PMEPR of resultant EB-ZCPs are upper bounded by 4.

In this paper, we constructed a class of low correlation zone sequence sets derived from the interleaved technique and DFT matrices. When p is a prime such that p > 3, p-ary LCZ sequence sets with parameters LCZ(pn-1,pm-1,(pn-1)/(pm-1),1) are constructed based on a DFT matrix with order pp, which is optimal with respect to the Tang-Fan-Matsufuji bound. When p is a prime such that p ≥ 2, pk-ary LCZ sequence sets with parameters LCZ(pn-1,pk-1,(pn-1)/(pk-1),1) are constructed based on a DFT matrix with order pkpk, which is also optimal. These sequence sets are useful in certain quasi-synchronous code-division mutiple access (QS-CDMA) communication systems.

An asymmetric zero correlation zone (A-ZCZ) sequence set can be regarded as a special type of ZCZ sequence set, which consists of multiple sequence subsets. Each subset is a ZCZ sequence set, and have a common zero cross-correlation zone (ZCCZ) between sequences from different subsets. This paper supplements an existing construction of A-ZCZ sequence sets and further improves the research results. Besides, a new construction of A-ZCZ sequence sets is proposed by matrices transformation. The obtained sequence sets are optimal with respect to theoretical bound, and the parameters can be chosen more flexibly, such as the number of subsets and the lengths of ZCCZ between sequences from different subsets. Moreover, as the diversity of the orthogonal matrices and the flexibility of initial matrix, more A-ZCZ sequence sets can be obtained. The resultant sequence sets presented in this paper can be applied to multi-cell quasi-synchronous code-division multiple-access (QS-CDMA) systems, to eliminate the interference not only from the same cell but also from adjacent cells.

A construction of shift sequence sets is proposed. Multiple distinct shift sequence sets are obtained by changing the parameters of the shift sequences. The shift sequences satisfy the conditions that P|L and P ≥ 2, where P is the length of the shift sequences, L is the length of the zero-correlation zone or low-correlation zone (ZCZ/LCZ). Then based on these shift sequence sets, many shift distinct ZCZ/LCZ sequence sets are constructed by using interleaving technique and complex Hadamard matrices. Furthermore, the new construction is optimal under the conditions proposed in this paper. Compared with previous constructions, the proposed construction extends the number of shift distinct ZCZ/LCZ sequence sets, so that more sequence sets are obtained for multi-cell quasi-synchronous code-division multiple access (QS-CDMA) systems.

Based on a ternary perfect sequence and a binary orthogonal matrix, the Z-periodic complementary sequence (ZPCS) sets over the 8-QAM+ constellation are constructed. The resultant sequences can be used in multi-carriers code division multiple access (MC-CDMA) systems to remove interference and increase the transmission rate. The proposed construction provides flexible choice for parameters so as to meet different requirements in the application. A construction of shift sequence sets is proposed and the number of 8-QAM ZPCS sets is extended by changing the parameters of shift sequences. As a result, more users can be accommodated in the system.

Two new families of balanced almost binary sequences with a single zero element of period L=2q are presented in this letter, where q=4d+1 is an odd prime number. These sequences have optimal autocorrelation value or optimal autocorrelation magnitude. Our constructions are based on cyclotomy and Chinese Remainder Theorem.