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.

In this letter, a generic method to construct mutually orthogonal binary zero correlation zone (ZCZ) sequence sets from mutually orthogonal complementary sequence sets (MOCSSs) with certain properties is presented at first. Then MOCSSs satisfying conditions are generated from binary orthogonal matrices with order N×N, where N=p-1, p is a prime. As a result, mutually orthogonal binary ZCZ sequence sets with parameters (2N2,N,N+1)-ZCZ can be obtained, the number of ZCZ sets is N. Note that each single ZCZ sequence set is optimal with respect to the theoretical bound.

By interleaving known Z-periodic complementary (ZPC) sequence set, a new ZPC sequence set is constructed with multiple ZPC sequence subsets based on an orthogonal matrix in this work. For this novel ZPC sequence set, which refer to as asymmetric ZPC (AZPC) sequence set, its inter-subset zero cross-correlation zone (ZCCZ) is larger than intra-subset zero correlation zone (ZCZ). In particular, if select a periodic perfect complementary (PC) sequence or PC sequence set and a discrete Fourier transform (DFT) matrix, the resultant sequence set is an inter-group complementary (IGC) sequence set. When a suitable shift sequence is chosen, the obtained IGC sequence set will be optimal in terms of the corresponding theoretical bound. Compared with the existing constructions of IGC sequence sets, the proposed method can provide not only flexible ZCZ width but also flexible choice of basic sequences, which works well in both synchronous and asynchronous operational modes. The proposed AZPC sequence sets are suitable for multiuser environments.

Based on the known binary and quaternary zero correlation zone (ZCZ) sequence sets, a class of 16-QAM sequence sets with ZCZ is presented, where the term “QAM sequence” means the sequence over the quadrature amplitude modulation (QAM) constellation. The sequence sets obtained by this method achieve an expansion in the number of 16-QAM sequence sets with ZCZ. The proposed sequence sets can be applied to quasi-synchronous code division multiple access (QS-CDMA) systems to eliminate the multiple access interference (MAI) and multipath interference (MPI) and improve the transmission data rate (TDR).

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).

An inter-subset uncorrelated zero-correlation zone (ZCZ) sequence pair set is one consisting of multiple ZCZ sequence pair subsets. What's more, two arbitrary sequence pairs which belong to different subsets should be uncorrelated sequence pairs in this set, i.e., the cross-correlation function (CCF) between arbitrary sequence pairs in different subsets are zeros at everywhere. Meanwhile, each subset is a typical ZCZ sequence pair set. First, a class of uncorrelated ZCZ (U-ZCZ) sequence pair sets is proposed from interleaving perfect sequence pairs. An U-ZCZ sequence pair set is a type of ZCZ sequence pair set, which of most important property is that the CCF between two arbitrary sequence pairs is zero at any shift. Then, a type of inter-subset uncorrelated ZCZ sequence pair set is obtained by interleaving proposed U-ZCZ sequence pair set. In particular, the novel inter-subset uncorrelated ZCZ sequence pair sets are expected to be useful for designing spreading codes for QS-CDMA systems.

The present paper introduces the construction of quadriphase sequences having a zero-correlation zone. For a zero-correlation zone sequence set of N sequences, each of length l, the cross-correlation function and the side lobe of the autocorrelation function of the proposed sequence set are zero for the phase shifts τ within the zero-correlation zone z, such that |τ|≤z (τ ≠ 0 for the autocorrelation function). The ratio $rac{N(z+1)}{ell}$ is theoretically limited to one. When l=N(z+1), the sequence set is called an optimal zero-correlation sequence set. The proposed zero-correlation zone sequence set can be generated from an arbitrary Hadamard matrix of order n. The length of the proposed sequence set can be extended by sequence interleaving, where m times interleaving can generate 4n sequences, each of length 2m+3n. The proposed sequence set is optimal for m=0,1 and almost optimal for m>1.

An uncorrelated asymmetric ZCZ (UA-ZCZ) sequence set is a special version of an asymmetric ZCZ (A-ZCZ) sequence set, which contains multiple subsets and each subset is a typical ZCZ sequence set. One of the most important properties of UA-ZCZ sequnence set is that two arbitrary sequences from different sequence subsets are uncorrelated sequences, whose cross-correlation function (CCF) is zeros at all shifts. Based on interleaved technique and an uncorrelated sequence set, a new UA-ZCZ sequence set is obtained via interleaving a perfect sequence. The uncorrelated property of the UA-ZCZ sequence sets is expected to be useful for avoiding inter-cell interference of QS-CDMA systems.

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.

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.

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.

In this letter, we present a general construction of sequence sets with low correlation zone, which is based on finite fields and the balance property of some functions. The construction is more flexible as far as the partition of parameters is concerned. A simple example is also given to interpret the construction.

In this correspondence, we devise a new method for constructing a ternary column sequence set of length 3m+1-1 form ternary sequences of period 3m-1 with ideal autocorrelation, and the ternary LCZ sequence set of period 3n-1 is constructed by using the column sequence set when (m+1)|n. In addition, the method is popularized to the p-ary LCZ sequence. The resultant LCZ sequence sets in this paper are optimal with respect to the Tang-Fan-Matsufuji bound.

In this correspondence, a new method to extend the number of quaternary low correlation zone (LCZ) sequence sets is presented. Based on the inverse Gray mapping and a binary sequence with ideal two-level auto-correlation function, numbers of quaternary LCZ sequence sets can be generated by choosing different parameters. There is at most one sequence cyclically equivalent in different LCZ sequence sets. The parameters of LCZ sequence sets are flexible.

In this letter, we propose a new construction of quaternary low correlation zone (LCZ) sequence set using binary LCZ sequence sets and an inverse Gray mapping. The new construction method provides optimal quaternary LCZ sequence sets even if the employed binary LCZ sequence set is suboptimal. The optimality is improved at the price of alphabet extension.

In this paper, two constructions of mutually orthogonal zero correlation zone polyphase sequence sets are presented. The first one is based on DFT matrices and interleaving iteration. After each recursive step, the period of sequence and the length of zero-correlation zone are two times larger than that in the last step. The second method, based on DFT matrices and orthogonal matrices, can generate numbers of mutually orthogonal optimal ZCZ sequence sets whose parameters reach the theoretical bounds by using interleaving and shifting techniques. As a result, the algorithms proposed can provide more sequences for the QS-CDMA (quasi-synchronous CDMA) systems.

Recently there has been a surge of interest in construction of low correlation zone sequences. The purpose of this paper is to survey the known results in the area and to present an interleaved construction of binary low correlation zone sequences. The interleaved construction unifies many constructions currently available in the literature. These sequences are useful in quasi-synchronous code-division multiple access (QS-CDMA) communication systems.

In this paper, we propose four new general constructions of LCZ/ZCZ sequence sets based on interleaving technique and affine transformations. A larger family of LCZ/ZCZ sequence sets with longer period are generated by these constructions, which are more flexible among the selection of the alphabet size, the period of the sequences and the length of LCZ/ZCZ, compared with those generated by the known constructions. Especially, two families of the newly constructed sequences can achieve or almost achieve the theoretic bound.

We propose an extension method of quaternary low correlation zone (LCZ) sequence set with odd period. From a quaternary LCZ sequence set with parameters (N, M, L, 1), the proposed method constructs a new quaternary LCZ sequence set with parameters (2N, 2M, L, 2), where N is odd. If the employed LCZ sequence set in the construction is optimal, the extended LCZ sequence set becomes also optimal where N = kL, L > 4, and k>2.

In this letter, new families of binary low correlation zone (LCZ) sequences based on the interleaving technique and quadratic form sequences are constructed, which include the binary LCZ sequence set derived from Gordon-Mills-Welch (GMW) sequences. The constructed sequences have the property that, in a specified zone, the out-of-phase autocorrelation and cross-correlation values are all equal to -1. Due to this property, such sequences are suitable for quasi-synchronous code-division multiple access (QS-CDMA) systems.