This letter proposes a class of polyphase zero correlation zone (ZCZ) sequence sets with low inter-set cross-correlation property. The proposed ZCZ sequence sets are constructed from DFT matrices and r-coincidence sequences. Each ZCZ sequence set is optimal, and the absolute value of the cross-correlation function of sequences from different sets is less than or equal to $rsqrt{N}$, where N denotes the length of each sequence. These ZCZ sequence sets are suitable for multiuser environments.

In this correspondence, a generic method of constructing optimal p2-ary low correlation zone sequence sets is proposed. Firstly p2-ary column sequence sets are constructed, then p2-ary LCZ sequence sets with parameters (pn-1, pm-1, (pn-1)/(pm-1),1) are constructed by using column sequences and interleaving technique. The resultant p2-ary LCZ sequence sets are optimal with respect to the Tang-Fan-Matsufuji bound.

Binary sequence pairs as a class of mismatched filtering of binary sequences can be applied in radar, sonar, and spread spectrum communication system. Binary sequence pairs with two-level periodic autocorrelation function (BSPT) are considered as the extension of usual binary sequences with two-level periodic autocorrelation function. Each of BSPT consists of two binary sequences of which all out-phase periodic crosscorrelation functions, also called periodic autocorrelation functions of sequence pairs, are the same constant. BSPT have an equivalent relationship with difference set pairs (DSP), a new concept of combinatorial mathematics, which means that difference set pairs can be used to research BSPT as a kind of important tool. Based on the equivalent relationship between BSPT and DSP, several families of BSPT including perfect binary sequence pairs are constructed by recursively constructing DSP on the integer ring. The discrete Fourier transform spectrum property of BSPT reveals a necessary condition of BSPT. By interleaving perfect binary sequence pairs and Hadamard matrix, a new family of binary sequence pairs with zero correlation zone used in quasi-synchronous code multiple division address is constructed, which is close to the upper theoretical bound with sequence length increasing.

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.

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, based on cyclic difference sets with parameters $(N,rac{N-1}{2},rac{N-3}{4})$ and complex transformations, a method for constructing degree-4 perfect Gaussian integer sequences (PGISs) with good balance property of length $N'equiv2( ext{mod}4)$ are presented. Furthermore, the elements distribution of the proposed Gaussian integer sequences (GISs) is derived.

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.

Quadriphase sequences with good correlation properties are required in higher order digital modulation schemes, e.g., for timing measurements, channel estimation or synchronization. In this letter, based on interleaving technique and pairs of mismatched binary sequences with perfect cross-correlation function (PCCF), two new methods for constructing quadriphase sequences with mismatched filtering which exist for even length N ≡ 2(mod4) are presented. The resultant perfect mismatched quadriphase sequences have high energy efficiencies. Compared with the existing methods, the new methods have flexible parameters and can give cyclically distinct perfect mismatched quadriphase sequences.

In this letter, several new families of binary sequence pairs with period N=np, where p is a prime and gcd(n,p)=1, and optimal correlation values 1 and -3 are constructed. These classes of binary sequence pairs are based on Chinese remainder theorem. The constructed sequence pairs have optimum balance among 0's and 1's.

A new class of almost quadriphase sequences with four zero elements of period 4N, where N ≡ 1(mod 4) being a prime, is constructed. The maximum nontrivial autocorrelations of the constructed almost quadriphase sequences are shown to be 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.

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, a new class of almost binary sequence pairs with a single zero element and three autocorrelation values is presented. The new almost binary sequence pairs are based on cyclic difference sets and difference set pairs. By applying the method to the binary sequence pairs, new binary sequence pairs with three-level autocorrelation are constructed. It is shown that new sequence pairs from our constructions are balanced or almost balanced and have optimal three-level autocorrelation when the characteristic sequences or sequence pairs of difference sets or difference set pairs are balanced or almost balanced and have optimal autocorrelations.

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 correspondence, a method of constructing optimal zero correlation zone (ZCZ) sequence sets over the 16-QAM+ constellation is presented. Based on 16-QAM orthogonal matrices and perfect ternary sequences, 16-QAM+ ZCZ sequence sets are obtained. The resulting ZCZ sequence sets are optimal with respect to the Tang-Fan-Matsufuji bound. Moreover, methods for transforming binary or quaternary orthogonal matrices into 16-QAM orthogonal matrices are proposed. The proposed 16-QAM+ ZCZ sequence sets can be potentially applied to communication systems using a 16-QAM constellation to remove the multiple access interference (MAI) and multi-path interference (MPI).

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.

A novel class of signal of perfect Gaussian integer sequence pairs are put forward in this paper. The constructions of obtaining perfect Gaussian integer sequence pairs of odd length by using Chinese remainder theorem as well as perfect Gaussian integer sequence pairs of even length by using complex transformation and interleaving techniques are presented. The constructed perfect Gaussian integer sequence pairs can not only expand the existence range of available perfect Gaussian integer sequences and perfect sequence pairs signals but also overcome the energy loss defects.

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.

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.

Zero correlation zone (ZCZ) aperiodic complementary sequence (ZACS) sets have potential applications in multi-carriers (MC) CDMA communication systems, which can support more users than traditional complementary sequence sets. In this letter, methods for constructing ZACS sets based on orthogonal matrices are proposed. The new constructions may propose ZACS sets with optimal parameters. The new ZACS sets can be applied in approximately synchronized MC-CDMA to remove interferences.