The timing synchronization scheme for massive MIMO systems is proposed with CCK (Complementary Code Keying) codes in this letter. Our proposed scheme is specifically designed to generate synchronization sequence with large family size. The optimal sequences can be constructed with ZCZ or LCZ based on the number of antennas. Furthermore Monte Carlo simulation results confirmed the expected detection probability for massive MIMO systems.

N-Shift Zero Correlation Zone (NS-ZCZ) sequence is defined with the N-shift zero correlation zone in the correlation function. Namely, the N-shift zero only appears within the correlation zone symmetrically distributed in the center of the correlation function. Moreover, the traditional ZCZ sequences can be considered as the N-shift ZCZ sequence with N=1. Similar to ZCZ sequence, NS-ZCZ sequences can be applied in sequence design for co-channel interference mitigation with more sequences in the sequence set compared with the traditional N-shift sequences. In this letter, the definition and construction algorithms are proposed. The corresponding theoretical bounds are analyzed.

The approximately synchronized code-division multiple-access (CDMA) communication system, using the QAM sequences with zero correlation zone (ZCZ) as its spreading sequences, not only can remove the multiple access interference (MAI) and multi-path interference (MPI) synchronously, but also has a higher transmission data rate than the one using traditional ZCZ sequences with the same sequence length. Based on Gray mapping and the known binary ZCZ sequences, in this letter, six families of 16-QAM sequences with ZCZ are presented. When the binary ZCZ sequences employed by this letter arrive at the theoretical bound on the binary ZCZ sequences, and their family size is a multiple of 4 or 2, two of the resultant six 16-QAM sequence sets satisfy the bound referred to above as well.

Based on the known quadriphase zero correlation zone (ZCZ) sequences ZCZ4(N,M,T), four families of 16-QAM sequences with ZCZ are presented, where the term "QAM sequences" means the sequences over the quadrature amplitude modulation (QAM) constellation. When the quadriphase ZCZ sequences employed by this letter arrive at the theoretical bound on the ZCZ sequences, and are of the even family size M or the odd width T of ZCZ, two of the resulting four 16-QAM sequence sets satisfy the bound referred to above. The proposed sequences can be potentially applied to communication systems using 16-QAM constellation as spreading sequences so that the multiple access interference (MAI) and multi-path interference (MPI) are removed synchronously.

Sequences with good correlation properties are of substantial interest in many applications. By interleaving a perfect array with shift sequences, a new method of constructing binary array set with zero correlation zone (ZCZ) is presented. The interleaving operation can be performed not only row-by-row but also column-by-column on the perfect array. The resultant ZCZ binary array set is optimal or almost optimal with respect to the theoretical bound. The new method provides a flexible choice for the rectangular ZCZ and the set size.

In this paper, we introduce a new general construction of zero correlation zone (ZCZ) sequence set, which is based on two given ZCZ sequence sets. Compared with the two given sequence sets, the resultant sequence set not only has larger family size and longer period, but also provides more flexible choices of basic sequences, ZCZ length and family size.

Aperiodic quadriphase Z-complementary sequences, which include the conventional complementary sequences as special cases, are introduced. It is shown that, the aperiodic quadriphase Z-complementary pairs are normally better than binary ones of the same length, in terms of the number of Z-complementary pairs, and the maximum zero correlation zone. New notions of elementary transformations on quadriphase sequences and elementary operations on sets of quadriphase Z-complementary sequences are presented. In particular, new methods for analyzing the relations among the formulas relative to sets of quadriphase Z-complementary sequences and for describing the sets are proposed. The existence problem of Z-complementary pairs of quadriphase sequences with zero correlation zone equal to 2, 3, and 4 is investigated. Constructions of sets of quadriphase Z-complementary sequences and their mates are given.

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.

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.

In approximately synchronous CDMA (AS-CDMA) systems, zero correlation zone (ZCZ) sequences are known as the sequences to eliminate co-channel and multi-path interferences. Therefore, numerous constructions of zero correlation zone (ZCZ) sequences have been introduced e.g. based on perfect sequences and complete complementary codes etc. However, the previous construction method which based on complete complementary code is lacking for merit figures when none of whose elements are zero. In this paper, a new construction method of ZCZ sequences based on complete complementary codes is proposed. By proposed method, non zero elements ZCZ sequences whose merit figure is greater than 1/2 are constructable.

In this paper, based on interleaved technique, we present a new method of constructing zero correlation zone (ZCZ) sequence sets. For any perfect sequence of length m(2k+1) with m > 2, k ≥ 0 and an arbitrary Hadamard matrix of order T > 2, the proposed construction can generate new optimal ZCZ sequence sets in which all the sequences are cyclically distinct.

Convolutional spreading CDMA with cyclic prefix (CS-CDMA/CP) is a multiuser interference-free (MUI-free) CDMA scheme proposed for multipath channels based on the convolution between user data and zero correlation zone (ZCZ) code, and its characteristics depend on the employed ZCZ codes. Although ternary ZCZ codes have more sequences than binary ZCZ codes in general, transmitted signal with ternary ZCZ codes give a slightly higher peak-to-average power ratio (PAPR). In this paper we propose the use of periodic ZCZ codes generated from an M-sequence which not only provides the same user capacity as ternary ZCZ codes but allows more design flexibility. Simulation results show that the new ZCZ code shows stronger robustness against an imperfect transmitter with clipping and enjoys better BER performances when used in CS-CDMA/CP compared to the conventional DS-CDMA with MRC-RAKE.

A Huffman sequence has a zero-sidelobe aperiodic autocorrelation function except at both shift ends. This paper presents orthogonal sets of the zero correlation zone (ZCZ) Huffman sequences and the application to a quasi-synchronous CDMA system with interferences suppressed. The sequences with low or large peak values are constructed on the basis of sequence spectra corresponding to multiple convolution of elementary sequences, and include the ZCZ sequences. The CDMA system is constructed from the ZCZ sequences, and suppresses intersymbol and interchannel interferences.

This paper presents constructions of two kinds of sets of sequences with a zero correlation zone, called ZCZ code, which can reach the upper bound of the member size of the sequence set. One is a ZCZ code which can be constructed by a unitary matrix and a perfect sequence. Especially, a ternary perfect sequence with elements 1 and zero can be used to construct the proposed ZCZ code. The other is a ZCZ code of pairs of ternary sequences and binary sequences which can be constructed by an orthogonal matrix that includes a Hadamard matrix and an orthogonal sequence pair. As a special case, an orthogonal sequence pair, which consists of a ternary sequence and a binary sequence, can be used to construct the proposed ZCZ code. These codes can provide CDMA systems without co-channel interference.

Sequences with ear zero correlation zones (EZCZs) are employed to suppress inter-symbol interference (ISI) and inter-user interference (IUI) in wireless communications. Theoretical limits on correlation functions of such sequences are investigated, lower bounds on the relations among length of sequence, width of EZCZs/ELCZs and family size are derived and presented, which play an important role in assessing performance of such sequences.

In order to judge the goodness of zero correlation zone sequence sets, a new concept, called ZCZ characteristic, is proposed. Then by defining a sequence operation, i.e. correlation product, and establishing its basic properties, a new approach to construct sets of sequences with a large zero correlation zone is presented.