Periodic Complementary Sequence Research Articles

Construction of Gaussian Integer Periodic Complementary Sequence Set with Zero Correlation Zone

Based on aperiodic complementary sequence (ACS) sets and orthogonal matrices, the construction of Gaussian integer (GI) zero correlation zone (ZCZ) periodic complementary sequence (ZPCS) sets is proposed. The constructed GI ZPCS sets can achieve the theoretical bound, and the length of ZCZ can be chosen flexibly. The GI ZPCS sets obtained by this paper can be used in multi-carrier code division multiple access system to obtain higher spectrum efficiency and eliminate interference.

Two Constructions of Quaternary Periodic Complementary Pairs

Two sequences are called a periodic (resp., an odd periodic) complementary pair if the sum of their periodic (resp., odd periodic) autocorrelation functions is a delta function. As a generalization of the well-known Golay sequence pairs, (odd) periodic complementary sequence pairs have important applications in radar, ranging, and communications. The objective of this letter is to present two generic constructions of quaternary periodic complementary pairs (PCPs). The first construction is based on binary odd PCPs and the Gray mapping. The second one is on the strength of the product sequences of a known quaternary sequence of odd length and a perfect quaternary sequence. Both constructions generate quaternary PCPs with new parameters which are not covered in the literature.

Two-Valued Periodic Complementary Sequences

We present a novel transform for periodic complementary sets (PCSs) over two-valued alphabets from a large set of difference families. This is achieved by generalizing Golomb's idea in 1992, which was for transformed perfect sequences with zero autocorrelations only. Based on the properties of difference family, a sufficient condition for such two-valued PCSs is derived. Systematic constructions of two-valued periodic complementary pairs are presented. It is shown that many lengths for which binary PCSs do not exist become admissible for our proposed two-valued PCSs.

Constructions of Gaussian Integer Periodic Complementary Sequences with ZCZ

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.

Inter-Group Complementary Sequence Set Based on Interleaved Periodic Complementary Sequences

By interleaving multiple shift versions of complementary sequence, a new method of constructing inter-group complementary (IGC) sequences is proposed. The resultant sequence set has zero correlation zone (ZCZ) properties in each sequence group and any two sequences from different sequence groups possess ideal periodic cross-correlation properties. When a suitable shift sequence is chosen, the constructed IGC sequence set will be optimal in terms of the corresponding theoretical bound. Compared with the existing constructions of IGC sequences, the proposed construction method may provide not only flexible ZCZ width but also flexible element sequence length, which will ensure a more freedom for the design and realization of IGC wireless communication systems.

QAM Periodic Complementary Sequence Sets

QAM Periodic Complementary Sequence Sets

A Method of Constructing Quaternary Periodic Complementary Sequence Sets for Suppression of Multiple Access Interference in CDMA Communication Systems

For suppressing multiple access interference (MAI) in a CDMA communication system, complementary sequence sets are employed as spreading sequences in such system. In this paper, we present a method for constructing a family of quaternary periodic complementary sequence sets, which arises from the conversion of the existing binary periodic complementary sequence sets with odd period of sub-sequences. The period of sub-sequences in the proposed sequence sets is twice as long as the one of the binary sequence sets employed, which is a drawback in the proposed method. Finally, some examples are given in order to illuminate the validity of the new method.

Constructions of Quaternary Periodic Complementary Sequence Sets with Zero Correlation Zone

摘要: 该文分别基于二元零相关区周期互补序列集和二元周期互补序列集做为初始序列，利用逆Gray映射构造了四元零相关区周期互补序列集。如果选取的初始序列集参数可以达到理论界限，得到的四元零相关区周期互补序列集接近甚至达到理论界限。零相关区互补序列集相比传统互补序列集具有更多的序列数目，应用到通信系统中可以支持更多的通信用户。 关键词: 四元序列 / 周期互补序列 / 零相关区 / 逆Gray映射

New Polyphase Complementary Sequence Sets for Wireless Communication Systems

In contemporary wireless communication systems, complementary sequences play fairly important roles. Based on polyphase perfect sequences (PPSs), this paper presents a construction method, whose basic idea is to sample a given PPS with equal space, for yielding a family of periodic polyphase complementary sequence sets (PPCSSs). The advantages of this method include the family size of resultant PPCSSs is the same as that of the PPSs employed, and the number and length of sub-sequences in the proposed PPCSSs can be altered on demand.

16-QAM periodic complementary sequence mates based on interleaving technique and quadriphase periodic complementary sequence mates

Based on an interleaving technique and quadriphase periodic complementary sequence (CS) mates, this paper presents a method for constructing a family of 16-quadrature amplitude modulation (QAM) periodic CS mates. The resulting mates arise from the conversion of quadriphase periodic CS mates, and the period of the former is twice as long as that of the latter. In addition, based on the existing binary periodic CS mates, a table on the existence of the proposed 16-QAM periodic CS mates is given. Furthermore, the proposed method can also transform a mutually orthogonal (MO) quadriphase CS set into an MO 16-QAM CS set. Finally, three examples are given to demonstrate the validity of the proposed method.

Compression of periodic complementary sequences and applications

A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence A=[a_0,a_1,...,a_{v-1}] of length v=dm we define the m-compressed sequence A^{(d)} of length d whose terms are the sums a_i + a_{i+d} + ... + a_{i+(m-1)d}. We prove that the m-compression of a complementary collection of sequences is also complementary. The compression procedure can be used to simplify the construction of complementary {+1,-1}-sequences of composite length. In particular, we construct several supplementary difference sets (v;r,s;lambda) with v even and lambda=(r+s)-v/2, given here for the first time. There are 15 normalized parameter sets (v;r,s;lambda) with v <= 50 for which the existence question was open. We resolve all but one of these cases.

Even periodic and odd periodic complementary sequence pairs from generalized Boolean functions

A pair of two sequences is called the even periodic (odd periodic)complementary sequence pair if the sum of their even periodic (oddperiodic) correlation function is a delta function. The well-knownGolay aperiodic complementary sequence pair (Golay pair) is aspecial case of even periodic (odd periodic) complementary sequencepair. In this paper, we presented several classes of even periodicand odd periodic complementary pairs based on the generalizedBoolean functions, but which do not form Gloay pairs. The proposedsequences could be used to design signal sets, which have beenapplied in direct sequence code division multiple (DS-CDMA) cellularcommunication systems.

New Constructions of 16-QAM Periodic Complementary Sequences

In this letter, we present a family of 16-QAM periodic complementary sequences (PCSs), including three constructions. Our basic idea is to transform the known quaternary PCSs/GCSs (Golay complementary sequences) into the required ones. In order to guarantee that such transformation of every construction is successful, the own sufficient conditions of three constructions are derived, respectively. Our methods can provide quite rich 16-QAM periodic PCSs, whose main parameters up to period 50 and number 12 of sub-sequences are given in Table 1, from a large number of available quaternary PCSs/GCSs, which can potentially satisfy the requirements of communication systems making use of 16-QAM constellation.

Construction of Periodic Complementary Multiphase Sequences Based on Perfect Sequences

This paper provides a construction method of periodic complementary multiphase sequences. The proposed method is based on perfect sequences possessing ideal periodic auto-correlation properties. By interleaving any two different perfect sequences with the same length, a kernel set of periodic complementary sequence with multiphase elements can be generated. Compared with the known periodic complementary binary sequences, the presented periodic complementary multiphase sequences may obtain much more lengths of element sequences, which will assure that the generated sequences can provide a more flexible choice of parameters for communication systems.

New construction method for quaternary aperiodic, periodic, and Z-complementary sequence sets

Based on the known binary sequence sets and Gray mapping, a new method for constructing quaternary sequence sets is presented and the resulting sequence sets' properties are investigated. As three direct applications of the proposed method, when we choose the binary aperiodic, periodic, and Z-complementary sequence sets as the known binary sequence sets, the resultant quaternary sequence sets are the quaternary aperiodic, periodic, and Z-complementary sequence sets, respectively. In comparison with the method proposed by Jang et al., the new method can cope with either both the aperiodic and periodic cases or both even and odd lengths of sub-sequences, whereas the former is only fit for the periodic case with even length of sub-sequences. As a consequence, by both our and Jang et al.'s methods, an arbitrary binary aperiodic, periodic, or Z-complementary sequence set can be transformed into a quaternary one no matter its length of sub-sequences is odd or even. Finally, a table on the existing quaternary periodic complementary sequence sets is given as well.

Constructions of Binary and Quaternary Periodic Complementary Sequence Sets with Zero Correlation Zone

摘要: 该文基于二元周期互补序列集，研究了二元和四元零相关区(ZCZ)周期互补序列集的构造方法。利用移位序列和交织法来构造二元ZCZ周期互补序列集，序列集的零相关区长度可以灵活设定。利用逆Gray映射构造了四元ZCZ周期互补序列集，零相关区长度同样可以灵活设定。如果采用的初始周期互补序列集参数达到理论界限，得到的二元和四元ZCZ周期互补序列集参数都是可以达到理论界限的。 关键词: 周期互补序列 / 零相关区(ZCZ) / 交织法 / 逆Gray映射 / 移位序列

Almost Perfect Sequences and Periodic Complementary Sequence Pairs over the 16-QAM Constellation

SUMMARY Based on quadriphase perfect sequences and their cyclical shift versions, three families of almost perfect 16-QAM sequences are presented. When one of two time shifts chosen equals half a period of quadriphase sequence employed and another is zero, two of the proposed three sequence families possess the property that their out-of-phase autocorrelation function values vanish except one. At the same time, to the other time shifts, the nontrivial autocorrelation function values in three families are zero except two or four. In addition, two classes of periodic complementary sequence (PCS) pairs over the 16-QAM constellation, whose autocorrelation is similar to the one of conventional PCS pairs, are constructed as

Quaternary periodic complementary/Z-complementary sequence sets based on interleaving technique and Gray mapping

A family of quaternary periodic complementary sequence (PCS) orZ-complementary sequence (PZCS) sets is presented. By combining aninterleaving technique and the inverse Gray mapping, the proposedmethod transforms the known binary PCS/PZCS sets with odd length ofsub-sequences into quaternary PCS/PZCS sets, but the length of newsub-sequences is twice as long as that of the originalsub-sequences, which is a drawback of this proposed method. However,the shortcoming that the method proposed by J. W. Jang, et al. ismerely fit for even length of sub-sequences is overcome. As aconsequence, the union of our and J. W. Jang, et al.'s methodsallows us to construct quaternary PCS/PZCS sets from binary PCS/PZCSsets with sub-sequences of arbitrary length.

New Construction Method and Low-Complexity Correlator for Binary Periodic Complementary Sequence Sets and Its Application to MIMO Channel Estimation

In this letter, we first present a new construction method for uncorrelated binary periodic Complementary sequence sets (CSS). Next, the uncorrelated periodic CSSs are used as pilot sequences for multiple-input multiple-output (MIMO) channel estimation. Later on, we propose a low-complexity periodic correlator. Finally, simulation results verify the optimality of pilot sequences for MIMO channel estimation.

8-QAM+ Periodic Complementary Sequence Sets

This letter presents three methods that can transform ternary complementary sequence sets (CSSs) into 8-QAM+ CSSs. Method 1 yields 8-QAM+ CSSs with sequences of even length. Method 2 works for sequences with an arbitrary period, but results in 8-QAM+ CSSs with a size twice that of the ternary sets. Method 3 transforms ternary CSSs with odd periods into 8-QAM+ CSSs, but with double the period. The resultant 8-QAM+ CSSs can be applied to signal processing, channel estimation, and synchronization.