Optimal Correlation Properties Research Articles

A METHOD FOR SYNTHESIS OF FAMILIES OF SETS OF PHASE MANIPULATED SIGNALS WITH OPTIMAL CORRELATION PROPERTIES

In the paper a method for synthesis of families of sets of phase manipulated signals with optimal correlation properties is substantiated. The method could be used in the development of new radar sensor networks, which exploit effectively the electromagnetic spectrum and can operate practically without self-interferences and multiaccess interferences

Optimal Constructions of Low-Hit-Zone Frequency-Hopping Sequence Sets via Cyclotomy

In complex environments of wireless communication, to improve the communication anti-interference performance, quasi-synchronous frequency-hopping (FH) communication system requires low-hit-zone (LHZ) FH sequence sets with optimal Hamming correlation (HC) properties and flexible parameters. In this paper, based upon cyclotomy theory, two classes of LHZ FH sequence sets with flexible parameters not included in the literatures are designed, and the periodic HC properties of which are analyzed. It turns out that the designed LHZ FH sequence sets are optimal on the maximum periodic HC. And thus the new constructions can be used to provide optimal FH sequence sets for quasi-synchronous FH communication system.

Optimal Low-Hit-Zone Frequency-Hopping Sequence Sets With Wide-Gap for FHMA Systems Under Follower Jamming

This letter is concerned with tackling both of the multi-access interference (MAI) and the follower jamming (FJ) in frequency-hopping multiple-access (FHMA) systems via novel FH sequence (FHS) design. We consider low-hit-zone (LHZ) FHS which provides lower MAIs in quasi-synchronous FHMA systems but suffers from FJ attack. We introduce an improved LHZ-FHS with wide-gap (i.e., WG-LHZ-FHS) for the neighboring carrier frequencies so as to combat the MAI and the FJ. We first present a general method to generate new WG-FHS sets and then construct the first known WG-LHZ-FHS sets with optimal periodic Hamming correlation (PHC) properties. Besides, the error-rate performance of the constructed WG-LHZ-FHS set imposed in an FHMA system under FJ is investigated. The numerical analysis and the system simulation results indicate that the proposed WG-LHZ-FHS set provides the better error-rate performance to combat the FJ as well as satisfactory capability of MAI suppression due to its combined merits of WG and LHZ.

On Optimal Estimates of Random Variables

A class of quasilinear, mean-square optimal estimates of random variables is indicated. Optimal correlation properties of the obtained estimates are established.

Frequency-hopping sequence sets with no-hit-zone through Cartesian product

For quasi-synchronous (QS) frequency-hopping multiple access (FHMA) systems, relative time delay between different users can be allowed to vary in a domain around the origin. On the other hand, for frequency-hopping sequence (FHS) sets with no-hit-zone (NHZ), there will be no hit between different sequences in case their time delay does not exceed a certain region known as NHZ. In such circumstances, NHZ-FHS sets can be well applied in QS-FHMA systems to eliminate the mutual interference (MI) and have great practical significance. In this paper, based on Cartesian product theory, three designs of NHZ-FHS sets are presented. It turns out that the newly constructed NHZ-FHS sets have optimal periodic Hamming correlation (PHC) properties and can offer help in improving the corresponding communication system performances in practice.

Low-Hit-Zone Frequency-Hopping Sequence Sets with Optimal Periodic Partial Hamming Correlation Properties

Low-Hit-Zone Frequency-Hopping Sequence Sets with Optimal Periodic Partial Hamming Correlation Properties

New families of optimal high-energy ternary sequences having good correlation properties

We employ algebraic methods to provide some new constructions of what we call optimal high-energy ternary sequences (a sequence with entries in $$\{0,1,-1\}$$ with a single zero, having optimal correlation properties). Our motivation for these constructions stems from their usefulness in several areas related to communication and radar systems.

Further Results on the Optimal Sequence Family $\mathcal {IP}_{8}$ Over 8-Ary Q-PAM Constellation

A family $\mathcal {IP}_{8}$ of sequences over the 8-ary quadrature-pulse amplitude modulation (Q-PAM) constellation with asymptotically optimal correlation property was presented by Anand and Kumar in 2008. This is the only known family of sequences over the quadrature amplitude modulation (QAM) constellation whose correlation magnitude asymptotically achieves the Welch bound. In this paper, a larger family $\mathcal {IP}_{8}^{\text {new}}$ of sequences with the same correlation magnitude as that of $\mathcal {IP}_{8}$ but double family size is obtained. Moreover, the correlation distributions of $\mathcal {IP}_{8}$ and $\mathcal {IP}_{8}^{\text {new}}$ are also determined for two particular cases in terms of the property of a class of exponential sums over Galois rings. It is also shown that more classes of QAM and Q-PAM sequences with low correlation and larger family size can be obtained from our approach.

Constructions of optimal low-hit-zone frequency hopping sequence sets

In recent years, the study relating to low-hit-zone frequency hopping sequence sets, including the bounds on the Hamming correlations within the low hit zone and the optimal constructions, has become a new research area attracting the attention of many related researchers. In this paper, two constructions of optimal frequency hopping sequence sets with low hit zone have been employed, one of which is based on m-sequence while the other is based on the decimated sequences of m-sequence. Moreover, in the special case of \(k=n-1\), the construction based on the decimated sequences of m-sequence also yields low-hit-zone frequency hopping sequence sets with optimal periodic partial Hamming correlation property.

Large low probability of intercept properties of the quaternary sequence with optimal correlation property constructed by legendre sequences

In this paper, we consider the Low Probability of Intercept(LPI) property of the quaternary sequence proposed by Kim, Jang, Kim, and No. We derive the LPI property of the sequence by calculating the triple autocorrelation bound of the sequence. The derived bound is approximately twice square root of the period of sequence that is similar to the triple correlation property of binary Legendre sequence.

СТАТИСТИЧЕСКИЕ ХАРАКТЕРИСТИКИ УСКОРЕННОГО ПОИСКА СИГНАЛОВ ПО ЗАДЕРЖКЕ С ИСПОЛЬЗОВАНИЕМ ПСЕВДОСЛУЧАЙНЫХ ПОСЛЕДОВАТЕЛЬНОСТЕЙ С ЛОКАЛЬНО ОПТИМАЛЬНЫМИ КОРРЕЛЯЦИОННЫМИ СВОЙСТВАМИ

СТАТИСТИЧЕСКИЕ ХАРАКТЕРИСТИКИ УСКОРЕННОГО ПОИСКА СИГНАЛОВ ПО ЗАДЕРЖКЕ С ИСПОЛЬЗОВАНИЕМ ПСЕВДОСЛУЧАЙНЫХ ПОСЛЕДОВАТЕЛЬНОСТЕЙ С ЛОКАЛЬНО ОПТИМАЛЬНЫМИ КОРРЕЛЯЦИОННЫМИ СВОЙСТВАМИ

New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation

Recently, Chung et al. gave a general method to construct frequency-hopping sequence set (FHS set) with low-hit-zone (LHZ FHS set) by the Cartesian product. In their paper, Theorems 5 and 8 claim that k FHS sets whose maximum periodic Hamming correlation is 0 at the origin result in an LHZ FHS set based on the Cartesian product, and Proposition 4 presented an upper bound of the maximum periodic Hamming correlation of FHSs. However, their statements are imperfect or incorrect. In this paper, we give counterexamples and make corrections to them. Furthermore, based on the Cartesian product, we construct two classes of LHZ FHS sets with optimal maximum periodic partial Hamming correlation property. It is shown that new FHS sets are optimal by the maximum periodic partial Hamming correlation bound of LHZ FHS set.

Families of multi‐dimensional arrays with optimal correlations between all members

Families of sequences with low off-peak autocorrelation and low cross-correlation are highly valued in spread-spectrum communication. Digital watermarking has an equal need for diverse families of orthogonal multi-dimensional (nD) arrays, where each array has optimal correlation properties. In this reported work, a 1D discrete projection method is used to construct new families of nD orthogonal arrays of size pn , with p a 4k − 1 prime. Finite field algebra and Hadamard matrices are applied to analyse these arrays. The periodic autocorrelation of each array is ‘perfect’ (p 2 − 1 peak value, with −1 off-peak for p × p arrays). The cross-correlation between any pair of the p members of each 2D family has the lowest possible values, 0 or ±p. The arrays can be synthesised for arbitrarily large p and outperform Kasami sequences. The alphabet values for these optimal arrays can be roots of unity or signed integers. The aperiodic autocorrelation of the p × p arrays can attain a merit factor of above 3 at shift (p/4, p/4), consistent with Golay's conjecture in 1D.

Set of Frequency-Hopping Sequence with Optimal Hamming Correlation

In wireless communication systems, frequency hopping (FH) spread spectrum and direct sequence spread spectrum are two main spread coding technologies. In this paper,by the Cartesian product, we construct one class of one-coincidence frequency-hopping sequence set. It is shown that this set has optimal balance property, optimal average periodic Hamming correlation properties and optimal average periodic partial Hamming correlation properties according to the bounds.

Efficient Architectures for the Generation and Correlation of Binary CSS Derived From Different Kernel Lengths

Complementary Sets of Sequences (CSS) are used as basic building blocks for the development of Generalized Orthogonal (GO) sequences. In the design of practical sequences are desirable both optimal correlation properties and an efficient implementation of their corresponding correlators (i.e., with a reduced number of operations per input sample). Traditionally, the efficient algorithms for the generation/correlation of K binary CSS have been constrained to those of lengths L=K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> , where K ≥ 2 and N is a non-negative integer. This constraint implies that many binary CSS of known lengths cannot be generated and correlated efficiently, thus limiting their practical application. This paper proposes novel efficient architectures for the generation and correlation of K binary CSS of length L=(K/2)·2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> ·10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sup> ·26 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sup> with N, M and P non-negative integers. The proposal allows the efficient generation and correlation of binary CSS of many more lengths than previous efficient architectures can handle. Therefore, the use of the proposed architectures allows selecting with more flexibility the processing gain needed for each particular application.

A Family of Alltop Functions that are EA-Inequivalent to the Cubic Function

Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (IEEE Trans. Inf. Theory 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed that these sequences were optimal with respect to the known bounds on auto and crosscorrelation. Subsequently these sequences were used to construct mutually unbiased bases (MUBs), a structure of importance in quantum information theory. The key feature of this cubic function is that its difference function is a planar function. Functions with planar difference functions have been called Alltop functions. This paper provides a new family of Alltop functions and establishes the use of Alltop functions for construction of sequence sets and MUBs.

Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties

In order to evaluate the goodness of frequency hopping sequence (FHS) design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FHS, so the study of the partial Hamming correlation of FHS is particularly important. In this paper, a class of low-hit-zone (LHZ) FHS sets with good partial Hamming correlation properties which has not yet been reported previously is constructed based on interleaving techniques. It is shown that new FHS sets are optimal with respect to the partial Hamming correlation bound of FHSs with LHZ.

A Generic Construction of Generalized Chirp-Like Sequence Sets with Optimal Zero Correlation Property

In this letter, a generic construction of optimal generalized chirp-like ZCZ sequence sets with reduced alphabet size is presented. Further, we can obtain multiple optimal quaternary ZCZ sequence sets with good inter-set cross-correlation property within the zero correlation zone, which outperforms the binary and ternary counterparts.

Frequency/time hopping sequence sets with optimal partial Hamming correlation properties

Frequency hopping/time hopping(FH/TH) sequences have found wide applications in various modern FH/TH spread spectrum communications, such as digital cellular mobile communication, short-range wireless communication, personal communication, and multi-user radar, sonar systems. In order to evaluate the goodness of FH/TH sequences design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen FH/TH sequence, so the study of the partial Hamming correlation of FH/TH sequence is particularly important. In this paper, a new class of FH/TH sequence sets with good partial Hamming correlation properties is proposed and investigated. The construction of new FH/TH sequence sets is based upon the generalized m-sequence and generalized Gordon-Mills-Welch sequence over a polynomial residue class ring. It is shown that new FH/TH sequence sets are optimal with respect to the partial Hamming correlation bound.

A New Set of Optimal Frequency-Hopping Sequences

In frequency-hopping (FH) multiple access systems, frequency-hopping sequences (FHSs) with optimal Hamming correlation properties are needed. Based on the d-form functions with ideal autocorrelation properties, a new set of FHSs is constructed. The new FHS set is optimal with respect to the Peng-Fan bounds and each FHS in the set is optimal with respect to the Lempel-Greenberger bound.