Low Correlation Zone Sequence Sets Research Articles

Millimeter-Wave Phase-Coded CW MIMO Radar Using Zero- and Low-Correlation-Zone Sequence Sets

A phase-coded continuous-wave multiple-input multiple-output (MIMO) radar based on code division multiplexing is presented. Zero-correlation-zone (ZCZ) and low-correlation-zone (LCZ) sequence sets are used to separate signals from multiple transmitters at the receivers. In particular, we investigate three different sequence set types: an equidistantly shifted almost-perfect autocorrelation sequence set, sequence sets based on mutually orthogonal Golay complementary sets, and a binary LCZ sequence set. The required sequence lengths are discussed according to the physical propagation behavior in a radar sensor scenario. Furthermore, we summarize the theoretical limitations of LCZ/ZCZ sequence sets and provide examples with regard to the chosen scenario. We present measurements carried out with a software-defined radar platform, which is equipped with 16 MIMO channels operating at a frequency of 77 GHz. We investigated the behavior of the sequence sets on real hardware in the range, cross-range, and range-Doppler domains.

New constructions of quaternary low correlation zone sequence sets

Sequence sets with low correlation have very important applications in modern communication systems. As in quasi-synchronous code-division multiple access (QS-CDMA) system, sequence sets with low correlation zone (LCZ) perform better than other well-known sequence sets. Furthermore, binary or quaternary sequence sets are preferred because of their easy implementation. In this paper, based on the inverse Gray mapping and special binary sequence pairs, new quaternary LCZ sequence sets were constructed. In the LCZ, the maximum of the nontrivial autocorrelation and crosscorrelation values is 1 which show that the QS-CDMA system used the new sequences sets can control the interference in a very low level.

A New Method for Constructing Quaternary Sequence Sets with Low Correlation Zone

A method of constructing multiple quaternary low correlation zone (LCZ) sequence sets with the same parameters is proposed. Two mappings which can map two binary variables to a quaternary one are presented. Based on different mappings, new quaternary LCZ sequence sets are constructed. Furthermore, based on the same mapping, the parameters of shift sequences are changed to extend the number of LCZ sequence sets and there is only one shift equivalent sequence from different sets. The parameters of the LCZ sequence sets can be flexibly chosen. Compared with previous methods, the proposed construction extends the number of quaternary LCZ sequence sets. As a result, more spreading sequences are provided for multi-cell quasi-synchronous code-division multiple-access systems.

New construction of perfect sequence set and low correlation zone sequence set

For a given binary ideal autocorrelation sequence, we construct a perfect sequence set by changing a few bits of the sequence. The set has a large size with respect to the period of its sequences. Based on the constructed perfect sequence set, a new class of low correlation zone sequence sets whose low correlation zone length can be chosen flexibly is obtained. Moreover, the new constructed low correlation zone sequence sets can attain Tang-Fan-Matsufuji’s bound with suitably chosen parameters.

Construction of Optimal Low Correlation Zone Sequence Sets Based on DFT Matrices

Construction of Optimal Low Correlation Zone Sequence Sets Based on DFT Matrices

A General Construction of Low Correlation Zone Sequence Sets Based on Finite Fields and Balanced Function

A General Construction of Low Correlation Zone Sequence Sets Based on Finite Fields and Balanced Function

A new class of quaternary LCZ sequence sets

In this article, we present a construction of low correlation zone (LCZ) sequence sets. This construction gives a new class of quaternary LCZ sequence sets. Furthermore, we observe a generalization of the LCZ sequence sets in Kim et al. (IEEE Trans Inform Theory 52(10):4607---4616, 2006) by using an orthogonal transformation. The obtained LCZ sequence sets are optimal with respect to the Tang, Fan and Matsufuji bound.

New Method to Extend the Number of Quaternary Low Correlation Zone Sequence Sets

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.

A Construction of Quaternary Low Correlation Zone Sequence Sets from Binary Low Correlation Zone Sequence Sets Improving Optimality

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.

New construction of quaternary low correlation zone sequence sets from binary low correlation zone sequence sets

In this paper, using binary (N, M, L, є) low correlation zone (LCZ) sequence sets, we construct new quaternary LCZ sequence sets with parameters (2N, 2M, L, 2є). Binary LCZ sequences for the construction should have period N ≡ 3 mod 4, L|N, and the balance property. The proposed method corresponds to a quaternary extension of the extended construction of binary LCZ sequence sets proposed by Kim, Jang, No, and Chung [1].

New Extension Method of Quaternary Low Correlation Zone Sequence Sets

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.

New Families of Binary Low Correlation Zone Sequences Based on Interleaved Quadratic Form Sequences

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.

A New Class of Sequences With Zero or Low Correlation Zone Based on Interleaving Technique

By interleaving one length-N perfect sequence or ideal sequence according to elaborate phases, a new method of construction of zero correlation zone (ZCZ) and low correlation zone (LCZ) sequence sets is presented. The resultant sequence sets are optimal or almost optimal with respect to Tang, Fan, and Matsufuji bound. Furthermore, the new method provides flexible choice for the ZCZ and LCZ lengths.

New Design of Quaternary Low-Correlation Zone Sequence Sets and Quaternary Hadamard Matrices

In this correspondence, we present new construction methods for quaternary low-correlation zone (LCZ) sequence sets from a binary sequence with good autocorrelation. We show that the sets obtained by our methods are optimal or nearly optimal with respect to the Tang-Fan-Matsufuji bound and that our construction methods are more flexible than any other previous constructions in the sense of period, family size, and zone size. We also give a construction method for a quaternary LCZ sequence set from a binary LCZ sequence set. Finally, we give a new construction method for quaternary Hadamard matrices by the inverse of the Gray map.

Butson Hadamard matrices with partially cyclic core

In this paper, we introduce a class of generalized Hadamard matrices, called a Butson Hadamard matrix with partially cyclic core. Then a new construction method for Butson Hadamard matrices with partially cyclic core is proposed. The proposed matrices are constructed from the optimal balanced low-correlation zone(LCZ) sequence set which has correlation value ?1 within LCZ.

New Sets of Optimal $p$-ary Low-Correlation Zone Sequences

In this correspondence, three methods of constructing low-correlation zone (LCZ) sequences are proposed. In the first method, we constructed binary LCZ sequence sets of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -1 using the Legendre sequences of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -1 as a column sequence when m|n. In the second method, we devise a column sequence set of length 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m+1</sup> -1 from a binary sequence of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -1 having ideal autocorrelation property and this column sequence set is used to construct binary LCZ sequence sets of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> -1 when (m+1)|n. In the third method, p-ary LCZ sequence sets are constructed by adopting p-ary sequence of period p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> -1 with ideal autocorrelation for integers n and m such that m|n as a column sequence. The second and third methods give us the optimal sets with respect to the bound by Tang, Fan, and Matsufuji. Finally, a construction method of p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> timesp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> p-ary Hadamard matrices from optimal LCZ sequence sets is proposed

New Design of Low-Correlation Zone Sequence Sets

In this paper, we present several construction methods for low-correlation zone (LCZ) sequence sets. First, we propose a design scheme for binary LCZ sequence sets with parameters (2n+1-2,M,L,2). In this scheme, we can freely set the LCZ length L and the resulting LCZ sequence sets have the size M, which is almost optimal with respect to Tang, Fan, and Matsufuji bound. Second, given a q-ary LCZ sequence set with parameters (N,M,L,epsi) and even q, we construct another q-ary LCZ sequence set with parameters (2N,2M,L,2epsi) or (2N,2M,L-1,2epsi). Especially, the new set with parameters (2N,2M,L,2) can be optimal in terms of the set size if a q-ary optimal LCZ sequence set with parameters (N,M,L,1) is used

A New Construction of Optimal p2-Ary Low Correlation Zone Sequences Using Unified Sequences

In this paper, given an integer e and n such that e|n, and a prime p, we propose a method of constructing optimal p2-ary low correlation zone (LCZ) sequence set with parameters (pn-1, pe-1, (pn-1)/(pe-1), 1) from a p-ary sequence of the same length with ideal autocorrelation. The resulting p2-ary LCZ sequence set can be viewed as the generalization of the optimal quaternary LCZ sequence set by Kim, Jang, No, and Chung in respect of the alphabet size. This generalization becomes possible due to a completely new proof comprising any prime p. Under this proof, the quaternary case can be considered as a specific example for p = 2.

Generalised Sarwate bounds on periodic autocorrelations and cross-correlations of binary sequences

A general periodic correlation bound named generalised Sarwate bound for binary zero or low correlation zone (ZCZ/LCZ) sequence set with respect to family size, sequence length, maximum autocorrelation sidelobe, maximum cross-correlation value and the zero or low correlation zone, are derived. It is shown that all the previous periodic sequence bounds, such as Sarwate bound, Welch bound and Tang-Fan bound, are only special cases of the generalised Sarwate bound.