Binary Complementary Sequence Research Articles

Binary Complementary Sequence Set With Low Correlation Zone

Recently, quasi-complementary sequence sets (QCSSs) including low correlation zone complementary sequence sets (LCZ-CSSs), and low correlation complementary sequence sets (LC-CSSs) have raised lots of concerns. According to the theoretical bounds, the set size of a QCSS is much larger than that of a traditional perfect complementary sequence set (PCSS). As a result, it is believed that QCSSs have potential applications in multi-carrier code-division multiple-access (MC-CDMA) systems to support more users. As binary sequences are desired in practice because of easier realization, we consider the design of binary QCSSs with large set size in this letter. A construction of aperiodic binary LCZ-CSSs is proposed, which leads to aperiodic binary LCZ-CSSs with asymptotically optimal parameters. Additional, aperiodic binary LC-CSSs with asymptotically optimal parameters can also be derived from the proposed construction.

Implementable phase‐coded radar waveforms featuring extra‐low range sidelobes and Doppler resilience

Golay binary complementary sequences are used to code quadriphase waveforms. The Gaussian minimum shift keying coding scheme is used to produce waveforms with constant amplitude, and continuous and differentiable phase. To satisfy spectral requirements, the waveforms are further spectrally optimised by a spectrum-optimisation process, making the final waveforms implementable. The extra-low sidelobe level is achieved by the use of an extended mismatched filter on receive of pulse compression. To improve Doppler tolerance, Doppler-resilient complementary waveforms are derived that provide first-order suppression to the raised range sidelobes introduced by the Doppler frequency shift in returned signals. This study is an expanded version of a conference paper presented at 2018 International Radar Conference held in Brisbane, Australia.

Matrix Completion and Performance Guarantees for Single Individual Haplotyping

Single individual haplotyping is an NP-hard problem that emerges when attempting to reconstruct an organism's inherited genetic variations using data typically generated by high-throughput DNA sequencing platforms. Genomes of diploid organisms, including humans, are organized into homologous pairs of chromosomes that differ from each other in a relatively small number of variant positions. Haplotypes are ordered sequences of the nucleotides in the variant positions of the chromosomes in a homologous pair; for diploids, haplotypes associated with a pair of chromosomes may be conveniently represented by means of complementary binary sequences. In this paper, we consider a binary matrix factorization formulation of the single individual haplotyping problem and efficiently solve it by means of alternating minimization. We analyze the convergence properties of the alternating minimization algorithm and establish theoretical bounds for the achievable haplotype reconstruction error. The proposed technique is shown to outperform existing methods when applied to synthetic as well as real-world Fosmid-based HapMap NA12878 datasets.

Phased unitary Golay pairs, Butson Hadamard matrices and a conjecture of Ito’s

Pairs of complementary binary or quaternary sequences of length v such as Golay pairs, complex Golay pairs and periodic Golay pairs may be used to construct Hadamard matrices and complex Hadamard matrices of order 2v. We generalize these and define unitary Golay pairs and phased unitary Golay pairs of length v with entries in the kth roots of unity for any $$k \ge 2$$ . This leads to a construction of Butson Hadamard matrices of order 2v over the kth roots of unity for even k. Ito conjectured that a central relative (4v, 2, 4v, 2v)-difference set exists in a dicyclic group of order 8v for all $$v \ge 1$$ , and this is known to imply the Hadamard conjecture. With our construction we prove that Ito’s conjecture also implies the stronger complex Hadamard conjecture. As a consequence, with this method we construct a complex Hadamard matrix of order 2v for any v for which Ito’s conjecture is verified, in particular, any $$v \le 46$$ .

Generation and correlation of orthogonal complementary pairs of sequences of lengths 2N10M26P based on an improved multilevel complementary sequences approach

SummaryBinary complementary pairs of sequences of lengths 2N10M26P posses some interesting properties for their application in signal detection in noisy channels. Nonetheless, they have not been broadly used because of their greater processing requirements as compared with binary complementary sequences with L = 2N. The present work introduces a new approach for generation and correlation of binary complementary pairs of sequences of length 2N10M26P that reduces the number of required operations. The proposed algorithm allows not only to optimize the number of arithmetic operations but also to correlate two orthogonal complementary pairs simultaneously with the use of a single architecture. Due to the fact that multilevel complementary sequences algorithms are used to generate and correlate binary complementary sequences of length 2N10M26P, the aforementioned algorithms are also improved. The proposal is theoretically proved and its arithmetic efficiency is assessed by comparing the number of operations with that of previously published architectures. Copyright © 2017 John Wiley & Sons, Ltd.

Research on Periodic Punctured Binary Complementary Sequence Pair Set

A new discrete perfect signal named periodic punctured binary complementary sequence pair set is proposed. Several construction methods are proposed, such as using perfect punctured binary sequence pair or array pair, column orthogonal matrix, mate set interleaved operation, and periodic production methods etc. More periodic punctured binary complementary sequence pair sets could be generated through these methods. Research results show that it has wider existent scope and could be applied in engineering as a kind of perfect signal with good correlation properties.

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.

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.

Noncoherent Radar Pulse Compression Based on Complementary Sequences

Noncoherent pulse compression (NCPC), suggested recently, uses on-off keying (OOK) signals, obtained from Manchester coding a binary sequence with favorable a-periodic autocorrelation. This paper investigates the use of binary complementary pairs as a basis for NCPC. It shows that a pair of Manchester coded, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> -element binary complementary sequences will yield a peak sidelobe (PSL) ratio of 1/(2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ).

Periodic complementary binary sequences and Combinatorial Optimization algorithms

We establish a new formalism for problems pertaining to the periodic autocorrelation function of finite sequences, which is suitable for Combinatorial Optimization methods. This allows one to bring to bear powerful Combinatorial Optimization methods in a wide array of problems that can be formulated via the periodic autocorrelation function. Using this new formalism we solve all remaining open problems regarding periodic complementary binary sequences, in the context of the Bomer and Antweiler diagram and thus complete the program that they started in 1990.

Optimal Training Sequences for Cyclic-Prefix-Based Single-Carrier Multi-Antenna Systems with Space-Time Block-Coding

In this paper, the requirement on optimal training sequences for single-carrier multi-antenna channel estimation with space-time block-coding is firstly derived based on time-domain analysis. It is then shown that the optimality requirement relates to a new concept called Z-periodic complementarity, and the desired optimal training sequences are in fact a class of Z-periodic complementary sequences which include the conventional periodic complementary sequences and L-perfect sequences as special cases. Definitions and constructions of the Z-periodic complementary binary sequences and their mates are given.

Odd-Periodic and Periodic Complementary binary sequences

Two or more sequences are called an Odd-Periodic Complementary binary sequences Set (OPCS) if the sum of their respective odd-periodic autocorrelation function is a delta function. In this paper, the definition of OPCS is given and the construction method of OPCS is discussed. The relation of the OPCS with the Periodic Complementary binary sequences Set (PCS) is pointed out, and some new PCSs are obtained based on such relation.

Complementary sequence inverse keying for indoor wireless infrared channels

Complementary sequence inverse keying is proposed to ameliorate multipath ISI effects in an indoor wireless infrared communication system. The method involves the transmission of a pair of complementary binary sequences. The system BER performance is presented in comparison with OOK and the results demonstrate that CSIK, unlike OOK, does not incur a power penalty due to ISI.

On aperiodic and periodic complementary binary sequences

We give direct and recursive constructions for aperiodic and periodic complementary sequences. Using these constructions, many missing entries in the table of Bomer and Antweiler (1990) can be filled.

On the existence of periodic complementary binary sequences

Using the connection between periodic complementary binary sequences and difference families given by Bomer and Antweiler [2], we use number theoretic techniques to obtain necessary conditions for their existence when two or three sequences are involved. Our results provide theoretical proof for the nonexistence of PCS320(ai) and settle the open case PCS236(ai) of [2], negatively.

Periodic complementary binary sequences

Existence conditions and recursive construction procedures for sets of periodic complementary binary sequences are given. Relationships to sets of aperiodic complementary binary sequences and to perfect binary arrays, whose two-dimensional periodic autocorrelation function is a delta function, are noted. The connections of periodic complementary binary sequences and difference families are given. Sets of periodic complementary binary sequences, which result from computer search, are presented. A diagram showing what is currently known about the existence of periodic complementary binary sequences with P<or=12 sequences of N<or=50 elements is given.<<ETX>>