Large Sets of Binary Spreading Sequences With Low Correlation and Low PAPR via Gold Functions

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.

Chaotic sequences have good correlation properties and they can be used as address sequences in Spread Spectrum Communication. Chaotic functions are highly sensitive to initial condition and exhibit non-linear behavior. In Chaotic spread spectrum communication systems, different user may be assigned different sequences generated with different initial conditions. Set of binary sequences with good pair wise cross- correlation property finds applications in Direct Sequence- Code Division Multiple Access (DS-CDMA) systems. Security in Direct Sequence-Code Division Multiple Access systems is relatively limited. To enhance security in Direct Sequence- Code Division Multiple Access systems, chaotic sequences are generated. In this paper we analyze the generation of chaotic binary sequences and study of auto correlation and cross correlation properties.

It is well known that jointly optimal multiuser detection for code division multiplex access (CDMA) systems has complexity which grows exponentially with the number of users. Recently, several authors [S. Ulukus and R. D. Yates, April 1998], [C. Sankaran and A. Ephremides, Sept. 1998], [C. Schlegel and A. Grant, 2000] have reported that, for certain special sets of spreading sequences, optimal multiuser detection in synchronous CDMA systems can be performed with computational complexity which is polynomial in the number of users. In this paper, we show that the existing polynomial complexity (PC) algorithms of [S. Ulukus and R. D. Yates, April 1998], [C. Sankaran and A. Ephremides, Sept. 1998], [C. Schlegel and A. Grant, 2000] lead to efficient algorithms for a wider class of spreading sequences than initially proposed. We identify these sequences and prove the existence of optimal polynomial-complexity algorithms for detecting synchronous CDMA signals using these sequences. We also give constructions of sets of binary antipodal spreading sequences for which optimal polynomial-complexity algorithms exist and show that for any sequence length N, we can construct at least N such 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

In recent years, fifth-generation (5G) is receiving attention in wide research and progress efforts from the wireless communication society. 5G provides a new frequency bands alongside amid the wider spectral bandwidth per frequency channel. To solve the new challenges in 5G, different kind of new modulation techniques and multiple access (MA) schemes have to be adopted. To increase spectral efficiency new techniques called orthogonal multiple access (OMA) and nonorthogonal multiple access (NOMA) techniques are used in 5G wireless system. Here, we propose a class of polyphase sequences called Zadoff Chu sequences which have uniform amplitude, and these sequences bear good correlation properties. Since these sequences are also identified as constant amplitude zero autocorrelation (CAZAC) sequences, Zadoff Chu sequences are used to spread data in OMA and NOMA schemes for 5G networks. The simulation result shows that Zadoff Chu sequence has good correlation properties, and ZCT precoded-based OFDM system is capable of reducing the PAPR significantly.

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.

This paper presents new binary spreading sequences, obtained by tabu search. These sequences exhibit odd correlation properties concerning the minimax criterion better than those of the classical sequence families, such as the well known Kasami and Gold sequences. In particular, the design process takes into account both odd and even correlation properties which means that global performance is compromised. These new sequences also have same mean-square correlation performance as classical ones.

A detailed study of the effects of binary spreading sequences (BSS) excitation in the magnetization dynamics of exchange-biased spin-valves driven by spin-transfer-torque has been carried out by full micromagnetic modeling. We show that the use of BSS allows to trigger the magnetization reversal by exciting its main precession modes. We compared our numerical results with the experimental ones reported by [Cui et al., Phys. Rev. B 77, 214440 (2008)], attaining quantitative agreement. Advantages of BSS as microwave source with respect to a sinusoidal signal are also reported and discussed.

The authors consider a direct-sequence spread-spectrum multiple-access (DS/SSMA) communication system with M-ary phase-shift keyed (MPSK) signaling. Users in the system use complex signature sequences. A bounding technique is used to obtain arbitrarily tight upper and lower bounds on the probability of bit error. Numerical results are presented for Frank-Zadoff-Chu (FZC) and near-optimal four-phase complex sequences, as well as binary Gold sequences, for binary phase shift keying, (BPSK), 4-PSK, and 8-PSK. Results show that complex sequences can yield better performance than binary sequences in MPSK signaling. Using complex sequences, the number of signature sequences with good correlation properties is greatly enlarged.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, for integers e and n such that e|n and 2e - 1 is a prime, we propose a method of constructing binary low correlation zone (LCZ) sequences of period 2n - 1 by using the extended form sequence with the same period. These new LCZ sequences use Legendre sequences as their column sequences

Welch-Gong (WG) transformation sequences are binary sequences of period 2n. 1 with 2-level auto correlation. These sequences were discovered by Golomb, Gong and Gaal in 1998 and verified for 5 ≤ n ≤ 20. Later on, No, Chung and Yun found another way to construct the WG sequences and verified their result for 5 ≤ n ≤ 23. Dillon first proved this result for odd n in 1998, and finally, Dobbertin and Dillon proved it for even n in 1999. In this paper, we investigate a two-faced property of the WG transformation sequences for application in stream ciphers and pseudo-random number generators. One is to present randomness or unpredictability of the WG transformation sequences. The other is to exhibit the security property of the WG transformations regarded as Boolean functions. It is shown that the WG transformation sequences, in addition to the known 2-level auto correlation, have threelevel cross correlation with m-sequences, large linear ! span increasing exponentially with n and efficient implementation. Thus this is the first type of pseudo-random sequences with good correlation and statistic properties, large linear span and efficient implementation. When the WG transformation are regarded as Boolean functions, it is proved that they have high nonlinearity. A criterion for whether the WG transformations regarded as Boolean functions are r-resilient is derived. It is shown that the WG transformations regarded as Boolean functions have large linear span (this concept will be defined in this paper) and high degree.

In this letter, we propose a novel scheme to construct a novel class of 2-D binary sequences with zero correlation zone, which is based on perfect arrays and orthogonal sequences. Compared with all existing 2-D binary sequences, the proposed construction can generate more sets of two-dimensional binary sequences with long zero correlation zone. Moreover, the constructed 2-D sequence sets could be applied directly, such as arrays of sound sources, position detection arrays, phased-array antennas, time-frequency coding, and spatial correlation.

The effects of a noise-like weak signal in the resonant switching of the magnetization driven by spin transfer torque have been systematically studied by means of micromagnetic simulations in both in-plane spin valves and out-of-plane magnetic tunnel junctions. The use of a noise-like resonant excitation allows the overpassing of some critical points compared to the traditional microwave assisted switching. In particular, the application of binary spreading sequences (BSS) does not require the precise knowledge of the resonant frequency and of the optimum relative phase, allowing the use of the same resonant excitation for all the devices in a matrix of memory cells, even if small variations of the physical and geometrical parameters are present. In addition, we also found that in spin valves the switching probabilities close to 100% can be achieved with a smaller current pulse, and in magnetic tunnel junctions a significant energy saving can be obtained.

Employing binary sequences with good autocorrelation properties leads to performance improvement for active sensing systems. Designing such sequences has been studied widely in the literature from optimization point of view. In this paper we consider the problem of designing binary sequences with good aperiodic/periodic auto-correlation functions in terms of Integrated Sidelobe Level (ISL) using machine learning method. Specifically, we propose a novel neural network structure which can learn an algorithm for designing binary sequences with small ISL. We also extend the resulting network, which we refer to as BiSCorN, by designing Low-Correlation Zone (LCZ) binary sequences. Numerical experiments show that our proposed method outperforms state-of-the-art algorithms in terms of ISL, and interestingly Peak Sidelobe Level (PSL).

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