Autocorrelation of two Legendre-Sidelnikov sequences

Sequences with nice pseudo-randomness play an important role in not only communication system but also cryptography system. Based on the Legendre-Sidelnikov sequence, a modified Legendre-Sidelnikov sequence was introduced. The exact value of the autocorrelation function was derived by strict computation. According to the values of the autocorrelation functions of the two Legendre-Sidelnikov sequences, it is proven that both of them have perfect pseudo-randomness. Furthermore, a detailed comparison between autocorrelation functions of the two Legendre-Sidelnikov sequences was deduced. It indicates that no matter which parameters are chosen, the modified sequence has pseudo-randomness as good as the primitive sequence, which is of great significance for applications.     

量子棒中电子的跃迁谱线的频率

The Hamiltonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation which changes the ellipsoidal boundary into a spherical one. We then study the first internal excited state energy, the excitation energy and the frequency of the transition spectral line between the first internal excited state and the ground state of the strong-coupling polaron in a quantum rod. The effects of the electron–phonon coupling strength, the aspect ratio of the ellipsoid, the transverse radius of quantum rods and the transverse and longitudinal effective confinement length are taken into consideration by using a linear combination operator and the unitary transformation methods. It is found that the first internal excited state energy, the excitation energy and the frequency of the transition spectral line are increasing functions of the electron–phonon coupling strength, whereas they are decreasing ones of the transverse radius of quantum rods and the aspect ratio. The first internal excited state energy, the excitation energy and the frequency of the transition spectral line increase with decreasing transverse and longitudinal effective confinement length. oindent     

Research on pulse edge extraction by using nonlinear optical fiber-loop mirror

The output characteristics of nonlinear optical fiber-loop mirror are analyzed in detail when the pump pulses with the same wavelength are input in the both directions for recovering the clock component of the signal spectrum.It is found that the double output pulses are produced in the transmission port of the nonlinear optical fiber-loop mirror.The output pulse peaks are located in time domain at the rising and falling edges of the pump pulses.It is demonstrated that the rising and falling edges of the pump pulse can be directly extracted by this method.Through numerical simulation,the effects of therelative delay of pump pulses and the dispersion of fiber on the characteristics of output pulses are studied.By spectrum analysis,it is found that the spectrum of output pulse sequence includes the clock components of the pump pulse sequence,and a new idea is provided for all-optical clock extraction.     

Some results on the algebraic immunity of Boolean functions

From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity(AI) of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed.     

Biased bearings-only parameter estimation for bistatic system

According to the biased angles provided by the bistatic sensors,the necessary condition of observability and Cramer-Rao low bounds for the bistatic system are derived and analyzed,respectively. Additionally,a dual Kalman filter method is presented with the purpose of eliminating the effect of biased angles on the state variable estimation. Finally,Monte-Carlo simulations are conducted in the observable scenario. Simulation results show that the proposed theory holds true,and the dual Kalman filter method can estimate state variable and biased angles simultaneously. Furthermore,the estimated results can achieve their Cramer-Rao low bounds.     

Optimal design and characteristics analysis of a polymer electro-optic switch with seven vertical-turning serial-cou- pled microrings

A novel 1 x2 polymer electro-optic （EO） switch based on seven vertical-mining serial-coupled microrings is proposed for dropping crosstalk and obtaining fiat boxlike spectrum. The device structure, theory and formulation are presented, and the microring resonance order and coupling gaps are optimized. The switching voltage of the device for obtaining crosstalk lower than -30 dB under through state is decided to be about 1.86 V. Under the operation voltages of 0 V （drop state） and 1.86 V （through state）, the switching performance is characterized, and the output spectrum is ana- lyzed. The calculation results show that the crosstalk at through state and that at drop state are -30.2 dB and -53.2 dB, respectively, while the insertion losses are 0.86 dB and 3.18 dB, respectively. Owning to the seven serial-coupled mi- crorings resonance structure, the proposed switch reveals the favorable boxlike spectrum compared with the simple device with only one microring, and thus the crosstalk under drop state is improved from -26.8 dB to -53.2 dB. Due to the low crosstalk, this device can be used in optical networks-on-chip for signal switching and routing.     

An ultra-compact cross/bar optical routing switch using two polymer electro-optic microrings

A 2×2 cross/bar polymer electro-optic(EO) routing switch is proposed,which is composed of two passive channel waveguides and two active EO polymer microrings with bending radius of only 13.76 μm.Detailed structure,theory and formulation are provided to characterize the output power of the switch.For obtaining fundamental mode propagation,small bending loss and phase-matching between channel waveguide and microring resonator(MRR) waveguide,the structural parameters are optimized under the wavelength of 1550 nm.Analyses and simulations on output power and output spectra indicate that a switching voltage of 5 V is desired to realize the exchange between cross state and bar state,the crosstalk under cross state and that under bar state are about 28.8 dB and 39.9 dB,respectively,and the insertion losses under these two states are about 2.42 dB and 0.13 dB,respectively.Compared with our four EO switches reported before,this device possesses ultra-compact size of 0.233 mm×0.233 mm as well as low crosstalk and insertion loss,and therefore it can serve as a good candidate for constructing large-scale optical routers or switching arrays in photonic network-on-chip(NoC).     

New concept for determining the orders of SAC and PC

The autocorrelation of a Boolean function possesses the capability to reflect such characteristics as linear structure, Strict Avalanche Criterion(SAC) and Propagation Criterion(PC) of degree k. But it can do nothing in determining the order of SAC or PC. A calculating table for the autocorrelation is constructed in this paper so as to show what is beyond the autocorrelation and how the three cryptographic characteristics are exhibited. A deeper study on the calculating table in a similar way has helped us to develop a new concept, named as the general autocorrelation, to address efficiently the problem how to determine the orders of SAC and PC. The application on the Advanced Encryption Standard(AES) shows the SAC and PC characteristicsof Boolean functions of AES S-box.     

Comparison of Three SVPWM Strategies

Three space vector pulse width modulation （SVPWM） schemes, called 7-segment space vector modulation （SVM）, 5-segment SVM and 3-segment SVM are studied in this paper. The basic principle of SVPWM is presented. The switching sequence of different scheme is described. The modulation signals, DC bus voltage utilization, and output line voltage harmonic of these schemes are analyzed by the MATLAB software with different modulation index M and frequency modulation index N. The simulation results are analyzed and show that discontinuous modulating functions lead a reduction of switching actions. The DC bus voltage utilization of three schemes is almost the same. For all three SVM, the frequency modulation index N will affect the harmonic characteristic, and the modulation index M will affect DC bus voltage utilization and the harmonic content. The experiment is implemented by the DSP of TMS320F2812. The results validate three algorithms and the simulation.     

A S-BAND 2.5 MW HIGH POWER BROADBAND KLYSTRON

In this paper,the design considerations of a high-efficiency high-gain broadband klystron aredescribed.Its buncher has been studied by using small signal gain and large signal efficiencyprograms.With small gain greater than 50dB,the buncher bandwidths of 10% and 10—15% can beobtained for 7 and 8 cavity klystrons respectively.The design methods and measured results ofoutput circuits of two types are introduced.The bandwidths of the filter type and the overlappingmode two gap cavity output circuits are about 7.5—10% and 10—12% respectively.Two types ofS-band broadband klystrons with the two respective output circuits described are constructed andtested,and the one with the former output circuit has 1dB equi-drive bandwidth of 7.5% with anefficiency of 38% and a gain of 43 dB,while the other with the later output circuit has 1dB equi-drive bandwidth of 10%.Their output power is greater than 2.5 MW.     

相控序列的改进——采用级连GMW序列 构造相控序列

本文介绍了一种新型伪随机序列－相控序列,相控序列具有线性复杂度很大,相关性好,序列平衡的优点.本文提出了对相控序列的改进,使用级连GMW序列代替原始定义中生成相控序列所需的GMW序列,并证明了这种改进的可行性.改进后的相控序列的线性复杂度进一步增大,族数增多但相关性和平衡性不变.     

Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences

Frequency hopping (FH) sequences have found wide applications in various modern FH spread-spectrum communications and radar systems. In FH spread-spectrum communications, the interference occurs when two distinct transmitters use the same frequency simultaneously. In order to evaluate the goodness of FH sequence design, the Hamming correlation function is used as an important measure. In this correspondence, by considering separately the maximum Hamming autocorrelation sidelobe H/sub a/, and the maximum Hamming cross correlation H/sub c/, several new lower bounds on the size p of the frequency slot set F, the sequence length L, the family size M, and correlation properties are established. The new periodic bounds include the known Lempel-Greenberger bounds as special case when M=2, and are tighter than the Seay bounds under certain conditions when M>2. Furthermore, the new bounds disclose more information on the relationship between the maximum autocorrelation sidelobe and the maximum cross correlation compared with the Lempel-Greenberger bounds and Seay bounds. Besides, the aperiodic FH bounds which have not yet been previously reported are also presented and discussed in this correspondence.     

具有二值自相关特性的p元伪随机序列族的构造

具有二值自相关特性的伪随机序列在扩频通信、流密码、雷达和声纳等领域中具有重要的应用。本文首先基于d-型序列的思想，给出了具有二值自相关特性的p元伪随机序列的构造表达式。此外，基于已有的具有二值自相关函数序列，本文提出了构造具有同样自相关特性的伪随机序列的方法。可以用来构造具有最佳Hamming相关特性的跳频序列族。     

自相关性和线性复杂度的关系

自相关性和线性复杂度是衡量序列伪随机性质的两个独立的指标.针对周期为2^<em>n的伪随机序列,本文首次指出了自相关性和线性复杂度之间存在的一个关系.该关系可应用于以下两个方面:(1)由序列的线性复杂度来估计/确定序列的自相关函数值;(2)通过线性复杂度来检验给定序列族的互相关性质.进一步的,针对一类周期为2^<em>n的伪随机序列,我们指出这类序列的自相关函数值和线性复杂度以及k-错线性复杂度存在着关系.     

环Zpl导出Kerdock-code序列的部分周期性质

对环Z_p^l导出的多元Kerdock-code序列的部分周期性质进行了研究,这里p为任意奇素数,l为任意正整数.利用特征为p^l的Galois环上不完全指数和的非平凡上界,对上述p元Kerdock-code序列的非周期自相关性及互相关性进行了估计,同时对序列的部分周期分布和部分周期独立r-样式分布也进行了刻画.结果表明,此类序列具有极低的非周期自相关性及互相关性,同时其部分周期分布和部分周期独立r-样式分布也是渐进均匀的,在密码学和通信领域具有潜在的应用价值.     

Optical orthogonal codes: design, analysis and applications

An optical orthogonal code (OOC) is a family of (0,1) sequences with good auto- and cross-correlation properties, i.e the autocorrelation of each sequence exhibits the `thumbtack' shape and the cross correlation between any two sequences remains low throughout. The use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably. The thumbtack-shaped autocorrelation facilitates the detection of the desired signal, and low-profile cross correlation reduces interference from unwanted signals. Theoretical upper and lower bounds on the maximum possible size of OOCs are derived. Methods for the design and analysis of OOCs, using tools from projective geometry, the greedy algorithm, iterative constructions, algebraic coding theory, block design, and various other combinational disciplines, are discussed     

Some randomness properties of cascaded sequences (Corresp.)

The autonomous response sequences of cascade coupled sequence generators are investigated. Them-tuple distribution and autocorrelation function of such sequences are related to them-tuple distribution of the component sequences. Cascade coupled pseudonoise (PN) sequence generators withtcumpunents have output sequences with anm-tuple distribution that approximates them-tuple distribution of a random sequence in which the probability of a one is2^{-t}. The phase shifts are almost uncorrelated for most shifts, but some shifts are highly correlated.     

Complementary Huffman sequences

The theories of complementary and Huffman sequences have been two distinct areas. It is shown that each Huffman sequence has its complementary pair. In radar applications, these pairs can be used, in the same way as other binary and nonbinary complementary sequences. They have the added advantage of zero autocorrelation sidelobes at all time shifts except the largest one. Even these sidelobes are cancelled if the autocorrelation functions are summed because of the complementarity.<>     

Bounds on partial correlations of sequences

Two approaches to bounding the partial auto- and crosscorrelations of binary sequences are considered. The first approach uses the discrete Fourier transform and bounds for character sums to obtain bounds on partial autocorrelations of m-sequences and on the partial auto- and crosscorrelations for the small Kasami sets and dual-BCH families of sequences. The second approach applies to binary sequences obtained by interleaving m-sequences. A bound on the peak partial correlation of such sequences is derived in terms of the peak partial autocorrelation of the underlying m-sequences. The bound is applied to GMW, No (1987), and other families of sequences for particular parameters. A comparison of the two approaches shows that the elementary method gives generally weaker results but is more widely applicable. On the other hand, both methods show that well-known sequence families can have favorable partial correlation characteristics, making them useful in certain spread-spectrum applications