The Research of Chaos-based M-ary Spreading Sequences

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.

The ratio of spectral power in two different bands and relative band power have been shown to be sometimes more discriminative features than the spectral power in a specific band for binary classification of a time series for seizure prediction. However, why and which ratio of spectral power and relative power features are better discriminators than a band power have not been understood. While general answers to why and which are difficult, this paper partially addresses the answer to these questions. Using auto-regressive modeling, this paper, for the first time, theoretically explains that for high signal-to-noise ratio (SNR) cases, the ratio features may sometime amplify the discriminability of one of the two states in a time series, as compared with a band power. This paper, also for the first time, introduces a novel frequency-domain model ratio (FDMR) that can be used to select the two frequency bands. The FDMR computes the ratio of the frequency responses of the two auto-regressive model filters that correspond to two different states. It is shown that the ratio implicitly cancels the effect of change of variance of the white noise that is input to the auto-regressive model in a non-stationary environment for high SNR conditions. It is also shown that under certain sufficient but not necessary conditions, the ratio of the spectral power and the relative band power, i.e., the band power divided by the total power spectral density, can be better discriminators than band power. Synthesized data and scalp EEG data from the MIT Physionet for patient-specific seizure prediction are used to explain why the ratios of spectral power obtained by a ranking algorithm in the prior literature satisfy the sufficient conditions for amplification of the ratio feature derived in this paper.

Gold functions are well-known for designing sequences with good correlation properties. This paper reveals a fascinating relationship between Gold functions and Golay-Davis-Jedwab (GDJ) Boolean functions to design sequences with low correlation and low PAPR, which is the first of its kind. The bent and semi-bent properties of the Gold functions are utilized to derive the correlation of the resultant binary spreading sequence sets, while the complementary properties of the GDJ Boolean functions are used to derive the low PAPR. Based on this idea we propose three new sets of binary spreading sequences with low PAPR and low correlation. The proposed sequence sets have the potential to be used as spreading sequences in non-orthogonal multiple access (NOMA). They have a very large set size, which in turn results in a high overloading factor as compared to the existing sequence sets with the same length and the same correlation, which are generated through systematic constructions.

In stream cipher systems, random key sequence generation is the primary task. The concept of chaotic systems can be considered in generating a random key sequence due to its inherent randomness property. Though the chaotic real sequences are random, the randomness will be lost after converting them to binary sequences. In this context, the authors propose a technique which uses a non‐linear feedback system to enhance the randomness of the binary sequences. In this work, three binary chaotic sequences using a logistic map are generated with three different initial conditions and each real value of the chaotic sequence is converted to ‘k’ bit binary value using a thresholding function. Some of the resulting sequences are not random. Hence, in this article a non‐linear structure is used to make the resulting sequence random. Here, a non‐linear function similar to the structure of the Simplified Data Encryption Standard is used to generate a sequence using two non‐random chaotic binary sequences. The resulting sequence is XORed with another non‐random chaotic binary sequence to get a random sequence. Sequences obtained from this nonlinear system are subjected to randomness tests and the results indicate that the sequences pass all the randomness tests. Hence, the sequences qualify as random key sequences, which can be used in a stream cipher based system to encrypt the data samples like audio, image, video, and so forth.

Binary sequences with good autocorrelation have many applications in raging systems, spread spectrum communication systems, multi-terminal system identification, code division multiple access communications systems, and stream ciphers. Magma is a large, well-supported software package designed for computations in algebra, number theory, algebraic geometry and algebraic combinatory. We design the system to compare and analysis the binary pseudorandom sequences. It is easy to analysis the existing binary sequence and new construction. And it can compare the performance of different sequences and draw the figure. We implement it on the C# and SQL database system.

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.

We discuss evaluations of bit error probabilities in SSMA (spread spectrum multiple access) communication systems using binary spreading sequences of Markov chains and the designing of binary spreading sequences of Markov chains optimal in terms of bit error probabilities. We study SSMA communication systems using binary spreading sequences of Markov chains and give a necessary and sufficient condition that the distribution of the normalized MAI (multiple-access interference) is Gaussian. Based on this result, we discuss theoretical evaluations of bit error probabilities in such systems based on the CLT (central limit theorem) and those based on the SGA (standard Gaussian approximation). We compare these theoretical evaluations with experimental results and also discuss the optimum spreading sequences of Markov chains in terms of bit error probabilities based on the CLT.

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.

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.

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.

Electroencephalogram-based emotion recognition (EEG-ER) has received increasing attention in the fields of health care, affective computing, and brain-computer interface (BCI). However, satisfactory ER performance within a bi-dimensional and non-discrete emotional space using single-trial EEG data remains a challenging task. To address this issue, we propose a three-layer scheme for single-trial EEG-ER. In the first layer, a set of spectral powers of different EEG frequency bands are extracted from multi-channel single-trial EEG signals. In the second layer, the kernel Fisher's discriminant analysis method is applied to further extract features with better discrimination ability from the EEG spectral powers. The feature vector produced by layer 2 is called a kernel Fisher's emotion pattern (KFEP), and is sent into layer 3 for further classification where the proposed imbalanced quasiconformal kernel support vector machine (IQK-SVM) serves as the emotion classifier. The outputs of the three layer EEG-ER system include labels of emotional valence and arousal. Furthermore, to collect effective training and testing datasets for the current EEG-ER system, we also use an emotion-induction paradigm in which a set of pictures selected from the International Affective Picture System (IAPS) are employed as emotion induction stimuli. The performance of the proposed three-layer solution is compared with that of other EEG spectral power-based features and emotion classifiers. Results on 10 healthy participants indicate that the proposed KFEP feature performs better than other spectral power features, and IQK-SVM outperforms traditional SVM in terms of the EEG-ER accuracy. Our findings also show that the proposed EEG-ER scheme achieves the highest classification accuracies of valence (82.68%) and arousal (84.79%) among all testing methods.

The information efficiency of communication systems using quadrature amplitude modulation is reduced because of the costs for data transmission necessary to provide frame synchronization and the required time to search for the sync signal and to go into the tracking mode of the synchronization system. One of the most effective schemes of constructing a frame synchronization system is the correlation diagram. In order for this diagram to operate, signal-code constructions with good aperiodic autocorrelation properties are required. The aim of this study is to develop an effective frame synchronization system for quadrature modulation communication systems based on binary signal-code sequences with an ideal sectioned non-periodic autocorrelation function. In this paper, we propose a frame synchronization scheme for QPSK modulation based on binary sequences of even length with an ideal autocorrelation function. All binary synchronous sequences of length N = 8 with the idealness of the autocorrelation function are analytically found in the study. On the basis of the chart of the code distance spectrum in the Hamming metric for binary sequences of N = 8 length, it was established that such sequences have a correcting ability that allows correcting single errors. Based on the structural properties of binary sequences of N = 8 length, sequences of a larger multiple length (N = 16, N = 32, etc.) can be synthesized. The practical value of the proposed scheme of frame synchronization is to reduce the complexity of technical implementation and increase the overall noise immunity of the communication system. The proposed approach can be successfully used to synchronize communication systems with QAM modulation with a large number of signal positions such as QAM 16, QAM 64, etc.

To address the inability to quantitatively analyze the performance of the direct sequence spread spectrum (DSSS) communication system in the presence of short-period pseudo-noise (PN) sequences, this study derives the interference components resulting from correlation processing of single-frequency interference. Given the short period of the spread spectrum sequence used in underwater acoustic systems, a theoretical expression is proposed for analyzing the anti-single-frequency interference performance of DSSS communication systems in underwater acoustics. This expression combines the interference power output by the system to enable quantitative analysis. Simulations are conducted to validate the accuracy of the theoretical expression. The results reveal that the interference sequence generated by correlation processing assumes either a direct current (DC) or sinusoidal distribution. The bit error rate (BER) of the system is influenced by signal-to-interference ratio (SIR), interference frequency offset, phase deviation, and the structure of the spreading code itself. The BER exhibits regular variation with changes in the interference phase. In all working conditions where the interference frequency offset is an integer multiple of the bit bandwidth, single-frequency interference with a frequency offset equivalent to the bit bandwidth has the greatest impact on the system. The concise theoretical expression presented in this study has significant practical value as it allows for quick prediction of variation in the anti-single-frequency interference performance of underwater acoustic DSSS communication systems using short-period PN sequences.

Zero Cross-Correlation (ZCC) code is a binary sequences with good auto- and cross correlation properties, i.e., the cross correlation between any two sequences remains zero throughout. In this paper, we evaluate the performance of ZCC based on Balanced Incomplete Block Design (BIBD) for Spectral Amplitude Coding Optical Code Division Multiple Access (SACOCDMA) system using direct detection. BER better than 10-9 at 622Mbps is obtained for five simultaneous users.

Criteria for selecting spreading codes for a downlink transmission in a direct sequence code division multiple access (DS-CDMA) system are reviewed. For the most general case of a non-code inversion keying system (CIK) it turns out that the codes must have good partial aperiodic cross and autocorrelation properties as far as the optimisation of the RAKE receiver performance is concerned. Codes generally used such as the Gold or Kasami codes have good cross and auto correlation properties on their whole period but do not have any particular partial correlation properties. In order to solve this limitation, the author proposes a method for building a set of so-called extended structured codes. Each long code is obtained by concatenation of cyclically different short codes of period the processing gain, the short codes of the initial set presenting good correlation properties. This construction is an extension of the structured codes proposed by T. O'Farrell (1991) that overcomes some of their drawbacks such as a short period and a small number of long codes in the constructed set. Simulation results show that the 'extended structured codes' bring a large improvement with respect to Gold and m-sequences.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>