Autocorrelation Sequence Research Articles

Sequential data classification by dynamic state warping

The ubiquity of sequences in many domains enhances significant recent interest in sequence learning, for which a basic problem is how to measure the distance between sequences. Dynamic time warping (DTW) aligns two sequences by nonlinear local warping and returns a distance value. DTW shows superior ability in many applications, e.g. video, image, etc. However, in DTW, two points are paired essentially based on point-to-point comparisons without considering the autocorrelation of sequences. Thus, points with different semantic meanings, e.g. peaks and valleys, may be matched providing their coordinate values are similar. As a result, DTW may be sensitive to noise and poorly interpretable. This paper proposes an improved alignment method, dynamic state warping (DSW). DSW integrates the dynamic information of sequences into DTW by converting each time point into a latent state. Alignment is performed by using the state sequences. Thus, DSW is able to yield alignment that is semantically more interpretable than that of DTW. Using one nearest neighbour classifier, DSW shows significant improvement on classification accuracy in comparison with Euclidean distance (68/85 wins), DTW (70/85 wins) and its variants. We also empirically demonstrate that DSW is more robust and scales better to long sequences than Euclidean distance and DTW.

Asymmetric multiscale multifractal analysis of wind speed signals

We develop a new method called asymmetric multiscale multifractal analysis (A-MMA) to explore the multifractality and asymmetric autocorrelations of the signals with a variable scale range. Three numerical experiments are provided to demonstrate the effectiveness of our approach. Then, the proposed method is applied to investigate multifractality and asymmetric autocorrelations of difference sequences between wind speed fluctuations with uptrends or downtrends. The results show that these sequences appear to be far more complex and contain abundant fractal dynamics information. Through analyzing the Hurst surfaces of nine difference sequences, we found that all series exhibit multifractal properties and multiscale structures. Meanwhile, the asymmetric autocorrelations are observed in all variable scale ranges and the asymmetry results are of good consistency within a certain spatial range. The sources of multifractality and asymmetry in nine difference series are further discussed using the corresponding shuffled series and surrogate series. We conclude that the multifractality of these series is due to both long-range autocorrelation and broad probability density function, but the major source of multifractality is long-range autocorrelation, and the source of asymmetry is affected by the spatial distance.

New quaternary sequences of even length with optimal auto-correlation

Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length $N$ can be obtained from two binary sequences of the same length, which are called component sequences. In this paper, using interleaving method, we present several classes of component sequences from twin-prime sequences pairs or GMW sequences pairs given by Tang and Ding in 2010; or two, three or four binary sequences defined by cyclotomic classes of order $4$. Hence we can obtain new classes of quaternary sequences, which are different from known ones, since known component sequences are constructed from a pair of binary sequences with optimal auto-correlation or Sidelnikov sequences.

Recurrence plots analysis of the CNY exchange markets based on phase space reconstruction

The employment of autocorrelation-based transformation to study the dynamics of the exchange rate system is meaningful because it benefits for chaotic prediction on the basis that the transformation from an exchange rate sequence to its associated autocorrelation sequence is reversible. This paper examines the influence of autocorrelation-based transformation on the systemic dynamics using exchange rates of CNY against different currencies among USD, EUR, JPY, GBP, MYR and RUB. First, we construct recurrence plots of exchange rate return sequences and autocorrelation sequences with a fixed sliding window length of 20. The recurrence quantification analysis (RQA) shows that the exchange rate return sequences exhibit lower degrees of determinism than the autocorrelation sequences. Further, by analyzing the RQA measures with bootstrap techniques and box plots, we reveal that the RQA measures of the exchange rate return systems and the autocorrelation sequence systems are mostly significant, and the vertical structures of recurrence plots of autocorrelation sequences are more sensitive to the shuffles of bootstrap techniques. Finally, we investigate the evolution of RQA measures with the changes of sliding window lengths. The analysis shows that appropriately adjusting the sliding window length can increase the systemic determinism.

Binary Complementary Code Structure via a Simple Necessary Condition

A complementary set of $K$ binary $\pm 1$ codes of length $N$ has the useful property that the sum of the autocorrelation sequences of the codes has only one nonvanishing element, its size- $KN$ peak. The $N\times K$ matrix whose columns are the codes of a binary complementary set, arranged in order, is the code set's complementary code matrix (CCM). One might ask for which $K$ and $N$ such matrices exist. A simple necessary condition for the existence of an $N\times K$ CCM is introduced, involving the sum of the squares of the imbalance values of the codes in the set (the imbalance of a binary $\pm 1$ code being the difference between the number of 1 and number of $-1$ s in the code). The one-to-one relationship between binary CCMs and binary complementary code sets allows the necessary condition for the $N\times K$ CCM existence to extend to a necessary condition for sets of $K$ complementary code sets of length $N$ . We examine the sum-of-squares condition for the separate cases of $N$ even and $N$ odd. The odd case is especially interesting, since representations in terms of sums of squares of odd integers are equivalent to representations as sums of triangular numbers, a subject of recent research in Number Theory. Furthermore, we exhibit a refinement of the existence condition in terms of the imbalance values of pairs of interlaced subcodes. This refinement is new, to the best of our knowledge. Finally, we investigate whether odd-length complementary code sets exist for $K>2$ , unlike the Golay case of $K=2$ where odd-length sets cannot exist. We easily find, by computer search, a four-code set of length 15, suggesting that these are likely not uncommon.

Generalized nonbinary sequences with perfect autocorrelation, flexible alphabets and new periods

We extend the parameters and generalize existing constructions of perfect autocorrelation sequences over complex alphabets. In particular, we address the PSK+ constellation (Boztas and Udaya 10) and present an extended number theoretic criterion which is sufficient for the existence of the new sequences with perfect autocorrelation. These sequences are shown to exist for nonprime alphabets and more general lengths in comparison to existing designs. The new perfect autocorrelation sequences provide novel alternatives for wireless communications and radar system designers for applications in ranging and synchronisation as well as channel identification.

A novel timing synchronization for CO-OFDM systems using CAZAC sequences

A novel symbol timing synchronization algorithm based on constant amplitude zero auto correlation (CAZAC) sequences is proposed for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The training symbol of the proposed algorithm is comprised of four different parts, utilizing even symmetry property of each part to accomplish timing synchronization. The performance of the proposed algorithm is demonstrated by means of simulations in OFDM and CO-OFDM systems. The proposed algorithm is shown to eliminate the timing sidelobes of Park’s algorithm and has a more accurate timing estimation. In the condition of chromatic dispersion (CD), the timing metric of the proposed method still maintains its peak value at the correct timing point, while the values are almost 0 at all the other positions. Meanwhile, the timing mean square error (MSE) of the proposed algorithm remains around 10-6.

Time and Frequency Synchronization with Channel Estimation for SC-FDMA Systems Over Time-Varying Channels

The constant amplitude zero autocorrelation sequence based synchronization and its usage in the block-type channel estimation for the single carrier frequency division multiple access (SC-FDMA) systems are vulnerable to the time-varying channels. Therefore, the channel estimation errors limit the performance of SC-FDMA systems in fast fading environments and result an irreducible error floor. In this paper, cyclic prefix based maximum likelihood estimator of time/frequency synchronization with comb-type channel estimation for the SC-FDMA systems are proposed to track the channel variations. Moreover, the residual time/frequency offsets calculations are derived for SC-FDMA systems. Simulation results confirm and illustrate that the proposed receiver is capable of tracking fast fading channel parameters and improving the overall performance as compared with the conventional receiver.

Symbol Misalignment Estimation in Asynchronous Physical-Layer Network Coding

Symbol misalignment is inevitable in asynchronous physical-layer network coding (PNC) systems. It is paramount that such symbol misalignment is taken into account in PNC decoding for good performance. Thus, accurate estimation of symbol misalignment is crucial. This paper argues that, when Nyquist pulses (i.e., intersymbol-interference (ISI)-free pulses) are adopted, signal samples only need to be collected at baud rate for optimal symbol misalignment estimation. Based on this principle, we propose a highly accurate symbol misalignment estimation method with low complexity. Our method makes use of the constant amplitude zero autocorrelation sequence (Zadoff–Chu sequence (ZC sequence)). We derive a maximum-likelihood (ML) estimator for symbol misalignment based on the cross-correlation result of the ZC sequence. Unlike previous methods that employ oversampling, our estimation method requires only baud-rate sampling, thus having much lower complexity. Extensive simulations show that our method can accurately estimate both integral and fractional symbol misalignments using sinc pulse and raised-cosine (RC) pulse. The root-mean-square error (RMSE) of the estimation is below 10−2 (in unit of symbol duration) when the SNR is above 15, 18, and 21 dB for 127-, 63-, and 31-bit-length ZC sequences, respectively. Furthermore, our method, being an ML estimation method, has no error floor in the high-SNR regime, whereas the prior methods exhibit an error floor.

Grouping modulation with different codes for improving performance in cVEP‐based brain–computer interfaces

A novel paradigm for building code modulated visual evoked potential (cVEP) brain–computer interfaces (BCIs) is proposed. The paradigm is based on grouping modulation of stimuli with different codes in order to increase the number of stimuli and resulting information transfer rate (ITR). In a single group, an original code and its circularly shifting codes are used for modulating 16 stimuli. To achieve good separability of stimuli, the original codes for different groups should have good autocorrelation and cross-correlation properties. A pair of Golay complementary series and an almost perfect autocorrelation sequence are used as the original codes to implement a three-group cVEP BCI with 48 targets. Four subjects participated in a simulated online experiment and a high ITR of 129.58 bits/min was achieved due to the sharp increase of the number of targets.

A Unified Framework for Low Autocorrelation Sequence Design via Majorization–Minimization

In this paper, we consider the low autocorrelation sequence design problem. We optimize a unified metric over a general constraint set. The unified metric includes the integrated sidelobe level (ISL) and the peak sidelobe level (PSL) as special cases, and the general constraint set contains the unimodular constraint, Peak-to-Average Ratio (PAR) constraint, and similarity constraint, to name a few. The optimization technique we employ is the majorization–minimization (MM) method, which is iterative and enjoys guaranteed convergence to a stationary solution. We carry out the MM method in two stages: in the majorization stage, we propose three majorizing functions: two for the unified metric and one for the ISL metric; in the minimization stage, we give closed-form solutions for algorithmic updates under different constraints. The update step can be implemented with a few Fast Fourier Transformations (FFTs) and/or Inverse FFTs (IFFTs). We also show the connections between the MM and gradient projection method under our algorithmic scheme. Numerical simulations have shown that the proposed MM-based algorithms can produce sequences with low autocorrelation and converge faster than the traditional gradient projection method and the state-of-the-art algorithms.

Random Error Reduction Scheme for Combinational Stochastic Circuit

In conventional stochastic computation, all the input streams are Bernoulli sequences (BSs), which may result in large random error. To reduce random error and improve computational accuracy, some other sequences have been reported as alternatives to BSs. However, these sequences only apply to the specific stochastic circuits, have difficulties in hardware generation, or have length constraints. To this end, new sequences without these disadvantages should be considered. This paper proposes the random error analysis method for stochastic computation based on autocorrelation sequence (AS), which is more general than the conventional one based on BS. The analysis results show that we can use the proper ASs as input streams of stochastic circuits to reduce random error. On the basis of that conclusion, we propose the random error reduction scheme based on maximal concentrated autocorrelation sequence (MCAS) and BS, both of which are ASs. MCAS and BS are applicable to any combinational stochastic circuit, are easily generated by hardware, and have no length constraints, which avoid the disadvantages of sequences in the previous work. Moreover, we apply the proposed random error reduction scheme into several typical stochastic circuits as case studies. The simulation results confirm the effectiveness of the proposed scheme.

Constructing Tight Gabor Frames Using CAZAC Sequences

The construction of finite tight Gabor frames plays an important role in many applications. These applications include significant ones in signal and image processing. We explore when constant amplitude zero autocorrelation (CAZAC) sequences can be used to generate tight Gabor frames. The main theorem uses Janssen’s representation and the zeros of the discrete periodic ambiguity function to give necessary and sufficient conditions for determining whether any Gabor frame is tight. The relevance of the theorem depends significantly on the construction of examples. These examples are necessarily intricate, and to a large extent, depend on CAZAC sequences. Finally, we present an alternative method for determining whether a Gabor system yields a tight frame. This alternative method does not prove tightness using the main theorem, but instead uses the Gram matrix of the Gabor system.

A multi-dimensional block-circulant perfect array construction

We present an N-dimensional generalisation of the two-dimensional block-circulant perfect array construction by Blake et al. As in Blake et al, the families of N-dimensional arrays possess pairwise good zero correlation zone (ZCZ) cross-correlation. Both constructions use a perfect autocorrelation sequence with the array orthogonality property (AOP).

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.

Correlation and spectral properties of chaotic signals generated by a piecewise-linear map with multiple segments

In recent decades, many studies with practical applications of chaotic signals in telecommunications and signal processing have been carried out. Although spectral analysis is of relevance in these areas, there are few analytical results concerning the spectral characterization of chaotic signals. In this work, we deduce analytical expressions for autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by a piecewise-linear map, with multiple segments. We present numerical simulations to confirm the theoretical results.

New Results on Generalized Fractional Programming Problems With Toeplitz Quadratics

We develop a polynomial-time procedure to handle a class of generalized fractional programming (GFP) problems with Toeplitz-Hermitian quadratics exploiting the linear matrix inequality (LMI) representation of the finite autocorrelation sequences cone, the spectral factorization theorem, and the Dinkelback's algorithm. For the special case of fractional quadratic programming (FQP) problems, we also provide a SemiDefinite programming (SDP) reformulation of the resulting non-convex optimization by means of the Charnes-Cooper transformation. Finally, we focus on an interesting radar signal processing application to assess the effectiveness of the devised optimization tool.

A Comparison of Imputation Techniques using Network Traffic Data

Abstract This paper presents a novel feature extraction approach for speaker identification when the speech is corrupted by additive noise. The environmental mismatch between training and testing data degrades the performance of speaker identification system. The performance degradation is primarily due to presence of background noise when try to match a given speaker to the set of known speakers in a database. Mel frequency cepstral coefficients (MFCCs) are perhaps the most widely used front ends in the state of the art speaker identification systems. One of the major issues with MFCCs is that they are very sensitive to additive noise. To overcome this bottleneck, a temporal filtering procedure on the autocorrelation sequence is proposed to minimize the effect of additive noise. The proposed feature is called Relative Autocorrelation Mel Frequency Cepstral Coefficients (A-MFCC) which is derived based on filtering the temporal trajectories of short time one sided autocorrelation sequence. This filtering process minimizes the effect of additive noise. No prior knowledge of noise characteristics is required. The additive noise can be a colored noise. For speaker identification, Hindi database was constructed from the speech samples of each known speaker. Feature vectors (MFCCs and A-MFCCs) were extracted from the samples by short-term spectral analysis, and processed further by vector quantization for locating the clusters in the feature space. Experimental results indicated that A-MFCCs significantly improved the performance of speaker identification system in noisy environment.

A Joint Timing Offset and Channel Estimation Using Fractional Fourier Transform and Cazac Sequences

This paper deals with symbol timing offset and channel estimation in OFDM (orthogonal frequency division multiplexing) system in fast varying channel. Symbol timing offset (STO) estimation is a major task in OFDM. Most of existing methods for estimating STO used cyclic prefix or training sequences. In this paper, we consider a new system for STO estimation using constant amplitude zero autocorrelation (CAZAC) sequences as pilot sequences in conjunction with fractional Fourier transform (FRFT). After STO estimation is done, timing compensation is made. Thereafter, channel is estimated to well recover the original transmitted signal. This method gives good results in terms of MSE in comparison with other known techniques, it estimated well the channel and it is important for fast varying channel. MATLAB Monte-Carlo simulations are used to evaluate the performance of the proposed estimator.

Dispersion-Tolerant DDO-OFDM System and Simplified Adaptive Modulation Scheme Using CAZAC Precoding

We apply the signal- and channel-independent constant amplitude zero autocorrelation sequence (CAZAC) precoding technique to a bandwidth-limited longer-reach DDO-OFDM system, and propose a simplified adaptive modulation scheme according to the equalized SNR per subcarrier after CAZAC precoding. Simulation results show that with the optimized modulation index, conventional 8.23-Gb/s double sideband (DSB) modulated QPSK-OFDM signal cannot realize 100 km standard single-mode fiber (SSMF) transmission at the given received optical power, while CAZAC precoding can enable 100 km SSMF transmission with dispersion-induced power penalty as low as 2.7 dB. The advantage becomes more obvious when CAZAC precoding is employed to 16.46-Gb/s 16QAM-OFDM systems. Thanks to the frequency diversity, OFDM system with CAZAC is proved to be more dispersion tolerant with improved receiver sensitivity. We also analyze the signal-to-noise ratio (SNR) of each individual subcarrier and its flatness is confirmed to be much improved independent of modulation formats and transmission distances when precoding is used. Based on the priori knowledge of flat SNR curve, we further propose a simplified adaptive modulation scheme using only three steps where bit loading can be applied with power loading omitted. Simulation and experimental results demonstrate that the BER performance can be further improved with negligible data rate reduction and system complexity aggravation using our proposed simplified adaptive modulation method.