Autocorrelation Sequence Research Articles

Maximum Likelihood Sequence Estimation Optimum Receiver Design with Channel Identification Based on Zero Distribution

In this paper, a novel maximum likelihood sequence estimation (MLSE) optimum receiver design is proposed to reduce the complexity of the conventional optimum receiver. We first propose a multipath channel classification method according to the zero distribution of the channel impulse response; that is, the multipath channel is divided into a minimum phase channel and a non-minimum phase channel. Then, an MLSE optimum receiver design with channel identification based on zero distribution is also proposed. In this design, the distribution of zero can be obtained directly by calculating the Z transform of the channel. Thus, the complexity is reduced. The number of the multiplication reduced is N(2N+1). In addition, 2N+1 memory units storing the autocorrelation sequence are reduced. The simulation results indicate that this channel classification method effectively represents the characteristics of the channel. Moreover, the MLSE optimum receiver proposed performs similarly and is less complex than the conventional one. The performance is greatly improved compared with the minimum mean square error (MMSE) equalizer.

State space reconstruction of Markov chains via autocorrelation structure

Understanding the state space of observed Markov processes is essential for advancing causal inference in a wide range of scientific fields. This paper demonstrates how the previously unknown state space can be reconstructed by exploring the spectrum of the time-delay embedding matrix derived from the autocorrelation sequence of the observed series. It also highlights that the eigenvector associated with the smallest eigenvalue can provide valuable insights into the hidden data generation process itself. The presented results provide a deeper understanding of the complex dynamics of Markov chains and hold promise for enhancing various scientific applications.

A traffic state prediction method based on spatial–temporal data mining of floating car data by using autoformer architecture

AbstractFloating car data (FCD), characterized by wide spatiotemporal coverage, low collection cost, and immunity to adverse weather conditions, are one of the key approaches for intelligent transportation systems to obtain real‐time urban road network traffic information. The research aims to utilize GPS data from taxis in Shanghai and vector geographic information data of the road network, with urban expressways as the research focus. Based on the different driving characteristics of expressways and the vehicles on the ramps below, a clustering analysis is employed to determine all floating vehicles traveling on the target road. Furthermore, an adaptive buffer zone consistent with the road orientation is established based on road vector geographic data. This allows for the extraction of FCD within segmented areas, and the average vehicle speed for that road segment is obtained through weighted calculations. This method fully exploits the natural characteristics of taxis in urban areas with a wide spatiotemporal distribution. The data effectiveness and coverage reach 90.2% and 85.7%, respectively, significantly surpassing the traditional grid‐based extraction method for FCD. Additionally, to capture the long‐term spatiotemporal dependencies of road network traffic states, a spatial–temporal autoformer (STAF) network based on spatial–temporal sequence autocorrelation is employed for traffic state prediction. The results indicate that the STAF method demonstrates good performance in medium‐ and long‐term prediction. We believe that the proposed FCD mining method in this paper provides a new approach for efficiently extracting large‐scale road network traffic states and conducting medium‐ to long‐term predictions.

A Fast Power Spectrum Sensing Solution for Generalized Coprime Sampling

With the growing scarcity of spectrum resources, wideband spectrum sensing is necessary to process a large volume of data at a high sampling rate. For some applications, only second-order statistics are required for spectrum estimation. In this case, a fast power spectrum sensing solution is proposed based on the generalized coprime sampling. The solution involves the inherent structure of the sensing vector to reconstruct the autocorrelation sequence of inputs from sub-Nyquist samples, which requires only parallel Fourier transform and simple multiplication operations. Thus, it takes less time than the state-of-the-art methods while maintaining the same performance, and it achieves higher performance than the existing methods within the same execution time without the need to pre-estimate the number of inputs. Furthermore, the influence of the model mismatch has only a minor impact on the estimation performance, allowing for more efficient use of the spectrum resource in a distributed swarm scenario. Simulation results demonstrate the low complexity in sampling and computation, thus making it a more practical solution for real-time and distributed wideband spectrum sensing applications.

Ideal Sequence Couple Design for Split Circle Classes with Different Cycle Lengths

Abstract The split-circle class and the generalized split-circle class are commonly utilized mathematical tools in sequence design. They have been extensively applied in the study of construction methods for almost different set couples and ideal sequence couples. In this paper, on the basis of sequence couplings and difference set couplings, the finite field, and Chinese remainder theorem are utilized to combine computers to carry out the design of the generalized subcircle class construction algorithm, and based on this algorithm, the search algorithm for sequence couplings is designed. In addition, based on the theory of fractional circle classes and fractional circle numbers, the article integrates the equivalence relations between difference families and ideal balanced binary almost complementary pairs. Then, it obtains the ideal sequence even construction method based on fractional circle classes. For the effectiveness of the sequence couple search algorithm, a search experiment is set up with a binary sequence couple as an example. Its efficiency is analyzed in comparison with that based on the difference table and the bit operation, and an example of the ideal sequence couple construction under different cycle lengths is analyzed based on the construction method. The search algorithm combined with the generalized fractional circle class can obtain the data sequences of optimal binary sequence couple pairs, pseudo-random binary sequence couples, and ideal three-valued autocorrelated binary sequence couples. The average computational efficiency of the algorithm is within 13ms and 3 when both s ≡ 1 (mod 4) and s ≡ 3 (mod 4), and the parameters of the binary and quadratic periodic ideal sequence couples obtained by the algorithm meet the parameters of (10,2,5)LACSP 3 4 when Z takes the value of 2 or R x 1 (γ) = –1 + 2t, respectively. Carrying out the construction of perfect sequence couples under different cycle lengths with the generalized fractional circle class the construction of ideal sequence couplings with varying lengths of cycle in the generalized fractional circle class can obtain a variety of forms of sequence coupling data, which enhances the application range of ideal sequence couplings.

Periodic autocorrelation of sequences

Periodic autocorrelation of sequences

Highly Efficient Waveform Design and Hybrid Duplex for Joint Communication and Sensing

Joint communication and sensing (JCAS) is a very promising 6G technology, which attracts more and more research attention. Compared with communication, radar has many unique features in terms of waveform design criteria, selfinterference cancellation (SIC), aperture-dependent resolution, and virtual aperture. This paper proposes a novel waveform design named max-aperture radar slicing (MaRS) to gain a large time-frequency aperture, which is generated by orthogonal frequency division multiplexing (OFDM) and occupies only a tiny fraction of OFDM resources. The proposed MaRS keeps the radar advantages of constant modulus, zero auto-correlation sequence, and simple SIC. As MaRS consumes much less resources, conventional processing methods fail, and novel angle-Doppler map based methods are proposed to obtain the rangevelocity-angle information from MaRS echos and strong clutters. To avoid complex full-duplex communication, this paper proposes a hybrid-duplex JCAS scheme composed of half-duplex communication and full-duplex radar. The half-duplex communication antenna array is reused, and a small sensingdedicated antenna array is added. Using these two arrays, a large space-domain sensing aperture is virtually formed to greatly improve the angle resolution. The numerical results show that the proposed MaRS and hybrid duplex can achieve a high sensing resolution with only 0.4% OFDM resources, which reduces the overheads of conventional methods to less than one tenth.

Trend Analysis of Civil Aviation Incidents Based on Causal Inference and Statistical Inference

The efficient management of aviation safety requires the precise analysis of trends in incidents. While classical statistical models often rely on the autocorrelation of indicator sequences for trend fitting, significant room remains for performance improvement. To enhance the accuracy and interpretability of trend analyses for aviation incidents, we propose the Causal-ARIMA model, which is grounded in causal inference theory, and we employ four distinct modeling strategies to fit the trend of incidents in China’s civil aviation sector between 1994 and 2020. The objective is to validate the performance of the Causal-ARIMA model and identify optimal trend analysis strategies. The four modeling strategies account for causation factors, stationarity, and causality with operational volume, incorporating models like AR, ARMA, ARIMA, and Causal-ARIMA. Our findings reveal that ensemble techniques incorporating the Causal-ARIMA model (Strategy 2 and 3) outperform classical trend analysis methods (Strategy 1) in terms of model fit. Specifically, the causality-based binary fitting technique (Strategy 3) achieves the most uniformly dispersed fitting performance. When the premises for using the Causal-ARIMA model are relaxed, applying it to variables without Granger causal relationships results in uneven model performance (Strategy 4). According to our study, the Causal-ARIMA model can serve as a potent tool for the analysis of trends in the domain of aviation safety. Modeling strategies based on the Causal-ARIMA model provide valuable insights for aviation safety management.

Arithmetic Autocorrelation Distribution of Binary m -Sequences

Binary <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -sequences are those with the largest period <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>m</i></sup> –1 among the binary sequences produced by linear shift registers with length <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> . They have a wide range of applications in communication since they have several desirable pseudorandom properties, such as balance, uniform pattern distribution, and ideal (classical) autocorrelation. In 1967, Mandelbaum introduced a 2-adic version of classical autocorrelation of binary sequences, called arithmetic autocorrelation, in his research on arithmetic codes. Later, Goresky and Klapper generalized this notion to the nonbinary case and got several properties of arithmetic autocorrelation related to linear shift registers with carry. Recently, Z. Chen et al. showed an upper bound on the arithmetic autocorrelation of binary <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -sequences and raised a conjecture on the absolute value distribution of the arithmetic autocorrelation of binary <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -sequences. In this paper, we present a general formula for computing arithmetic autocorrelation, from which we completely determine the arithmetic autocorrelation distribution of arbitrary binary <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -sequences. In particular, the conjecture raised by Z. Chen et al. is verified.

Applying deep learning to predict SST variation and tropical cyclone patterns that influence coral bleaching

South Penghu Marine National Park, Taiwan experienced severe coral bleaching in 2020 that may lead to coral mortality. Corals are important animals that enrich marine biodiversity, but several studies have shown that the range of sea surface temperature (SST) corals can survive is narrow, and recovery time can be as long as 10 years. The influences of climate change induced extreme weather should not be underestimated, and it is critical to accurately predict SST variations. In this study, a deep learning model, convolutional long short-term memory (ConvLSTM), which is a newer model suitable for estimating autocorrelated sequences, was built to predict daily SST for the next day, next week, and next two weeks, with the highest achieved 99.22% accuracy and a RMSE values of 0.2579. On the other hand, Penghu was not directly impacted by tropical cyclones in 2020; hence the lack of typhoon-induced SST cooling could be one of the reasons for extensive coral bleaching. The wind intensity, speed, as well as the thickness of ocean mixed layer all affect the variation of SST cooling. The results show that the degree heating weeks (DHWs) near Penghu achieved its highest level in 2020, and according to the analysis of the study, there is a clear association between climate change and coral bleaching risk increase in recent years. Therefore, we applied Random Forest to establish a machine learning model to classify whether a typhoon can trigger significant cooling. Model accuracy achieved 92.90% in the testing set, and empirical orthogonal function (EOF) analysis contributed the most to the SST cooling pattern among typhoons. This study provides a predictive contribution to global coral conservation for relevant institutions to know the risk beforehand, and they can discuss corresponding strategies and early warnings.

Pseudorandom Noise Sequence Time-Modulated Reflective Metasurfaces for Target Recognition

In this article, pseudorandom noise (PN) sequence time-modulated reflective metasurfaces are proposed to provide a low-cost, low-complexity, simple solution for target recognition. By covering the target to be recognized with a time-modulated metasurface modulated by a PN time sequence, the metasurface scatters the interrogating harmonic wave into a binary PN-modulated wave. As a result, the radar detector with the foreknowledge of the modulating PN sequence may recognize the target by applying the properties of strong autocorrelation and weak cross correlation of PN sequences and performing cross correlation between the modulating PN sequence and the picked-up signal after downshifting its frequency without actually decoding and reading the scattered information. A 1-bit reconfigurable metasurface unit cell operating at 2.4 GHz is proposed and full-wave simulated to achieve out-of-phase reflective responses by controlling the ON and OFF states of the p-i-n diode for PN time modulation. The target recognition is demonstrated by experiment in two different scenarios where only one metasurface and multiple metasurfaces are present for recognition. The experimental results show that by providing an appropriate threshold in the cross-correlation detecting results, the proposed method can recognize the targets well in both scenarios.

Remote fault detection and location of power fiber optic cable based on a logistic regression model

Abstract The current fiber optic communication network presents the characteristics of network scale, complexity, and efficiency, and the use of traditional means for the maintenance of power fiber optic cable has been greatly limited. In this paper, based on the characteristics of simple structure, convenient construction, strong randomness, strong sequence autocorrelation, and good iterative performance of chaos theory in a logistic regression model, a logistic-based remote fault detection and location system for power fiber optic cables is proposed. The fault location test is carried out through with TMS200 series fiber optic cable automatic monitoring management system and GIS method. The fault location error of the logistic-based fault detection method is less than ±3m, that of the GIS method is less than ±10m, and that of the TMS200 series cable automatic monitoring and management system is less than ±15. The comparison shows that this paper’s fault detection and location system is more accurate and can help maintenance personnel have a faster and more comprehensive understanding of the line situation. Realize the rapid repair work of faults, which provides great help to maintain the fiber optic cable lines.

Almost perfect autocorrelation sequences with small number of pauses for applications in magnetic resonance

Almost perfect autocorrelation sequences with small number of pauses for applications in magnetic resonance

Constructions of Complementary Sequence Sets and Complete Complementary Codes by Ideal Two-Level Autocorrelation Sequences and Permutation Polynomials

In this paper, we further investigate the constructions of complementary sequence sets (CSSs) and complete complementary codes (CCCs) by Butson-type Hadamard matrices. By taking the algebraic structure of Butson-type Hadamard (BH) matrices into consideration, we obtain the explicit representation of the δ-linear terms and δ-quadratic terms, which are ingredients to construct CSSs and CCCs. In particular, we derive the δ-quadratic terms determined by DFT matrices and BH matrices constructed from 2-level autocorrelation sequences, which yields two type of new contructions. We show that inequivalent BH matrices produce different CSSs and CCCs, which proves that our constructed CSSs and CCCs are new. As a consequence of the first type of the constructions, not only a large number of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -ary CSSs and CCCs of size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> prime) have been proposed, which were never reported in the literature, but also a theory linking these CSSs of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -ary sequences and the generalized Reed-Muller codes proposed by Kasami <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i> . is shown. These codes enjoy good error-correcting capability, tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pⁿ</i> subcarriers. As a consequence of the second type of the constructions, we reveal an extremely fascinating hidden connection between the sequences in aperiodic CSSs and CCCs and the sequences with ideal period 2-level autocorrelation, through their trace representations and permutation polynomials over finite fields.

A Redundant Measurement-Based Maximum Correntropy Extended Kalman Filter for the Noise Covariance Estimation in INS/GNSS Integration

The resolution accuracy of the inertial navigation system/global navigation satellite system (INS/GNSS) integrated system would be degraded in challenging areas. This paper proposed a novel algorithm, which combines the second-order mutual difference method with the maximum correntropy criteria extended Kalman filter to address the following problems (1) the GNSS measurement noise estimation cannot be isolated from the state estimation and suffers from the auto-correlated statistic sequences, and (2) the performance of EKF would be degraded under the non-Gaussian condition. In detail, the proposed algorithm determines the possible distribution of the measurement noise by a kernel density function detection, then depending on the detection result, either the difference sequences–based method or an autoregressive correction algorithm’s result is utilized for calculating the noise covariance. Then, the obtained measurement noise covariance is used in MCEKF instead of EKF to enhance filter adaptiveness. Meanwhile, to enhance the numerical stability of the MCEKF, we adopted the Cholesky decomposition to calculate the matrix inverse in the kernel function. The road experiment verified that our proposed method could achieve more accurate navigation resolutions than the compared ones.

OPTIMAL SIGNAL-CODE CONSTRUCTIONS FOR INCREASE EFFICIENCY OF 5G AND 6G MOBILE INFOCOMMUNICATION RADIO SYSTEMS

The article discusses methods of increasing the efficiency of information communication radio systems of mobile communication, which includes increasing spectral efficiency and energy efficiency when used for telecommunication radio equipment. A comparison of block error coefficient values for f-OFDM, W-OFDM and OFDM methods with mixed numerology of uplink and downlink subscriber channels of access to information resources of the telecommunications network was made. As a result of the study of compression methods using several carriers, the dominant compression method for mobile communication systems, in particular, the CP-OFDM method due to its high efficiency of spectrum use, scalability and flexibility due to the introduction of a cyclic prefix, has been determined. It is proved that the CP-OFDM compression method is free from the Doppler range shift problem, thus the range and Doppler shift estimations can be considered as independent tasks in CP-OFDM. In addition, CP-OFDM parameters such as carrier distance, guard interval size, frame length, and pilot shape can be tailored to optimize the performance and robustness of detection and data transmission. However, such advantages are based on perfect synchronization (time and frequency) between the transmitter and receiver – although perfect synchronization may not be possible, especially for bistatic scanning, where the transmitter and receiver of the scan signal are not adjacent. In this case, the cyclic prefix may not provide any advantage for quality scanning, and multiple unprefixed waveforms may be considered. The main disadvantage of rejecting the prefix is the difficulty of data detection (due to intersymbol interference), which must be eliminated. Another important challenge for scanning, where energy efficiency is extremely important, is the large PAPR of multi-carrier (prefixed or unprefixed) signals. Single-carrier compression methods, which are based on the expansion of the code area of common radar signals and communication, in which the radar characteristics are affected by sequence autocorrelation, have been studied. However, the long spreading code, which leads to good autocorrelation, reduces the spectrum utilization efficiency for communication systems. In this case, the estimation of the Doppler effect is not trivial and requires more complex algorithms. The justification of the choice of the signal modulation scheme in 5/6G radio systems has been made.

Unimodular Perfect and Nearly Perfect Sequences: a Variation of Björck’s Scheme

Constant Amplitude (CA), Zero Auto Correlation (ZAC) sequences (or CAZAC sequences, aka perfect sequences) have numerous applications. We generalize the CAZAC notion to what we term as CASAC by permitting small autocorrelations (SAC). We extend Björck’s classification result of two-valued CAZAC sequences by providing a complete classification of all almost 2-valued (i.e., two-valued except for the first position which uses a third value) CASAC sequences. While Björck’s original work dealt only with primes p, we extend his ideas to any abelian group of order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v\equiv 1\pmod {4}$ </tex-math></inline-formula> , as opposed to restricting just to the prime fields GF(p). Björck sequences have better ambiguity function than Zadoff-Chu sequences, making them suitable for radar and communications applications in the presence of high Doppler shifts. In fact, the discrete narrow band ambiguity function has an optimal bound in case of Björck sequences (as opposed to Gauss sequences). A one-parameter infinite family of CASAC we construct would have applications in Multiple-Input Multiple-Output (MIMO) areas. Toward MIMO applications, we introduce a performance measure we term as cross merit factor to study cross correlation behavior, generalizing the well-known notion of Golay Merit Factor (GMF).

Additive averages of multiplicative correlation sequences and applications

We study sets of recurrence, in both measurable and topological settings, for actions of (ℕ, ×) and (ℚ>0, ×). In particular, we show that autocorrelation sequences of positive functions arising from multiplicative systems have positive additive averages. We also give criteria for when sets of the form {(an+b)1/(cn+d)ℓ: n ∈ ℕ} are sets of multiplicative recurrence, and consequently we recover two recent results in number theory regarding completely multiplicative functions and the Omega function.

Correlation properties of interleaved Legendre sequences and Ding-Helleseth-Lam sequences

&lt;abstract&gt;&lt;p&gt;Sequences with optimal autocorrelation properties play an important role in wireless communication, radar and cryptography. Interleaving is a very important method in constructing the optimal autocorrelation sequence. Tang and Gong gave three different constructions of interleaved sequences (generalized GMW sequences, twin prime sequences and Legendre sequences). Su et al. constructed a series of sequences with optimal autocorrelation magnitude via interleaving Ding-Helleseth-Lam sequences. In this paper we further study the correlation properties of interleaved Legendre sequences and Ding-Helleseth-Lam sequences.&lt;/p&gt;&lt;/abstract&gt;

Study on Rainfall Distribution in Yunnan Province Based on ARIMA Model by Big Data Computation

Taking the monthly rainfall data of 16 prefectures and cities in Yunnan Province from 2012 to 2020 as the research object, an ARIMA time series model is established based on big data calculation. First, we use the cluster analysis method to divide all regions into three categories according to the distribution characteristics of rainfall and select a representative city from each category to study the rainfall distribution. Then, according to the results of the ADF test, the method using phase and seasonal differences is used to eliminate the non-stationary and seasonal trends of the series. Finally, the ARIMA prediction model of rainfall distribution in Kunming, Dali, and Pu'er is obtained by combining the sequence autocorrelation and partial autocorrelation analysis diagram to determine the values of various parameters in the ARIMA model. The prediction accuracy of the model is high, and the residual sequence is a white noise sequence, which has a good fitting effect. It effectively predicts the fluctuation law of rainfall and provides an early warning mechanism for drought, flood, debris flow, and other disasters.