Cyclic Autocorrelation Research Articles

Multivariate Fusion Covariance Matrix Network and Its Application in Multichannel Fault Diagnosis With Fewer Training Samples.

Due to the large number of monitoring variables in engineering, it is extremely to reflect fault information in machinery and equipment with a single channel signal, which poses a significant challenge for fault diagnosis. Furthermore, most existing intelligent recognition methods rely on label samples, yet ignore the high cost of label interpretation in practical engineering. In this work, a novel multivariate fusion covariance matrix network (MFCMN) is developed for multichannel fault diagnosis with fewer training samples. First, the collected multichannel signals are separated into mode functions by using cyclic autocorrelation analysis. Thereafter, the acquired mode functions are utilized to construct the multivariate fusion covariance matrix (MFCM), which retains the linkage of signals from different channels. Finally, MFCM is fed into the standard autoencoder to form the MFCMN network, which is applied to implement multichannel fault diagnosis. To assess effectiveness, the MFCMN is compared with the deep residual network (ResNet), convolutional neural network (CNN), long short-term memory (LSTM), and K-nearest neighbor (KNN) in two experimental cases with fewer training samples. The results clarify that the MFCMN offers excellent performance and high accuracy in multichannel fault diagnosis.

Multimodality-aided Multicarrier Waveform Recognition in low SNR Regimes based on Denoised Cyclic Autocorrelation Transformation

Wireless signal recognition driven by artificial intelligence (AI) plays a pivotal role in 6G ultra-reliable wireless communications, facilitating spectrum surveillance to impede illegal radio interference. As a promising wireless technique, multicarrier waveform recognition (MWR) has been explored to enhance the reliability of wireless data transmission. However, existing works fail to achieve reliable recognition accuracy under strong noise. It remains a daunting task for MWR in signal-to-noise ratio (SNR) regimes. To deal with this issue, we propose a denoised cyclic autocorrelation-based multimodality fusion network (DCA-MFNet). Specifically, we first leverage the cyclic autocorrelation transformation to convert intercepted signals into cyclic autocorrelation (CA) features in cyclic frequency domains, which have the robust property of being insensitive to low SNR. Next, the singular value decomposition (SVD) method is employed to weaken the strong noise effects on useful CA peak values. Based on the denoised CA matrix (DCAM), the projection accumulation strategy is proposed to generate the time delay accumulation vector (TDV) and cyclic frequency accumulation vector (CFV), which can enlarge the discrimination among multicarrier signals. Finally, we fed the multimodality features of DCAM, TDV, and CFV into the developed DCA-MFNet to perform hierarchical learning, feature aggregation training, and multicarrier type prediction. Experimental results demonstrate that the proposed DCA-MFNet obtains better recognition performance than existing algorithms. Moreover, DCA-MFNet can effectively identify six multicarrier signals with a recognition accuracy of 100% at a low SNR of even -2 dB.

Application of IPSO-MCKD-IVMD-CAF in the compound fault diagnosis of rolling bearing

The vibration signals of rolling bearings are mixed with a variety of noises and a variety of faults which are coupled to each other, and which make the fault frequencies interfere with each other. This in turn leads to difficulty of accurate extraction of the features of composite faults. Therefore, it is necessary not only to suppress the noise of vibration signals but also to separate and extract the features of compound faults. A compound fault feature extraction method based on improved particle swarm optimization (IPSO) algorithm optimized maximum correlation kurtosis deconvolution (MCKD), improved variational mode decomposition (IVMD) and cyclic autocorrelation function (CAF), named IPSO-MCKD-IVMD-CAF is proposed. Firstly, the parameters of MCKD are selected adaptively by the IPSO, and the original signal is pre-processed by the parameterized MCKD. Secondly, the IVMD is utilized to decompose the signal, several intrinsic mode functions (IMFs) are obtained, the kurtosis and correlation coefficients of each IMF component are calculated. Finally, appropriate IMF components are selected by kurtosis and correlation coefficient to be superimposed into the reconstructed signals, and the reconstructed signals are analyzed by CAF. The proposed method has been successfully applied in simulation and measured vibration signal analysis, and the features of compound faults can be separated and extracted with high accuracy. The IPSO algorithm shortens the optimization time, and the IVMD solves the parameter selection problem. The analysis results of simulation case and measured data show the advantages of the proposed method IPSO-MCKD-IVMD-CAF. Compared to existing methods, the proposed method not only increases the accuracy of compound fault feature extraction, but also has a very good performance on the separation and extraction of compound fault features. More importantly, the improved algorithm reduces the computational complexity.

Toeplitz Cyclic-MUSIC Algorithms for DOA Estimation of the SOCS Correlated Signals

This letter addresses the problem of direction-of-arrival (DOA) estimation for cyclostationary signal when the second-order cyclic statistics (SOCS) of signals are correlated. We first present a Toeplitz Cyclic-MUSIC algorithm for multichannels receiver by exploiting signal cyclostationarity. Based on cyclic autocorrelation of the received signal, a new pesudocyclic covriance matrix, which is Toeplitz, is constructed. The rank of Toeplitz matrix is equal to the number of signals even if the SOCS of signals are correlated. So the MUSIC algorithm can be used to estimate the DOAs of sources. Moreover, a single channel Toeplitz Cyclic-MUSIC algorithm for the the single-channel receiver is proposed to avoid the affect of channel inconsistency. The effectiveness of the proposed algorithms is verified by computer simulation, and the performance of the proposed algorithms is compared with the existing algorithms correspondingly.

An optimised hardware architecture of the angular-domain cyclostationary detector for cognitive radio communications

This paper proposes a novel method to improve the performance and reduce the implementation design complexity of the angular domain cyclostationary feature detection (CFD). This method implements Orthogonal Frequency Division Multiplexing (OFDM) signal detection for cognitive radio applications. The originality of this work is based on using a selective sampling process for the OFDM signal detection by using only samples related to the cyclic prefix (CP). Using only the first NCP (CP length) angles of the angular domain cyclic autocorrelation function and eliminating the remaining angles has significantly improved the detector sensitivity. Results from Matlab simulations revealed that the proposed method reaches a detection probability of 100% at an SNR (signal-to-noise ratio) equal to −16 dB in the case of an additive white Gaussian noise (AWGN) channel. Moreover, the proposed method outperforms the other CFD methods with a performance range up to 5 dB. The proposed algorithm is coded using the VHDL language and implemented with the minimum of counters and comparators on Field-programmable gate array (FPGA) platform without using multipliers and DSP blocks. The proposed design requires a lesser power, logic and memory bits by 5.95, 60.96 and 87.5%, respectively, compared to the conventional angular domain CFD design. The proposed hardware architecture can be more efficient for spectrum sensing in many communication systems, such as LTE-Advanced and the L-band Digital Aeronautical Communication System (LDACS).

Channel Randomness-Based Adaptive Cyclic Prefix Selection for Secure OFDM System

A novel method for cyclic prefix (CP) adaptation based on wireless channel randomness is proposed for orthogonal frequency-division multiplexing (OFDM) systems in urban areas. Especially, a quantization algorithm and an adaptive window-based strong subcarriers selection are designed on the sorted channel frequency response of the legitimate party to select randomly the secure CP (SCP) length for each OFDM symbol without the need to share any information between legitimate nodes. The proposed method creates a problem for illegitimate user’s synchronization as it does not have any information about SCP length for every OFDM symbol, even if it uses blind synchronization techniques. The effectiveness of the proposed mechanism is evaluated through representative metrics, such as bit error rate (BER), throughput in both perfect and imperfect channel estimation scenarios, mismatch probability (MP), and cyclic autocorrelation function (CAF). Also, the performance for the presence of a correlated eavesdropper (Eve) in the system is evaluated. Simulation results show a huge secrecy gap between BER and throughput performance of legitimate and illegitimate users in all scenarios.

Informative singular value decomposition and its application in fault detection of planetary gearbox

The fault features of planetary gearboxes are modulated complexly and are submerged by other signal components, for its vibration signal has the characteristics of multi-source and multi transmission path. A fault detection method of planetary gearboxes based on informative singular value decomposition and envelope spectrum analysis (ISVD-ESA) is proposed in this paper. In this method, the advantage of blind source separation of singular value decomposition (SVD) method is combined with the ability of negentropy and cyclic autocorrelation (CA) in non-Gaussian characteristics recognition. The fast SVD is firstly performed to decompose the vibration signal into a series of singular value decomposition component signals (SVCSs). Secondly, the detector of negentropy combined with CA is applied to estimate the fault informativeness of each SVCS. The SVCSs are amplified by the fault informativeness and reconstructed to the out signal of ISVD. Finally, the fault features can be extracted by the ESA from the output signal of ISVD. The performance of the proposed method is verified by simulation and experimental studies. Results show that the proposed ISVD-ESA strategy can enhance the weak features of multi-modulation and accurately extract the faults of tooth tip pitting and misalignment of sun gear of the planetary gearbox.

Initial Fault Diagnosis of Rolling Bearing Based on Second-Order Cyclic Autocorrelation and DCAE Combined With Transfer Learning

Under actual working conditions, the initial faults of rolling bearings are difficult to be predicted effectively because of the lack of prior fault knowledge, weak fault information, and strong noise interference. How to enhance the fault characteristics while removing the vibration signal noise of rolling bearings has become the key challenge to the field of early fault diagnosis of rolling bearings. Based on the above problems, a rolling bearing initial fault diagnosis model based on second-order cyclic autocorrelation (Soca) and deep auto-encoder (AE) combined with transfer learning (TL) was proposed to improve the overall performance of rolling bearing fault identification. First, the Soca is used to estimate the second-order cyclic statistics of the vibration signal, which can better highlight the periodic pulse characteristics of rolling bearings and suppress random noise to a certain extent. After that, the dataset containing the valuable health state information of the rolling bearing is input into the denoising and contraction auto-encoder (DCAE). The advantages of denoising AEs (DAEs) and contraction AEs are fully utilized to extract the initial fault characteristics of rolling bearings. Finally, the balanced distribution adaptation (BDA) is used to reduce the distribution difference and class spacing of the transferable features extracted from the original datasets and the target datasets, and the initial fault diagnosis of the target rolling bearing is diagnosed according to the feature knowledge of the source rolling bearing. In three experimental datasets, six TL experiments were carried out to verify that the Soca-Denoising auto-encoder, Contraction auto-encoder and Transfer learning (DCT) model can effectively enhance the initial fault characteristics of rolling bearings, and has higher diagnostic accuracy and robustness compared with the existing initial fault diagnosis methods of rolling bearings. This method has a good application prospect in the field of early fault diagnosis of rolling bearings.

On Infinite Past Predictability of Cyclostationary Signals

This paper explores the asymptotic spectral decomposition of periodically Toeplitz matrices with finite summable elements. As an alternative to polyphase decomposition and other approaches based on Gladyshev representation, the proposed route exploits the Toeplitz structure of cyclic autocorrelation matrices, thus leveraging on known asymptotic results and providing a more direct link to the cyclic spectrum and spectral coherence. As a concrete application, the problem of cyclic linear prediction is revisited, concluding with a generalized Kolmogorov-Szegö theorem on the predictability of cyclostationary signals. These results are finally tested experimentally in a prediction setting for an asynchronous mixture of two cyclostationary pulse-amplitude modulation signals.

Symbol rate estimation of PSK signals under cyclostationary framework based on compressing transform function in alpha-stable noise

A novel compressing transform (CT) function based cyclic autocorrelation (CTCA) under the cyclostationary framework is presented, which is intended for the symbol rate estimation of phase-shift keying (PSK) signals in the presence of alpha-stable noise. The domain of the CT function built in this paper can be divided into the approximate linear zone (ALZ) and the suppression zone (SZ). The ALZ helps the proposed CT function keep the useful information of signals-of-interest unchanged and because of the SZ, the CT function can mitigate effectively the large amplitudes of the impulsive noise. Subsequently, motivated by the excellent parameter estimation performance of the cyclic autocorrelation and based on the constructed CT function, the CTCA is proposed for symbol rate estimation in alpha-stable noise. Afterwards, the estimation accuracy of the proposed CTCA is measured by the normalized root mean square error in Monte Carlo simulations. According to the simulation results, the proposed method is feasible for PSK symbol rate estimation, and it distinctively outperforms the equivalent cyclic autocorrelation based counterparts especially in a strong impulsive noise environment.

A study on the extraction of characteristics of compound faults of rolling bearings based on ITD-AF-CAF

In view of the cyclostationary characteristics of vibration signals from aero-engine, the combination of cyclic autocorrelation function and intrinsic timescale decomposition (ITD) has been proposed. According to the proposed method, vibration signals are decomposed by ITD algorithm to obtain the autocorrelation function of proper rotation components (PRC), based on which characteristic extraction and identification of compound faults of rolling bearings is made possible. To validate the effectiveness of method, an analysis has been given to the vibration signals of rolling bearings collected by sensors of different positions in different compound fault modes. As shown by results, the method combining ITD and cyclostationary theory can precisely and effectively extract the characteristic frequency relative to the type of faults and identify the compound faults.

Modified square timing error detector with large chromatic dispersion tolerance for optical coherent receivers

Clock recovery plays an important role in the digital signal processing (DSP) chain of modern coherent optical receivers. It references the local sampling clock with the signal baudrate and finds the optimal sampling instances by performing endless timing error corrections. At the core of clock recovery, a timing error detector (TED) is used to provide instantaneous error tracking. However, usual TEDs suffer from effects such as chromatic dispersion (CD) and polarization rotation, thus requiring additional efforts to remove those effects before TED. Here we propose a modified square TED based on the signal's cyclic autocorrelation function (CAF), which generalizes its classical counterpart and exhibits a much larger CD tolerance. It provides a time-domain solution of the CD-tolerant TED. The previously analyzed equivalence among the time-domain and the frequency-domain TEDs is reestablished in the framework of spectral correlation. The modified square TED demands a minimum extra complexity. Both numerical simulation and experiments are performed to study the performance of the proposed TED.

High-Impedance Fault Identification Using Cyclostationary Characteristic Analysis

Conventional overcurrent-based protection systems are generally not sensitive to high impedance faults (HIFs) since they have a low overcurrent amplitude. This type of fault causes damages to dealers and can provoke the deaths of people and animals. Therefore, different methods for identifying HIFs in electric power distribution systems have been proposed. However, besides the low fault overcurrent level be still a problem, the noise interference on signals is also a difficulty for non-conventional methods. Therefore, this work proposes a reliable method based on statistical characteristics for identifying HIFs regardless of the noise interference and the overcurrent level. Specifically, the method uses cyclostationary characteristic analysis to extract cyclic autocorrelation information from the signals of interest by calculating the cyclic spectral density function. From this information, HIFs can be properly identified among other power system disturbances. The performance of the method was assessed with actual HIF data and with realistic HIF simulations, presenting promising results.

Interference‐to‐noise ratio estimation in long‐term evolution passive radar based on cyclic auto‐correlation

This letter considers the interference-to-noise ratio (INR) estimation problem in long-term evolution (LTE)-based passive bistatic radar. The INR is of great importance in the evaluation of interference level, the prediction of the target detection capability and the target parameter estimation. Traditional passive radar uses the cross-correlation function between the reference and surveillance signals to estimate the INR. This is not applicable to LTE-based passive radar due to the uncorrelation between the interference and reference signals in LTE-based passive radar. In this letter, we propose a cyclic auto-correlation method to estimate the INR. Simulation results show the effectiveness of the proposed method.

Cyclostationary Analysis of Irregular Statistical Cyclicity and Extraction of Rotating Speed for Bearing Diagnostics With Speed Fluctuations

Mechanical fault diagnosis under nonstationary conditions is one of the hotspots in the condition monitoring research field, presenting still several difficulties. Vibration signals of faulty bearings exhibit second-order cyclostationarity when rotating speed and load are constant. Due to the time-varying rotating speed, the original cyclostationary signal becomes a special type of nonstationary signal. Considering the superiority of cyclostationary analysis in bearing fault diagnosis, it is interesting to extend the cyclostationary paradigm to make it suitable for particular signals that show irregular statistical cyclicity (ISC). Modeling bearing vibrations with speed fluctuation, however, is a controversial topic, which further sparked a debate on how to process bearing signals with ISC. Therefore, in this article, a detailed comparison of two signal models is made, the pace irregularity and the time warping, to illustrate the advantages and disadvantages of the modeling ideas. Based on these models, two novel tacholess diagnostic methods, the synchronization-sequence method and the dewarping method, are proposed for bearing diagnosis in nonstationary operations. By identifying the impact points with the same cyclic feature, the synchronization-sequence method shifts the impulse patches to the same interval, so the signal becomes cyclostationary. Using another strategy, the dewarping method recovers the regular statistical property by maximizing the squared modulus of the cyclic autocorrelation of specific feature points. The results show that both models can help diagnose local bearing faults, and the classical cyclostationary diagnostic tools become more powerful when extending to nonstationary operation conditions. In addition, the speed fluctuation curve can also be estimated by the two methods without using a tachometer. The characteristic of the proposed methods for speed estimation is that only the second-order cyclostationary information is utilized. Besides, the methods are robust to noise, so they are suitable for processing bearing data in the incipient failure stage. Numerical simulations and experimental data analyses corroborate the theoretical results.

Using two-dimensional fast Fourier transform for estimating spectral correlation function

The paper presents the algorithm for estimating spectral correlation function (SCF) of a wide-sense cyclostationary random process. SCF provides the quantitative representation of the correlation in frequency domain and relates to cyclic autocorrelation function via Fourier transform. The algorithm is based on two-dimensional Fourier transform, which is being applied to the discrete diadic correlation function weighted by a two-dimensional windowing function, chosen rectangular in the direction orthogonal to the current-time axis. This transform can be implemented by means of the fast Fourier transform (FFT) algorithm, which is built-in in a variety of modern mathematical platforms. A pulse-amplitude modulated process masked by the additive stationary Gaussian noise was considered as an example of a random process exhibiting strong cyclostationarity. The numerical simulation where the estimation of spectral correlation function of such process is conducted, and it proved the effectiveness of the proposed algorithm.

Blind Parameters Estimation Algorithm Based on SC-FDE Cyclic Autocorrelation

This paper analyzes properties of Single-Carrier Frequency Domain Equilibrium (SC-FDE) signal’s cyclic autocorrelation section. The relationship between cyclic autocorrelation, useful signal length, cyclic prefix length is studied. The blind estimation algorithm is proposed for the useful signal length and cyclic prefix length without prior information. According to zero point symmetry property and the relationship between cyclic prefix length and spectral line, the area of spectral peak search is limited. So that the length of cyclic prefix and the number of cyclic prefix symbols are estimated. Simulation results show that the algorithm can improve the estimation accuracy and have better estimation performance at low signal-to-noise ratio.

Cyclic-Auto-Correlation Based Timing Estimation Algorithm for Time-Frequency Overlapping Multi-Carrier Signals

In recent years, the time-frequency overlapping multi-carrier signal has been a novel and valuable topic in blind signal processing, especially in the non-cooperative receiving field. But there is little related research in public published papers. This paper proposes two timing estimation algorithms, which are non-data-aided and based on the cyclic auto-correlation function. In order to evaluate the performance of the proposed algorithms, the theoretical bound of the timing estimation is derived. According to the analyses and simulation results, the effectiveness of the proposed algorithms has been demonstrated. It shows that Method I has better performance than Method II. However, Method II does not need prior information, so it has a wider range of applications.

Estimation of Modulation Parameters of LPI Radar Using Cyclostationary Method

Low Probability of intercept (LPI) radars work on the principle of low peak-power and wide bandwidth. To achieve this, the LPI radars use special type of modulated waveforms which are difficult to intercept. The main tasks of intercept receivers are to detect, estimate and classify LPI signals even in the presence of high noise. Accurate estimation of the modulation parameters also provides information about threat to radar so that necessary counter measures could be initiated against the enemy radars. In the present work, Cyclo-stationary (CS) method is used to estimate the parameters of Polytime coded LPI signals. CS method is efficient for the analysis of periodic waveforms like LPI signals and finds applications in many fields such as array signal processing, estimation of direction of arrival, signal detection. Cyclic auto correlation function and the spectral correlation density function (SCD) which are the basis for CS analysis are computed for all the four types of polytime codes. Generation of all the four types of Polytime codes and computation of SCD coefficients are carried out using MATLAB. From the contour plot of SCD function, the parameters carrier frequency, bandwidth and code rate are measured. It is assumed that the received signal is not corrupted with any noise. The simulation results are compared with the values available in the literature. The maximum error of estimation is well within ± 6% for all the codes in the proposed method whereas the maximum error reported in the literature is 25.7%. Hence the proposed method is better. Since CS method is sensitive to sampling frequency, the analysis is repeated for three different sampling frequencies and in all cases, the estimation error is less than 6%.

Cyclostationary-Based Vital Signs Detection Using Microwave Radar at 2.5 GHz.

Non-contact detection and estimation of vital signs such as respiratory and cardiac frequencies is a powerful tool for surveillance applications. In particular, the continuous wave bio-radar has been widely investigated to determine the physiological parameters in a non-contact manner. Since the RF-reflected signal from the human body is corrupted by noise and random body movements, traditional Fourier analysis fails to detect the heart and breathing frequencies. In this effort, cyclostationary analysis has been used to improve the radar performance for non-invasive measurement of respiratory rate and heart rate. However, the preliminary works focus only on one frequency and do not include the impact of attenuation and random movement of the body in the analysis. Hence in this paper, we evaluate the impact of distance and noise on the cyclic features of the reflected signal. Furthermore, we explore the assessment of second order cyclostationary signal processing performance by developing the cyclic mean, the conjugate cyclic autocorrelation and the cyclic cumulant. In addition, the analysis is carried out using a reduced number of samples to reduce the response time. Implementation of the cyclostationary technique using a bi-static radar configuration at 2.5 GHz is shown as an example to demonstrate the proposed approach.