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In underwater acoustic applications, the conventional cyclic direction of arrival algorithm faces challenges, including a low signal-to-noise ratio and high bandwidth when compared with modulated frequencies. In response to these issues, this paper introduces a novel, robust, and broadband cyclic beamforming algorithm. The proposed method substitutes the conventional cyclic covariance matrix with the variance of the cyclic covariance matrix as its primary feature. Assuming that the same frequency band shares a common steering vector, the new algorithm achieves superior detection performance for targets with specific modulation frequencies while suppressing interference signals and background noise. Experimental results demonstrate a significant enhancement in the directibity index by 81% and 181% when compared with the traditional Capon beamforming algorithm and the traditional extended wideband spectral cyclic MUSIC (EWSCM) algorithm, respectively. Moreover, the proposed algorithm substantially reduces computational complexity to 1/40th of that of the EWSCM algorithm, employing frequency band statistical averaging and covariance matrix variance. [ABSTRACT FROM AUTHOR]

The article investigates the complexities associated with spectrum analysis in cognitive radio networks (CRNs). It begins by acknowledging the evolving challenges of spectrum sensing due to the dynamic nature of wireless environments and the increasing demand for efficient spectrum utilization. The study thoroughly examines various traditional spectrum sensing methods, including Energy Detector Based Sensing, Waveform-Based Sensing, Cyclostationarity-Based Sensing, and Matched Filtering. The focus of the research is on the Variable Time Segment Monitoring (VTSM) method, a novel approach that optimizes spectrum sensing by dynamically adjusting the time segments used for analyzing spectral characteristics. The paper highlights the VTSM method's ability to enhance detection accuracy and reduce false alarms by adapting to different signal environments, making it particularly suited for complex and dynamic CRN scenarios. Furthermore, the article compares VTSM with traditional methods across key performance metrics such as detection accuracy, false alarm rate, latency, and computational complexity. The analysis reveals that while traditional methods have their strengths, VTSM offers a balanced approach, combining flexibility, accuracy, and moderate computational demands, thereby providing a versatile solution for modern spectrum sensing challenges. The findings contribute to the broader understanding and advancement of cognitive radio technologies, supporting the development of more robust and efficient spectrum sensing solutions, which are crucial for optimizing network performance and ensuring reliable communication in increasingly congested and complex wireless environments. The article concludes by emphasizing the importance of selecting the appropriate spectrum sensing method based on the specific requirements of the CRN application, considering factors such as accuracy, computational resources, and environmental dynamics. The findings contribute to the broader understanding and advancement of cognitive radio technologies, supporting the development of more robust and efficient spectrum sensing solutions. [ABSTRACT FROM AUTHOR]

The paper deals with the estimation methodology for the α-stable periodic autoregressive (PAR) models. For the classical (Gaussian) PAR time series is cyclostationary systems the periodicity is manifested in the model characteristics. One of the most common characteristics used in this context is the autocovariance function. One of the methods of the PAR model estimation utilizes the Yule-Walker equations that contain the autocovariance function of the given process. However, for the infinite variance version of the PAR model (i.e., α-stable-distributed) it is expected that the autocovariance function is not properly defined. Thus, alternative measures need to be used. In this paper, we present the general idea of the modified Yule-Walker equations for the considered model. It is proposed to replace the classical dependency measure by the dependency measures properly defined for infinite variance models. We demonstrate two possible modifications based on the covariation and fractional lower order covariance. The first approach was recently proposed in the literature while the latter is a novel algorithm. We compare the effectiveness of both estimation methods for the considered model. Finally, the results are compared with the classical Yule-Walker approach. We demonstrate the limitations of the classical method for the considered model. The possible application for real data analysis is demonstrated. [ABSTRACT FROM AUTHOR]

Purpose: The implementation of conditional and preventive maintenance of rotating machines based on accurate vibration monitoring appears to be a suitable solution for the early detection of mechanical defects, something which is unfortunately not always obvious. Methods: In this study, we propose an advanced and recent method for processing no stationary and nonlinear signals in an industrial environment, based on cyclostationary analysis. The proposed technique is initially used to signals measured on defective bearings on a test bench. Finally, the industrial application realized on a valid production machine for large-scale, beyond that of the laboratory. The main objective of this work is to respond to the demand of a large FERTIAL industrial group where vibration analysis has been used to analyze the signal vibration measured on the journal bearings of a reducer GVAB420 of a turbo alternator GZ1164. Results: The problem encountered in this case is due to the reduction in the generation of the electrical load from six to five MVA, resulting in a sharp rise in the vibration level on all frequency bands of the turbine and machine bearings. To remedy this problem, a vibration analysis has been used for analyzing measured signals on this turbo-alternator which operates in true conditions. The results obtained proved the ability of the proposed approach to highlight the exact nature of the mechanical fault studied and its gravity in various setups, whatever the type of faults: on the outer and inner races; and journal bearings in an industrial environment. Conclusions: This significant contribution highlights the potential of advanced vibration analysis, using plots of its two indicators MID and IMID created with the proposed approach can be easily interpreted by maintenance engineers as a simple spectrum, for significantly improving the reliability and operational lifespan of critical machines, which is of utmost importance in various industries. [ABSTRACT FROM AUTHOR]

The signal detection problem for cyclostationary signals is addressed within the fraction-of-time probability framework, where statistical functions are constructed starting from a single time series, without introducing the concept of stochastic process. Single-cycle detectors and quadratic-form detectors based on measurements of the Fourier coefficients of the almost-periodically time-variant cumulative distribution and probability density functions are proposed. The adopted fraction-of-time approach provides both methodological and implementation advantages for the proposed detectors. For single-cycle detectors, the decision statistic is a function of the received signal and the threshold is derived using side data under the null hypothesis. For quadratic-form detectors, the decision statistic can be expressed as a function of the received signal without using side data, at the cost of some performance degradation. The threshold can be derived analytically. Performance analysis is carried out using Monte Carlo simulations in severe noise and interference environments, where the proposed detectors provide better performance with respect to the analogous detectors based on second- and higher-order cyclic statistic measurements. [ABSTRACT FROM AUTHOR]

AbstractPeriodic autoregressive (PAR) time series with finite variance is considered as one of the most common models of second-order cyclostationary processes. However, in the real applications, the signals with periodic characteristics may be disturbed by additional noise related to measurement device disturbances or to other external sources. Thus, the known estimation techniques dedicated for PAR models may be inefficient for such cases. When the variance of the additive noise is relatively small, it can be ignored and the classical estimation techniques can be applied. However, for extreme cases, the additive noise can have a significant influence on the estimation results. In this paper, we propose four estimation techniques for the noise-corrupted PAR models with finite-variance distributions. The methodology is based on Yule-Walker equations utilizing the autocovariance function. It can be used for any type of the finite-variance additive noise. The presented simulation study clearly indicates the efficiency of the proposed techniques, also for extreme case, when the additive noise is a sum of the Gaussian additive noise and additive outliers. The proposed estimation techniques are also applied for testing if the data correspond to noise-corrupted PAR model. This issue is strongly related to the identification of informative component in the data in case when the model is disturbed by additive non-informative noise. The power of the test is studied for simulated data. Finally, the testing procedure is applied for two real time series describing particulate matter concentration in the air. [ABSTRACT FROM AUTHOR]

Block timing synchronization, which could be data-aided or non-data-aided, is a critical part of space–time block codes (STBCs) for recovery of transmitted symbols. The data-aided schemes are not suited for some problems like bandwidth efficiency and most of the existing non-data-aided techniques rely on the received signals statistics and channel coefficients estimation increasing their complexity. In this paper, a non-data-aided cyclostationary-based approach is proposed for block timing estimation in Alamouti STBC employing frequency-shifted versions of the received signals. The method is non-statistical with low complexity and requires no knowledge of channel coefficients. Simulation results confirm the effectiveness of the method.

Fatigue pitting can reduce the gear surface durability and induce other severe failures, which will eventually lead to the complete loss of transmission function of the transmission system. Thus, monitoring fatigue pitting progression is vital to avoid unexpected economic losses and incidents. Thanks to the unique characteristics of the gear meshing process, there is a close relationship between the tribological features of fatigue pitting and gear vibration cyclostationarity. Based on the vibration cyclostationarity, this paper develops a novel second-order cyclostationary (CS2) fatigue pitting monitoring indicator, which can accurately assess the degradation status of the gear system and benefit subsequent health management. The advantage of the developed cyclostationary indicator in evaluating and monitoring the process of fatigue pitting propagation is demonstrated with the natural fatigue pitting progression test, through comparisons with other conventional indicators. [ABSTRACT FROM AUTHOR]

This paper presents a novel deep-learning (DL)-based approach for classifying digitally modulated signals, which involves the use of capsule networks (CAPs) together with the cyclic cumulant (CC) features of the signals. These were blindly estimated using cyclostationary signal processing (CSP) and were then input into the CAP for training and classification. The classification performance and the generalization abilities of the proposed approach were tested using two distinct datasets that contained the same types of digitally modulated signals, but had distinct generation parameters. The results showed that the classification of digitally modulated signals using CAPs and CCs proposed in the paper outperformed alternative approaches for classifying digitally modulated signals that included conventional classifiers that employed CSP-based techniques, as well as alternative DL-based classifiers that used convolutional neural networks (CNNs) or residual networks (RESNETs) with the in-phase/quadrature (I/Q) data used for training and classification. [ABSTRACT FROM AUTHOR]

Driven by increasing food demand and the urgent need for intelligent land use, the size and complexity of agricultural machinery has increased significantly. Monitoring the operation of machines during long working days is a very challenging task for the operators. Automatic monitoring systems can lighten the load and also pave the way towards fully autonomous machines. This paper proposes an automatic condition monitoring system for detecting operation anomalies on agricultural machine components with reciprocating motion, and applies it to a use-case on a combine harvester header cutter bar. Cyclostationary analysis techniques are employed to develop filtering algorithms to extract informative features, which are monitored through the implementation of statistical process control (SPC) using control charts. Together with a comparison of several filtering and feature extraction techniques, an analysis is provided on the influence of sensor type and position on anomaly detection performance. Filtering benefit was found to be highly dependent on the considered sensor type and its location, with increases in Matthews correlation coefficient (MCC) ranging from 0 to 50%, resulting in maximal MCC values of 1. Suitable feature calculation resulted in average prediction performance improvements over 10% in MCC values for nearly all considered sensor types and their locations. These results highlight the importance of intelligent sensor selection for condition monitoring purposes on agricultural machinery and the added value of SPC involving cyclostationary analysis techniques for anomaly detection. • Knife impacts are detected with a Matthews correlation coefficient of 0.995. • Sensors mounted closer to the cutter bar performed best. • The proposed synchronous filters clearly improved performance. • The standard deviation per rotation captured the signal response during impact well. [ABSTRACT FROM AUTHOR]

This article addresses the problem of estimating the spectral correlation function (SCF), which provides quantitative characterization in the frequency domain of wide-sense cyclostationary properties of random processes which are considered to be the theoretical models of observed time series or discrete-time signals. The theoretical framework behind the SCF estimation is briefly reviewed so that an important difference between the width of the resolution cell in bifrequency plane and the step between the centers of neighboring cells is highlighted. The outline of the proposed double-number fast Fourier transform algorithm (2N-FFT) is described in the paper as a sequence of steps directly leading to a digital signal processing technique. The 2N-FFT algorithm is derived from the time-smoothing approach to cyclic periodogram estimation where the spectral interpolation based on doubling the FFT base is employed. This guarantees that no cyclic frequency is left out of the coverage grid so that at least one resolution element intersects it. A numerical simulation involving two processes, a harmonic amplitude modulated by stationary noise and a binary-pulse amplitude-modulated train, demonstrated that their cyclic frequencies are estimated with a high accuracy, reaching the size of step between resolution cells. In addition, the SCF components estimated by the proposed algorithm are shown to be similar to the curves provided by the theoretical models of the observed processes. The comparison between the proposed algorithm and the well-known FFT accumulation method in terms of computational complexity and required memory size reveals the cases where the 2N-FFT algorithm offers a reasonable trade-off. [ABSTRACT FROM AUTHOR]

Time series arising from measurements in many fields of physics, engineering, chemistry, biology, and econometrics, are commonly modeled as sample paths from an ensemble which, together with a probability measure, is called a stochastic process. Stationarity and ergodicity assumptions about this model are generally made for analytical convenience and mathematical tractability of the model. In this article, it is shown that a dichotomy, which can be very misleading in practice, exists between the properties of a stochastic process and those of its individual sample paths. This dichotomy can be eliminated by adopting the fraction-of-time (FOT) probability approach reviewed in this article for which a probabilistic model is constructed from a single time series without introducing the abstraction of the stochastic process. Two FOT-probability models are reviewed. The first considers probabilistic functions that do not depend on time and employs the relative measure on the real line as a probability measure and the time average as an expectation operator. Such time series are called stationary signals. The second considers periodic, poly-periodic, and almost periodic probabilistic functions and employs the operator that extracts the finite-strength additive sine-wave components of its argument as an expectation operator. This latter model is appropriate for describing time series originating from phenomena involving a combination of periodic and random phenomena. Such time series are called cyclostationary, poly-cyclostationary, and almost cyclostationary signals. The FOT-probability alternative provides a means for circumventing two standard but undesirable practices: (1) Adopting the Kolmogorov stochastic process model by using its Axiom VI without being able to verify its validity for the specific application and (2) Assuming Birkhoff’s ergodicity condition holds without being able to verify its validity for the specific application.

A new model for the electrocardiogram (ECG) signal is proposed. Specifically, the ECG signal is modeled as an amplitude-modulated and time-warped version of a cyclostationary process which is the sum of a periodic signal and a zero-mean cyclostationary term. For the proposed model, the second-order characterization is derived in both time and frequency domains. The autocorrelation function is shown to be the superposition of amplitude- and angle-modulated sine waves and the Loève bifrequency spectrum a spread version of that of the underlying cyclostationary process. The signal model belongs the recently introduced class of the oscillatory almost-cyclostationary processes. A procedure for estimating the second-order statistical functions in both time and frequency domains is outlined. The effectiveness of the proposed model and of the estimation procedure is corroborated by measurements on real ECG signals. These measurements are in full agreement with the theoretical analytical expressions. The proposed model is shown to be effective with observation intervals much larger than those adopted up to now with the classical cyclostationary model and is suitable to be exploited for arrhythmia modeling and characterization, and for diagnosis and biometric purposes.

The signal detection problem for cyclostationary signals is addressed within the fraction-of-time probability framework, where statistical functions are constructed starting from a single time series, without introducing the concept of stochastic process. Single-cycle detectors and quadratic-form detectors based on measurements of the Fourier coefficients of the almost-periodically time-variant cumulative distribution and probability density functions are proposed. The adopted fraction-of-time approach provides both methodological and implementation advantages for the proposed detectors. For single-cycle detectors, the decision statistic is a function of the received signal and the threshold is derived using side data under the null hypothesis. For quadratic-form detectors, the decision statistic can be expressed as a function of the received signal without using side data, at the cost of some performance degradation. The threshold can be derived analytically. Performance analysis is carried out using Monte Carlo simulations in severe noise and interference environments, where the proposed detectors provide better performance with respect to the analogous detectors based on second- and higher-order cyclic statistic measurements.

Due to the interference of various strong background signals, it is often difficult to extract effective features by using conventional methods such as envelope spectrum analysis when early weak fault arises in rolling bearing. Inspired by the current two main research directions of weak fault diagnosis of rolling bearing, that is, the enhancement of impulse features of faulty vibration signal through vibration analysis and the selection of fault information sensitive frequency band for further envelope spectrum analysis, and based on the second-order cyclostationary characteristic of the vibration signal of faulty bearing, a two-stage method for weak feature extraction of rolling bearing combining cyclic Wiener filter with improved enhanced envelope spectrum (IEES) is proposed in the paper. Firstly, the original vibration signal of the rolling bearing's early weak fault is handled by cyclic Wiener filter exploiting the spectral coherence (SCoh) theory and the noise components are filtered out. Then, SCoh is applied on the filtered signal. Subsequently, an IEES method obtained by integrating over the selected fault information sensitive spectral frequency band of the SCoh spectral is used to extract the fault features. The innovation of the proposed method is to fully excavate the advantages of cyclic Wiener filter and IEES simultaneously. The feasibility of the proposed method is verified by simulation firstly, and vibration signals collected from accelerated bearing degradation tests and engineering machines are used to further verify its effectiveness. Additionally, its superiority over the other state-of-the-art methods is also compared. [ABSTRACT FROM AUTHOR]

Francis turbine is one of the most commonly used hydraulic machinery for hydroelectric power generation, but its stability is frequently jeopardized by vortex rope. It is crucial to promptly and accurately detect vortex rope for the reliable operation of turbine unit. To address this challenge, the Cyclostationary Extended Dictionary Learning (CEDL) approach is proposed to identify vortex rope in Francis turbine. CEDL utilizes the Fisher discrimination criterion and low-rank constraints through the preprocessing and extending strategies to achieve accurate identification. Preprocessing specifically refers to the construction of filter for raw data based on cyclostationarity Then, the trained dictionary is used to extract features, and a linear classifier is developed based on these features. To evaluate the proposed method, vortex rope experiments are conducted in a Francis turbine under five conditions, and every condition includes four states: normal state, initial vortex rope, stable vortex rope and severe vortex rope. The results reveal three main findings. Firstly, the trained atoms in each sub-dictionary exhibit unique characteristics such as tonal frequency at 7 kHz and broadband frequency during 12–20 kHz, which are linked to the evolution stages of vortex rope. Secondly, the dictionary trained for a specific condition can achieve a classification accuracy of up to 90%, and even exceed 97% in some cases. Finally, the dictionary trained in a specific working condition can achieve relatively high classification accuracy in the scenarios of other working conditions. • Cyclostationary extended dictionary learning is proposed to characterize vortex rope state. • The raw data is preprocessed by filters based on cyclostationarity. • The atoms of each sub-dictionary can reflect the signal features of vortex rope. • A linear classifier is designed to identify vortex rope state in Francis turbine. • Few-shot learning can achieve high classification accuracy even between different conditions. [ABSTRACT FROM AUTHOR]

Cyclostationary analysis has been strongly recognized as an effective demodulation tool in identifying fault features of rotating machinery based on vibration signature analysis. This study improves two current mature cyclostationary approaches, cyclic modulation spectrum (CMS) and fast spectral correlation (Fast-SC), combined with the novel frequency-domain application of Teager Kaiser energy operator (TKEO). They can enhance fault feature identification with the lower computational burden. Firstly, the raw vibration signal is transformed into the time–frequency domain through the short-time Fourier transform (STFT) to realize the conversion of the multi-carrier signal to a multiple signal-carrier signal. Secondly, the TKEO is utilized to enhance the fault feature by taking full advantage of demodulating the mono-component. Finally, the spectral coherence and enhanced envelope spectrum (EES) are calculated to effectively exhibit fault features. The superiority of the proposed methods is successfully validated by the simulation study and diagnosing the broken rotor bar (BRB) and bearing outer race faults of induction motors (IMs) under various operating conditions. • The frequency domain TKEO is proposed for processing the single carrier signal. • The fault extraction capabilities of CMS and Fast-SC are enhanced using TKEO. • The optimized methods have high computational efficiency. • The results validate the effectiveness of the proposed methods for IM fault diagnosis. [ABSTRACT FROM AUTHOR]

Due to short frames of short-term burst signals, the performance of conventional non-data-aided feedforward timing estimators is unsatisfactory. This letter investigates an estimator based on multiple cyclic correlations addressing this issue. The cyclic correlations at high-valued timing lags provide the timing information for estimating timing offset. Motivated by it, we combine the timing information at various timing lags, utilizing the second-order statistical characteristics of the limited sample data for accurate estimation. Considering the estimation range of roll-off factors and computational complexity, an asymptotically unbiased estimation using four correlations is deduced. Simulation results show that the proposed estimator outperforms other estimators. [ABSTRACT FROM AUTHOR]

Safety, security, and privacy are three critical concerns affiliated with the use of drones in everyday life. Considering their ever-shrinking sizes and capabilities, being aware of drone activities in the vicinity becomes an important surveillance item. Therefore, keeping track of drones and preferably their controllers should be included into the already-existing security measures. In this study, a frequency hopping spread spectrum (FHSS) type drone controller signal detection and emitter direction finding framework is proposed to achieve aforementioned goals. Since drone communications signals generally coexist with other FHSS signals in 2.4 GHz industrial, scientific, and medical (ISM) band, first, a method based on cyclostationarity analysis is proposed to distinguish the drone radio controller signals from other signals utilizing 2.4 GHz ISM band. Then, a variant of short-term Fourier transform is introduced to extract the parameters of detected drone remote controller signals. The correct hopping signals are then aggregated based on the clustered parameters to obtain their combined baseband equivalent signal. Furthermore, the resampling process is applied to reduce the unrelated samples in the spectrum and represent the spectrum with the reconstructed signal, which has a much lower bandwidth than the spread bandwidth. Finally, two different multiple signal classification algorithms are utilized to estimate the direction of the drone controller relative to the receiving system. In order to validate the overall performance of the proposed method, the introduced framework is implemented on hardware platforms and tested under real-world conditions. A uniform linear antenna array is utilized to capture over-the-air signals in hilly terrain suburban environments by considering both line-of-sight and non-line–of-sight cases. Direction estimation performance is presented in a comparative manner and relevant discussions are provided.

Automatic signal recognition (ASR) plays an important role in various applications such as dynamic spectrum access and cognitive radio, hence it will be a key enabler for beyond 5G communications. Recently, many research works have been exploring deep learning (DL) based ASR, where it has been shown that simple convolutional neural networks (CNN) can outperform expert features based techniques. However, such works have been primarily focusing on single-carrier signals. With the advent of spectrally efficient filtered multicarrier waveforms, we propose in this paper, to revisit the DL based ASR to account for the variety and complexity of these new transmission schemes. Specifically, we design two types of classification algorithms. The first one relies on the cyclostationarity characteristics of the investigated waveforms combined with a support vector machine (SVM) classifier; while the second one explores the use of a four-layer CNN which performs both features extraction and classification. The proposed approaches do not require any a priori knowledge of the received signal parameters, and their performance is evaluated in a multipath channel through simulations for a signal-to-noise ratio (SNR) ranging from −8 to 20 dB. The simulation results show that, despite cyclostationary characteristics being highly discriminative, the CNN outperforms the cyclostationary based classification especially for short time received signals, and low SNR levels.

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. [ABSTRACT FROM AUTHOR]

In this study, an attempt has been made to develop an automated muscle fatigue detection system using cyclostationary based geometric features of surface electromyography (sEMG) signals. For this purpose, signals are acquired from fifty-eight healthy volunteers under dynamic muscle fatiguing contractions. The sEMG signals are preprocessed and the epochs of signals under nonfatigue and fatigue conditions are considered for the analysis. A computationally effective Fast Fourier transform based accumulation algorithm is adapted to compute the spectral correlation density coefficients. The boundary of spectral density coefficients in the complex plane is obtained using alpha shape method. The geometric features, namely, perimeter, area, circularity, bending energy, eccentricity and inertia are extracted from the shape and the machine learning models based on multilayer perceptron (MLP) and extreme learning machine (ELM) are developed using these biomarkers. The results show that the cyclostationarity increases in fatigue condition. All the extracted features are found to have significant difference in the two conditions. It is found that the ELM model based on prominent features classifies the sEMG signals with a maximum accuracy of 94.09% and F-score of 93.75%. Therefore, the proposed approach appears to be useful for analysing the fatiguing contractions in neuromuscular conditions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel low-complexity scheme to extract cyclic features of wideband signals from sub-Nyquist samples as Nyquist rates push contemporary analog-to-digital converters to their performance limits. Due to the sparse spectrum occupancy in wideband, sub-Nyquist sampling is performed and cyclostationary feature extraction is achieved at baseband to identify the modulation scheme with low computational complexity. The multichannel sub-Nyquist sampling structure of the modulated wideband converter (MWC) is used to perform spectrum sensing. Automatic modulation identification and classification are done based on cyclostationary feature detection for the efficient use of available spectrum bands. The computational complexity is reduced as the aliased copy of the signal in baseband obtained in each channel of MWC is only used to estimate the cyclic spectrum of the signal and identify the modulation scheme. Simulations performed validate the proposed method for various modulation schemes. [ABSTRACT FROM AUTHOR]

This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving the frequency domain counterpart of CCF—voltage–current cross spectrum correlation function (CSCF). Not only does the latter exhibit the complete representation of voltage–current interaction in the element, but it can be systematically exploited for evaluating all commonly used power measures, including instantaneous power, in the form of Fourier series expansion. Simulation examples, which are given for the parallel resonant circuit excited by the periodic currents expressed as a finite sum of sinusoids and periodic train of pulses with distorted edges, numerically illustrate the components of voltage–current CSCF and the characteristics derived from it. In addition, the generalization of Tellegen's theorem, suggested in the paper, leads to the immediate formulation of the power conservation law for each CSCF component separately. [ABSTRACT FROM AUTHOR]

Spectrum sensing is one of the means of utilizing the scarce source of wireless spectrum efficiently. In this paper, a convolutional neural network (CNN) model employing spectral correlation function (SCF) which is an effective characterization of cyclostationarity property, is proposed for wireless spectrum sensing and signal identification. The proposed method classifies wireless signals without a priori information and it is implemented in two different settings entitled CASE1 and CASE2. In CASE1, signals are jointly sensed and classified. In CASE2, sensing and classification are conducted in a sequential manner. In contrary to the classical spectrum sensing techniques, the proposed CNN method does not require a statistical decision process and does not need to know the distinct features of signals beforehand. Implementation of the method on the measured over-the-air real-world signals in cellular bands indicates important performance gains when compared to the signal classifying deep learning networks available in the literature and against classical sensing methods. Even though the implementation herein is over cellular signals, the proposed approach can be extended to the detection and classification of any signal that exhibits cyclostationary features. Finally, the measurement-based dataset which is utilized to validate the method is shared for the purposes of reproduction of the results and further research and development. [ABSTRACT FROM AUTHOR]

• Diagnostic information in vibration signals is distorted by transfer functions. • Cepstrum-based OMA can be utilised to estimate forcing functions for SIMO systems. • In MIMO situations, responses to a CS2 source with unique cyclic frequency can be separated. • Previous method required phase unwrapping the CSD, but often not possible with excessive noise. • Proposed new method based on the real cyclic cepstrum avoids phase unwrapping the CSD. • Results of application to extraction of gearmesh forcing functions greatly improved. Operational modal analysis aims at identifying modal parameters of a system from response measurements only. Cepstrum-based operational modal analysis (OMA) has an advantage over conventional OMA methods, since it relaxes the assumption of white noise excitation and is able to retain the relative scaling between modes, which is important in many applications such as force identification. In previous research, the cepstrum-based OMA has been applied to reconstruct the forcing functions generated by a gear pair from response measurements, in order to obtain more direct diagnostic information. However, the cepstrum-based OMA can only cope with systems with a single excitation. To overcome this challenge, this paper proposes a novel technique, which can be applied to minimum-phase multiple input systems that have a cyclostationary excitation with a unique cyclic frequency. The technique first extracts the single-input system from the multiple-input case using the cyclic spectral density (CSD) of the measurement, equal to the spectral correlation density (SCD) evaluated at a particular cyclic frequency. The method then identifies the frequency response function (FRF) by fitting the real cyclic cepstrum of the measurement, this being the inverse Fourier transform of the log magnitude of the CSD. This method elaborates on a technique developed in previous research, which extracted the signal of interest from the complex cyclic cepstrum instead, this being the inverse Fourier transform of the logarithm of the CSD with unwrapped phase. In this paper, a limitation of the previously developed technique is identified and discussed for the first time, viz. problems with the phase unwrapping of the CSD. The technique in this paper overcomes the drawback in the previous research and exhibits better performance in noisy conditions. Both methods have been validated on synthetic signals as well as vibration measurements from a beam test rig. An attempt has also been made to apply them to vibration signals from a single-stage spur gear test rig. The method based on the real cyclic cepstrum is considered to have great potential to reconstruct the forcing functions from vibration signals measured from multi-stage gearboxes. [ABSTRACT FROM AUTHOR]

One significant fact familiar to the signal processing-based diagnostic community but generally ignored by the transfer learning-based diagnostic community is that the cyclostationarity of the monitored signal conveys the actual diagnostic information. Popular network architectures, e.g. , ResNet, and domain discrepancy metrics, e.g. , maximum mean discrepancy, in current transfer diagnostic research are generally borrowed from the transfer learning community yet do not explicitly consider machine fault physics. As Jérôme Antoni points out, signal processing and machine learning methods are not mutually exclusive but should complement each other. The current article aims to develop an interpretable domain adaptation method for transfer diagnostic tasks by simultaneously exploiting the ideas of cyclostationary signal processing and domain adaptation techniques. By taking NTScatNet as the network backbone and scattering moment distance as the domain discrepancy metric, the proposed scattering moment matching-based domain adaptation method is more interpretable and matches fault physics better than conventional deep transfer learning methods. Besides, the proposed method does not require target domain data during the training phase, thus relaxing the assumption of standard domain adaptation. The effectiveness and superiority of the proposed domain adaptation method were verified on four transfer diagnostic case studies, i.e. , transfer diagnostic across bearing specifications, transfer diagnostic across escalator roller specifications, transfer diagnostic across transducers on bearing datasets, and transfer diagnostic across transducers on the gearbox datasets. [ABSTRACT FROM AUTHOR]

Abstract The problem of spectrum sensing in multiple-input multiple-output (MIMO) cognitive radio systems using the cyclostationarity property is considered. Since the noise is not a cyclostationary signal and the interference exhibits distinct cyclostationarity as primary user (PU) signals, spectrum sensing based on cyclostationarity is superior to traditional methods. To detect the presence of PU signals, cyclostationarity-based methods tend to use the second-order cyclostationarity property of cyclostationary signals. However, the computation of cyclostationary statistics is complicated. Thus, the complexity of conventional cyclostationary feature detection methods is challenging, especially for MIMO systems. A new improved algorithm that jointly utilizes the cyclostationarity property and the multiple antenna combining technique of MIMO systems is proposed in this paper. The proposed methods simplify the complexity of spectrum sensing and provide robust detection performance. The performance of the proposed schemes compared with conventional cyclic combining methods is evaluated via Monte-Carlo simulation. The simulation results indicate that the proposed method is preferred under some severe noise and interference presence scenarios.

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. [ABSTRACT FROM AUTHOR]

Often, the condition of a machine tool is detected indirectly in the reduced quality of manufactured parts upon visual inspection. Reliable and efficient machine tool condition monitoring is indispensable for manufacturing. Furthermore, issues affecting machine tools are closely related to pathologies associated with many other industrial electromechanical systems. An instrumentation and measurement solution for tool condition monitoring is presented in this article. A signal processing algorithm and instrumentation hardware are proposed to avoid intrusive sensor installations or modifications of the machine under test. The cyclostationary properties of machine vibration signals drive fault-detection approaches in the proposed sensing hardware and signal processing chain. A sample of end mills from an industrial facility is used to validate the tool condition monitoring system. [ABSTRACT FROM AUTHOR]

Easily and flexibly deployable ad-hoc communication networks emerging in tactical military or even civilian contexts, frequently suffer from poor synchronization due to lack of coordinating infrastructure. In addition to synchronization issues, and especially in military settings, security from the aspect of detectability is also of crucial importance. Imperfect synchronization can be dealt with by making use of Quasi-Synchronous Code Division Multiple Access (QS-CDMA), relying on Loosely Synchronous Codes to maintain orthogonality in the presence of limited time delays. Security, in terms of low probability of detection (LPD) from the standpoint of a malicious adversary, can be improved (reduced detection) by employing randomization techniques that disrupt the inherent structure of the transmitted QS-CDMA signals. This is based on the fact that QS-CDMA signals are Cyclostationary, having (almost) periodic Auto-Correlation functions (ACF) due to eminent signal periodicities (such as spreading code repetition). In this paper, we propose techniques to disturb the ACF and equivalently the Spectral Correlation function, and reduce the Degree of Cyclostationarity (DCS), our LPD measure. Specifically, we investigate randomization via 1) random per symbol time dithering and 2) random selection of spreading sequences, as well as a hybrid approach combining time dithering and code randomization. In all proposed techniques knowledge of the randomization pattern is not required at the legitimate receiver. We derive the Spectral Correlation function of the QS-CDMA signal under the proposed randomization schemes and compare it to simulations. We show through analysis and extensive numerical simulations that the proposed technique can reduce the DCS by almost two orders of magnitude. We also show that enhanced LPD can be achieved using the proposed techniques while sacrificing a part of the reduced time synchronization requirement. We further analyze the implications of the friendly receiver not knowing the randomization pattern and present results on the resulting communication performance. [ABSTRACT FROM AUTHOR]

Abstract Estimating direction of arrival (DOA) is important in a variety of practical applications. Conventional cyclostationarity-based coherent DOA estimation algorithms are not robust to non-Gaussian α-stable impulsive noise. Additionally, fractional lower-order statistics (FLOS)-based algorithms are tolerant to impulsive noise; however, they experience performance degradation for coherent signals and interference. To overcome these drawbacks, two types of fractional lower-order cyclostationarity-based subspace DOA estimation methods are proposed for coherent signals in the presence of interference and α-stable impulsive noise. The new proposed algorithms exploit the fractional lower-order cyclostationarity properties of the signals and are immune to the impulsive noise and interference. Moreover, they can provide more accurate DOA estimates of coherent signals than conventional cyclostationarity-based and FLOS-based methods. The simulation results illustrate the robustness and effectiveness of the proposed methods for coherent signals based on a comparison with traditional methods. The new algorithms can be used in the presence of a wide range of interference, Gaussian noise, and α-stable distribution impulsive noise environments.

This paper addresses the problem of direction-of-arrival (DOA) estimation for cyclostationary signals using less reception channel in comparison with the number of sensors. The system is considered to be realized by using the reception channel(s) to receive the signal reached each sensor in turn. Such simplification results in a cost reduction of the system and the effect of inconsistency among different channels are removed. However, non-synchronized sampling also makes the traditional DOA estimation algorithms ineffective. To cope with the problem, the signal models for DOA estimation using a single channel and dual channels are formulated based on signal cyclostationary, and the single channel cyclic MUSIC (SC-Cyclic-MUSIC) algorithm and the dual channels cyclic MUSIC (DC-Cyclic-MUSIC) algorithm are proposed correspondingly. This paper shows that both SC-Cyclic-MUSIC algorithm and DC-Cyclic-MUSIC algorithm work well when the switching interval is known, and a satisfied performance can also be obtained by DC-Cyclic-MUSIC algorithm when the uncertainty of the switching interval exists. Moreover, the proposed estimators are suitable for both narrow-band and wide-band signals. The computer simulations are provided to verify the effectiveness of the proposed algorithms.

Radio air interface identification provides necessary information for dynamically and efficiently exploiting the wireless radio frequency spectrum. In this study, a general machine learning framework is proposed for Global System for Mobile communications (GSM), Wideband Code Division Multiple Access (WCDMA), and Long Term Evolution (LTE) signal identification by utilizing the outputs of the spectral correlation function (SCF), fast Fourier Transform (FFT), auto-correlation function (ACF), and power spectral density (PSD) as the training inputs for the support vector machines (SVMs). In order to show the robustness and practicality of the proposed method, the performance of the classifier is investigated with respect to different fading channels by using simulation data. Various over-the-air real- world measurements are taken to show that wireless signals can be successfully distinguished from each other without any prior information while accounting for a comprehensive set of parameters such as different kernel types, number of in-phase/quadrature (I/Q) samples, training set size, or signal-to-noise ratio (SNR) values. Furthermore, the performance of the proposed classifier is compared to the existing well-known deep learning (DL) networks. The comparative performance of the proposed method is also quantified by classification confusion matrices and Precision/Recall/F1-scores. It is shown that the investigated system can be also utilized for spectrum sensing and its performance is also compared with that of cyclostationary feature detection spectrum sensing.

Spectrum scarcity is a challenging problem in wireless communications: high data rates are needed to support 5G new technologies. However, the spectrum is underutilized. To address this problem, cognitive radio (CR) is proposed to exploit the underutilized spectrum. The main requirement for the future CR networks is wideband spectrum sensing, which provides secondary users with the available frequency bands across a wide frequency range. Secondary users should fill these bands without causing interference to licensed users. Thus, new waveforms are proposed for the 5G physical layer. Generalized frequency division multiplexing (GFDM) is considered to be a contender for the 5G new physical layer. The GFDM is a block-based waveform that is suitable for fragmented spectrum scenarios and is designed to overcome the drawbacks of orthogonal frequency-division multiplexing (OFDM) used in 4G. The GFDM is the perfect candidate for 5G and CR technologies. Considering the cyclostationarity properties of modulated signals, we propose an optimized recovery method for the GFDM signals in the wideband regime. By exploiting the signal sparsity, we can recover the spectral correlation function (SCF) of the GFDM from digital samples of the GFDM taken at a sub-Nyquist rate to reduce the sampling time. Furthermore, a generalized likelihood ratio test is applied to the recovered function to detect multiple signal sources and identify the spectrum occupancy. The numerical results show that our method achieves a high probability of detection at a low signal-to-noise ratio (SNR) with robustness in terms of rate reduction in wireless networks.

In signal processing research, cyclostationarity and fractional lower-order statistics (FLOS) are two important solutions to non-stationary signals and non-Gaussian noises, respectively. In the last five years, many methodologies combining the two technologies were proposed to achieve the two tasks simultaneously. Unfortunately, these methodologies need to be based on the Shannon/Nyquist sampling theorem. As phased fractional lower-order cyclic moment (PFLOCM) theoretically cooperates with compressive signal processing (CSP), this paper studies PFLOCM to apply in CSP at sub-Nyquist sampling rates. Using this technical foundation, a complete procedure is novelly proposed to rebuild phased fractional lower-order cyclic moment spectrum (PFLOCMS), which functions as a crucial factor in signal detection, system identification, parameter estimation, and other applications. In addition, various experiments verify the performance of the proposed procedure. It is believed that this paper will have implications for non-stationary and non-Gaussian signal processing at sub-Nyquist sampling rates.

Abstract Statistically inferred time-warping functions are proposed for transforming data exhibiting irregular statistical cyclicity (ISC) into data exhibiting regular statistical cyclicity (RSC). This type of transformation enables the application of the theory of cyclostationarity (CS) and polyCS to be extended from data with RSC to data with ISC. The non-extended theory, introduced only a few decades ago, has led to the development of numerous data processing techniques/algorithms for statistical inference that outperform predecessors that are based on the theory of stationarity. So, the proposed extension to ISC data is expected to greatly broaden the already diverse applications of this theory and methodology to measurements/observations of RSC data throughout many fields of engineering and science. This extends the CS paradigm to data with inherent ISC, due to biological and other natural origins of irregular cyclicity. It also extends this paradigm to data with inherent regular cyclicity that has been rendered irregular by time warping due, for example, to sensor motion or other dynamics affecting the data. Graphical abstract ᅟ