Cyclic Autocorrelation Function Research Articles

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.

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.

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.

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.

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%.

Time-Difference-of-Arrival Estimation Algorithms by Employing Cyclostationary Property of LFM Signals

In this letter, two time-difference-of-arrival (TDOA) estimation algorithms are studied by employing the cyclostationary property of LFM signals. First, the multicycle frequency phase TDOA (MCFP-TDOA) estimation algorithm is developed by using the phase difference of the cyclic auto-correlation function of each cycle frequency, followed by an analysis on the phase ambiguity problem. By taking advantage of multiple cycle frequencies and the linear relationship between each cycle frequency, it was found to have smaller estimation error compared with the traditional cyclic phase difference (CPD) method. Second, based on the characteristics of LFM signals in the cyclic frequency domain, the spectral correlation TDOA (SC-TDOA) estimation algorithm is devised, which has good antinoise ability. The improved performances of the proposed algorithms are demonstrated through detailed theoretical analysis and simulations.

Fragmental weight-conservation combining scheme for statistical signal transmissions under fast time-varying channels

Statistical Signal Transmission (SST) is a technique based on orthogonal frequency-division multiplexing (OFDM) and adopts cyclostationary features, which can transmit extra information without additional bandwidth. However, the more complicated environment in 5G communication systems, especially the fast time-varying scenarios, will dramatically degrade the performance of the SST. In this paper, we propose a fragmental weight-conservation combining (FWCC) scheme for SST, to overcome its performance degradation under fast time-varying channels. The proposed FWCC scheme consists of three phases: 1) incise the received OFDM stream into pieces; 2) endue different weights for fine and contaminated pieces, respectively; 3) combine cyclic autocorrelation function energies of all the pieces; and 4) compute the final feature and demodulate data of SST. Through these procedures above, the detection accuracy of SST will be theoretically refined under fast time-varying channels. Such an inference is confirmed through numerical results in this paper. It is demonstrated that the BER performance of proposed scheme outperforms that of the original scheme both in ideal channel estimation conditions and in imperfect channel estimation conditions. In addition, we also find the experiential optimal weight distribution strategy for the proposed FWCC scheme, which facilitates practical applications.

Symmetric Peaks-Based Spectrum Sensing Algorithm for Detecting Modulated Signals

Cognitive radio is considered an effective solution to spectrum shortages, which has been a significant issue in the next generation of wireless communications. In this paper, we focus on spectrum sensing under a low signal-to-noise-ratio (SNR) and noise fluctuation and propose a symmetric peaks-based spectrum sensing algorithm for modulated signals. First, we analyze the characteristics of the cyclic autocorrelation function of modulated signals, and construct a detection domain for detecting primary users based on the characteristics of the cyclic autocorrelation function of primary signals. Then, we introduce the significance level factor into the spectrum sensing, and develop a symmetric peaks criterion. Following this criterion, we propose a symmetric peaks-based spectrum sensing algorithm. Finally, we give the probabilities of detection and false alarm of the spectrum sensing algorithm, discuss the effect of the significance level factor on the spectrum sensing performance, and compare the complexity of the algorithm with that of other algorithms. The spectrum sensing algorithm proposed does not require any prior knowledge of primary user signals or noise in the systems, and can sense modulated signals under very low SNR. Simulation results are provided to verify the performance of the algorithm proposed under a low SNR and noise fluctuation. Compared with the maximum and minimum eigenvalue (MME) algorithm, frequency domain autocorrelation-based (FD-AC) algorithm and statistical knowledge autocorrelation-based (SKAB) algorithm, it improves about 4 dB margin in SNR.

A comparative example of cyclostationary description of a non-stationary random process

The paper deals with cyclostationarity as a natural extension of stationarity as the key property in designing the widely-used models of random processes. The comparative example of two processes, one is wide-sense stationary and the other is wide-sense cyclostationary, is given in the paper and reveals the lack of the conventional stationary description based on one-dimensional autocorrelation functions. It is shown that two significantly different random processes appear to be characterized by exactly the same autocorrelation function while their two-dimensional autocorrelation functions provide outlook where the difference between processes of two above-mentioned classes becomes much clearer. More concise representation by expanding the two-dimensional autocorrelation function to its Fourier series where the cyclic frequency appears as the transform parameter is illustrated. The closed-form expression for the components of the cyclic autocorrelation function is also given for the random process which is an infinite pulse train made of rectangular pulses with randomly varying amplitudes.

IEEE 802.11p MAC with spectrum sensing scheme reliable for VANET using intelligent transportation system

In congested areas, enough spectrum is needed to transmit safety and non-safety messages. Spectrum Sensing with Distributed TDMA (SSD-TDMA) accesses the channel in a distributed fashion to avoid the collision and the cyclic autocorrelation function is used to detect the energy at the vehicle level for broadcast signal. All information is aggregated for making a decision for data delivery in vehicular environments. The spectrum sensing method is employed to sense broadcast signals for finding out the occupancy status of the spectrum and availability of the licensed frequency bands. The performance of spectrum sensing technique and slot allocation based on the timestamp of a vehicle entering in the RSU coverage area in distributed manner is judged at a congested city state of affairs using the ns2 simulator. The proposed approach SSD-TDMA represents an effective and warranted conversation over Vehicular Adhoc Network (VANET) measured through the reduced delay and overhead of packet constraints.

IEEE 802.11p MAC with spectrum sensing scheme reliable for VANET using the intelligent transportation system

In congested areas, enough spectrum is needed to transmit safety and non-safety messages. Spectrum Sensing with Distributed TDMA (SSD-TDMA) accesses the channel in a distributed fashion to avoid the collision and the cyclic autocorrelation function is used to detect the energy at the vehicle level for broadcast signal. All information is aggregated for making a decision for data delivery in vehicular environments. The spectrum sensing method is employed to sense broadcast signals for finding out the occupancy status of the spectrum and availability of the licensed frequency bands. The performance of spectrum sensing technique and slot allocation based on the timestamp of a vehicle entering in the RSU coverage area in distributed manner is judged at a congested city state of affairs using the ns2 simulator. The proposed approach SSD-TDMA represents an effective and warranted conversation over Vehicular Adhoc Network (VANET) measured through the reduced delay and overhead of packet constraints.

Automatic Modulation Classification Architectures Based on Cyclostationary Features in Impulsive Environments

Cyclostationary analysis has several applications in communications, e.g., spectral sensing, signal parameter estimation, and modulation classification. Most of them consider the additive white Gaussian noise (AWGN) channel model, although wireless communication systems may also be subject to non-Gaussian interference and impulsive noise. In this context, the communication channel can be better modeled by heavy-tailed distributions, such as the non-Gaussian alpha-stable one. Some applications of the cyclostationary approach based on the spatial sign cyclic correlation function (SSCCF), fractional lower-order cyclic autocorrelation function (FLOCAF), and cyclic correntropy function (CCF) demonstrate that these are promising solutions for the analysis of signals in the presence of impulsive non-Gaussian noise. However, the investigation of functions above applied to digital modulation recognition in impulsive environments, and the comparison among them are topics that did not adequately explore yet. This work demonstrates that SSCCF is a particular case of the FLOCAF. Besides, a detailed analysis of the use of the FLOCAF and CCF is presented to obtain cyclostationary descriptors for the recognition of digital modulations BPSK, QPSK, 8-QAM, 16-QAM, and 32-QAM. Automatic modulation classification (AMC) architectures, based on the functions mentioned above, are also proposed. Besides, another contribution showed is that both the FLOCAF and CCF allow the symbol rate parameter estimation. The performances of AMC architectures were evaluated in the scenario with modulated signals contaminated with additive non-Gaussian alpha-stable noise. The results demonstrate that both architectures can classify signals in different contamination scenarios. However, the architecture based on the CCF is more efficient than the FLOCAF-based one.

Multiple Cycle Frequencies Estimation Under Cochannel Interference

In this letter, two cycle frequencies estimation algorithms are proposed to estimate the number of weak cyclostationary signals and their cycle frequencies in the presence of higher power interferer signal. Both cycle frequencies estimation algorithms are eigenanalysis-based methods that use the cyclic autocorrelation function of the received signals. In particular, a new eigen-analysis cyclic null spectrum is introduced to determine the number of cyclostationary signals and estimate their cycle frequencies. The performances of the proposed cycle frequency estimation algorithms are demonstrated with numerical examples and compared with the existing cycle frequency estimation algorithms. It is shown that both the proposed cycle frequencies estimation algorithms have better accuracy than the existing methods and could work with small sample size for faster estimation.

Characterization of cavitation and seal damage during pump operation by vibration and motor current signal spectra

Cyclic spectral analysis is conducted to extract the frequency characteristic components from nonstationary current signals under cavitation and seal damage conditions as indicators of fault characterization. Specifically, vibration and current signals are both acquired and pre-processed by envelope extraction and singular value decomposition methods, respectively. Since there are more noise waves in vibration power spectral density spectra in comparison with current signals, the cyclic spectral analysis is conducted for the current signal analysis. Cyclic autocorrelation functions of signals are firstly calculated then corresponding slices are extracted from the cyclic autocorrelation functions and processed by fast Fourier transform method. Consequently from the spectra, indicators for characterization are extracted to demonstrate the occurrence and severity of faults. Results show that the rotating frequency component shows obvious tendency as the flow rate deviates from the designed point without any faults. The indicators for seal damage characterization are 250 Hz and 350 Hz frequency components related with rotating frequency and blade passing frequency in the current signals. Meanwhile, the occurrence and development status of cavitation are indicated by the frequency component of 100 Hz in the slice spectra of cyclic autocorrelation functions. Additionally, the effect of instability caused by off-design, seal damage, as well as cavitation operation conditions is distinguished by cyclic spectral analysis. Characteristic components are innovatively extracted at specific frequencies to avoid the effect from modulated and noise components in the current signals. And the results about the recognition of different types of faults could provide important evidences for fault detection during pump operation.

Cyclic Spectral Analysis of Vibration Signals for Centrifugal Pump Fault Characterization

Seal damage and cavitation are common faults during centrifugal pump operation. The characterization and recognition of these faults are investigated in this paper to improve the efficiency and reliability of pumps. A time-frequency signal analysis method based on the cyclostationary theory is adopted to extract the frequency characteristic components from non-stationary vibration signals under cavitation and seal damage conditions. Specifically, the signal analysis was conducted preliminarily based on the calculation of cyclic autocorrelation functions (CAFs) for various signals. Corresponding slices are extracted from the CAFs and processed by fast Fourier transform (FFT) method. Consequently from the FFT spectra, indicators for characterization are extracted to demonstrate the occurrence and severity of faults. Results show that the indicators for seal damage characterization are 100 and 600-Hz frequency components in slice $\alpha =600$ Hz of CAF corresponding to shaft and blade passing frequency in the frequency domain of vibration signals. Meanwhile, the occurrence and development status of cavitation are indicated by the frequency component of 200 Hz in slice $\alpha =600$ Hz of CAF. Additionally, the effect of instability caused by off-design, seal damage, and cavitation operation conditions are distinguished by cyclic spectra analysis. Characteristic components are innovatively extracted at specific frequencies to avoid the effect from modulated and noise components in vibration signals. And the results about recognition of different types of faults could provide important evidences for fault detection during pump operation.

Performance of Hybrid Sensing Method in Environment with Noise Uncertainty

The paper presents a novel hybrid spectrum sensing method used in cognitive radio and presents a hybrid detector (HD) which improves the sensing performance. The proposed HD takes advantage of the energy detection (ED) principle and a method based on Covariance Absolute Value (CAV), as well as on Cyclic Autocorrelation Function (CAF). The paper shows the limitations of using ED, resulting from the uncertainty of spectral density of noise power estimation, known as the SNR wall. The paper describes a system model and presents simulation results for the OFDM signal of a WiMAX-based communications system. The simulation results refer to an ideal environment with well-known parameters, and to an environment with uncertain spectral density of noise power estimation.

The Influence of Noise Uncertainty and SNR Wall on the Performance of Hybrid Sensing Method

The paper discusses the hybrid sensing method and presents the hybrid detector (HD) which improves the sensing performance. The proposed HD takes advantage of the energy detection (ED) and a method based on the Covariance Absolute Value (CAV) or Cyclic Autocorrelation Function (CAF). The paper chara