Autocorrelation Function Of Signal Research Articles

A Synchronization Algorithm for MBOC Signal Based on Reconstructed Correlation Function

In order to address the ambiguous synchronization problem caused by the multi-peak nature of the autocorrelation function of the modulated signal of the Multiplexed Binary Offset Carrier (MBOC) in the Global Navigation Satellite System (GNSS), a new synchronization algorithm for MBOC signals is presented in this paper, which uses a reconstruction correlation function to effectively handle synchronization ambiguities associated with multi-peak signals. The paper proposes an algorithm for reconstructing the correlation function of the MBOC signal by analyzing its characteristics. The algorithm generates three local auxiliary signals, namely, pseudo-random codes (PRN), BOC(1,1) signals, and MBOC signals, which are correlated with the received signal. By combining the three correlation functions, the algorithm produces a reconstructed correlation function based on reconstruction rules, eliminating side peaks and achieving unambiguous synchronization. Simulation results show that the proposed algorithm in this paper eliminates all side peaks while maintaining a high detection probability, and its deblurring capability is optimal compared to other algorithms. In addition, the discriminant curve shows that the algorithm in this paper successfully eliminates all the mis-locked points, and the slope gain is improved by more than 2.5 dB compared with other algorithms, and the anti-multipath performance of the algorithm in this paper is better than that of other traditional algorithms, such as ASPeCT (Autocorrelation Side-Peak Cancellation Technique).

High covertness camouflage covert underwater acoustic communication based on masking technique

In marine military operations, it is very important to ensure the safe transmission of underwater information, so it is urgent to improve the covertness of underwater communication. In order to meet the requirement of high covertness in underwater acoustic communication, according to the natural characteristics of superimposed interference of marine ambient noise, a high covertness camouflage covert underwater acoustic communication (CUWAC) method based on masking technique using ship-radiated noise as communication carrier is proposed in this paper. This method leverages innovative audio digital technology to embed information into the DCT domain of ship-radiated noise, creating a disguised signal that is hard to detect, thereby significantly enhancing stealth without compromising communication effectiveness. In order to improve the demodulation performance of this camouflage CUWAC, this paper proposes a variable step size p-norm-like LMP sparse adaptive filtering algorithm to offset the interference of the masking signal at the receiving end. This adaptive filtering algorithm is based on the improved modified Gaussian function to construct step size. Furthermore, it introduces the error signal autocorrelation function to adjust the step size and zero-attracting term dynamically. The proposed adaptive filtering algorithm obtains excellent anti-noise performance. Through a series of simulation experiments, this paper not only validates the feasibility of the CUWAC method but also demonstrates its stability and reliability under various marine environmental conditions, providing robust theoretical support for practical applications, proving its efficiency and reliability in complex marine environments.

METHOD OF MINIMIZATION SIDELOBES LEVEL AUTOCORRELATION FUNCTIONS OF SIGNALS WITH NON-LINEAR FREQUENCY MODULATION

Context. At present, when creating new and upgrading existing radar systems, solid-state generator devices are widely used, which imposes certain restrictions on the peak power of probing signals. To overcome this limitation, longer duration signals with internal pulse modulation are used. The main efforts of the researchers are focused on reducing the maximum level of the side lobes of the autocorrelation function of such signals, which, without taking additional measures, has a significant level, which complicates the work of systems for detecting and stabilizing the level of false alarms. Attention is paid to signals with non-linear frequency modulation, which consist of two and three linearly frequency-modulated fragments. The maximum level of the side lobes of such signals depends significantly on the frequency-time parameters of the fragments, and therefore it is very difficult to obtain its stable value. Searching for signals with minimal side lobe level values by optimizing their time-frequency parameters is a difficult task, because changing the parameters of previous signal fragments leads to changes in the parameters of subsequent fragments
 Objective. The aim of the work is to develop a method for simplifying the search for local minima of the level of side lobes of two- and three-fragment signals with nonlinear frequency modulation by using a modified mathematical model with a whole number of periods of radio oscillations of linear-frequency modulated fragments.
 Method. The developed method is based on the proposed modification of the mathematical model, which corrects the frequencytime parameters of two- and three-fragment signals with non-linear frequency modulation by modifying the values of the frequency modulation speed while providing an integer number of complete periods of radio frequency oscillations for each of the fragments, which simplifies the process of finding local minima of the level of side lobes.
 Results. Modification of the initial mathematical model leads to the expansion of the possible range of values of frequency-time parameters, ratios of durations and frequency deviations of linearly-frequency modulated fragments and ensures stability of the mathematical model with a decrease in the maximum level of side lobes of the autocorrelation function.
 Conclusions. It has been experimentally confirmed that the use of the proposed method of modifying the input frequency-time parameters of signals with non-linear frequency modulation in the vast majority of cases reduces the maximum level of side lobes and simpli-fies the process of finding its local minima. The optimal ratios of durations and deviations of the frequency of the signal frag-ments are determined, subject to these, stable operation of the models is ensured and, in most cases, - less than the value of the maximum level of the side lobes.

Effective reduction of sidelobes in pulse compression radars using NLFM signal processing approaches

Pulse compression techniques are widely used in modern radar systems to enhance range resolution and detection capability. As signal design is one of the basic factors of an efficient radar system, the problem of designing a radar signal with good characteristics using pulse compression is addressed in this paper. A linear frequency modulated (LFM) waveform has been widely used for conventional radars. However, it has a higher sidelobe level which makes the detection of weak targets very difficult in presence of strong targets returns and as a result the problem of masking occurs. In order to get suppressed sidelobes of radar matched filter output as well as preserve the main lobe resolution and level to overcome the problem of masking, nonlinear frequency modulated (NLFM) signals are used in modern radars. In this paper, we will introduce two different approaches to design an optimized NLFM signal which is characterized by optimized sidelobe level (SLL). The first is the exponential piecewise linear function (EPWL) which is the modification of piecewise linear (PWL) functions relying on an exponential predistortioning function. The second is the odd-term polynomial approximation (OTPA) in which the generation of NLFM signal depends only on odd-powered terms of the polynomial function. Furthermore, the simulation results of autocorrelation functions (ACF) of the proposed signals show its superiority over the traditional LFM signals and significantly enhancement compared to the recent background work. The Doppler sensitivity of the designed signals has been evaluated, revealing that the first approach offers Doppler tolerance and is suitable for surveillance radar systems, while the second approach with a lower sidelobe level is used in applications such as Synthetic Aperture Radar (SAR). Finally, the ambiguity function of the designed signals has been measured to illustrate the effect of the Doppler effect relative to different velocities.

Dual-use baseband signal design for RadCom with position index and phase modulation

This paper deals with the synthesis of dual-use signal to simultaneously achieve detection and communication for a dual-function radar communication (DFRC) system. A new position index and phase (PIP) modulation is proposed for information embedding, where position index modulation is realized by selecting the information embedding subpulses (InSp) positions. Moreover, differential phase modulation is utilized to distinguish InSp from other available subpulses. As for radar detectability, peak sidelobes level (PSL) of signal auto-correlation function is minimized. Meanwhile, constant-envelope and phases constraints are forced to ensure compatibility with the current hardware technique and modulation demand, respectively. To tackle the resulting nonconvex and NP-hard optimization problem, a spectral majorization-minimization (SM) dual-use baseband signal design method is proposed. In each iteration, the original problem is approximated by a tractable problem with a closed-form solution. Finally, simulation and semi-physical experimental results demonstrate the designed dual-use signal is capable of realizing high data rate communication and ensuring acceptable radar performance.

Time-Resolved Hanbury Brown–Twiss Interferometry of On-Chip Biphoton Frequency Combs Using Vernier Phase Modulation

Biphoton frequency combs (BFCs) are promising quantum sources for large-scale and high-dimensional quantum information and networking systems. In this context, the spectral purity of individual frequency bins will be critical for realizing quantum networking protocols like teleportation and entanglement swapping. Measurement of the temporal autocorrelation function of the unheralded signal or idler photons comprising the BFC is a key tool for characterizing their spectral purity and in turn verifying the utility of the biphoton state for networking protocols. Yet the experimentally obtainable precision for measuring BFC correlation functions is often severely limited by detector jitter. The fine temporal features in the correlation function---not only of practical value in quantum information, but also of fundamental interest in the study of quantum optics---are lost as a result. We propose a scheme to circumvent this challenge through electro-optic phase modulation, experimentally demonstrating time-resolved Hanbury Brown--Twiss characterization of BFCs generated from an integrated 40.5-GHz ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ microring, up to a $3\ifmmode\times\else\texttimes\fi{}3$-dimensional two-qutrit Hilbert space. Through slight detuning of the electro-optic drive frequency from the comb's free spectral range, our approach leverages Vernier principles to magnify temporal features, which would otherwise be averaged out by detector jitter. We demonstrate our approach under both continuous-wave and pulsed-pumping regimes, finding excellent agreement with theory. Our method reveals not only the collective statistics of the contributing frequency bins but also their temporal shapes---features lost in standard fully integrated autocorrelation measurements.

Optimized weights spectrum autocorrelation: A new and promising method for fault characteristic frequency identification for rotating Machine fault diagnosis

Since fault characteristic frequencies (FCFs) and their harmonics are closely connected with specific fault types of rotating machines, identification of FCFs and their harmonics is a very crucial step for signal processing-based rotating machine fault diagnosis. Nowadays, Hilbert transform (HT) based square envelope spectrum (SES) and spectral coherence (SC) based SES are two main tools for FCF identification. Since the HT demodulates signals by calculating envelope signals in the time domain and the SC is based on the temporal instantaneous autocorrelation function of demodulated signals, the temporal waveform of a demodulated signal must be purified by using fault signature extraction methods, e.g., fast kurtogram, blind deconvolution, and their variants, etc. However, it has been extensively reported that these fault signature extraction methods are prone to be affected by interference components such as impulsive noise. Unlike the HT and SC which demodulate from the time domain, this paper aims to demodulate signals from the frequency domain to identify FCFs and their harmonics for rotating machine fault diagnosis. Firstly, it is demonstrated that Fourier spectrum autocorrelation is possible to indicate FCFs and their harmonics. Nevertheless, a troublesome problem is that interference spectral lines and noise spectral lines of real-world signals in the frequency domain will severely affect the performance of the Fourier spectrum autocorrelation. To solve such problem, this paper introduces a recently developed optimized weights spectrum (OWS) and innovatively designs an adaptive threshold method to respectively eliminate an influence of interference spectral lines and noise spectral lines. Thus, a new FCF identification method named optimized weights spectrum autocorrelation (OWSAC) is accordingly proposed. One main merit of the proposed OWSAC is that it does not need any fault signature extraction methods to do signal preprocessing. Two experimental case studies respectively on incipient bearing and gearbox diagnosis validate the effectiveness of the proposed OWSAC. The proposed OWSAC can achieve satisfactory performance respectively in two case studies and it is superior to five methods including HT-based SES, SC-based SES, optimized SES, fast kurtogram guided SES, and Fourier spectrum autocorrelation.

STATISTICAL CHARACTERISTICS OF TWO-DIMENSIONAL AUTOCORRELATION FUNCTIONS IN NOISE-LIKE COMPLEX SIGNALS

For various terrestrial and satellite radio systems, the task of detecting complex signals under conditions of a priori uncertainty, when their parameters, including the modulation law, is unknown, is relevant. Detection of such signals can be combined with estimation (measurement) of their parameters, such as carrier frequency and delay time. A method for calculating two-dimensional autocorrelation functions of noise-like complex signals has been developed and their types have been studied depending on the type of pseudo-random sequences on the basis of which they are formed, as well as the modes of emission of these signals in radio systems. Regularities have been revealed in the statistical characteristics of side peaks of various types of complex signals depending on the length of pseudo-random sequences and radiation modes. The developed methodology for calculating the two-dimensional correlation function of complex signals made it possible to identify the relationship between the values of the side peaks of the correlation functions of pseudo-random sequences used in their formation and the peaks of the modules of their two-dimensional correlation function. This approach allows, without a detailed calculation of the two-dimensional correlation functions themselves in various modes of emission of complex signals, to determine their statistical characteristics using the corresponding parameters of the distribution functions of the side peaks of the correlation functions. The two-dimensional correlation function of various complex signals was calculated and their statistical characteristics were studied.

Experiments on direct chaotic differentially coherent data transmission in a wired communication channel

Methods of differentially coherent information transmission using noise signals are of interest because of the impossibility of implementing the known methods of correlation reception for such signals. With a potentially higher noise immunity compared to the methods of information transmission based on chaotic synchronization, however, they have a feature that does not allow transceivers to be implemented in practice. The transmitter and receiver of the scheme, based on already known methods of differentially coherent transmission, require a time delay comparable to the duration of the transmitted bits. With an analog implementation of the scheme this leads to a physical length of the delay line of tens of meters or more. Previously, the authors proposed and studied a differentially coherent transmission scheme in which there are no long delays. In this scheme, the duration of delays in the transmitter and receiver is determined not by the duration of the bit, but by the decay time of the autocorrelation function of the chaotic signal. Purpose of this work is to experimentally demonstrate the possibility of physical implementation of a direct-chaotic differentially coherent information transmission scheme in a wired communication channel. Methods. For this, a layout of the communication scheme, transmitting a binary data stream in the frequency range from 200 to 500 MHz, was designed and assembled. The layout is an ultrawideband differentially coherent transmitter and receiver connected via a wired channel. Results of the experiment are in full agreement with the previously obtained results of the analytical evaluations, as well as with the data of computer simulation. Conclusion. In the course of the research, a transceiver layout of a differentially coherent ultra-wideband direct chaotic communication scheme was developed, designed and manufactured. For the first time, experiments on the transmission of digital information were carried out on it, and thereby the practical feasibility and operability of the proposed direct chaotic differentially coherent transmission scheme were proved.

Dual High Resolution Correlators for Multipath Mitigation in BOC Signals

Multipath is a dominant source of positioning errors in global navigation satellite system receivers. It is difficult to design multipath mitigation techniques for binary offset carrier (BOC) signals due to the complicated autocorrelation function of BOC signals and localized variations of multipath. In this paper, a dual high resolution correlators (DHRC) technique is proposed for BOC signals to mitigate code and subcarrier multipath errors, as well as the carrier multipath error that is neglected by common techniques. Based on the concept of dual binary phase-shift keying (BPSK) tracking, the BOC signal is decomposed into two BPSK signals located in the upper and lower sidebands, respectively, thereby transforming the multipath mitigation in the BOC signal into the multipath mitigation in the upper and lower sidebands. Two narrow correlation functions of the upper and lower sidebands are synthesized using multiple correlation values, so the multipath outside the main peak of the synthesized correlation function is eliminated. The peak value of the synthesized correlation function is reduced from the original ACF, resulting in a large noise error. Therefore, a complementary filter is designed to compensate the noise error. Theoretical analysis and simulation results demonstrate that the DHRC technique with complementary filters can significantly mitigate multipath errors for BOC signals with slight thermal noise performance loss.

Pseudo-Passive Time-of-Flight Imaging: Simultaneous Illumination, Communication, and 3D Sensing

The 3D time-of-flight (ToF) cameras have recently received a lot of attention due to their wide range of applications. Despite remarkable advancements in ToF imaging, state-of-the-art ToF cameras are still afflicted by the power hungriness of their illumination sources. To tackle this problem, we exploited existing lighting infrastructure, which ensures the ubiquitous presence of modulated light sources in indoor spaces that serve as opportunity illuminators. We explored the bistatic geometry for passive imaging using the pulse-based ToF approach. Our work is inspired by the recently introduced visible light communication (VLC) or light-fidelity (Li-Fi) infrastructure. VLC allows the infrastructure to provide indoor simultaneous illumination, communication, and sensing (SICS). To this end, we designed a bistatic geometry for the purpose of attaining passive 3D imaging. Such capabilities are achieved by exploiting the pulse shape of the autocorrelation function of real optical signals generated by VLC/Li-Fi modules (e.g., OpenVLC and LiFiMAX). We demonstrated passive imaging by means of matched filtering. In this work, we also studied different sampling strategies in the time-shift domain, including uniform, random, and sparse rulers, which is another step forward toward preserving high depth accuracy with a minimal number of measurements. The proposed methodology achieved successful depth reconstruction with negligible root-mean-square error (RMSE) for the low signal-to-noise ratio (SNR) of the measurements. Parametric models, such as Gaussian and sum of sines, are used to characterize the cross correlation functions and allow for robust parametric depth retrieval from a few measurements. Moreover, we attained a 20-mm worst case error for a target at 25 cm. The experiment proved that the bistatic passive depth reconstruction is feasible.

Stride-to-stride time intervals are independently affected by the temporal pattern and probability distribution of visual cues

The temporal structure of the variability of the stride-to-stride time intervals during paced walking is affected by the underlying autocorrelation function (ACF) of the pacing signal. This effect could be accounted for by differences in the underlying probability distribution function (PDF) of the pacing signal. We investigated the isolated and combined effect of the ACF and PDF of the pacing signals on the temporal structure of the stride-to-stride time intervals during visually guided paced overground walking. Ten young, healthy participants completed four walking trials while synchronizing their footstep to a visual pacing signal with a temporal pattern of either pink or white noise (different ACF) and either a Gaussian or normal probability distribution (different PDF). The scaling exponent from the Detrended Fluctuation Analysis was used to quantify the temporal structure of the stride-to-stride time intervals. The ACF and PDF of the pacing signals had independent effects on the scaling exponent of the stride-to-stride time intervals. The scaling exponent was higher during the pink noise pacing trials compared to the white noise pacing trials and higher during the trials with the Gaussian probability distribution compared to the uniform distribution. The results suggest that the sensorimotor system in healthy young individuals has an affinity towards external cues with a pink noise pattern and a Gaussian probability distribution during paced walking.

Bubble Behaviors in a Dense Gas‐Solids Fluidized Bed: Analysis of Pressure Fluctuation

AbstractThe pressure signals were analyzed by time‐domain and frequency‐domain methods, including standard deviation, autocorrelation function, and power spectral density function, to investigate the bubble behavior and determine the regime transition. Results indicated that the autocorrelation function of pressure signals derived from bubbles was periodic fluctuation. The periodic nature of the autocorrelation function disappeared and the dominant frequency increased when the transition from bubbling to the turbulent regime occurred. The decrease of static bed height facilitated the explosion of bubbles, which accelerated the transition from the bubbling to the turbulent regime. The fluidization index was used as an indicator for the bubble state in the dense fluidized bed.

Maximum average impulse energy ratio deconvolution and its application for periodic fault impulses enhancement of rolling bearing

Periodic fault impulses, inevitably occurring along with a localized defect, are crucial for incipient fault diagnosis of rotating machinery. Whereas, they are awfully weak and masked by other interferences in industrial applications. Blind deconvolution methods (BDMs) are diffusely used in enhancing periodic fault impulses submerged in vibration signals. Due to some drawbacks, the applications of traditional BDMs are restricted. Therefore, the maximum average impulse energy ratio deconvolution (MAIERD) method is proposed, where the maximization of a new index called average impulse energy ratio (AIER) is tailored as the objective function. AIER takes the sampling point with the largest amplitude in every fault period as the location of fault impulse. Also, the fault period is detected by the autocorrelation function of the envelope signal. Furthermore, the Morlet wavelet is appointed as the initial filter. The synthesized signals and experimental data collected from two different rolling bearing test rigs are processed for verification. The results show that the proposed MAIERD method is superior in enhancing periodic fault impulses compared with five popular deconvolution methods.

The study of the vibration under different lubrication states based on Stribeck curve

The tribology system is a complex nonlinear dynamical system. To study the vibration under different lubrication states, the experiments on full-film lubrication state and mixed lubrication state are designed based on Stribeck curve. In full-film lubrication state, vibration signal energy does not increase, but in mixed lubrication state, vibration signal energy increases with the increase of loading force. Under the condition of full-film lubrication, the autocorrelation function of vibration signal is similar to that of noise signal, which has smooth characteristics. In mixed lubrication state, the autocorrelation function of vibration signals has the characteristics of narrow convergence. Results reflect that for smaller loads there are no friction-induced vibrations due to full-film lubrication and for higher loads the friction-induced vibration comes into existence as the rough peaks between pin and disk surfaces come into play.

Correlation Technologies for Emerging Wireless Applications

In this article, we introduce correlation technologies both at RF/mmWave and baseband frequencies. At RF and mmWave frequencies, power-spectra and energy-spectra metrics are introduced for measuring the power-density of mobile devices and systems. New ASIC-embedded smart connectors are developed for bringing correlation-based signal processing close to antenna modules. At baseband frequencies, DSP-based convolutional accelerators are proposed for fast and accurate measurement of EVM (error vector magnitude) using correlation technologies. Porting of the DSP-based convolutional accelerators into advanced fully depleted silicon-on-insulator (FDSOI)-based ASIC platforms for co-integration with adaptive RF/mmWave front-end modules will enable real-time extraction of auto-correlation and cross-correlation functions of stochastic signals. Perspectives for optically synchronized interferometric-correlation technologies are drawn for accurate measurements in noisy environments of stochastic EM fields using power-spectra and energy-spectra metrics. Adoption of correlation technologies will foster new paradigms relative to interactions of humans with smart devices and systems in randomly fluctuating environments. The resulting new paradigms will open new possibilities in communication theory for properly combining and reconciling information signal theory (Shannon information-based entropy) and physical information theory (statistical-physics-based entropy) into a unified framework.

Autocorrelation functions of navigation signals with meander modulation at two subcarrier frequencies

Autocorrelation functions of navigation signals with meander modulation at two subcarrier frequencies

Weak Signal Detection Based on Lifting Wavelet Threshold Denoising and Multi-Layer Autocorrelation Method

To solve the problem that the weak signal is difficult to detect under a strong background noise, a detection method based on lifting wavelet threshold denoising and multi-layer autocorrelation method is proposed. Firstly, the original signal is denoised by lifting wavelet threshold to improve the signal-to-noise ratio. Secondly, the multi-layer autocorrelation function of the noise-reconstructed signal is calculated, and its time-frequency signature are analyzed. Finally, the combined algorithm is used on weak signals with low signal-to-noise ratio to extract weak signal features. Simulation and experimental results demonstrate that the proposed method can detect weak signal features buried in the heavy noise effectively. The proposed method is compared with the traditional noise reduction method, which reflects its effectiveness and superiority.

Effects of Timing Noise on Square-Wave Optoelectronic Oscillators

Optoelectronic oscillators produce microwave-modulated optical beams without external modulation. The most commonly studied types produces narrow-band output, i.e., optical output modulated by a sinusoid, in which case phase noise determines key figures of merit that limit device performance. Nonetheless, other types of modulated signals have been exhibited by optoelectronic oscillators, including square waves. In this work we provide a theoretical treatment of the power spectral density of a microwave self-modulated optical periodic, but non-sinusoidal, oscillator in the presence of timing noise (as phase noise is only defined for a single sinusoid) and focus on the case of square waves. We consider the effects of timing noise on the power spectral density and autocorrelation function of the modulation signal.

A Novel Blind Deconvolution Method with Adaptive Period Estimation Technique and Its Application to Fault Feature Enhancement of Bearing

Minimum correlated generalized Lp/Lq deconvolution (MCG-Lp/Lq-D) is an important tool to detect periodic impulses in vibration mixture. It is proved to be a more stable technique than maximum correlated kurtosis deconvolution (MCKD) to recover the fault impulse under strong noise conditions. However, MCG-Lp/Lq-D still has limitations. One of the necessary conditions for the success of MCG-Lp/Lq-D is to provide a precise period of fault. An imprecise prior period will lead to performance degradation or even failure of the method. Therefore, in this paper, a MCG-Lp/Lq-D with adaptive fault period estimation capability is proposed, adaptive minimum correlated generalized Lp/Lq deconvolution (AMCG-Lp/Lq-D). The proposed method uses the autocorrelation function of envelope signal to estimate the fault period adaptively in each iteration and then takes the estimated period as the input parameter of MCG-Lp/Lq-D for the next iteration optimization. The proposed method does not require precise prior fault period input, which greatly improves the fault recovery accuracy and application range of MCG-Lp/Lq-D. Eventually, simulated and experimental data verify the effectiveness and superiority of AMCG-Lp/Lq-D.