Cross-correlation Peak Research Articles

MIMO radar sequence design with constant envelope and low correlation side-lobe levels

Transmit sequence design plays a significant role in multiple-input multiple-output (MIMO) radar to suppress correlation function side-lobe levels. This paper investigates two practical constraints, namely, constant envelope constraint to reduce the effect of nonlinear amplifiers, and low side-lobe levels to reduce the effect of interference among various transmitting sequences. To facilitate this, new Legendre sequences (L-seq) are designed that uses Legendre orthogonal polynomial (LOP). Superiority of the proposed L-seq is proven for peak side-lobe level (PSL) and cross-correlation level (CCL) performance parameters. Further, the signal cross-interference in MIMO radar is minimized by generating orthogonal L-seq. The impact of designed L-seq on the delay-Doppler plane is observed using the ambiguity function (AF). Simulation results show that the proposed L-seq has a constant envelope and suppressed side-lobe levels compared to the existing popular methods.

Radar waveform diversity using nonlinear chirp with improved sidelobe level performance

Radar system with high range-resolution can be obtained through discrete frequency-coding waveform (DFCW). In this paper, we investigate the design process of DFCW using nonlinear chirp (DFCW-NLC), with improved autocorrelation sidelobe peak (ASP) and cross-correlation peak (CCP) levels, to attain radar waveform diversity. In this context, we present a parameterized waveform design model and derive NLC functions for designing the required NLC waveform, thereby simplifying the waveform design process. We derive analytical expressions of autocorrelation and cross-correlation functions for the NLC waveform. To achieve a waveform with desired properties, we present an optimization process based on genetic algorithm, and the optimization of parameterized NLC waveforms attains improved ASP performance over existing designs. Subsequently, we propose the design of a set of DFCW-NLC, double the number as compared to the reported designs. We derive analytical expressions of ambiguity function to investigate waveform performance. We perform a joint optimization of frequency hopping sequence and associated chirp-pulse type of the DFCW-NLC. Numerical results prove that the designed DFCWs-NLC achieve significant improvement in ASP and CCP levels of ≈5.0 dB and ≈5.47 dB, respectively in comparison with the state-of-the-art designs, and makes the proposed waveforms a superior candidate for multiple-input-multiple-output (MIMO) and multiuser radar applications.

Discrete stationary wavelet transform and SVD-based digital image watermarking for improved security

Digital image watermarking plays an important role in digital content protection and security related applications. Embedding watermark is helpful to identify the copyright of an image or ownership of the digital multimedia content. Both the grey images and colour images are used in digital image watermarking. In this work, discrete stationary wavelet transform and singular value decomposition (SVD) are used to embed watermark into an image. One colour image and one watermark image are considered here for watermarking. Three level wavelet decomposition and SVD are applied and watermarked image is tested under various attacks such as noise attacks, filtering attacks and geometric transformations. The proposed work exhibits good robustness against these attacks and obtained simulation results show that proposed approach is better than the existing methods in terms of bit error rate, normalised cross correlation coefficient and peak signal to noise ratio.

Automated structural dynamic modelling using model-free health monitoring results

Structural health monitoring (SHM) methods provide damage metrics and localisation, but not a means of answering subsequent questions concerning immediate or long-term damage mitigation, risk, or safety in re-occupancy. Models based on the SHM results would provide a means to test these issues, but typically require extensive human input, which is not available immediately after an event to enhance and optimise immediate decision-making. This work presents a simple, readily automated modelling approach to translate SHM results from the proven hysteresis loop analysis (HLA) method into foundation models for immediate use. Experimental data from a 3-storey structure tested at the E-Defense facility in Japan are used to assess model performance. The model’s ability to capture the essential dynamics is assessed by comparing peak dynamic displacement and cross correlation coefficient (Rcoeff). For all 6 events, 3 storeys, and 2 directions, median (5-95% Range) of peak displacement error was 0.82 (0.17, 4.09) mm, and average Rcoeff = 0.82, all of which were significantly improved if the worst event was excluded. Overall, accurate nonlinear, time-varying baseline models were created using data from SHM damage identification and localisation methods using relatively quite simple model structures. The method is readily automated via algorithm, and the models were suitable for initial investigation and analysis on safety, damage mitigation, and thus re-occupancy. Such models could take SHM from being a tool for damage identification and extend it into further decision-making, creating far greater utility for engineers and owners, which could further spur impetus for investment in monitoring.

Bandwidth-Enhanced Quasi-Distributed Acoustic Sensing With Interleaved Chirped Pulses

In this letter, to break through the response bandwidth limit of quasi-distributed acoustic sensing system, a novel interleaved chirped pulses (ICP) approach is proposed on the basis of pulse compression ${\Phi }$ -OTDR with coherent detection. As shown in the theoretical analysis, for ultra-weak fiber Bragg grating (UWFBG) array with fixed positions and intervals, the space between any two FBGs can be used to multiplex probing pulses, without occupying extra detection bandwidth. The cross-correlation peak of probe pulses can be separated from each other in the time domain with matched filtering. By injecting probe pulses which are evenly interleaved as positive-chirped and negative-chirped, crosstalk of the cross-correlation peaks can be suppressed. In the proof-of-principle experiment, the response bandwidth is 3 times as that of the traditional single pulse probing scheme, all with the same detection bandwidth; 860 m sensing range with 166.4 kHz response bandwidth has been achieved, with 5 m spatial resolution and 1.8 p ${\varepsilon /\sqrt {Hz}}$ strain sensitivity.

Generations of chaos-modulated pulses based on a gain-switched semiconductor laser subject to delay-synchronized optical feedback for pulsed chaos lidar applications.

We generate and analyze chaos-modulated pulses based on a gain-switched semiconductor laser subject to delay-synchronized optical feedback for pulsed chaos lidar applications. Benefited by the aperiodic and uncorrelated chaos waveforms, chaos lidar possesses the advantages of no range ambiguity and immunity to interference and jamming. To improve the detection range while in compliance with the eye-safe regulation, generating chaos-modulated pulses with higher peak power rather than chaos in its CW form is desired. While using an acousto-optic modulator to time-gate the CW chaos into pulses could be lossy and energy inefficient, in this paper, we study the generation of chaos-modulated pulses using a gain-switched laser subject to delay-synchronized optical feedback. Under different feedback strengths and modulation currents of gain-switching, we investigate the quality of the chaos-modulated pulses generated by analyzing their ratio of chaos oscillations, peak sidelobe levels (PSLs), and cross-correlation peaks under different mismatching conditions between the pulse repetition interval (PRI) and the feedback time delay τ. With proper feedback strengths and modulation currents, we find that synchronizing the gain-switching modulation with the delayed feedback (PRI = τ) is essential in generating the chaos-modulated pulses suitable for the pulsed chaos lidar applications. When mismatching occurs, we identify sequences of dynamical periods including stable, periodic, and chaos oscillations evolved within a pulse.

A mathematical model of ultrasonic cross correlation flow meters based on industrial experience

A new model for Ultrasonic Cross Correlation Flow Meters (USCCFM) has been developed as result of industrial experience at Ontario Power Generation (OPG). Industrial applications of USCCFM have encountered cases where the frozen pattern model failed. The new model is based on the mathematical properties of turbulent velocity fields and correlation functions. It contains a proof that USCCFM measurement in a particular situation is successful, if and only if certain mathematical conditions are satisfied. In this document, the term “successful” means that the USCCFM is able to obtain a consistent cross correlation peak, and a stable time delay from the flow condition; otherwise the measurement is considered unsuccessful. This model applies to all measurement conditions encountered so far.

A Method of Improving the Correlation Properties of OFDM Chirp Waveform Diversity

In this letter, an orthogonal frequency-division multiplexing (OFDM) chirp waveform diversity design scheme is proposed to achieve better correlation properties. First, the subchirp duration and bandwidth are optimized simultaneously to increase the degree of freedom in waveform diversity. Second, an optimization procedure is proposed based on the idea of Gram-Schmidt orthogonalization. To reduce the problem complexity, the design problem is separated into several subproblems. Each subproblem corresponds to designing an OFDM chirp composite waveform and is optimized by the Pareto optimization framework. Simulation results show that the proposed method outperforms the conventional methods in terms of both autocorrelation peak sidelobe level (APSL) and cross correlation peak level (CPL) under the circumstance of the same mainlobe width.

OFDM Chirp Waveform Design Based on Imitating the Time–Frequency Structure of NLFM for Low Correlation Interference in MIMO Radar

The orthogonal frequency division multiplexing (OFDM) chirp signal has its special merits of high-range resolution by exploiting a full bandwidth as multiple input multiple output (MIMO) radar signal. After simulation, there are some high peaks in the autocorrelation function and cross correlation function of conventional OFDM chirp signals, which may increase the correlation interference and reduce the detection performance of MIMO radar signal. This letter proposes to reduce the autocorrelation sidelobe peak (ASP) of OFDM chirp signal by subsection imitating the nonlinear frequency modulation (NLFM) signal's time-frequency structure. Since a suitable difference should be made between the subchirp rates and subchirp carrier frequencies of each of the two designed OFDM chirp signals for reducing the cross correlation peaks (CP), the imitated NLFM waveforms' design problem is solved by the proposed optimized method. At last, subchirps of the designed signals are coded by a group of optimized codes. The simulation shows the designed OFDM chirp signals have lower ASP and CP than the conventional ones and referenced previous OFDM signals, and their ASP decreases as the number of subchirps increases.

Fin whale 40‐Hz calling behavior studied with an acoustic tracking array

Fin whale 40‐Hz calling behavior studied with an acoustic tracking array

Swaying to the complex motion of a visual target affects postural sway variability

BackgroundVoluntary shifting body weight in the anteroposterior direction is an important element of daily life activities, such as rising from a chair or initiating a step. In order to accommodate the daily-life challenges of such tasks, voluntary postural sway needs to be flexible and variable. Research questionIn this study we asked how whole-body tracking of a complex visual target motion with the concurrent provision of feedback modulates the variability of voluntary sway. MethodsTwenty young adults (age: 27.10 ± 9.15years, height: 170.73 ± 9.40 cm, mass: 62.84 ± 11.48 kg) performed 132 cycles of voluntary antero-posterior sway, on a force platform, under two conditions: a) self-paced sway and b) swaying while tracking the complex motion of a visual target. Magnitude and temporal structure of variability of postural sway were investigated with the Coefficient of Variance (CoV) and the fractal exponent α, respectively. This analysis was performed for sway cycle duration, amplitude and velocity. The cross-correlation function between the target and sway cycle parameters was computed as a measure of visuo-postural coupling. ResultsThe CoV of sway cycle amplitude, duration and velocity increased during active tracking of the complex target. Fractal exponent α increased for sway cycle amplitude but decreased for cycle duration and remained unchanged for sway velocity. The cross-correlation function revealed a consistent peak at lag+1 indicating an asynchrony between the target and sway cycle duration, while the peak cross-correlation for cycle amplitude was noted at lag 0. SignificanceSwaying to the complex motion of a visual target improves the variability of sway cycle amplitude, at the cost of cycle duration. This is associated with a more synchronous spatial than temporal coupling to the visual target motion. This knowledge could inform the design of postural tracking paradigms as appropriate exercise interventions, for improving voluntary sway in populations with reduced limits of stability (i.e. older adults).

Sequential optimisation of orthogonal waveforms for MIMO radar

The existing methods to design orthogonal waveforms for multiple-input multiple-output radar mainly focus on the optimisation of autocorrelation and cross-correlation properties. Their performance will degrade severely in the presence of Doppler shifts. To overcome this limitation, the authors take an unknown Doppler shifts range into consideration and formulate a new waveform optimisation problem. Since the optimisation problem is highly non-linear, the authors propose an algorithm, called sequential cone programming, to tackle it. The key idea is to use the first-order Taylor expansion to approximate the constraints at each iteration. The authors show that the approximation can be solved via second-order cone programming. In addition, the autocorrelation peak sidelobe level and cross-correlation peak level could be further reduced by setting an appropriate threshold function. Simulation results demonstrate the efficiency of the proposed method compared with state-of-art methods.

Fine Timing Synchronization Based on Modified Expectation Maximization Clustering Algorithm for OFDM Systems

A novel fine timing synchronization method based on the modified expectation-maximization (EM) clustering algorithm is proposed for orthogonal frequency-division multiplexing systems. Using the cross-correlation metrics of one preamble symbol, the cross-correlation peaks corresponding to the channel arriving paths are identified by the proposed modified EM clustering algorithm, the position of the first coherent cross-correlation peak is then chosen as the start of the frame. Computer simulations show that the proposed method is robust in multipath dispersive channels and achieves superior performance to existing techniques in terms of timing accuracy.

Review on Time Delay Estimate Subsample Interpolation in Frequency Domain.

Time delay or the time-of-flight is a most frequently used parameter in many ultrasonic applications. Delay estimation is based on the sampled signal, so the resolution is limited by the sampling grid. Higher accuracy is available if the signal-to-noise ratio is high, then the subsample estimate is desired. Techniques used for subsample interpolation suffer from bias error. Time-of-flight estimation that is free from bias errors is required. The proposed subsample estimation works in the frequency domain; it is based on the cross-correlation peak temporal position. The phase of the cross-correlation frequency response becomes linear thanks to multiplication by the complex conjugate, and its inclination angle is proportional to the delay. Then, subsample interpolation becomes free from the bias error. Twelve algorithmic implementations of this technique have been proposed in this paper. All algorithmic implementations have been analyzed for bias and random errors using simulation and MATLAB codes are given as supplementary material. Comparison with best-performing interpolation techniques (spline approximation, cosine interpolation, carrier phase) is given for both bias and random errors. It was demonstrated that frequency domain interpolation has no bias errors, and noise performance is better or comparable to other subsample estimation techniques. Weighted regression using L2 norm minimization has the best performance: total errors (bias and random) are within 3% of theoretical lower bound.

Comments on “Automated Determination of Snow Water Equivalent by Acoustic Reflectometry”

This paper presents the issues in snow water equivalent (SWE) determination using acoustic reflectometry. To determine SWE, the density and the depth of each layer of snow in a snow pack need to be estimated. A noninvasive acoustic reflectometry technique to estimate the SWE is proposed in the mentioned paper, in which it is shown that SWE of the snowpacks with approximately 100 cm depth can be determined using a maximum length sequence (MLS) of length 7 as a probe signal. We performed similar experiments as reported in the mentioned paper to determine SWE using acoustic reflectometry but failed to replicate the given method. The signal processing-related issues such as design of probe signal, direct pickup problem, and so on of the mentioned paper are investigated and presented in this communication. We show that it is not possible to extract the reflection response by using the MLS of length 7 as a probe signal. The amount of sound attenuation and absorption in the snow medium is very high, of the order of 1 dB/cm and greater depending on the frequency, as reported in the literature and measured by us. Hence, the depth of snowpack investigated in the mentioned paper is practically difficult to achieve using conventional loudspeaker and microphone. Also, it has been explained how the cross-correlation peak width and, hence, the layer resolution achieved by the authors of the mentioned paper is not practically feasible by their reported method. We have also demonstrated that Wiener spiking deconvolution-based technique is not able to obtain the sharp peaks as shown in the mentioned paper.

OFDM Chirp Waveform Design Based on Subchirp Bandwidth Overlap and Segmented Transmitting for Low Correlation Interference in MIMO Radar

There are some special merits for the orthogonal frequency division multiplexing (OFDM) chirp waveform as multiple input multiple output (MIMO) signals. This signal has high range resolution, good Doppler tolerance, and constant modulus superiority since it exploits a full bandwidth and is based on chirp signals. The correlation sidelobe peaks level are critical for the detection requirement of MIMO radar signals, however conventional OFDM chirp signals produce high autocorrelation sidelobe peaks (ASP) and cross-correlation peaks (CP), which reduces detection performance. In this paper, we explore the structure of OFDM chirp signals’ autocorrelation function and proposed a scheme to reduce the designed signal’s ASP by a designing suitable range of subchirp bandwidth and a segmented transmit-receive mode. Next, we explore a suitable range of interval between the chirp rates of each two signals to reduce the CP. The simulation of designed signals verifies the effectiveness of the proposed methods in the reduction of ASP and CP, with the correlation performance being compared with recent relate studies. In addition, the multiple signals detection and one-dimensional range image simulation show the good detection performance of a designed signal in MIMO radar detection.

Characteristics of Turbulent Coherent Structures in Atmospheric Flow Under Different Shear–Buoyancy Conditions

Turbulent coherent structures in the atmospheric boundary layer exert unsteady loads on mechanical and civil structures and greatly contribute to pollutant dispersion and heat dissipation. Much has been deduced about the characteristics of these structures at the laboratory scale in pure shear-driven flows. We examine the influence of atmospheric stability (shear–buoyancy variation) on the newly discovered properties of these turbulence features using observations obtained from a test facility at an onshore site on the east coast of Malaysia. Three ultrasonic anemometers placed at 1.7, 3 and 12 m above ground collected 124 30-min samples of the undisturbed flow. Contrary to expectations, the decline in shear stress in stable stratification reduced the time delay of the peak cross-correlation, implying an increase in the inclination angle of these structures. A wavelet analysis shows that, although the time scale of the vortex packets decreases as the atmosphere becomes increasingly stable, the super-streak time scale increases. The monotonic increase in the energy content in the convective direction results in an enhanced modulating effect for the large super-streaks on the small vortex packets. Analyzing the structure coherence defined as the temporal extension of the streamwise velocity depression reveals two stages of the life cycle of convective rolls. In the first stage, a super-streak couple consisting of a warm updraft and a cold downdraft appears simultaneously at a Monin–Obukhov stability parameter $$\zeta = -\,3.5$$ . In the second stage, the warm updraft strengthens and the cold downdraft weakens.

The Interrogation of Quasi-Distributed Optical FBG Sensing System Through Adopting a Wavelength-Tunable Fiber Chaotic Laser

Wavelength scanning- and optical time domain reflectometer (OTDR)-based methods have been widely used as sensor interrogation schemes for quasi-distributed fiber Bragg grating (FBG) sensing systems. However, wavelength scanning based technique mainly provides the information of wavelength shift at each FBG sensor, whereas it does not have the locating ability. For OTDR-based technique, the spatial resolution is typically several meters, which is not sufficient for high-resolution sensor locating where a centimeter resolution is usually required. Moreover, both of these two interrogation techniques lack the ability of real-time fiber fault monitoring. To address these problems, a novel interrogation technique for quasi-distributed optical FBG sensors based on a wavelength-tunable fiber chaotic laser is proposed and experimentally demonstrated. In the proposed technique, the wavelength shift at each FBG sensor can be obtained through differentially calculating the cross-correlation peaks at two separate wavelength of input light. The positions of FBG sensors can also be determined by the delay time of the corresponding cross-correlation peak. The proposed technique has the advantages of wide wavelength tunable range (40 nm in our works), tunable strain-sensing sensitivity, stability against source power fluctuation, and capability of interrogating both identical and wavelength division multiplexing-based FBG arrays. Strain sensing experiments show a sensitivity of up to 0.0076 dB/ μ ϵ in the range of 0∼1200 μ ϵ with a good linearity. At the same time, a spatial resolution of 18.86 cm is demonstrated in the real-time fiber fault monitoring, which can be further improved with a higher sampling rate.

Multiple water band detections in the CARMENES near-infrared transmission spectrum of HD 189733 b

Aims. We explore the capabilities of CARMENES for characterising hot-Jupiter atmospheres by targeting multiple water bands, in particular, those at 1.15 and 1.4 μm. Hubble Space Telescope observations suggest that this wavelength region is relevant for distinguishing between hazy and/or cloudy and clear atmospheres. Methods. We observed one transit of the hot Jupiter HD 189733 b with CARMENES. Telluric and stellar absorption lines were removed using SYSREM, which performs a principal component analysis including proper error propagation. The residual spectra were analysed for water absorption with cross-correlation techniques using synthetic atmospheric absorption models. Results. We report a cross-correlation peak at a signal-to-noise ratio (S/N) of 6.6, revealing the presence of water in the transmission spectrum of HD 189733 b. The absorption signal appeared slightly blueshifted at –3.9 ± 1.3 km s−1. We measured the individual cross-correlation signals of the water bands at 1.15 and 1.4 μm, finding cross-correlation peaks at S/N of 4.9 and 4.4, respectively. The 1.4 μm feature is consistent with that observed with the Hubble Space Telescope. Conclusions. The water bands studied in this work have been mainly observed in a handful of planets from space. Being able also to detect them individually from the ground at higher spectral resolution can provide insightful information to constrain the properties of exoplanet atmospheres. Although the current multi-band detections can not yet constrain atmospheric haze models for HD 189733 b, future observations at higher S/N could provide an alternative way to achieve this aim.

Distributed temperature measurement with millimeter-level high spatial resolution based on chaotic laser

The high-precision structural health monitoring of large civil structures and materials are increasingly demanded with widely using the distributed fiber sensors. A Brillouin optical correlation domain analysis for millimeter-levelhigh spatial resolution sensing using broadband chaotic laser is proposed and demonstrated. Through the analysis of the influence of polarization state and feedback strength on the chaotic laser, we experimentally achieve a broadband chaotic laser with a spectrum over 7.5 GHz in –3 dB which means that the theoretical spatial resolution is 3 mm, and we also successfully measure the distribution of fiber Brillouin gain spectrum with a temperature over 300 m measurement range with 7.05 mm spatial resolution, which is the first time that the sensor system based on chaotic laser has achieved the measurement with millimeter-level. However, there is still a difference in spatial resolution between the experimental and theoretical values. We can find that the chaotic laser has a time-delay feature; besides, with the broadening of chaotic laser, the threshold of stimulated Brillouin scattering in optical fibers increases while the Brillouin gain will weaken if the pump power is not enough here, and the cross-correlation peak of chaotic laser will narrow. All these problems cause the Brillouin gain signal to be easily submerged by noise, so the performance of the chaotic Brillouin optical correlation domain analysis system will decrease ultimately. Therefore, we also propose an optimization of Brillouin optical correlation domain analysis system by introducing the time-gated scheme into pump branch. It is obvious that the peak power of the pump wave is heightened by more than 9.5 dB after being amplitude-modulated by a square pulse with a pulse width of greater than acoustic phonon lifetime, and the signal-to-back ground noise ratio of the gain spectrum is improved effectively in theory; the cross correlation between chaotic pump wave and probe waveis locked within a pulse duration time, and the residual stimulated Brillouin scattering interactions existing outside the central correlation peak can be largely inhibited. In this optimized setup, the performance of the distributed temperature sensing is improved to 3.12 mm spatial resolution, which corresponds well to the theoretical value. The improved chaotic Brillouin optical correlation domain analysis technology will have a great potential application in high-precision structural health monitoring of large civil structures.