Nonlinear Waveform Research Articles

Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation

Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation

Impact of Receiver Bandwidth on the Performance of Nonlinear Volterra Equalizer in IM/DD Systems

Nonlinear electrical equalization is an effective means to compensate for nonlinear waveform distortions in short-haul intensity-modulation (IM)/direct-detection (DD) optical transmission systems. Nonlinear distortions contain broader spectral components than the original signal. Thus, a wide receiver bandwidth and high sampling rate are beneficial to effective compensation of nonlinear distortions. However, this leads to poor signal-to-noise ratio at the receiver. In this paper, we investigate the impact of receiver bandwidth on the performance of 2nd-order nonlinear Volterra equalizer in IM/DD transmission systems. Through the computer simulation and the experimental verification performed with 4-ary pulse amplitude modulation signals, we show that an optimum receiver bandwidth for bit-error ratio performance increases with the amount of nonlinear distortions in IM/DD systems. We also show that the sampling rate should also be increased to avoid the aliasing of the nonlinear distortion components. The cost of the receiver increased by the wider receiver bandwidth and higher sampling rate could be offset in part by the non-integer fractionally sampled nonlinear Volterra equalizer.

Ultrasonic imaging of concrete-embedded corroded steel liners using linear and nonlinear evaluation

ABSTRACT This study explores the efficacy of horizontally polarised shear (SH) waves in ultrasonic inspection of concrete-embedded steel liner plates, focusing on corrosion detection. SH-waves are found to significantly improve the localisation and potential dimensional assessment of embedded plate-like structures compared to compressional (P) waves, as evidenced by SH C-scans. Anomalies corresponding to severe corrosion are discernible in SH C-scans, whereas they are minimally visible in P-wave scans. Nonlinear evaluation explores harmonic-based imaging, including second harmonic generation (SHG) and third harmonic generation. Nonlinear SH-wave evaluation accurately locates the most severely corroded embedded plate, whereas comparative P-wave evaluations fail. However, potential FFT sidelobe contamination in the results warrants consideration. These results suggest a promising use for nonlinear waveform distortion in SH-wave-based corrosion detection though conclusive evidence of the source of SHG is uncertain. Experiments utilised an automatic scanner system for consistent control. The concrete specimen investigated herein contained pre-corroded plates which hint at heightened nonlinear effects when corrosion occurs post-embedment due to corrosion-induced cracking. These findings encourage further investigation into SH-waves for nonlinear ultrasonic detection of concrete-embedded steel liner plates and the development of instrumentation tailored to such methods.

Upper mantle structure beneath the Mongolian region from multimode surface waves: Implications for the western margin of Amurian plate

Multimode phase speeds of surface waves are used to build a new radially anisotropic S wave model in the eastern Eurasian and Mongolian regions. Our dataset includes seismic waveforms of over 1655 teleseismic events (Mw≥5.8) from 2009 to 2021, recorded at permanent and temporary stations in and around Mongolia. The multimode dispersion curves of Love and Rayleigh waves were extracted using the nonlinear waveform fitting method for individual seismograms. Then, we retrieved phase speed maps for each mode and frequency, incorporating finite-frequency effects. Finally, localized multimode dispersion curves extracted from the phase speed maps were inverted for local 1-D SV and SH wave profiles, which are combined into a radially anisotropic 3-D shear wave model. Our new model exhibits significant lateral variations of S wave speeds at 70–100 km depth beneath Mongolia, i.e., slow anomalies in the tectonically active western Mongolia in contrast to fast anomalies in stable eastern Mongolia. In the radial anisotropy model, SH waves are faster than SV waves in most areas of the Mongolian lithosphere above 100 km depth, except for the northeast of the Altay Mountains. The Hangay Dome region is characterized by significantly slower velocities that may relate to its uplifting. A large-scale low velocity beneath the northeast of the Hangay Dome with a slower SV wave speed than SH may indicate the existence of partially molten layers. This study also reveals distinct lateral variations of S wave speeds across the boundary between the Amurian and Eurasian plates, characterized by the fast anomaly in eastern Mongolia, corresponding to the lithosphere in the western Amurian plate.

Sub-rate sampled, non-integer fractionally spaced Volterra nonlinear equalizer for IM/DD systems.

As high-speed analog-to-digital converters (ADC) account for a significant portion of the receiver's cost in intensity-modulation (IM)/direct-detection (DD) systems, there have been substantial efforts to employ an ADC operating at a relatively low sampling rate. However, half-symbol-spaced electronic nonlinear equalizers used to compensate for nonlinear waveform distortions commonly operate at 2 samples/symbols, and thus require digital upsampling before the equalization. This implies that the digital signal processing (DSP) at the receiver should also operate at 2 sample/symbol even though the ADC operates at the sub-rate (i.e., < 2 sample/symbol). Hence, we propose and experimentally demonstrate the sub-rate sampled, non-integer fractionally spaced Volterra nonlinear equalizer (VNLE). This equalizer does not require the digital upsampling, and thus makes the entire receiver DSP block operating at the sub-rate, the same as the sampling rate of ADC. We estimate the complexity of the proposed equalizer by the number of multipliers required for its implementation. We also evaluate the performance of the proposed VNLE over a 64-Gb/s 4-ary pulse amplitude modulation link and compare the performance with the conventional VNLE (requiring digital upsampling). The results show that the proposed VNLE incurs a very slight performance degradation compared with the conventional VNLE, but reduces the implementation complexity considerably since it obviates the need for digital upsampling at the receiver.

Localized structures in optical media and Bose-Einstein condensates: an overview of recent theoretical and experimental results

A survey of recent theoretical and experimental studies on localized structures that form and propagate in a broad class of optical and matter-wave media is presented. The article is structured as a resource paper that overviews a large series of theoretical and experimental results obtained in diverse research areas: linear and nonlinear optical waveforms, nonlinear surface waves, ultrashort few-cycle optical pulses, localized structures in fractional systems, rogue (freak) waves, and matter-wave localized states.

Few- and single-molecule reservoir computing experimentally demonstrated with surface-enhanced Raman scattering and ion gating.

Molecule-based reservoir computing (RC) is promising for achieving low power consumption neuromorphic computing, although the information-processing capability of small numbers of molecules is not clear. Here, we report a few- and single-molecule RC that uses the molecular vibration dynamics in the para-mercaptobenzoic acid (pMBA) detected by surface-enhanced Raman scattering (SERS) with tungsten oxide nanorod/silver nanoparticles. The Raman signals of the pMBA molecules, adsorbed at the SERS active site of the nanorod, were reversibly perturbated by the application of voltage-induced local pH changes near the molecules, and then used to perform time-series analysis tasks. Despite the small number of molecules used, our system achieved good performance, including >95% accuracy in various nonlinear waveform transformations, 94.3% accuracy in solving a second-order nonlinear dynamic system, and a prediction error of 25.0 milligrams per deciliter in a 15-minute-ahead blood glucose level prediction. Our work provides a concept of few-molecular computing with practical computation capabilities.

Nonlinear waveform steepening in time reversal focusing of airborne, one-dimensional sound waves, and the absence of Mach stems

Time reversal (TR) is a process that can be used to generate high amplitude focusing of sound. Previous research has shown that TR in reverberant environments can generate peak levels that exceed 200 dB with airborne, audible sound [Patchett and Anderson, J. Acoust. Soc. Am. 151(6), (2022)], and 134 dB with airborne ultrasound [Wallace and Anderson, J. Acoust. Soc. Am. 150(2), (2021)]. Particularly, in the focusing of audible sound, these high amplitude focused waveforms exhibit multiple nonlinear properties including waveform steepening and a nonlinear increase in compressions due to the generation of free space Mach stems. This study attempts to remove the Mach stems by generating the focus in a 1D system, since Mach stems require higher dimensional spaces to form. The system of pipes used ensures a planar 1D reverberant environment. Results show that waveform steepening remains as expected but that the nonlinear increase in compression amplitudes disappears without the ability for Mach stems to form. This provides further confirmation that Mach stems are the cause of the nonlinear increase in compression amplitudes observed with high amplitude TR.

Dynamic prediction of nonlinear waveform transitions in a thalamo-cortical neural network under a square sensory control

Dynamic prediction of nonlinear waveform transitions in a thalamo-cortical neural network under a square sensory control

Quantitative Relationship between Data Dimensionality and Information Processing Capability Revealed via Principal Component Analysis for Nonlinear Current Waveforms with Nonideality Derived from Ionic Liquid-Based Physical Reservoir Device

Quantitative Relationship between Data Dimensionality and Information Processing Capability Revealed via Principal Component Analysis for Nonlinear Current Waveforms with Nonideality Derived from Ionic Liquid-Based Physical Reservoir Device

Adaptive optimal control of under-actuated robotic systems using a self-regulating nonlinear weight-adjustment scheme: Formulation and experimental verification.

This paper formulates an innovative model-free self-organizing weight adaptation that strengthens the robustness of a Linear Quadratic Regulator (LQR) for inverted pendulum-like mechatronic systems against perturbations and parametric uncertainties. The proposed control procedure is devised by using an online adaptation law to dynamically adjust the state weighting factors of LQR's quadratic performance index via pre-calibrated state-error-dependent hyperbolic secant functions (HSFs). The updated state-weighting factors re-compute the optimal control problem to modify the state-compensator gains online. The novelty of the proposed article lies in adaptively adjusting the variation rates of the said HSFs via an auxiliary model-free online self-regulation law that uses dissipative and anti-dissipative terms to flexibly re-calibrate the nonlinear function's waveforms as the state errors vary. This augmentation increases the controller's design flexibility and enhances the system's disturbance rejection capacity while economizing control energy expenditure under every operating condition. The proposed self-organizing LQR is analyzed via customized hardware-in-loop (HIL) experiments conducted on the Quanser's single-link rotational inverted pendulum. As compared to the fixed-gain LQR, the proposed SR-EM-STC delivers an improvement of 52.2%, 16.4%, 55.2%, and 42.7% in the pendulum's position regulation behavior, control energy expenditure, transient recovery duration, and peak overshoot, respectively. The experimental outcomes validate the superior robustness of the proposed scheme against exogenous disturbances.

Photonic generation of Barker encoded dual-nonlinear frequency modulated RADAR waveforms

Photonics enables the development of versatile waveform generators with carrier frequency tunability and broad bandwidths, allowing for high-range resolution for modern radar systems. Linear frequency-modulated waveforms are widely employed in various radar applications due to their large time-bandwidth products but are limited in functionality due to high sidelobe levels, resulting in a poor signal-to-noise ratio (SNR). On the other hand, non-linear frequency-modulated waveforms (NLFM) have a faster sweep rate at the edges than at the center, resulting in high SNRs, which can be boosted further through encoding techniques. A photonic approach for generating Barker-encoded dual-NLFM waveforms through a dual-drive Mach Zehnder modulator is proposed with improved range resolution, pulse compression ratio, and peak-to-sidelobe ratio. A theoretical analysis is performed, which is then modeled, and experimentally confirmed. Barker-encoded dual-NLFM waveforms are generated at 6 GHz with 500 MHz chirp bandwidth showing a maximum range resolution of 19.89 cm with PCR of 9803.

A two-level classification diagnosis method for AC arc faults based on data random fusion and MC-MGCNN network

The series arc faults of the electric lines in the low-voltage distribution network can lead to devastating fires, posing a significant threat to the lives and safety of residents. Aiming at the problems that arc faults are challenging to identify due to the variety of load types in the lines, a new diagnosis method of two-level classification for arc faults based on data random fusion and MC-MGCNN network is proposed. Firstly, the first level of load classification is carried out. Extreme weighted fuzzy entropy is calculated to separate the dimmer load that could easily lead to misjudgment from the total load pool, and the concepts of simple load pool and complex load pool are established. Secondly, the corresponding classifiers are designed for the two different load pools for the second level of diagnosis classification. Specifically, the time–frequency domain features are extracted for the load waveforms in a simple load pool, and extreme gradient boosting (XGBoost) is used for rapid diagnosis. On the contrary, for the nonlinear load waveforms and multi-load combination waveforms in the complex load pool, the random fusion mechanism of data is applied for feature enhancement, and a new one-dimensional data set is constructed. Finally, the latest data is input into the multi-channel convolution neural network combining multi-head attention and gated recurrent unit (MC-MGCNN) network for arc fault diagnosis. The experimental results show that the first level of load classification can effectively reduce the number of misjudgment samples in the complex load pool and improve the overall binary classification accuracy by 7.54 %. The new data set gains different degrees of improvement in the identification accuracy of other comparative networks. In addition, the new network has good feature learning ability and diagnostic accuracy of arc faults. The accuracy of the multi-classification is up to 99.5 %, and the binary classification accuracy is up to 99.94 %. The test is carried out in the Raspberry PI 4b environment, and the detection time is 52.3 ms, which verified the feasibility of hardware deployment.

New wave behaviors of the Fokas-Lenells model using three integration techniques.

In this investigation, we apply the improved Kudryashov, the novel Kudryashov, and the unified methods to demonstrate new wave behaviors of the Fokas-Lenells nonlinear waveform arising in birefringent fibers. Through the application of these techniques, we obtain numerous previously unreported novel dynamic optical soliton solutions in mixed hyperbolic, trigonometric, and rational forms of the governing model. These solutions encompass periodic waves with W-shaped profiles, gradually increasing amplitudes, rapidly increasing amplitudes, double-periodic waves, and breather waves with symmetrical or asymmetrical amplitudes. Singular solitons with single and multiple breather waves are also derived. Based on these findings, we can say that our implemented methods are more reliable and useful when retrieving optical soliton results for complicated nonlinear systems. Various potential features of the derived solutions are presented graphically.

Interacting Solitons, Periodic Waves and Breather for Modified Korteweg–de Vries Equation

We theoretically demonstrate a rich and significant new families of exact spatially localized and periodic wave solutions for a modified Korteweg–de Vries equation. The model applies for the description of different nonlinear structures which include breathers, interacting solitons and interacting periodic wave solutions. A joint parameter which can take both positive and negative values of unity appeared in the functional forms of those closed form solutions, thus implying that every solution is determined for each value of this parameter. The results indicate that the existence of newly derived structures depend on whether the type of nonlinearity of the medium should be considered self-focusing or defocusing. The obtained nonlinear waveforms show interesting properties that may find practical applications.

Phase-Domain Injected Training for Channel Estimation in Constant Envelope OFDM

Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a multi-carrier waveform with 0 dB peak-to-average power ratio (PAPR). This property enables the exploitation of multi-carrier waveforms with non-linear power amplifiers, avoiding the undesirable clipping effects. However, the existing channel estimation techniques designed for OFDM cannot be reused, since the use of a phase modulator makes CE-OFDM a non-linear waveform. Previous works assumed that the channel estimation process relies on the transmission of preambles, and the data symbols are equalized using a frequency domain equalizer (FDE). To avoid the overhead induced by preambles, a phase-domain injected training (PIT) is proposed, where the pilot sequence is embedded in the phase dimension of the data symbols. This novel approach does not waste time and/or frequency resources as in preamble-based schemes. Moreover, it does not require additional power for the training. The received symbols are averaged with a dual procedure, and owing to the particular structure of CE-OFDM, the channel estimates are recovered. Also, the analytical expression of the channel estimation mean squared error (MSE) is derived. Finally, several numerical results illustrate the performance of the proposal, showing that the MSE, bit error rate (BER) and achievable rate are improved, as compared to the existing works.

Relative Entropy-Based Waveform Optimization for Rician Target Detection With Dual-Function Radar Communication Systems

In this paper, we consider waveform design for dual-function radar-communication systems based on multiple-input-multiple-out arrays. To achieve better Rician target detection performance, we use the relative entropy associated with the formulated detection problem as the design metric. We also impose a multi-user interference energy constraint on the waveforms to ensure the achievable sum-rate of the communications. Two algorithms are presented to tackle the nonlinear non-convex waveform design problem. In the first algorithm, we derive a quadratic function to minorize the objective function. To tackle the quadratically constrained quadratic programming problem at each iteration, a semidefinite relaxation approach followed by a rank-one decomposition procedure and an efficient alternating direction method of multipliers (ADMM) are proposed, respectively. In the second algorithm, we present a novel ADMM algorithm to tackle the optimization problem and employ an efficient minorization-maximization approach in the inner loop of the ADMM algorithm. Numerical results demonstrate the superiority of both algorithms. Moreover, the presented algorithms can be extended to synthesize peak-to-average-power ratio constrained waveforms, which allows the radio frequency amplifier to operate at an increased efficiency.

Remote Sensing Small Explosives With an Ionospheric Radar

AbstractEarth's ionosphere has long been targeted as a medium for remote sensing of explosive terrestrial events such as earthquakes, volcanic eruptions, and nuclear/conventional weapon detonations. Until now, the only confirmed ionospheric detections have been of very large events that were easily detectable through other traditional global sensor systems (e.g., seismic). We present the first clear, confirmed detections of relatively low yield 1‐ton TNT‐equivalent chemical explosions using pulsed Doppler radar observations of isodensity layers in the ionospheric E region. The shape and spectra of the detected waveforms closely match predictions from the acoustic ray tracing and weakly nonlinear waveform propagation models. The explosions were roughly three orders of magnitude lower yield than any previous confirmed ionospheric detection and represent the first conclusive evidence that explosions of this size can have clear impacts on the ionosphere. This technique could improve the remote detection of both anthropogenic and natural explosive events.

Propagation of chirped gray solitons in weakly nonlocal media with parabolic law nonlinearity and spatio-temporal dispersion

In our research, we have examined the existence and stability of chirped periodic and solitary waves in a weakly nonlocal nonlinear medium, which exhibits various types of effects, including inter-modal dispersion, nonlinear dispersion, detuning, spatio-temporal, and parabolic law nonlinearity. By studying the nonlinear Schrödinger equation that describes the field dynamics in this system, a class of nonlinearly chirped periodic waves is derived in the presence of all physical processes. In addition, we have obtained solitary waves of the gray type in the long-wave limit of these nonlinear waveforms. We have found that the frequency chirp associated with these optical waves depends on their intensity and its magnitude can be controlled by manipulating the nonlinear dispersion parameter. Furthermore, we have numerically studied the stability of the gray soliton solution under finite initial perturbations. Our results indicate that the nonlinear waves we have identified represent new types of extremely robust chirped localized structures in weakly nonlocal nonlinear parabolic law media.

A characteristic nonlinear distortion length for broadband Gaussian noise

The nonlinear evolution of high-amplitude broadband noise is important to the psychoacoustic perception, usually annoyance, of high-speed jet noise. One method to characterize the nonlinear evolution of such noise is to consider a characteristic nonlinear waveform distortion length for the signal. A common length scale for this analysis is the shock formation distance of an initially sinusoidal signal. However, application of this length scale to broadband noise, even with the amplitude and source frequency replaced with characteristic values, may lead to underestimates of the overall nonlinear waveform distortion of the noise as indicated by the skewness of the time derivative of the acoustic pressure (or derivative skewness). This paper provides an alternative length scale derived directly from the evolution of the derivative skewness of Gaussian noise that may be more appropriate when analyzing the nonlinear evolution of broadband noise signals. This Gaussian-based length scale is shown to be a useful metric for its relative consistency and its physical interpretation. Various analytical predictions of the evolution of the derivative skewness for an ensemble of numerical simulations of noise propagation are used to highlight various aspects of this new length scale definition.