Hyperbolic Frequency Research Articles

Parameter estimation of the hyperbolic frequency-modulated bat calls using hyperbolic scale transform

Echolocating bats are known to vary their waveforms at the phases of searching, approaching, and capturing the prey. It is meaningful to estimate the parameters of the calls for bat species identification and the technological improvements of the synthetic systems, such as radar and sonar. The type of bat calls is species-related, and many calls can be modeled as hyperbolic frequency- modulated (HFM) signals. To obtain the parameters of the HFM-modeled bat calls, a reversible integral transform, i.e., hyperbolic scale transform (HST), is proposed to transform a call into two-dimensional peaks in the “delay-scale” domain, based on which harmonic separation and parameter estimation are realized. Compared with the methods based on time-frequency analysis, the HST-based method does not need to extract the instantaneous frequency of the bat calls, only searching for peaks. The verification results show that the HST is suitable for analyzing the HFM-modeled bat calls containing multiple harmonics with a large energy difference, and the estimated parameters imply that the use of the waveforms from the searching phase to the capturing phase is beneficial to reduce the ranging bias, and the trends in parameters may be useful for bat species identification.

VCH: A Velocity Measurement Method Combining HFM Signals

During sonar detection, the fuzzy function of hyperbolic frequency modulation (HFM) in the waveform of active signal is in the shape of a “oblique blade,” which leads to the coupling characteristics of its fuzzy function in the time dimension and frequency dimension. Doppler causes a frequency shift in the frequency dimension and a time delay in the time dimension, which makes it impossible for a single HFM signal to measure speed accurately. However, the time delay caused by the same moving target to HFM signals with different frequency bands and different pulse widths is also different. A velocity measurement method combining HFM signals (VCH) is proposed, which employs the time delay correlation between the combined HFM signals to achieve the target distance and speed. In the VCH method, the echo signal is no longer matched and filtered as a whole but is divided into two channels and matched and filtered separately. And then, the combined HFM signals are used to obtain the distance and speed of the target. Extensive simulation results show that the proposed method can estimate the distance and speed of moving targets accurately, and it has reference value for engineering application.

PHS: A Pulse Sequence Method Based on Hyperbolic Frequency Modulation for Speed Measurement

The channel in the marine environment is a time-varying and space-varying channel. Pulse-truncated continuous wave (PCW) speed measurement is often used in sonar, but the instability effect of PCW signal in the channel limits the effectiveness of speed measurement. Hyperbolic frequency modulation (HFM) signal is insensitive to Doppler; therefore, HFM signals are widely used in ranging and velocity measurement of sonar and radar. However, due to the filtering effect of the marine environment, the HFM signal of a single frequency band may cause excessive transmission loss, and the echo energy may be too weak to detect the target. Based on the analysis of the influence of speed on the distance measurement of HFM signal, a pulse sequence method based on HFM for speed measurement (PHS) is proposed, which uses HFM signals of different frequency bands and pulse widths in the pulse sequence to perform speed measurement. Extensive simulation results show that PHS method not only guarantees the speed measurement but also makes full use of the energy of the HFM sequence to improve the accuracy of the distance measurement. And PHS method is valuable to the practical application of engineering.

An improved parameter estimation of HFM signals based on IRLS linear fitting of extracted group delay

To address the issue of robust parameter estimation of hyperbolic frequency modulated (HFM) signals under low signal-to-noise ratios (SNRs), an improved algorithm based on iteratively reweighted least squares (IRLS) linear fitting of extracted group delay is proposed. The algorithm includes three main steps. First, a novel method for estimating the frequency distribution range (FDR) of an HFM signal is presented, which involves analyzing the transient features of the amplitude spectrum (AS). Second, the spectrum phase (SP) is unwrapped in the estimated FDR to extract the group delay (GD) of the HFM signal. Last, parameter estimation of the HFM signal is achieved by fitting the GD, which is a linear function of the reciprocal of the frequency, using the IRLS linear fitting method. The simulation results have shown that for SNR ≥ -14 dB, the normalized root mean square errors (NRMSEs) estimated by the proposed estimator are 1.5 dB lower than those estimated by the spectrum phase unwrapping (SPU) estimator, including the starting frequency and period slope. Furthermore, experimental results based on sea trial data have also verified the validity and feasibility of the proposed estimator.

Quasi-maximum likelihood-based estimator of the hyperbolic frequency modulated signals

The quasi-maximum likelihood (QML) algorithm has been extended to estimate the phase parameters and the instantaneous frequency (IF) of the hyperbolic frequency modulated (HFM) signals. The Nelder-Mead simplex algorithm (NMSA) is adopted for a fine estimation. The obtained accuracy is excellent with the estimates achieving the Cramer-Rao lower bound (CRLB) above the signal-to-noise (SNR) threshold of 0 dB. The proposed technique is capable of functioning with signals that are sampled below the requirements of the sampling theorem, which is particularly important for HFM signals. Additionally, there are no limitations for signals with monotonic IF and/or group delay (GD) functions.

Hyperbolic linear canonical transforms of quaternion signals and uncertainty

This paper is concerned with Linear Canonical Transforms (LCTs) associated with two-dimensional quaternion-valued signals defined in an open rectangle of the Euclidean plane endowed with a hyperbolic measure, which we call Quaternion Hyperbolic Linear Canonical Transforms (QHLCTs). These transforms are defined by replacing the Euclidean plane wave with a corresponding hyperbolic relativistic plane wave in one dimension multiplied by quadratic modulations in both the hyperbolic spatial and frequency domains, giving the hyperbolic counterpart of the Euclidean LCTs. We prove the fundamental properties of the partial QHLCTs and the right-sided QHLCT by employing hyperbolic geometry tools and establish main results such as the Riemann–Lebesgue Lemma, the Plancherel and Parseval Theorems, and inversion formulas. The analysis is carried out in terms of novel hyperbolic derivative and hyperbolic primitive concepts, which lead to the differentiation and integration properties of the QHLCTs. The results are applied to establish two quaternionic versions of the Heisenberg uncertainty principle for the right-sided QHLCT. These uncertainty principles prescribe a lower bound on the product of the effective widths of quaternion-valued signals in the hyperbolic spatial and frequency domains. It is shown that only hyperbolic Gaussian quaternion functions minimize the uncertainty relations.

Incoherent Integration of Hyperbolic Frequency Modulated Pulses by the Radon Transform

We herein investigate the incoherent integration of hyperbolic frequency modulated (HFM) pulses for improvement of detection performance under heavy ocean noise. In active sonar systems, combining wideband transmit signals and matched filtering offers considerable processing gain. However, when relative motion exists between the target and sonar system, the processing gain decreases due to the mismatch caused by the Doppler distortion. As a Doppler invariant signal, the HFM waveform gets the property at the cost of a bias in the matched filter output. We propose an incoherent pulse integration method based on the Radon transform to take advantage of the property of HFM signals and handle the bias in outputs of matched filters. In the proposed method, return pulses are first matched filtered, and the Radon transform is performed on the outputs afterward. After that, range bias compensation is performed based on the transform results. The proposed method offers reliable detection performance under heavy ambient ocean noise thanks to the processing gain obtained by both pulse integration and matched filtering. Also, with the help of the Radon transform, detection, bias compensation, and target parameter (range and radial velocity) estimation could be carried out simultaneously.

A Low Complexity Estimator of Hyperbolic Frequency Modulated Signals

A Low Complexity Estimator of Hyperbolic Frequency Modulated Signals

Spread Spectrum Modulation with Grassmannian Constellations for Mobile Multiple Access Underwater Acoustic Channels.

The objective of this study is to evaluate Grassmannian constellations combined with a spread spectrum multiple access scheme for underwater acoustic mobile multiple access communication systems. These communication systems enable the coordination of a fleet of Autonomous Underwater Vehicles (AUVs) from a surface or bottom control unit, e.g., a boat. Due to its robustness against phase rotation, the demodulator of Grassmannian constellations uses non-coherent detection, and the main advantage of such modulation lies in the spectrum efficiency gain with respect to conventional differential modulation. The communication system under study in this paper consists of (i), at the transmitter side, a Grassmannian modulation used in an orthogonal spread spectrum multiple access scheme called Multiuser Hyperbolic Frequency Modulation (MU-HFM) and (ii), at the receiver side, a non-coherent array decoder. The modulation and demodulation are presented as well as the considered spreading sequences. Finally, performances of the proposed transmission scheme are evaluated over replayed underwater acoustic channel responses collected at sea by a multi-sensor acoustic acquisition system.

Deep reinforcement learning for cognitive active-sonar employment

We introduce a framework to leverage deep reinforcement learning (RL) for active sonar employment, wherein we train an RL agent to select waveform parameters, which maximize the probability of single-target detection. We first simulate raw sonar returns of targets and clutter in reverberation and noise using a physics-based sonar-simulation model, the Sonar Simulation Toolkit (SST), then process the resulting signatures into network inputs via an in-house signal and information processing model of an archetypal antisubmarine warfare (ASW) processing chain. We demonstrate that the trained RL agent is able to appropriately select between continuous wave (CW) and hyperbolic frequency modulated (HFM) waveforms depending on target trajectory, as well as select an optimal bandwidth and pulse length trade-off (when constrained by a constant time-bandwidth product), when presented with sonar returns from a reverb-limited or noise-limited environment.

Joint Range-Doppler Estimation Based on Multipulse Processing of Composite Hyperbolic Frequency Modulated Waveforms

We herein investigate the joint estimation of range and Doppler based on multipulse processing of composite hyperbolic frequency-modulated (HFM) waveforms. The composite HFM waveform solves the range bias problem in the HFM waveform by using the mapping relationship between the radial velocity and the peak-to-peak interval in the outputs of matched filters. However, the result may be inaccurate in the presence of multiple false peaks. In this letter, we fit matched filter outputs into a hidden Markov model by utilizing the kinetic model of the target. We can subsequently solve the peak-pair selection problem and perform the joint range-Doppler estimation by using the Viterbi algorithm. The proposed method, by multipulse processing, lowers the signal-to-noise ratio (SNR) requirement, and exact detection of the target in each return pulse is no longer necessary. We prove the effectiveness of the proposed method via numerical simulations, and the simulation results demonstrate that this method outperforms existing methods in low SNR environments.

Influence of tropical dipole in the East Indian Ocean on acoustic convergence region

The physical ocean phenomena in the ocean affect the changes of water body, which has an important influence on the sound propagation. A hyperbolic frequency modulation (HFM) signal sound propagation experiment of towed sound source in the East Indian Ocean (EIO) was conducted in summer 2019. The center frequency of the towed sound source is 300 Hz, and the hydrophone receives the data from 4130 m far. This is the first time that we have conducted the underwater acoustic survey in the Indian Ocean. The influence of the physical ocean phenomenon—Indian Ocean Dipole (IOD) on sound propagation is observed. The experimental data of sound propagation from the IOD are processed and analyzed, the effects of sound source depth and water fluctuation on the deep-sea convergence zone (CZ) are analyzed, and the formation mechanism of sound propagation phenomenon in the experiment is explained theoretically. The results show that the second CZ is not formed under the influence of the warm water mass formed by the IOD and the depth of the sound source in the incomplete deep channel environment of the EIO. Owing to the fluctuation of the sound source depth, the deep-sea CZ disappears at the distance where it should have appeared. When the depth of the sound source becomes deeper, it is easier to form the deep-sea CZ. Under the influence of the IOD, the thermocline fluctuation at the location of the second CZ has an important influence on the formation and location of the third CZ. It is found that the location of the third CZ shifts 2–3 km toward the sound source in the experiment. The research results have important significance in guiding the applications in detection and communication sonar in deep-sea complex environment.

Time reversal pulse position modulation communication in shallow water acoustic channels

The remote sensing and control of biomimetic robot fishes is an important but challenging task because the available underwater acoustic communication cannot accommodate their size, power consumption, and price. Hence, we propose a power-efficient, low-complexity time reversal pulse position modulation communication scheme, which partitions the available bandwidth of a transducer into several different sub-bands using different linear frequency modulated (LFM) pulses. The information is reflected by the position of the LFM pulses with different start and end frequencies for adjacent symbols. In the receiver, the Doppler factor is obtained by cross-correlating two hyperbolic frequency modulation signals transmitted before and after the modulated signal, and the channel response is estimated by match filtering the sync preamble. Furthermore, time reversal and bandpass filtering are performed to mitigate intrasymbol and intersymbol interferences caused by the multipath effects of underwater acoustic channels, respectively. The effectiveness and robustness of the proposed communication scheme are confirmed experimentally.

A novel parameter estimation for hyperbolic frequency modulated signals using group delay

A two-stage technique for estimating hyperbolic frequency modulated (HFM) signal parameters is proposed. In the first stage, coarse parameter estimations are performed through a regression of the group delay estimate obtained from an unwrapped spectrum phase due to its robustness to noise. In the second stage, the coarse estimates are refined by a combination of the Newton-Raphson strategy and O'Shea refinement method. The proposed technique reaches the Cramér-Rao lower bound for HFM signal parameters, and it has better performance and lower computational complexity with respect to current state-of-the-art algorithms.

(Invited) Raman Spectroscopy of Confined Hyperbolic and Surface Phonon-Polaritons in 2D Materials

Phonon-polaritons are quasiparticles resulting from the strong coupling between polar phonons and the electromagnetic field. This hybrid matter-light quasiparticle exhibits remarkable characteristics enabling new or enhanced nanophotonics functionalities. Polaritons in 2D materials are particularly promising: the natural anisotropy leads to a hyperbolic frequency dispersion and enables for example sub-wavelength imaging, low-loss propagation, spontaneous emission enhancement, and extreme field confinement. In addition, 2D heterostructures allow unprecedented opportunities for polariton dispersion engineering.Due to the large momentum mismatch between polaritons and free space propagating fields, polariton measurements require either near-field coupling to its evanescent wave or a direct coupling to the underlying polar oscillation. So far, polaritons in 2D materials have been largely studied using the near-field coupling mediated by an AFM tip. This technique has been extensively applied to h-BN, where imaging of polaritons allows determining the dispersion relation, propagative behaviour, and confinement of polaritons. In contrast, Raman scattering probes polar phonons directly. However, polaritonic effects are manifest at very low wavenumber and can be observed only in a forward scattering configuration, which has made until now this important and ubiquitous characterization techniques ineffective for the study of polaritons in 2D materials.In this work, we demonstrate for the first time that Raman spectroscopy in a backscattering configuration is in fact an extraordinarily powerful and versatile tool for polariton studies in 2D materials. Usually forbidden, they can be readily observed due selection rule relaxation occurring in thin samples and the deep sub-wavelength confinement typical of hyperbolic materials. For the demonstration, we used gallium selenide owing to its strong polar resonances, its two hyperbolic regions and its nested reststrahlen structure.Polariton Raman scattering spectra are both calculated and experimentally measured, allowing an unambiguous identification of the polaritons involved. Measurements as function of incident angle directly reveal the dispersion of the upper extraordinary and surface polaritons. The dependence of polariton frequencies on sample thickness is reported and agrees very well with the calculated values, as long as the silicon oxide and silicon substrate on which the sample is deposited are included in the calculation. This demonstrates that polaritons are quite sensitive to their dielectric environment.Excitation near the 1s-exciton leads to a strong exaltation of the upper extraordinary polariton and the otherwise unobserved lower ordinary polariton. This resonant enhancement allows probing subtle effects related to propagation and confinement along lateral directions. The scattering efficiency, initially isotropic for large samples, becomes polarized along the weaker confinement direction. In addition, the polariton frequency becomes polarization dependent and is highest along the strongly confined direction. From these results, we find low propagation losses and a propagation figure of merit of γ-1 ≥ 39 is found. This value is among the highest reported and establishes GaSe as a promising 2D materials.More significantly, these results demonstrate that Raman spectroscopy, a simple, rapid, non-invasive and widely available technique, can effectively probe confined polariton states. Compatible with high spatial imaging and energy resolution, Raman spectroscopy will undoubtedly accelerate the development of a wider variety of polaritonic materials and complex 2D heterostructures for mid-infrared nanophotonics applications.

SCH: A Speed Measurement Method of Combined Hyperbolic Frequency Modulation Signals

Hyperbolic Frequency Modulation (HFM) signal has certain tolerance to Doppler shift. However, during ranging, the unidirectional modulated HFM signal cannot eliminate the Doppler delay at the output of the matched filtering, and thus there is a ranging error. After the combined positive and negative HFM echo signals are matched and filtered, the Doppler-induced delay is closely related and proportional to the frequency, bandwidth and pulse width of the transmitted signals. By using the combined signals, the ranging error in the ranging of single modulated HFM signal can be eliminated. In this paper, a Speed measurement method of Combined HFM signals (SCH) is proposed, which employs positive and negative frequency modulation signals for speed measurement and ranging. Moreover, the SCH method relaxes the requirements of bandwidth and pulse width, which makes it more suitable for general conditions. Extensive simulation results show that the proposed approach can better estimate the speed and distance of moving targets, and it has reference value for engineering application.

Highly anisotropic two-dimensional metal in monolayer MoOCl2

Anisotropy is a general feature in materials. Strong anisotropy could lead to interesting physical properties and useful applications. Here, based on first-principles calculations and theoretical analysis, we predict a stable two-dimensional (2D) material---the monolayer ${\mathrm{MoOCl}}_{2}$---and show that it possesses intriguing properties related to its high anisotropy. Monolayer ${\mathrm{MoOCl}}_{2}$ can be readily exfoliated from the van der Waals layered bulk, which has already been synthesized. We show that a high in-plane anisotropy manifests in the structural, phononic, mechanical, electronic, and optical properties of monolayer ${\mathrm{MoOCl}}_{2}$. The material is a metal with highly anisotropic Fermi surfaces, giving rise to open orbits at the Fermi level, which can be probed in magnetotransport. Remarkably, the combination of high anisotropy and metallic character makes monolayer ${\mathrm{MoOCl}}_{2}$ an almost ideal hyperbolic material. It has two very wide hyperbolic frequency windows from 0.41 eV (99 THz) to 2.90 eV (701 THz), and from 3.63 eV (878 THz) to 5.54 eV (1340 THz). The former window has a large overlap with the visible spectrum, and the dissipation for most of this window is very small. The window can be further tuned by the applied strain, such as that at a chosen frequency, a transition between elliptic and hyperbolic character can be induced by strain. Our work discovers a highly anisotropic 2D metal with extraordinary properties, which holds great potential for electronic and optical applications.

Modulation of spontaneous emission near graphene/hBN multilayers

The spontaneous emissions of a quantum emitter near three different samples, namely, graphene-covered hexagonal boron nitride (hBN) bulk (monocell), graphene/hBN/graphene sandwich (sandwich), and graphene/hBN/graphene/hBN (double-cell), are investigated in detail. The spontaneous emission decay rate near the graphene/hBN samples can be increased by several orders of magnitude because of the hyperbolic characteristics of hBN. For the monocell, two sharp peaks appear in the Purcell factor curve, corresponding to the hyperbolic frequency ranges of hBN. The Purcell factor can be actively controlled by the chemical potential of graphene via the coupling of surface plasmons (SPs) supported by graphene and hyperbolic phonon polaritons (HPPs) supported by hBN. As the chemical potential increases, the Purcell factor decreases when the distance between the quantum emitter and the sample is less than 1/1000 transition wavelength. Conversely, the Purcell factor increases when the distance ranges from 1/1000 to 1/100 transition wavelength. The interaction between two quantum emitters in the proximity of different samples in reflective configuration is investigated, and the interaction exhibits an oscillation between superradiant and subradiant states in accordance with the separation between the two emitters. The interaction between quantum emitters can also be controlled freely with the chemical potential of graphene. This work provides a meaningful basis for modulating the spontaneous emission, and could be valuable in expanding the application of new and emerging materials in the field of light–matter interaction.

JLHS: A Joint Linear Frequency Modulation and Hyperbolic Frequency Modulation Approach for Speed Measurement

In the waveform design, the distance measurement and resolution are a pair of irreconcilable contradictions. Linear Frequency Modulation (LFM) can alleviate this contradiction. LFM is widely used in radar and sonar, however, its Doppler tolerance is not ideal. Hyperbolic Frequency Modulation (HFM) signal has a particularly strong tolerance towards Doppler frequency shift. When the unidirectionally modulated HFM signal is in distance measurement, the Doppler delay of the matched filtering output cannot be eliminated, and there is a ranging error. After matched filtering of the positive and negative frequency modulation (HFM+LFM) echo signal based on the same frequency band, the Doppler-induced delay is the same but opposite in direction, and the delay is closely related to the frequency, bandwidth, and pulse width of the transmitted signal. By using the inverse time delay difference of the positive and negative frequency modulation, the ranging error in the ranging of unidirectionally modulated LFM signal can be eliminated. In this paper, a Joint Linear frequency modulation and Hyperbolic frequency modulation approach for Speed measurement (JLHS) is proposed, which employs the same frequency band of positive and negative frequency modulation signals for speed measurement and ranging. Extensive simulation results show that the proposed approach can better estimate the speed and distance of moving targets, and it has reference value for engineering application.

Tunable broadband hyperbolic light dispersion in metal diborides.

The naturally hyperbolic materials that conquer the limitations of artificially structured hyperbolic metamaterials are promising candidates for the emerging devices based on light. However, the variety of natural hyperbolic materials and their hyperbolic frequency regime are presently limited. Here, on the basis of first-principles calculations, we demonstrated a family of natural hyperbolic materials, graphite-like metal diborides, with a broadband hyperbolic region from near-IR (∼2.5µm) to the ultraviolet regime (∼248 nm). The operating hyperbolic window and negative refraction can be effectively modulated by extracting electrons from the materials, offering a promising strategy for regulating the optical properties.