Hyperbolic Frequency Modulation Research Articles

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.

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.

Performance analysis on the speed spectrum estimation based on dual-HFM waveform

Real-time Doppler estimation of sonar signals is of great significance to underwater communication and detection. The Hyperbolic-Frequency-Modulated (HFM) waveform-based speed spectrum estimation is one of the modern methods for underwater Doppler estimation, and this paper presents a detailed analyses of the derivation and the performance of this method. The analyzing results show the robustness of the method on multipath channels and multi-highlight targets and provide the main lobe width of the speed spectrum. Moreover, the paper examines the spectral properties of the HFM signal from the frequency-domain Doppler invariance property, which could provide insights for better understanding and utilization of this Doppler invariant waveform.

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.

Timing estimation of multiple hyperbolic frequency‐modulated signals based on multicarrier underwater acoustic communication

AbstractUnderwater acoustic channel is much more complex than radio channel. Background noise, multipath extension, and Doppler frequency shift are all factors that affect high‐speed and stability for underwater communication. Orthogonal frequency division multiplexing (OFDM) is a modulation technology with high spectrum efficiency and strong anti‐multipath ability, usually used in high‐speed underwater acoustic communication. Signal arrival time detection and timing estimation before receiving data is an essential module in an underwater communication system. Timing estimation error will seriously affect the demodulation of the signal. In order to solve the problem of a complex channel environment in underwater acoustic communication system, a timing estimation method is proposed based on multiple hyperbolic frequency‐modulated (MHFM) signals. In order to improve the performance of underwater acoustic communication systems, this article proposes an iterative method of correlation‐sum‐mean absolute error (MAE) based on hyperbolic frequency‐modulated (HFM). The simulation results show that the proposed method can provide better performance and higher timing estimation accuracy under the conditions of low signal‐to‐noise ratio (SNR) and Doppler effect under oceanic noise channel and Doppler spread channel.

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.

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.

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.

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.

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.

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.

A Bioinspired Twin Inverted Multiscale Matched Filtering Method for Detecting an Underwater Moving Target in a Reverberant Environment.

To this day, biological sonar systems still have great performance advantages over artificial sonar systems, especially for detection in environments with clutter, strong reverberation, and a low signal to noise ratio (SNR). Therefore, mammal sonar systems, for instance, bats and toothed whales, have many characteristics worth learning from. This paper proposes a bioinspired twin inverted multiscale matched filtering method to detect underwater moving targets. This method can be mainly divided into three parts. Firstly, a hyperbolic frequency modulation (HFM) continuous wave (CW) multiharmonic detection signal was adopted after analyzing signals from bats and dolphins. This signal combines the advantages of CW and HFM signals and has excellent time measurement and speed measurement performance when detecting a moving target. Secondly, the twin inverted waveform was introduced to suppress strong linear reverberation and highlight moving targets. The pulse interval was determined by assessing the reverberation reduction time. Thirdly, when processing echoes, a multiscale matched filtering method was proposed to make use of multiharmonic information and improve detection performance. Finally, a channel pool experiment was carried out to test the performance of the proposed method. The experimental result demonstrates that the proposed method has better performance when detecting a moving target in a reverberant environment compared to the conventional matched filtering method. Related results can be applied to small underwater platforms or sensor network platforms for target detection and coastal defense applications.

Practical Multiple User System Using Heterogeneous Frequency Modulation for High Data Rate in Underwater Sensor Network

The goal of this paper is to improve the data rate in a multiple user (MU) underwater system. Toward this goal, we propose a new modulation, a combination of hyperbolic frequency modulation (HFM) and power frequency modulation (PFM) signals. By overlapping the heterogeneous signals, the number of bits which can be transferred during a symbol duration increase. In addition, by finely dividing the bandwidth into sub-channels, we increase the size of available modulation order per each user. Owing to the Doppler invariant characteristic of HFM signal, the Doppler shift can be estimated and it is utilized to compensate for the Doppler distortion occurred at the PFM signal. To take acoustic channel properties into account the system evaluation, we develop an acoustic network simulator involving well-defined propagation physics. The simulation results substantiate that our modulation scheme significantly increases data rate as compared with the existing MU systems.

On the Doppler Bias of Hyperbolic Frequency Modulation Matched Filter Time of Arrival Estimates

The purpose of this paper is to introduce an extended matched filter for hyperbolic frequency modulation (HFM) waveforms in active sonar systems, along with an exact closed-form solution for the Doppler bias in time of arrival estimates when using this filter. Conventional HFM matched filtering employs a single undilated replica of the transmitted signal and estimates the time of an echo's arrival using the peak squared magnitude of the processed data. It is well known that when the echo is dilated (the term dilate is used in a generic sense to mean either stretching or compressing) due to the Doppler effect, such an estimate of the time of arrival is biased by an amount depending on the range rate $v$ , however, a closed-form solution for this Doppler bias does not exist. Using the extended HFM matched filter in place of a conventional one allows for an exact closed-form solution for the Doppler bias. The closed-form solution for the Doppler bias of time of arrival estimates using the extended HFM matched filter is presented. This solution applies to both broadband and narrowband HFM signals, and suggests that a previously published approximation of the bias for a conventional HFM matched filter is valid only for narrowband HFM signals.

Biosonar inspiration for radar waveform design

Bat biosonar offers a natural source for biomimetic design of radar waveforms with inspirations falling into two categories: (1) biosonar principles similar to ones already employed in radar and (2) principles used by bats that operate in ways not yet understood or not yet embraced yet for radar. This second type offers the possibility for driving radar innovation. Hyperbolic frequency modulation (HFM) waveforms were one of the first aspects of bat biosonar to catch the attention of the radar community. Relative to the popular linear frequency modulation (LFM) waveform, HFM is less vulnerable to Doppler shifts from targets' relative velocities. Another promising possibility for biomimetics is the remarkable ability of some bats to resolve closely-spaced objects using acoustic frequencies on a small platform. Bats' ability to operate in swarms is of interest to radar designers concerned about mutual interference between ships or planes using the same waveforms and frequencies. As bat researchers approach an understanding of the mechanisms behind these, and other, abilities of bats, their results will find a ready audience. This talk will discuss aspects of bat biosonar offering payoffs for radar design, including but not limited to improved resolution, Doppler tolerance and mitigation of inter-system interference.Bat biosonar offers a natural source for biomimetic design of radar waveforms with inspirations falling into two categories: (1) biosonar principles similar to ones already employed in radar and (2) principles used by bats that operate in ways not yet understood or not yet embraced yet for radar. This second type offers the possibility for driving radar innovation. Hyperbolic frequency modulation (HFM) waveforms were one of the first aspects of bat biosonar to catch the attention of the radar community. Relative to the popular linear frequency modulation (LFM) waveform, HFM is less vulnerable to Doppler shifts from targets' relative velocities. Another promising possibility for biomimetics is the remarkable ability of some bats to resolve closely-spaced objects using acoustic frequencies on a small platform. Bats' ability to operate in swarms is of interest to radar designers concerned about mutual interference between ships or planes using the same waveforms and frequencies. As bat researchers approach a...

Characteristics of convergence zone formed by bottom reflection in deep water

There appears a convergence effect on the sound filed under the condition of sound channel in the deep sea due to the refraction effect of the sea water. For the deep water environment with an incomplete channel, sea bottom has an important influence on sound propagation. A long-range sound propagation experiment was conducted in the South China Sea in April 2018. Hyperbolic frequency modulated (HFM) signals with a frequency band of 250-350 Hz are transmitted by an acoustic source which is towed at a speed of 4 knots away from a vertical line array (VLA). The VLA consists of 20 hydrophones which are arranged from 85 m to 3400 m with an unequal depth space. Using the data collected in the experiment, the effects of bathymetry variation on sound propagation are studied. The physical causes of the seafloor reflection convergence phenomenon are explained by using the parabolic equation combined with ray theory. The observed phenomenon is different from the convergence phenomenon in the typical deep water environment, the spatial variation of bathymetry contributes to the formation of the seafloor reflection convergence zone in advance, and the sound intensity in part of shadow zone is significantly increased. Due to the reflection from the seabed, two obvious seafloor reflection convergence zones are observed near the range of 20 km and 40 km respectively, in which both gains increase up to 10 dB, and a high sound intensity area is formed in the shadow zone near the range of 11 km, where the gain is less than the gains in the two convergence zones. In addition, the grazing angle of the sound ray reaching the second convergence zone is smaller than that reaching the first convergence zone when the receiving depth is the same as the source depth, and the rays with smaller glancing angle have less reflection loss, which leads to a higher gain in the second convergence zone. As the water depth becomes gradually shallower with range increasing, the convergence zone near the range of 51 km under the SOFAR channel is destroyed, and the sound field energy in the corresponding range is much smaller since the number of arriving refracted sound rays is reduced. In the first convergence zone, the path of arriving rays is gradually increased as the receiver becomes deeper. Therefore, the arrival structure tends to be complicated, and the multi-path effect is more obvious. The study result is meaningful for the performance analysis of sonar in complex deep water environment.