Hyperbolic Frequency Modulation Signal 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.

Wideband Lv's Distribution: A signal processing tool for hyperbolic frequency modulated signal analysis

Wideband Lv's Distribution: A signal processing tool for hyperbolic frequency modulated signal analysis

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.

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.

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.

An Improved Velocity Estimation Method for Wideband Multi-Highlight Target Echoes in Active Sonar Systems

In active sonar systems, the target echoes are usually equivalent to a superposition of the Doppler-scaled reflections from multiple highlights. The reflections overlap with each other both in the time and frequency domain, which results in a decreased velocity estimation performance. Recently, the hyperbolic-frequency modulated signal has been widely employed in sonar systems for moving targets due to its Doppler tolerance, while the precise velocity estimation becomes a great challenge under such conditions. In this paper, the echo c is modeled onsidering a target with a constant velocity and multi-highlights. The velocity estimation performance is analyzed though the signal’s matched filter and the wideband ambiguity function. An improved method based on the sliding window matching algorithm is proposed to improve the performance. The method controls the energy of environmental noise and interference by focusing on the dominant target highlight, and applying a designed window which utilizes the Doppler characteristics of hyperbolic-frequency modulated signals. Simulations and lake experiment allow us to compare between the improved method and the conventional matched filter method. The results verify the influence of the multi-highlights in velocity estimation and indicate that the improved method has more effective performance.

쌍곡선 주파수 변조신호 기반 매체접속지연에 자유로운 AUV 위치추정

쌍곡선 주파수 변조신호 기반 매체접속지연에 자유로운 AUV 위치추정

Impact of MAC Delay on AUV Localization: Underwater Localization Based on Hyperbolic Frequency Modulation Signal.

Medium Access Control (MAC) delay which occurs between the anchor node’s transmissions is one of the error sources in underwater localization. In particular, in AUV localization, the MAC delay significantly degrades the ranging accuracy. The Cramer-Rao Low Bound (CRLB) definition theoretically proves that the MAC delay significantly degrades the localization performance. This paper proposes underwater localization combined with multiple access technology to decouple the localization performance from the MAC delay. Towards this goal, we adopt hyperbolic frequency modulation (HFM) signal that provides multiplexing based on its good property, high-temporal correlation. Owing to the multiplexing ability of the HFM signal, the anchor nodes can transmit packets without MAC delay, i.e., simultaneous transmission is possible. In addition, the simulation results show that the simultaneous transmission is not an optional communication scheme, but essential for the localization of mobile object in underwater.

A method of velocity estimation using composite hyperbolic frequency-modulated signals in active sonar.

This paper proposes a method to estimate the target velocity using a combination of two hyperbolic frequency-modulated (HFM) signals. The Doppler-shifted time-delay between the two signals compared with the original time-delay is used to estimate the target velocity. One finds that a HFM with an increasing frequency sweep (positive HFM) and one with a decreasing frequency sweep (negative HFM) yield a different time. And a better Doppler estimation can be obtained by using a negative HFM signal followed by a positive HFM signal than the other way around. The method is applied to real data and performance is demonstrated via simulated data.

A joint synchronization parameter estimation in fractional Fourier transform orthogonal frequency division multiplexing underwater acoustic communication system

In the conditions of Gaussian noise, symmetric alpha stable impulse noise, multipath propagation, Doppler effect, and so on, a joint synchronization algorithm is proposed for underwater acoustic communication system based on fractional Fourier transform orthogonal frequency division multiplexing. The algorithm realizes the orthogonal multicarrier underwater acoustic communication system synchronization based on that the symmetrical triangular linear frequency modulation signal has the energy convergence in the domain of fractional Fourier transform. In order to verify the effectiveness of the algorithm, hyperbolic frequency modulation signal and linear frequency modulation signal are used as the evaluation index, and the synchronization performance of bit error rate of them is compared by simulation and pool experiments. The simulation results show that the proposed algorithm in this article is resistant to Gaussian noise, symmetric alpha stable pulse noise, multipath propagation, and Doppler effect, compared with traditional synchronization algorithms; the synchronization error probability is low at the same signal-to-noise ratio.

Parameter estimation for HFM signals using combined STFT and iteratively reweighted least squares linear fitting

This paper presents a fast and robust method for estimating the starting frequency and period slope of hyperbolic frequency modulated (HFM) signals. The method involves, first, the instantaneous frequency (IF) estimation of HFM signals based on the peak of short-time Fourier transform (STFT) and, second, taking reciprocal of the estimated IF to get the zero crossing interval (ZCI). Parameter estimation of HFM signals is then achieved by using iteratively reweighted least squares (IRLS) linear fitting method to fit the ZCI which is a linear function of time. Both the approximate analysis of the magnitude spectrum and the formula used to determine the window length of STFT are derived for HFM signals. The lower bound of the estimator's variance and bias of the parameters of HFM signals are also derived in order to compare the performance of the proposed method. At last, both the simulation results and processing of sea trial data are presented to justify the validity and feasibility of the proposed method.

Underwater Acoustic Communication Using Nonlinear Chirp Signal

This paper presents an underwater acoustic communication with nonlinear chirp modulation. The information is carried by the carrier amplitude, frequency or phase in the most common underwater acoustic communications. However, the proposed method includes the information within frequency variation of carrier wave for a symbol. Especially, as carrier wave the hyperbolic frequency modulated signal, one of the nonlinear chirp signal, is used and it is robust in the Doppler channel. The proposed method was analyzed and compared to conventional method by simulation. When the doppler shift existed, the error probability of the proposed method is reduced by 5~12 % than conventional method with linear frequency modulated signal. Sea trial was performed to analyze the performance of the proposed method.

An Iterative Parameters Estimation Method for Hyperbolic Frequency Modulated Signals with Colored Noise

This paper presents an iterative method for estimating the starting frequency and period slope of hyperbolic frequency modulated (HFM) signals with underwater acoustic platform colored noise. The method involves, firstly, whitening of the colored noise and, secondly, instantaneous frequency (IF) estimation of HFM signals based on the peak of short-time Fourier transform (STFT) and taking reciprocal of the estimated IF to get the zero crossing interval (ZCI). Parameters estimation of HFM signals is then achieved by using iteratively reweighted least squares (IRLS) linear fitting method to fit the ZCI. The main contributions of our work are three-fold: (1) A simple and effective method is proposed to whiten the underwater acoustic platform colored noise; (2) A complex nonlinear problem is transformed into a linear one by the proposed parameters estimation method; (3) The proposed method is applicable for the practical engineering applications.

Characteristics Analysis of HFM Signal over Underwater Acoustic Channels

For pulse compression characteristics and not easily affected by noise, linear frequency modulation signal are widely used in underwater acoustic communication. This paper analyzes the characteristics of hyperbolic frequency modulation signal over underwater acoustic channels. Compared with linear frequency modulation signal, hyperbolic frequency modulation has the same performance of strong anti-noise and anti-multipath, what’s more, hyperbolic frequency modulation signal is better resist the influence of doppler. And discussed the influence of doppler on signal, simulation results show that the hyperbolic frequency modulation signal detection rate is better than linear frequency modulation signal in the doppler environment. DOI: http://dx.doi.org/10.11591/telkomnika.v11i3.2183 Full Text: PDF