Wideband Ambiguity Function Research Articles

High-Resolution Wideband Waveform Design for Sonar Based on Multi-Parameter Modulation

The design of transmitting waveforms is an effective way to improve the detection performance of sonar systems. For the problem of high-range sidelobe when designing reverberation-resistant waveforms, this paper proposes a high-resolution wideband composite waveform design with reverberation suppression performance and a waveform parameter improvement method. Firstly, we propose a novel wideband waveform, which utilizes linear frequency modulation (LFM) as the fundamental pulse, referred to as multi-parameter coded modulation LFM pulse (MPCM-LFM). Additionally, we deduce the wideband ambiguity function for waveform design. Then, we deduce the constraint relations of the waveform parameters for different sub-band overlaps, and according to the mathematical expressions of the obtained range ambiguity function, we analyze in detail the effects of the waveform parameters on the range ambiguity function under different constraints. Secondly, on the basis of the analysis, we also propose a hopping carrier frequency constraint rule to optimize the spectral performance, and the range sidelobe is restrained effectively in significant measure by this parameter improvement method. Finally, we analyze the computer simulation results. It is obvious that our proposed waveform parameter improvement method leads to good results. The proposed improved MPCM-LFM signal shows a “near-thumbtack” ambiguity function, whose sidelobe suppression performance is superior to other classical waveforms in the desired region, and it can realize high-precision parameter estimation. In addition, the proposed improved MPCM-LFM signal possesses good performance in detecting stationary and low Doppler targets in the background of reverberation.

Cramér–Rao Lower Bounds for Estimating Time Delay and Doppler Stretch for Monostatic and Bistatic Impulse Radar Systems Using Ultrawideband-Throb Signal

In this article, the wideband ambiguity function (WBAF) of monostatic radar and that of bistatic radar, both operating with ultrawideband (UWB)-throb signals, are presented and used to calculate Cramér–Rao lower bounds (CRLBs) on the estimation accuracy of time delay and Doppler stretch in the case of monostatic radar and CRLBs on the estimation accuracy of receiver-to-target range and relative-velocity of a moving point target in the case of bistatic radar. Performance analysis is carried out to investigate the effects of the parameters that characterize the UWB-throb signal, i.e., pulse scaling factor, initial pulse repetition frequency (PRF), throb rate, and signal duration, and the parameters defining the bistatic-radar geometry, i.e., receiver-to-target range, baseline distance, and elevation angle, on the estimation accuracy of the monostatic-CRLBs and on that of the bistatic-CRLBs. Computer plots demonstrate that the estimation accuracy of the monostatic-CRLBs and the bistatic-CRLBs is influenced by the aforementioned radar parameters. It is also shown that target relative velocity has no major effects on the estimation performance of monostatic-CRLBs and bistatic-CRLBs.

A performance comparison between m-sequences and linear frequency-modulated sweeps for the estimation of travel-time with a moving source.

This manuscript discusses the utility of maximal period linear binary pseudorandom sequences [also referred to as m-sequences or maximum length sequences (MLSs)] and linear frequency-modulated (LFM) sweeps for the purpose of measuring travel-time in ocean-acoustic experiments involving moving sources. Signal design and waveform response to unknown Doppler (waveform dilation or scale factor) are reviewed. For this two-parameter estimation problem, the well-known wide-band ambiguity function indicates, and moving-source observations corroborate, a significant performance benefit from using MLS over LFM waveforms of similar time duration and bandwidth. The comparison is illustrated with a typical experimental setup of a source suspended aft of the R/V Sally Ride to a depth of∼10 m and towed at∼1 m/s speed. Accounting for constant source motion, the root mean square travel-time variability over a 30 min observation interval is 53 μs (MLS) and 141 μs (LFM). For these high signal-to-noise ratio channel impulse response data, LFM arrival-time fluctuations mostly appear random while MLS results exhibit structure believed to be consistent with source (i.e., towed transducer) dynamics. We conclude with a discussion on signal coherence with integration times up to 11 MLS waveform periods corresponding to ∼27 s.

Study of the relationship between sound signals and behaviors of a sperm whale during the hunting process

In order to study the relationship between the vocal law and the hunting demand of a sperm whale in the process of approaching and capturing prey, time domain characteristics such as waveform amplitude and inter click interval (ICI) and frequency domain characteristics such as centroid frequency and rms bandwidth of the sperm whale pulses are calculated firstly. Secondly, the sonar waveform parameters such as range resolution, speed resolution and Doppler tolerance are calculated using the wideband ambiguity function (WAF). Finally, variation of the above seven parameters is analyzed. The results show that the seven parameters change continuously during the hunting process. When switching from the approaching stage to the capture stage, the values of waveform amplitude, inter click interval, centroid frequency and range resolution will decrease, the values of speed resolution and rms bandwidth will increase, and the values of Doppler tolerance remain relatively unchanged. By analyzing variation of the seven parameters of the pulses and the hunting demand of the sperm whale in different hunting stages, we can better understand the relationship between the vocal law of the sperm whale and its hunting demand. We prove that the click pulses of the sperm whale transmitted during the stage of approaching and capturing prey are Doppler tolerant signals. The sperm whale constantly changes the ICI and signal forms of the transmitted signals during the approach and capture stages to adapt to different hunting demands at different hunting stages. Unlike the sonar signals of bats, the sperm whale does not change the length of the signals when switching from approach stage to capture stage, and instead it will reduce the peak pressure of the clicks significantly. The click pulses of the sperm whale in the process of approaching and capturing prey are more likely specially designed to accurately distinguish the position rather than the speed between targets, which is similar to the results of the previous research on dolphins.

Iterative matching-based parameter estimation for time-scale underwater acoustic multipath echo

In this paper, a wideband underwater acoustic multipath channel is investigated with a sonar-target relative movement. The underwater environment causes time delay, amplitude and Doppler factor changes on the transmitted signals, as a result, the signal components from the respective paths may be differentiated from these parameters. The Doppler factor of a specific path is analyzed in a moving condition, and the impulse responses of the propagation paths are illustrated by the wideband ambiguity function. Since different Doppler factors should be taken into consideration, an effective iterative method is proposed for parameter estimation of multipath echo. The proposed method retrieves a signal component by searching for the optimal scale factor from the resampling matching outputs, and eliminates the matching output of the estimated signal to analyze the next component. The effectiveness of the method is confirmed by some simulation results. It is also effective for various wideband signals with a broad range of frequencies, because the method prevents the time-domain subtractions of the received signals for providing a higher robustness. Therefore, it can be applied in many fields including active target detection and underwater communication.

Ambisonics and wideband matched-filter approach for bat biosonar study

We previously introduced a method of bat echolocation signal measurement and analysis for target angle estimation using a custom-built high-frequency (20–80 kHz) soundfield microphone and spatial audio techniques. The method provided precise angle estimates of multiple targets. This presentation will provide details and results of expanding the processing of these spatial audio signals using a wideband matched-filter. The custom-built ultrasonic soundfield microphone recorded a static bat’s echolocation signals directly in front of the bat’s head. The measured audio signal in B-format was processed and reproduced for all directions with an increment of 1 deg in azimuth and elevation using Ambisonic audio processing techniques. A matched-filter algorithm was developed and produced wideband ambiguity functions (WAF) of transmitted signals from a high-frequency transmitter or bats. The wideband matched-filter outputs filter responses of the reproduced signals in time domain for all directions. The target estimate accompanying the strongest filter response provides the range, normal velocity, angle, and elevation of the target. This presentation shows the hardware and software development including experimental validation to establish this new method for bat biosonar study.We previously introduced a method of bat echolocation signal measurement and analysis for target angle estimation using a custom-built high-frequency (20–80 kHz) soundfield microphone and spatial audio techniques. The method provided precise angle estimates of multiple targets. This presentation will provide details and results of expanding the processing of these spatial audio signals using a wideband matched-filter. The custom-built ultrasonic soundfield microphone recorded a static bat’s echolocation signals directly in front of the bat’s head. The measured audio signal in B-format was processed and reproduced for all directions with an increment of 1 deg in azimuth and elevation using Ambisonic audio processing techniques. A matched-filter algorithm was developed and produced wideband ambiguity functions (WAF) of transmitted signals from a high-frequency transmitter or bats. The wideband matched-filter outputs filter responses of the reproduced signals in time domain for all directions. The target est...

Ambiguity function analysis of human echolocator waveform by using gammatone filter processing

Human echolocation is a technique used by small group of people (normally blind persons) to observe their surrounding via emitting an active signal (usually tongue click) and analyse the return echo. This skill allows them to navigate safely by ‘seeing through sound’. Remarkable performances upon echolocating have attracted scholars’ attention from multidiscipline field including psychophysical and engineering. Study of waveform diversity has reported the signal is wideband, consisting of multiple frequency components with exponential decay factor that probably made up the entire unique signal. As such, wideband perspective is considered during ambiguity function analysis using wide-band ambiguity function method. The waveform analysis continues and reported optimum autocorrelation function is achieved by adopting a bio-inspired technique, which incorporated gammatone-filter processing. It will be interesting to synthesise the waveform using gammatone-filter approaches prior to relay it into ambiguity function process for analysis. Therefore, it is worth to explore its output results in this paper, which hold new findings that may help to understand how these humans achieve an optimum performance upon echolocating including ambiguity function characteristic. Thus, the new knowledge explored in this paper could be beneficial in emerging concept for new development in radar and sonar system application in near future.

Parameter Estimation Based on Sigmoid Transform in Wideband Bistatic MIMO Radar System under Impulsive Noise Environment.

Since second-order statistics-based methods rely heavily on Gaussianity assumption and fractional lower-order statistics-based methods depend on a priori knowledge of non-Gaussian noise, there remains a void in wideband bistatic multiple-input/multiple-output (MIMO) radar systems under impulsive noise. In this paper, a novel method based on Sigmoid transform was used to estimate target parameters, which do not need a priori knowledge of the noise in an impulsive noise environment. Firstly, a novel wideband ambiguity function, termed Sigmoid wideband ambiguity function (Sigmoid-WBAF), is proposed to estimate the Doppler stretch and time delay by searching the peak of the Sigmoid-WBAF. A novel Sigmoid correlation function is proposed. Furthermore, a new MUSIC algorithm based on the Sigmoid correlation function (Sigmoid-MUSIC) is proposed to estimate the direction-of-departure (DOD) and direction-of-arrival (DOA). Then, the boundness of the Sigmoid-WBAF to the symmetric alpha stable () noise, the feasibility analysis of the Sigmoid-WBAF, and complexity analysis of the Sigmoid-WBAF and Sigmoid-MUSIC are presented to evaluate the performance of the proposed method. In addition, the Cramér–Rao bound for parameter estimation was derived and computed in closed form, which shows that better performance was achieved. Simulation results and theoretical analyses are presented to verify the effectiveness of the proposed method.

Waveform Design for Dual-Function Radar-Communication System With Golay Block Coding

In view of the defects that high range side lobes and high peak-to-average power radio (PAPR) in radar and communication integrated systems based on traditional orthogonal frequency division multiplexing (OFDM), a co-designed OFDM waveform based on Golay block coding for joint radar-communication system is proposed in this paper. The communication information is coded into Golay complementary sequences by Reed-Muller codes, which can not only reduce the PAPR of the system, but also can improve the error correction capability. However, the code rate of the algorithm will decrease rapidly with the increase of the number of subcarriers. Furthermore, the traditional block coding would impact on the final superimposed waveform performance due to phase randomness. Hence, a self-disarrange block coding algorithm is proposed. The radar and communication performance of the designed waveform, including wideband ambiguity function, range profile, PAPR, and bit error rate, is analyzed and simulated. The results demonstrate that the PAPR of the waveform and BER can be reduced effectively, while the range side lobes can be decreased for better radar detection performance.

Study of the relationship between pilot whale (Globicephala melas) behaviour and the ambiguity function of its sounds

Pilot whales produce clicks, whistles and pulsed calls, which form a key component of their social lives. The three types of sound driven by their behavioural states are not directly observable. The mathematical tools which compute properties of sound are natural candidates for analysing the possible relationship between pilot whale sound and behaviour. In this paper, the wideband ambiguity function is used to compute the range resolution, speed resolution, Doppler tolerance, sidelobe-to-mainlobe suppression ratio of the range ambiguity function and sidelobe-to-mainlobe suppression ratio of the speed ambiguity function for pilot whale sound, which can be used to evaluate the abilities of pilot whale sound in detecting targets and resisting the influence of relative speed. Statistical results show that clicks have the best range resolution and its range ambiguity functions have the lowest sidelobe-to-mainlobe suppression ratio. Pulsed calls and part of the whistles have the best speed resolution and its speed ambiguity functions have the lowest sidelobe-to-mainlobe suppression ratio. The other part of whistles has a large Doppler tolerance. Analyzing the five parameters of different types of sound and the corresponding behaviour, we then reach a better understanding of the relationship between pilot whale sound and pilot whale behaviour.

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.

An efficient algorithm for WBAF estimation based on linear interpolation and its estimation error

Wideband ambiguity function (WBAF) plays an important role in radar, sonar, and GPS. However, the computational complexity of the conventional algorithms for WBAF is high. Moreover, because the signal is discretized the values between two sampling points of the sampled signal are unknown. These situations cause significant difficulty for the computation of the WBAF with Doppler stretch changing. To solve these problems, an algorithm based on linear interpolation is proposed to estimate the WBAF. According to the values of Doppler stretch and time delay, the locations of interpolation can be determined Based on these interpolation locations, the algorithm calculates the signal values, which are unknown but essential for WBAF, with linear interpolation; and then use the recovered values and original sampled values to estimate the WBAF. By using the linear interpolation, the algorithm does not need to utilize a great deal of the matched filters, and the conventional multirate sampling method is avoided. Therefore, the computational complexity of the algorithm can be reduced greatly. We analyzed the estimation error of WBAF to examine the performance of the algorithm. Moreover, we obtained the following results: the estimation error of the WBAF is mainly affected by the linear interpolation error, while the linear interpolation error depends on the time delay, Doppler stretch and sampling frequency. The estimation error is acceptable in the case of high sampling frequency. Numerical experiments verified the validity of the algorithm.

Statistical Characteristics of Signal Parameter Estimation by Normalized Correlation Function Maximization

In this paper differences between Fisher Information Matrix (FIM) and inverse covariation matrix of normalized correlation estimations for white and colored noise are investigated. It’s shown that implementation of normalized correlation function estimation leads to modification of maximum likelihood estimation FIM elements, so in case of arbitrary energy affected parameter vector, variance of estimation by normalized correlation function maximization is not equal to Cramer–Rao lower bound. Statistical characteristics of joint Doppler stretch and delay estimation by maximization of normalized correlation function for signal with nuisance parameters are derived in this paper. It’s shown that normalized correlator is equal to wideband ambiguity function, but this method of estimation follows from Cauchy–Schwarz inequality without using energy conservation assumptions. Besides, it is proved that estimation of Doppler stretch and delay by normalized correlation function or WBAF of signal with random initial phase and gain is asymptotically unbiased and effective.

An Active Detection Method for Buried Target Based on LFMCW Waveform

Underwater clutter is the main interference for active sonar to detect buried target. Anti-clutter waveform designing and processing method play a significant role in clutter suppression. This paper proposes a processing framework for detecting buried target. The linear-frequency-modulated continuous wave (LFMCW) signal is selected as the detecting waveform, and the properties of time-frequency distribution, spectrum, periodic fractional Fourier transform (PFRFT) and wideband ambiguity function (WAF) for LFMCW are analysed, then the waveform parameters is designed to well detect buried target. Furthermore, on the basis of PFRFT and WAF, this paper proposes a processing method for LFMCW. Both the theoretical analysis and simulation results validate the proposed method. Sine-square weighted LFMCW outperforms the rectangular weighted one.

Estimating the delay-Doppler of target echo in a high clutter underwater environment using wideband linear chirp signals: Evaluation of performance with experimental data.

A chirp signal is a signal with linearly varying instantaneous frequency over the signal bandwidth, also known as a linear frequency modulated (LFM) signal. It is widely used in communication, radar, active sonar, and other applications due to its Doppler tolerance property in signal detection using the matched filter (MF) processing. Modern sonar uses high-gain, wideband signals to improve the signal to reverberation ratio. High gain implies a high product of the signal bandwidth and duration. However, wideband and/or long duration LFM signals are no longer Doppler tolerant. The shortcoming of the standard MF processing is loss of performance, and bias in range estimation. This paper uses the wideband ambiguity function and the fractional Fourier transform method to estimate the target velocity and restore the performance. Target velocity or Doppler provides a clue for differentiating the target from the background reverberation and clutter. The methods are applied to simulated and experimental data.

Frequency shifting reduces but does not eliminate acoustic interference between echolocating bats: A theoretical analysis.

Bats have been observed to shift the frequency of their echolocation calls in the presence of other echolocating bats, ostensibly as a way to reduce acoustic interference. Few studies, however, have examined the theoretical efficacy of such jamming avoidance responses. The present study uses the wideband ambiguity function to analyze the effects of acoustic interference from conspecifics and congeneric heterospecifics on the target acquisition ability of Myotis californicus and Myotis yumanensis, specifically whether unilateral or bilateral frequency shifts reduce the effects of such interference. Model results suggest that in conspecific interactions, M. yumanensis recovers its target acquisition ability more completely and with less absolute frequency shift than does M. californicus, but that alternative methods of jamming avoidance may be easier to implement. The optimal strategy for reducing heterospecific interference is for M. californicus to downshift its call and M. yumanensis to upshift its call, which exaggerates a preexisting difference in mean frequency between the calls of the two species. Further empirical research would elucidate whether these species do in practice actively employ frequency shifting or other means for jamming avoidance, as well as illuminate the role of acoustic interference in niche partitioning.

Human echolocation: waveform analysis of tongue clicks

Some blind individuals have the ability to detect and classify objects in complex scenes by using echolocation based on ‘tongue clicks’. A waveform analysis of the tongue clicks collected from three blind individuals is presented who use tongue-click based echolocation on a daily basis. It is found that the tongue clicks are wideband signals and that that the spectrum of clicks varies within and between individuals. However, by using the wideband ambiguity function, it is found that all of the clicks from three different individuals share some common characteristics.

The Mellin Matched Filter

In propagation channels signals are undergone translation and dilation changes. The Fourier and Mellin transforms are natural foundations of the analysis of wideband signals. Three interconnected problems, where the Mellin transform plays a key role, are considered in the paper: i) synthesis of a linear matched filter that is invariant to signal scale; ii) estimation of the signal scale; and iii) the wideband ambiguity function and its properties. The filter that is invariant to the signal scale and maximizes the output SNR is synthesized in the paper using the Mellin transform. The filter is named the Mellin matched filter. Introduction of the Mellin matched filter allows to give a new interpretation of the signal scale estimation and the wideband ambiguity function. Concept of the Mellin matched filter facilitates to produce a physical interpretation of the resolution of wideband signals and the time-frequency-scale uncertainties.

Cramer-Rao Lower Bounds for the Joint Delay-Doppler Estimation of an Extended Target

The problem on the Cramer-Rao Lower Bounds (CRLBs) for the joint time delay and Doppler stretch estimation of an extended target is considered in this paper. The integral representations of the CRLBs for both the time delay and the Doppler stretch are derived. To facilitate computation and analysis, series representations and approximations of the CRLBs are introduced. According to these series representations, the impact of several waveform parameters on the estimation accuracy is investigated, which reveals that the CRLB of the Doppler stretch is inversely proportional to the effective time-bandwidth product of the waveform. This conclusion generalizes a previous result in the narrowband case. The popular wideband ambiguity function (WBAF) based delay-Doppler estimator is evaluated and compared with the CRLBs through numerical experiments. Our results indicate that the WBAF estimator, originally derived from a single scatterer model, is not suitable for the parameter estimation of an extended target.

Analysis of Tracking Performance about DS/FH TT&C Based on Ambiguity Function

After introducing the ambiguity function theory of radar analysis, wideband ambiguity function about Direct Spread/Frequency Hopping (DS/FH) signal is derived out in this paper. From the point of signal simulation ambiguity figure, the tracking performance is studied and analyzed, that includes ambiguity character and signal resolution under the influence of frequency switching time and phase discontinuous. Conclusion shows the following design difficulty based on feasibility in DS/FH TT&C.