Ambiguity Function Research Articles

A Particle Fuzzy Decisive Framework for Moving Target Detection in the Multichannel SAR Framework

Target detection is one of the important subfields in the research of Synthetic Aperture Radar (SAR). It faces several challenges, due to the stationary objects, leading to the presence of scatter signal. Many researchers have succeeded on target detection, and this work introduces an approach for moving target detection in SAR. The newly developed scheme named Adaptive Particle Fuzzy System for Moving Target Detection (APFS-MTD) as the scheme utilizes the particle swarm optimization (PSO), adaptive, and fuzzy linguistic rules in APFS for identifying the target location. Initially, the received signals from the SAR are fed through the Generalized Radon-Fourier Transform (GRFT), Fractional Fourier Transform (FrFT), and matched filter to calculate the correlation using Ambiguity Function (AF). Then, the location of target is identified in the search space and is forwarded to the proposed APFS. The proposed APFS is the modification of standard Adaptive genetic fuzzy system using PSO. The performance of the MTD based on APFS is evaluated based on detection time, missed target rate, and Mean Square Error (MSE). The developed method achieves the minimal detection time of 4.13[Formula: see text]s, minimal MSE of 677.19, and the minimal moving target rate of 0.145, respectively.

Determination of the Appropriate Kernel Structure in Electroencephalography Analysis of Alcoholic Subjects

Alcoholism is one of the major health problems in the world. The organ most affected by alcohol is the brain. It has been shown that alcohol causes neuronal loss in the brain and reduces brain blood flow and oxygen use. Electroencephalography is a method that measures the instantaneous electrical activity of the brain. It is known that valuable information can be obtained by observing the biological effects of alcohol through EEG. As their methods of signal processing and analysis have evolved, Electroencephalography signals have attracted the attention of researchers in this field. In this study, methods of the time-frequency analysis were applied to Electroencephalography signals obtained from normal and alcoholic subjects. For this purpose, the Cohen’s class distribution was examined. Ambiguity function analysis, which was in the structure of the distribution, was applied to the signals. Then, from the kernel structure inside the distribution, the Wigner-Ville distribution, which was very common, was reached and this distribution was examined. The inadequacy of the distribution resolution was seen and analysis of the new time-frequency distributions, which were obtained by making convolution with 4 types of kernel functions (nonseparable, separable, Doppler independent, lag independent), was performed. As a result, it was shown that the resolution of time-frequency distributions could be improved with proper kernel functions. Thus, at the end of these analyses, changes that alcohol caused in brain functions were revealed.

Instantaneous Ambiguity Reinitialization and Fast Ambiguity Initialization for L1-L2 GPS Measurements.

This paper presents a PREcise and Fast Method of Ambiguity Reinitialization/Resolution (PREFMAR) for L1 and L2 in GPS measurements. The method determines and ambiguities based on the ambiguity functions: and . These ambiguity functions have been described in detail in this work. The developed method of ambiguity initialization and reinitialization in relative positioning can use Global Positioning System (GPS) measurements from only two satellites and one measurement epoch. To resolve and ambiguities, a variance-covariance (VC) matrix of the float solution is not needed. The size of the search area in the PREFMAR method depends on code and phase accuracy as well as on the GNSS signal frequencies. Therefore, the search area is specific for every double or triple Global Navigation Satellite Systems (GNSS) data frequency. However, this part of the research only presents the ambiguity search area for L1 and L2 of GPS measurements. Additionally, a numerical example has been analyzed in detail with the use of the PREFMAR method and a float solution (, ). Finally, the elaborated algorithms were successfully tested on real L1 and L2 GPS measurements for instantaneous ambiguity reinitialization. The PREFMAR method allows instantaneous ambiguity reinitialization if all satellites lose contact with a GNSS antenna, for short and long baselines. Therefore, the PREFMAR has a great potential for precise real-time kinematic GNSS navigation.

Multi-Functional Radar Waveform Generation Based on Optical Frequency-Time Stitching Method

A photonic-assisted multi-functional radar waveform generator for single-chirped, counter-chirped, and dual-band linear frequency-modulated (LFM) microwave waveforms generation is proposed and experimentally demonstrated based on an optical frequency-stepped waveform (FSW) generator. The optical FSW generator is realized by an optical switch and an optical frequency shifting loop (OFSL). When an electrical rectangular LFM pulse is applied to the proposed signal generator, an optical frequency-stepped LFM signal would be generated. By carefully setting the time length and the bandwidth of the rectangular LFM pulse, we can achieve an optical linearly-chirped continuous wave. Optical frequency-time stitching is thus realized. Combining the optical linear-chirped signal with one or more optical wavelengths, and meticulously adjusting the value of the optical wavelengths, single-chirped, counter-chirped or dual-band LFM signals can be produced. An experiment is carried out. Single-chirped and counter-chirped LFM signals of 8-32 GHz over a time duration of 5 μs, and dual-band LFM signals of 8-16 GHz & 15-23 GHz and 8-20 GHz & 20-32 GHz are generated. The ambiguity functions of the generated signals are investigated.

Formulation for renormalon-free perturbative predictions beyond large-\u03b20 approximation

We present a formulation to give renormalon-free predictions consistently with fixed order perturbative results. The formulation has a similarity to Lee’s method in that the renormalon-free part consists of two parts: one is given by a series expansion which does not contain renormalons and the other is the real part of the Borel integral of a singular Borel transform. The main novel aspect is to evaluate the latter object using a dispersion relation technique, which was possible only in the large-β0 approximation. Here, we introduce an “ ambiguity function,” which is defined by inverse Mellin transform of the singular Borel transform. With the ambiguity function, we can rewrite the Borel integral in an alternative formula, which allows us to obtain the real part using analytic techniques similarly to the case of the large-β0 approximation. We also present detailed studies of renormalization group properties of the formulation. As an example, we apply our formulation to the fixed-order result of the static QCD potential, whose closest renormalon is already visible.

Moving target localization for multistatic passive radar using delay, Doppler and Doppler rate measurements

Time delay and Doppler shift between the echo signal and the reference signal are two most commonly used measurements in target localization for the passive radar. Doppler rate, which can be obtained from the extended cross ambiguity function, offers an opportunity to further enhance the localization accuracy. This paper considers using the measurement Doppler rate in addition to measurements of time delay and Doppler shift to locate a moving target. A closed-form solution is developed to accurately and efficiently estimate the target position and velocity. The proposed solution establishes a pseudolinear set of equations by introducing some additional variables, imposes weighted least squares formulation to yield a rough estimate, and utilizes the function relation among the target location parameters and additional variables to improve the estimation accuracy. Theoretical covariance and Cramer-Rao lower bound (CRLB) are derived and compared, analytically indicating that the proposed solution attains the CRLB. Numerical simulations corroborate this analysis and demonstrate that the proposed solution outperforms existing methods.

High-Accuracy Multinode Ranging For Coherent Distributed Antenna Arrays

The design and experimental implementation of a waveform for high-accuracy internode ranging in a coherent distributed antenna array is presented. Based on a spectrally sparse high-accuracy ranging waveform, the presented multifrequency waveform enables high-accuracy ranging between multiple nodes in an array simultaneously, without interference. The waveform is based on a unique time–frequency duplexing approach combining a stepped-frequency waveform with different step cycles per node pair. The waveform also inherently includes beneficial disambiguation properties. The ambiguity function of the waveform is derived, and theoretical bounds on the ranging accuracy are obtained. Measurements were conducted in software-defined radio-based nodes in a three-element distributed array, demonstrating high-accuracy unambiguous ranging between two slave nodes and one master node.

Sidelobe improvement of Golay set sequences by using SA for radar applications

This study has been made to improve the detection capacity of radar using phase coded waveforms especially the Golay set sequence while keeping the sidelobe ambiguity function to the possible minimum. This Letter begins with a description of Golay complementary sets construction from a graph and a determination of the parameters on which they depend to be optimised after. Then, the simulated annealing (SA) algorithm has been proposed to deal with low ambiguity problem of the Golay set, due to its simplicity and also to its effectiveness to solve this kind of problem. Simulation results show that the optimisation with SA has impressively improved the sidelobe rejection of Golay set sequences with a gain of up to 20 dB.

A New Compact Delay, Doppler Stretch and Phase Estimation CRB with a Band-Limited Signal for Generic Remote Sensing Applications

Since time-delay, Doppler effect and phase estimation are fundamental tasks in a plethora of engineering fields, tractable lower performance bounds for this problem are key tools of broad interest for a large variety of remote sensing applications. In the large sample regime and/or the high signal-to-noise ratio regime of the Gaussian conditional signal model, the Cramér–Rao bound (CRB) provides an accurate lower bound in the mean square error sense. In this contribution, we introduce firstly a new compact CRB expression for the joint time-delay and Doppler stretch estimation, considering a generic delayed and dilated band-limited signal. This generalizes known results for both wideband signals and the standard narrowband signal model where the Doppler effect on the band-limited baseband signal is not considered and amounts to a frequency shift. General compact closed-form CRB expressions for the amplitude and phase are also provided. These compact CRBs are expressed in terms of the baseband signal samples, making them especially easy to use whatever the baseband signal considered, therefore being valid for a variety of remote sensors. The new CRB expressions are validated in a positioning case study, both using synthetic and real data. These results show that the maximum likelihood estimator converges to the CRB at high signal-to-noise ratios, which confirms the exactness of the CRB. The CRB is further validated by comparing the ambiguity function and its 2nd order Taylor expansion where the perfect match also proves its exactness.

Uniqueness of STFT phase retrieval for bandlimited functions

We consider the problem of phase retrieval from magnitudes of short-time Fourier transform (STFT) measurements. It is well-known that signals are uniquely determined (up to global phase) by their STFT magnitude when the underlying window has an ambiguity function that is nowhere vanishing. It is less clear, however, what can be said in terms of unique phase-retrievability when the ambiguity function of the underlying window vanishes on some of the time-frequency plane. In this note, we demonstrate that by considering signals in Paley–Wiener spaces, it is possible to prove new uniqueness results for STFT phase retrieval. Among those, we establish a first uniqueness theorem for STFT phase retrieval from magnitude-only samples for real-valued signals.

Dual-Use Signal Design for Radar and Communication via Ambiguity Function Sidelobe Control

This article considers the dual-use unimodular signal design for a novel dual-functional radar-communication (DFRC) architecture. The information of downlink communication is modulated via the ambiguity function (AF) sidelobe nulling in the prescribed range-Doppler cells. At the same time, the sidelobe around the AF mainlobe is suppressed to ensure the radar detection performance. User equipment (UE) computes the AF of the received signal to make a judgment of the position of nulling for achieving demodulation. To this end, an objective function to evaluate the depth of nulling in AF is developed as figure of merit accounting for the worst-case sidelobe level ratio over the range-Doppler cells of interest. The resultant design is very challenging to solve due to the non-convex and non-smooth quartic fractional objective function and the NP-hard constant modulus constraint. Herein, we develop a fractional-alternating direction penalty method (FADPM) algorithm that invokes the fractional program theory and the ADPM framework. Specifically, we formulate a new ADPM form through introducing an auxiliary variable and resorting to the Dinkelbach's procedure. In each iteration, we transform the original quartic fractional program into two quadratic optimization subproblems both of which are approximated successively through a series of convex subproblems. We also provide the analytical convergence guarantee of the proposed FADPM algorithm. The simulation results verify the performance of the proposed algorithm and exhibit the effectiveness of the DFRC framework in modulation and demodulation process guaranteeing that a high data rate is achievable.

Frequency Hopping Signal Sorting Algorithm Based on Global Feature of Ambiguity Function

Aiming at the problem that the traditional feature parameters are difficult to meet the fastness and effectiveness of frequency-hopping signal sorting recognition, a feature extraction method based on ambiguity function theory is proposed. The algorithm applies the ambiguity function theory to the frequency hopping signal sorting and identification. Firstly, the ambiguity function of the single-hop signal is calculated, then the AFMR slice of the signal is extracted by the PSO algorithm, and the global features of the AFMR slice are extracted to form the feature vector. The results of FCM clustering experiments show that the extracted feature parameters have higher sorting accuracy and can adapt to the larger dynamic signal-to-noise ratio.

Doppler Resilient Complementary Waveform Design for Active Sensing

Active sensing systems prefer probing waveforms with good auto-correlation properties. Faced with the difficulty in getting individual sequences with impulse-like aperiodic auto-correlation functions, we resort to the temporal waveform diversity based on complementary sets of sequences (CSS). It seems an ideal solution, but has rarely been used due to the extreme sensitivity of CSS to Doppler shifts. This paper is devoted to applying numerical methods to the design of Doppler resilient complementary waveforms (DRCW) whose ambiguity functions are almost free of range sidelobes along modest Doppler shifts. We formulate the problem as minimizing the worst-case peak sidelobe level (PSL) with low peak-to-average power ratio (PAR) constraints, and then approximate the min-max problem by a ${l}_{p}$ -norm minimization problem. A hierarchical strategy is developed to tackle the phase optimization and the amplitude-phase optimization respectively. Correspondingly, two algorithms based on phase-gradient and Majorization-Minimization are proposed, both of which can be efficiently computed via FFT. Numerical experiments show our method is effective and superior to existing ones. The DRCWs thus obtained have their range sidelobes at all lags suppressed below −60dB, and are expected to bring significant performance improvements in active sensing. Two application examples, detecting weak targets in heavy clutter and estimating the high-resolution range profile of an extended target by active radars, are given.

Using the perceptual past to predict the perceptual future influences the perceived present - A novel ERP paradigm.

The information available through our senses is noisy, incomplete, and to varying degrees ambiguous. The perceptual system must create stable and reliable percepts out of this restricted information. It solves this perceptual inference problem by integrating memories of previous percepts and making predictions about the perceptual future.Using ambiguous figures and a new experimental approach, we studied whether generating predictions based on regularities in the past affects processing of the present and how this is done. Event-related potentials (ERPs) were measured to investigate whether a highly regular temporal context of either ambiguous or unambiguous stimulus variants differently affects processing of a current stimulus and/or task execution. Further, we tested whether symbolic announcements about the immediate perceptual future can replace the past experience of regularities as a source for making predictions. Both ERP and reaction time varied as a function of stimulus ambiguity in the temporal context of a present stimulus. No such effects were found with symbolic announcements.Our results indicate that predictions about the future automatically alter processing of the present, even if the predictions are irrelevant for the present percept and task. However, direct experiences of past regularities are necessary for predicting the future whereas symbolic information about the future is not sufficient.

Conveying symbolic relations: Children’s ability to evaluate and create informative legends

Two studies were conducted to examine 4- to 6-year-old children’s understanding of how to convey symbol–referent relations using legends. Study 1 investigated children’s ability to evaluate legends in terms of whether or not they clearly convey information (N = 74). In this study, 41% of children were successful, with performance uniquely differentiated by sensitivity to ambiguity and executive function. Study 2 investigated children’s ability to create informative legends (N = 115), with 39% being successful. Nearly half of those who were unsuccessful improved after exposure to exemplars (relative to only 9% in the baseline group). Sensitivity to ambiguity uniquely differentiated their ability to create a legend and improve after exposure. These studies provide insight into children’s developing understanding of how symbol meanings are effectively conveyed and the contributions of other cognitive factors.

Ambiguity Function Analysis of Random Frequency and PRI Agile Signals

Random frequency and pulse repetition interval (PRI) agile (RFPA) signals bring excellent performance of electronic counter-countermeasures to radar systems and have been received considerable attention in recent years. However, the research on their ambiguity function (AF) is not comprehensive. In this article, the analytical expressions of the AF expectation and variance are given. According to the expressions, the direct relationships between the key metrics of the AF and the waveform parameters of RFPA signals are specified. The results in this article are verified by Monte Carlo simulations and provide some insights into RFPA waveform design.

A Novel Data-Driven Specific Emitter Identification Feature Based on Machine Cognition

Machine learning becomes increasingly promising in specific emitter identification (SEI), particularly in feature extraction and target recognition. Traditional features, such as radio frequency (RF), pulse amplitude (PA), power spectral density (PSD), and etc., usually show limited recognition effects when only a slight difference exists in radar signals. Numerous two-dimensional features on transform domain, like various time-frequency representation and ambiguity function are used to augment information abundance, whereas the unacceptable computational burden usually emerges. To solve this problem, some artfully handcrafted features in transformed domain are proposed, like representative slice of ambiguity function (AF-RS) and compressed sensing mask (CS-MASK), to extract representative information that contributes to machine recognition task. However, most handcrafted features only utilizing neural network as a classifier, few of them focus on mining deep informative features from the perspective of machine cognition. Such feature extraction that is based on human cognition instead of machine cognition may probably miss some seemingly nominal texture information which actually contributes greatly to recognition, or collect too much redundant information. In this paper, a novel data-driven feature extraction is proposed based on machine cognition (MC-Feature) resort to saliency detection. Saliency detection exhibits positive contributions and suppresses irrelevant contributions in a transform domain with the help of a saliency map calculated from the accumulated gradients of each neuron to input data. Finally, positive and irrelevant contributions in the saliency map are merged into a new feature. Numerous experimental results demonstrate that the MC-feature can greatly strengthen the slight intra-class difference in SEI and provides a possibility of interpretation of CNN.

Evaluation of phase-frequency instability when processing complex radar signals

A new radar system for digital signal processing before detection is proposed. These are the guidelines for selecting an intermediate frequency for signal processing. The features of signal processing in the case of echo-signal selection by the features of the correlation properties of their complex bypass are described. This paper presents the study of ambiguity function (AF) when processing complex radar signals. In this work, the AF synthesis was performed considering non-determined components and the presence of phase-frequency instability. The received result enhances the potentials for distinguishing an incoherent radar signal. The numerical simulation results of received AF are presented. Considering fluctuation components in the complex AF, depending on the laws of the distribution of amplitude and frequency fluctuations and their parameters, allowed to get the gain in the width of the main lobe from the units to tens of times. Paper represents original analytical expressions for AF of radio-signals modulated by narrow band random processes with various distribution laws.

Identification of Energy-Hidden Chirp Signals of Telecommunication Systems in Conditions of Parametric Uncertainty

The ambiguity diagram of rectangular chirp RF pulse has been analyzed. The characteristic point of ambiguity diagram was identified. It was proposed to identify the signal on the basis of correlation level at the characteristic point of ellipsoidal ambiguity diagram built in a special coordinate system. The quasi-optimal autocorrelation algorithm with quadrature processing is proposed. This algorithm is resistant to a priori uncertainty of parameters of input energy-hidden signals with unknown waveform and unknown initial phase against the background of Gaussian stationary noise. The tuning parameters of identification scheme and the decision-making rule regarding the availability of chirp signal in the input mixture were determined. The simulation modeling of identification procedure was conducted using the software package Matlab R2016a. The simulation results confirmed the ability of the proposed algorithm to identify the chirp signal in the input mixture at small values of the signal-to-noise ratio.

Radar code design to optimise detection under whitened similarity constraint

An active sensing system, such as radar, extracts the useful features of the targets of interest, by transmitting a certain waveform to a particular area and analysing the returned signal. There are two factors that are critical to the system performance, namely the receive filter and the transmitted waveform. Transmitted signal is among the most interesting factor affecting the radar system performance in complex environments. The waveform design problem is an important stage in the performance of cognitive radars. Here, the matched illumination approach is studied which specially addresses the issue of adaptive waveform design to maximise the signal-to-disturbance ratio that finally leads to an increased probability of detection. Different constraints on the designed waveform have been introduced in the literature. However, the focus is on the similarity constraint that controls the ambiguity function and modulus variations of the devised code. In more details, it is shown that this kind of constraint should be written based on the estimated background covariance matrix leading to a proposed whitened similarity constraint. It is shown by simulation that the proposed whitened constraint outperforms the well-known similarity one in resultant ambiguity function properties and probability of detection, assuming the same environmental conditions.