Space–time Radon–Fourier transform and applications in radar target detection

The multivariate range function of the high-speed maneuvering target induces modulations on both the envelop and phase, i.e., the range cell migration (RCM) and Doppler frequency migration (DFM) which degrade the long-time coherent integration used for detection and localization. To solve this problem, many long-time coherent integration methods have been proposed. Based on mechanisms of typical methods, this paper names two signal processing modes, i.e., processing unification (PU) mode and processing separation (PS) mode, and presents their general forms. Thereafter, based on the principle of the PS mode, a novel long-time coherent integration method, known as the generalized dechirp-keystone transform (GDKT), is proposed for radar high-speed maneuvering target detection and localization. The computational cost, energy integration, peak-to-sidelobe level (PSL), resolution, and anti-noise performance of the GDKT are analyzed and compared with those of the maximum likelihood estimation (MLE) method and keystone transform-dechirp (KTD) method. With mathematical analyses and numerical simulations, we validate two main superiorities of the GDKT, including (1) the statistically optimal anti-noise performance, and (2) the low computational cost. The real radar data is also used to validate the GDKT. It is worthwhile noting that, based on closed analytical formulae of the MLE method, KTD method, and GDKT, several doubts in radar high-speed maneuvering target detection and localization are mathematically interpreted, such as the blind speed sidelobe (BSSL) and the relationship between the PU and PS modes.

Radar fast long-time coherent integration via TR-SKT and robust sparse FRFT

The digital array radar (DAR) is a fully digitized phased array radar in which digital beam forming technique is used both in receive and transmit. A lot of simulations are made about the influence of amplitude-phase error on the antenna pattern, since amplitude-phase error of the antenna will severely affect the performances of the digital array radar. Based on the far-field external monitoring principle, the amplitude-phase error calibration method of the digital processing is studied, and the “in-the-field calibration” method, combining the reference data and the mid-field monitoring, is finally presented. Besides, the key techniques of the real-time DBF based on the FPGA processing platform are analyzed. The test results show that by using the method proposed, the high-precise calibration data can be obtained and the antenna beam after calibration can meet the digital array radar's requirements, and moreover the FPGA processing platform can realize the real-time multi-beam processing. It is a probe that the method combines the reference data and the mid-field monitoring, which is a simple, feasible and effective method for the digital array radar in the field calibration.

This paper introduces a new concept of focus-before-detect (FBD) with long-time coherent integration to improve detection of low-SNR and high-speed radar target. By modeling the target range migration function with limited motion and position parameters, the target's echo energy can be focused and projected into a low-dimensional parameter space via the proposed FBD method. Compared to the existing Doppler filter bank and track-before-detect (TBD) method, the proposed FBD method may obtain higher SNR gain and effectively overcome the non-desired effects of across range unit and across Doppler unit for the long-time coherent integration. Therefore, larger coverage diagram and smaller detectable radar cross-section may be obtained for an FBD-based radar system.

Coherent integration is a conventional approach to improve detection ability in radar applications, whereas its performance is decreased by migration through range cell due to the motion of target, limiting the time of integration. This problem becomes more severe in terahertz band. This paper introduces Keystone transform to terahertz radar in order to realize long-time coherent integration, aiming to get a successful detection of targets. Moreover, doppler ambiguity is resolved based on intra-pulse interference processing. A simulation is conducted to demonstrate the effective improvement for target detection using Keystone transform in terahertz radar.

Deep neural network-aided coherent integration method for maneuvering target detection

Signal integration, as an effective method of detecting weak target, is widely used in areas of radar, sonar, etc. In previous studies of long-time coherent integration, researchers usually established a multi-pulse echo model with linear frequency modulation (LFM) signal due to its good compression performance and large Doppler tolerance. Then, perfect analytical formula can be deduced to compensate for range migration and Doppler spread, which is helpful in analyzing the mechanism of long-time coherent integration in depth. However, besides LFM, a wide variety of signal waveforms are also used in modern sonar and underwater guidance system to meet the requirements for diverse applications. For instance, continuous wave (CW) pulse is often used in signal detection, high resolution direction of arrival (DOA) estimation, and velocity estimation, while large time-bandwidth product waveforms such as modulated signal, coded signal, and pseudo-random signal are utilized for special tasks like anti-interference detection, channel matching, and active concealed detection. Therefore, the formulas and corresponding instructive conclusions deduced by LFM have no generality when other sonar waveforms are used in pulse integration. In this paper, we focus on long-time coherent integration for arbitrary signal reflected by underwater target moving with a uniform velocity and propose a motion-compensated coherent integration method for arbitrary complex envelop signal. A kind of general ambiguity function (GAF) for transmitted signal is defined to present a unified expression based on GAF for the output of the matched filter. The operation not only helps us to describe and calculate the pulse compression form of the arbitrary complex envelop by using a general mathematical model, but also provides information about the range migration and Doppler frequency shift of the multi-pulse echo, which is needed in pulse range alignment and FFT integration. For the matched filter output expressed by the GAF, Keystone transform is utilized to correct the complex envelop of the multi-pulse echo and eliminate the range walk. Then, Doppler frequency shift is compensated for by performing FFT transform, and the long-time coherent integration for arbitrary complex envelop is realized. To verify the correctness of the proposed method, we carry out the computer simulation on both signal integration and detection performance by using four sonar waveforms, i.e., CW signal, LFM signal, m-sequence phase-coded signal, and Costas frequency hop coded signal. The simulation results show that the proposed motion-compensated coherent integration method is applicable to arbitrary complex envelop signal. We also design an anechoic water tank experiment scheme which can successfully obtain the multi-pulse echoes of constant moving target. The motion-compensated coherent integration of the experimental data of the above-mentioned four waveforms further validates the effectiveness of the proposed method.

Long-time coherent integration can remarkably improve the detection and motion parameter estimation ability of radar for maneuvering targets. Unfortunately, the linear range migration, quadratic range migration (QRM), and Doppler frequency migration (DFM) within the coherent processing interval seriously degrade the target detection and parameter estimation performance. In this regard, a novel coherent integration approach based on frequency autocorrelation function (FAF) and Lv’s distribution (LVD), i.e., FAF–LVD, is proposed in this paper. The QRM is firstly removed by the second-order keystone transform. Then, the FAF with a variable delay is introduced to remove the DFM, followed by the scaled Fourier transform to achieve coherent integration. Finally, the acceleration and velocity are estimated simultaneously by LVD. Analysis demonstrates that FAF–LVD could be efficiently implemented via complex multiplications, the fast Fourier transform (FFT) and inverse FFT. Detailed comparisons with several representative methods indicate that FAF–LVD achieves a better balance among computational complexity, detection ability, and parameter estimation performance. Extensive simulations are presented to validate the effectiveness of FAF–LVD method.

Based on constant acceleration radial distance model, a novel approach to long-time coherent integration is provided. This technique focuses on detecting high speed targets with ARU walk, by compensating the phase fluctuations of target echoes after pulse compression along slow time dimension. The numerical experiments are provided to demonstrate the effectiveness of the proposed method.

The Discrete Fourier Transform (DFT), which can be calculated efficiently by the Fast Fourier Transform (FFT), is one of the most commonly used tools for frequency estimation of a multi-frequency exponential signal. However, the performance of the FFT is inherently affected by spectral leakage when non-coherent sampling occurs. The Chirp-Z Transform (CZT), which can refine the spectrum to the narrowband range of the source signal accurately, can be generalized to a special form of DFT. This paper proposes a CZT based algorithm which can estimate frequencies of the multi-frequency exponential signal accurately. In our method, the CZT bin, as a nonlinear equation, is firstly used to describe the correspondence among the frequencies, amplitudes, phases and the observed spectrum. Then, the above nonlinear equation is rewritten as a linear equation with unknown frequencies. We further extend the proposed method to the Discrete-time Fourier Transform (DTFT), zero-padding FFT and DFT, which are the special cases of the CZT. We also give the derivation procedure of theoretical variance of our method. In our method, the spectrum leakage is fully considered as useful information to establish the linear equation set. Therefore, it can estimate the frequencies of multi-frequency exponential signal with high accuracy. Simulation results verify the performance of the proposed method.

In order to make full use of the digital array radar (DAR), effective dwell scheduling must be implemented. According to the signal processing characteristics of DAR, an adaptive dwell scheduling algorithm is proposed. In this algorithm, time and energy vectors are introduced to implement pulse interleaving and the scheduling analysis, which breaks the limitations of strict interleaving conditions, and reduces the complexity of scheduling analysis compared with existing algorithms based on pulse interleaving technique. Meanwhile, the synthetic priority of the task and the validity of scheduling it are considered comprehensively. Simulation results demonstrate that the proposed algorithm can effectively improve the scheduling performance for DAR.

Nondestructive testing (NDT) methods for identifying stress levels in materials mostly rely on the theory of acoustoelasticity. However, the sensitivity and the accuracy of acoustoelasticity are affected by several factors such as the (1) type, (2) propagation, and (3) polarization directions of the used signals. This paper presents the results of an experimental investigation of longitudinal waves propagating perpendicular to the applied uniaxial tensile stresses in structural steel specimens. The changes in four ultrasonic signal characteristics were investigated with increasing stress levels ranging from below to above the yield stress of steel. The considered signal characteristics were the peak amplitudes and signal energy in the time domain, and the fast Fourier transform (FFT) and chirp-Z transform (CZT) in the frequency domain. Even though the acoustoelastic effect on the type ultrasonic signal used is very small, clear distinctions between prior to and postyielding are observed for all investigated parameters. The results are presented with a detailed statistical and receiver operating characteristics (ROCs) analyses. The results show that identifying damage to steel structures due to local yielding is possible using the simple ultrasonic signal classification.

In this paper, we discuss two effective methods for computing optical propagations using two-dimensional (2D) discrete Fourier transforms: the matrix triple product (MTP) and the chirp z-transform (CZT) and analyze their performance both in theory and via benchmarks compared to the performance of a traditional padded fast Fourier transform (FFT). We show that, in many regimes of interest for phase-retrieval algorithms, the MTP or CZT is comparable to or better than the FFT in terms of run time while offering more flexible control over the sampling. We propose that for many applications, the CZT makes a robust general purpose alternative to the padded 2D FFT.

Digital Array Module (DAM) is one of the key components of digital array radar (DAR). Usually, a DAR contains tens to hundreds of DAMs, which is making it increasingly difficult for human operators to test them in limited time. Therefore, the technique for automatic test of DAMs is in urgent demand. This paper presents a DAM automatic test system (ATS) that has proved successful in several radar test projects. We first analyze the requirement of automatic test according to characters of DAM. After that we propose a brief of comprehensive framework as well as the design scheme of hardware and software. We finally discuss the method of testing data acquisition and algorithm for calculating performance indexes. Application examples have shown that the system can meet the great demand of testing tasks with high automation, efficiency, and accuracy.

An Entropy-based PSO for DAR task scheduling problem