Long-time coherent integration for target detection in terahertz radar

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

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.

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.

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.

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.

This study proposes the Space–time Radon–Fourier transform (STRFT) for wideband digital array radar (DAR). It is a novel coherent detection technique that jointly realise wideband digital beamforming (DBF), range compression and long-time coherent integration. The likelihood ratio detector (LRT) is first derived based on the three-dimensional (3D) signal model of moving targets, which is the output of the STRFT on the 3D range-compressed echoes. Some transform properties of the proposed STRFT are also discussed. This include the 3D impulse response, 3D translational invariance, multi-target linear additivity, linear SNR gain in additive white Gaussian noise (AWGN), as well as the 3D correlation function of transformed AWGN. Also, the fast implementation of STRFT is proposed in the element-pulse-range frequency domain, which is realised via the two dimensional Chirp-Z transform (CZT) based on fast Fourier transform (FFT) operators. The proposed method may remarkably reduce the computational burden for modern wideband DAR. Finally, some numerical experiments are provided to demonstrate the effectiveness of the proposed methods.

Long-time coherent integration using frequency hopping signals is a challenging problem for passive bistatic radar due to its frequency hopping characteristics. Apart from range walk, range curve, and Doppler frequency migration, Doppler diffusion caused by frequency hopping characteristics occurs within the observation time, which also lowers the detection performance. To deal with this problem, a novel coherent integration method for frequency hopping signals based on passive bistatic radar is proposed in this paper. In this novel method, range curve and range walk are eliminated by applying generalized Keystone transform. Then, Doppler frequency migration caused by the target's acceleration is compensated for by a parameter search with a designed search scope. Finally, Doppler frequency migration caused by frequency hopping characteristics is compensated for by designing a new acceleration compensation function and a revised rotation factor for Fourier transform. Since migration effects caused by frequency hopping characteristics are considered and compensated for when using frequency hopping signals, the weak target echo can be better integrated in the observation time compared to when using the existing methods. The simulation results and performance analysis illustrate the effectiveness of the proposed 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.

Terahertz radar has unique advantages, including large bandwidth, high resolution, Doppler sensitivity, and anti-interference; it is a significant development in the field of target detection. Herein, the history of electronic and optical terahertz radar systems is introduced, and the current situation and latest progress pertaining to these systems are reviewed. The target characteristics of terahertz radar are summarized based on its mechanism, calculation, and measurement. Moreover, the current research status of terahertz SAR, ISAR, array, and aperture encoding imaging are discussed, and the applications of terahertz radar, such as early warning detection and security anti-terrorism systems, are briefly introduced. Finally, the development direction of terahertz radar technology is forecast.

Currently, target detection usually requires long-time coherent integration and suffers the Doppler shift, due to the velocity of maneuvering targets. This paper has proposed a complete scheme, applying the fractional Fourier transform into the estimation of range and velocity parameters of targets. The radar signal processing technique is developed to measure the range and velocity of moving targets simultaneously in a single frequency-stepped burst without the long-time integration and avert the negative effect of Doppler shift.

High-speed, low-observable, and maneuvering target detection is always the difficult problem for the early warning and detection of space target, ballistic target, and passive radar signal processing. The high-order motion information of maneuvering target is employed in this paper, such as acceleration and jerk. Accordingly, several long-time coherent integration methods are demonstrated and illustrated, i.e., Radon-fractional Fourier transform (RFRFT), Radon fractional ambiguity function (RFRAF), Radon-linear canonical ambiguity function (RLCAF), and phase differentiation-Radon-Lv's distribution (PD-RLVD). These methods can compensate the across range unit (ARU) and Doppler frequency migration (DFM) effects simultaneously during the long-time integration. The background clutter and noise can be well suppressed with higher integration gain. Experimental results using real radar data show the superiority of the proposed methods.

The Doppler mismatch, range migration and Doppler frequency migration (DFM) correction problem for realizing the long-time coherent integration of space moving target with high-speed manoeuvring performance in passive bistatic radar is considered. A novel method based on intra-partition range-Doppler (RD) processing is proposed, where the intra-partition RD processing is first performed to achieve the pre-accumulation of target’s energy in each partition and eliminate the Doppler mismatch. Then, the generalized keystone transform is employed to correct the range curvature. After that, the residual range walk is removed with the centre frequency of the coarse Doppler filter related to the target velocity. Furthermore, matched filtering process is carried out to compensate the DFM. The advantage of the method is that it can obtain superior coherent integration and detection performance in comparison with the existing algorithms. Numerical simulations are presented to demonstrate the coherent integration and the detection performance for a high-speed target.

This paper considers the coherent integration problem for a low-observable maneuvering target, where the velocity and acceleration result in range migration (RM) and Doppler frequency migration (DFM) within the coherent pulse interval. A novel method based on the frequency spectrum segment processing (FSSP) and the segmental Lv's distribution (SLVD) is proposed to realize the long-time coherent integration for multiple maneuvering targets. In this method, FSSP is proposed to eliminate the RM effect by dividing the received signal into several subband signals and expanding the range resolution of the subband signals. Then SLVD is applied to achieve the coherent integration of the subband signals and accumulate the energy of all the subband signals coherently. The proposed method can realize the coherent integration for multiple maneuvering targets without any prior knowledge of the targets' motion. The simulation and experimental results demonstrate the effectiveness of the proposed algorithm.

The synthetic-wideband and pulse repetition frequency jittering radar systems are receiving increasing attention due to the relatively low construction costs and good anti-jamming performance. However, the inter-pulse random hopping of the carrier frequency and pulse repetition frequency introduces challenges to the long-time coherent integration and motion parameter estimation of the high-speed weak targets for these radar systems. A modified generalized Radon Fourier transform for weak target detection and motion parameter estimation is proposed. The proposed method can achieve full coherent integration gain for the high-speed weak target and has a good parameter estimation accuracy. After the target motion has been well compensated, the well-focused high-resolution range profile of the target can be obtained by synthetic-wideband processing. The effectiveness of the proposed method is verified by Monte Carlo simulations. In addition, experimental data collected using an X-band radar system are processed and analyzed to illustrate the practical performance of the proposed method.