A Novel Technique for Long-Time Coherent Integration of Supersonic 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.

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

Long-time coherent integration works to significantly increase the detection probability for maneuvering targets. However, during the observation time, the problems that often tend to occur are range cell migration (RCM) and Doppler frequency cell migration (DFCM), due to the high velocity and acceleration of the maneuvering target, which can reduce the detection of the maneuvering targets. In this regard, we propose a new coherent integration approach, based on the product scale zoom discrete chirp Fourier transform (PSZDCFT). Specifically, by introducing the zoom operation into the modified discrete chirp Fourier transform (MDCFT), the zoom discrete chirp Fourier transform (ZDCFT) can correctly estimate the centroid frequency and chirp rate of the linear frequency-modulated signal (LFM), regardless of whether the parameters of the LFM signal are outside the estimation scopes. Then, the scale operation, combined with ZDCFT, is performed on the radar echo signal in the range frequency slow time domain, to remove the coupling. Thereafter, a product operation is executed along the range frequency to inhibit spurious peaks and reinforce the true peak. Finally, the velocity and acceleration of the target estimated from the true peak position, are used to construct a phase compensation function to eliminate the RCM and DFCM, thus achieving coherent integration. The method is a linear transform without energy loss, and is suitable for low signal-to-noise (SNR) environments. Moreover, the method can be effectively fulfilled based on the chirp-z transform (CZT), which prevents the brute-force search. Thus, the method reaches a favorable tradeoff between anti-noise performance and computational load. Intensive simulations demonstrate the effectiveness of the proposed method.

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.

In coherent radar system, maneuvering target with complex motions usually confronts the issues of range cell migration (RCM) and Doppler frequency spread (DFS) within the long-time coherent integration process. To address these issues and achieve reliable detection and estimation performance, this paper proposes a novel fast approach without motion parameters searching. Particularly, the proposed approach performs the third-order keystone transform (TKT) to eliminate the third-order RCM (TRCM). Then, the bilinear parametric symmetric self-correlation function (BPSSF), scaled Fourier transform (SCFT) and inverse Fourier transform (IFT) are successively operated to estimate target's velocity and acceleration. Afterwards, the improved second-order phase differentiation (ISPD) is performed to estimate target's jerk. Utilizing the estimated parameters, the compensation functions could be constructed to eliminate the remaining RCMs and DFSs as well as to obtain the energy coherent integration. By contrast, analyses of several classical approaches and the proposed one are provided concerning computational complexity, coherent integration performance, detection performance and estimation performance, which confirm that the proposed approach can balance the computational burden and the detection/estimation capabilities. Additionally, the proposed approach can avoid the effect of blind speed side-lobe (BSSL). Eventually, simulated data verification and raw data processing are conducted to evaluate the efficacy of the presented approach.