Coherent radon transform based weak target detection for phased array radar

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.

As a special system of early warning radar, high-frequency sky-wave over-the-horizon (OTH) radar usually needs to detect sea and airborne targets in the same direction simultaneously. However, the long coherent integration time (CIT) required by the sea target makes the echo data about high-speed moving airborne target in the same direction incompletely coherent, which is not conductive to the detection and tracking of airborne target. To overcome this problem, this paper proposes a novel track-before-detect (TBD) algorithm for airborne target. Firstly, the motion prior knowledge of the airborne target is utilized to select the number of pulses in the CIT to perform coherent integration processing. Then TBD based on dynamic programming (DP-TBD) technique is used to realize the noncoherent integration for the detection and tracking of the airborne target. Simulation results show that compared with the traditional method, the proposed algorithm effectively improve the detection and tracking performance of the airborne target.

Axis rotation MTD algorithm for weak target detection

The airborne coherent multi-input multi-output (MIMO) radar benefiting from coherent integration (including intra-channel integration and inter-channel integration) of multi-channel echoes can obtain superior detection performance for high-speed maneuvering targets. However, due to the coupling motion characteristic between multiple airborne platforms and high-speed targets, the range walk (RW) and Doppler walk (DW) will occur within the intra-channel integration. Besides, the inter-channel signals also exist envelope and phase differences, which will lead to the difficulty in multi-channel integration. We make contributions towards addressing these limitations. On the one hand, we establish a three-dimensional (3-D) geometrical model for high-speed maneuvering target detection with airborne coherent MIMO radar and derive the mathematical expression of radar echoes, while the generalized Radon-Fourier transform (GRFT) is utilized to simultaneously correct the RW and DW for acquiring intra-channel integration. On the other hand, we analyze the properties of GRFT outputs and propose a GRFT-domain integration method to achieve the multi-channel coherent integration. More specifically, the proposed method first constructs a set of coupling equations for the estimation of target motion parameters (i.e., position, velocity and acceleration), then, the target's motion parameters can be estimated by Newton-Raphson method and solving the linear equations. Second, in order to settle the envelope and phase differences between multi-channel echoes, the envelope alignment and phase compensation functions of inter-channel echoes are constituted based on the estimated parameters. Finally, the coherent accumulation of multi-channel echoes can be implemented. Numerical simulations demonstrate the effectiveness of the proposed method.

Differential Coherent Integration method is an effective method for weak GPS acquisition. But the traditional differential method has a problem that the coherent integration time could not be too long and can hardly acquire very weak GPS signal. This paper introduces an improved differential coherent integration algorithm based on optimum path method, which can find the path of the maximum sum of differential blocks by estimating every possible product of the adjacent navigation data bits. So it could overcome the influence of navigation data bit transition and the long time coherent integration can be used in the differential method. Another advantage of this new method is that the loss of the square is reduced, because of the differential operation. Simulations show that, in the weak signal environment, if the same C/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> and processing data length are provided, the performance of the new method is much better than the legacy half-bits method and full-bits method. With the increasing of the processing data length, the advantage of the new method on signal to noise ratio improvement is more significant.

A fundamental task of radar is the detection of targets in noise and clutter. It is very difficult to detect weak targets in heavy sea clutter. In this paper we apply the discrete wavelet transform (WT), along with multilayer feedforward neural networks, to the detection of radar weak targets. The wavelet transform employs the Haar scaling function, which is well matched to the signals from targets. The hard threshold filter is adopted to remove sea clutter. The neural networks are trained with the back-propagation rule, which are used to detect weak targets. The simulated results show that the proposed method is very effective for radar detection of weak targets.

Long-term coherent integration (CI) can effectively improve the radar detection capability for high-speed targets. However, the range walk (RW) effect caused by high-speed motion significantly degrades the detection performance. To improve detection performance, this study proposes an improved algorithm based on the modified Radon inverse Fourier transform (denoted as IMRIFT). The proposed algorithm uses parameter searching for velocity estimation, designs a compensation function based on the relationship between velocity and distance walk and Doppler ambiguity terms, and performs CI based on the compensated signal. IMRIFT can achieve RW correction, avoid the blind-speed sidelobe (BSSL) effect caused by velocity mismatch, and improve detection performance, while ensuring low computational complexity. In addition, considering the relationship between energy concentration regions and bandwidth in the 2D frequency domain, a fast method based on IMIRFT is proposed, which can balance computational cost and detection capacity. Finally, a series of comparative experiments are conducted to demonstrate the effectiveness of the proposed algorithm and the fast method.

This paper considers the coherent integration problem for maneuvering target detection and motion parameters estimation, involving range migration (RM) and Doppler frequency migration (DFM) within the coherent pulse interval. A fast non-searching method based on adjacent cross correlation function (ACCF) and Lv's distribution (LVD) is proposed, where the adjacent correlation operation is first employed to remove the RM and reduce the order of DFM. After that, LVD is applied to realize the coherent integration, target detection and parameters estimation. In addition, at the cost of some performance loss, another fast method via ACCF iteratively is also introduced to further reduce the computational complexity and obtain the motion parameters estimation. The proposed two methods are fast in that they can be easily implemented by using complex multiplications, the fast Fourier transform (FFT) and inverse FFT (IFFT). Compared with the existing methods, the presented algorithms can obtain the motion parameters estimation without any searching procedure and can achieve a good balance between the computational cost and the detection ability as well as parameters estimation performance. Finally, several simulation experiments are provided to demonstrate the effectiveness.

HighlightsWhat are the main findings?This paper presents a high-order phase compensation and parameter estimation algorithm designed for maneuvering targets, which effectively balances detection performance and computational efficiency.The proposed method achieves precise compensation of high-order range migrations without the need for exhaustive parameter search, thereby circumventing the blind speed sidelobe effect. Futhermore, the incorporation of a time-delay variable significantly improves the anti-noise capability of the approach.What is the implication of the main finding?This algorithm introduces a novel motion compensation technique to address the challenges of range migration, Doppler frequency migration, and Doppler ambiguity in detecting weak maneuvering targets. It achieves precise range migration compensation with enhanced accuracy and robustness, forming a vital preprocessing step for high-quality SAR imaging.The algorithm supports simultaneous multi-target processing and holds promising application potential in fields such as airborne radar detection, maritime moving target indication, cooperative observation by UAV formations, and other fields.This study focuses on the key challenges in detecting and estimating motion parameters of ground maneuvering targets for airborne radar sensors. The complex unknown motion states of the ground maneuvering target, including velocity, acceleration, and jerk, result in range migrations (RMs) and Doppler frequency migrations (DFMs). These effects severely degrade the long-time coherent accumulation performance of the airborne radar, thereby limiting the reliable detection and precise parameter estimation of maneuvering targets. To address this issue, a new detection and motion parameter estimation method based on the range frequency reversal transform (RFRT) and searching Lv’s distribution (SLVD), i.e., RFRT-SLVD, is proposed. Specifically, the third-order RM (TRM) and quadratic DFM (QDFM) are considered. The proposed method operates as follows: First, RMs are eliminated simultaneously via the RFRT operation, which multiplies the echo by its reversed data in the range frequency and slow-time domains, leveraging the symmetric equal-interval sampling property of the range frequency. Subsequently, a phase compensation function (PCF) related to the jerk is constructed to compensate the QDFM. Finally, the LVD is performed to remove residual DFMs and achieve effective signal energy accumulation. Additionally, the case of a fast-moving target with Doppler ambiguity is analyzed, and a method for estimating three motion parameters is provided. A key advantage of the proposed technique is its ability to directly compensate the RMs without requiring prior knowledge of the maneuvering target, while also avoiding the blind speed sidelobe (BSSL) effect. In comparison with existing algorithms, RFRT-SLVD achieves a balanced trade-off between parameter estimation performance and computational efficiency. Numerical analyses and experiments are conducted to validate the method, assessing its detection capability for ground maneuvering targets, Doppler ambiguity resolution in parameter estimation, computational complexity, and method applicability in multi-target scenarios.

The target motion parameter estimation is an important index to measure the performance of radar system. Accurate estimation of acceleration parameter has important influence on improving the detection and tracking performance of high maneuvering target. When radar transmits a signal with fixed frequency, the maneuvering target echo signal can be approximated as linear frequency modulation signal. Therefore, the acceleration parameter estimation of maneuvering target is transformed into the parameter estimation of linear frequency modulation signal. In this paper, a novel method for acceleration parameter estimation of maneuvering target is proposed based on the compressed sensing theory. The linear frequency modulation signal has sparse characteristic in fractional Fourier transform domain and compressed sensing theory asserts that we can employ nonadaptive linear projections to preserve the structure of the signal and reconstruct the signal with these projections using an optimization process. Theoretical analysis and experimental results verify that the method can effectively solve the precision problem of parameter estimation caused by the large sampling rate in the traditional signal processing method, and effectively reduce the data storage and transmission pressure in radar signal processing.

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.

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

Hypersonic vehicle-borne radar target detection will suffer from time-varying plasma sheath which is formed during hypersonic flight. In this study, effect of time-varying plasma sheath on hypersonic vehicle-borne radar target detection is investigated. First, the radar echo model coupling time-varying plasma sheath effect is proposed using an analytical computation method. The regulation of electron density variation is based on flow parameters. Coherent integration result with the present of time-varying plasma sheath effect is derived. The degradations of hypersonic vehicle-borne radar target detection under time-varying plasma sheath are studied through real hypersonic vehicle flight cases. Simulation results shows that high electron density of time-varying plasma sheath will cause significant attenuation, which will lead to decrease of detection probability. In some cases, the signal-noise ratio (SNR) threshold that target can be detected increases more than 40 dB compared with situation without time-varying plasma sheath. Moreover, time-varying plasma sheath will cause time-varying amplitude and phase in pulse and between different pulses, causing intra-pulse and inter-pulse modulation phenomena. These phenomena lead to the disappearance of peak value in range-Doppler plane which will degrade the coherent accumulation as well as target detection performance. By using plasma sheath electron density diagnosis method on vehicle, compensation factor according to the electron density can be established to compensate plasma sheath effect in radar echoes. Simulations results based on real hypersonic vehicle flight flow parameters confirm the conclusions above. The work in this paper will benefit the design and application of hypersonic vehicle-borne radar in the future.

Space time coding plays quite an important role in the design of multi-input multi-output (MIMO) radar. It has been shown that the correlation characteristics of waveform set have a great impact on the performance of target detection and localisation for MIMO radar. In this study, the target detection and localisation performance of co-located MIMO radar is analysed theoretically and experimentally, when correlated (not ideally orthogonal or fully coherent) waveforms are transmitted. The relationship between transmit–receive beam pattern improvement and correlation coefficients of transmitted waveforms is investigated. The signal to interference and noise ratio varying with correlation coefficients in range-Doppler matched processing is defined and analysed. Furthermore, Cramer–Rao bound for target direction of arrival estimation and target detection probability in the Neyman–Pearson criteria are derived when transmitting correlated waveforms. It is shown that the MIMO radar detection and localisation performance is much dependent with the correlation level of transmitted waveforms, which can be quite useful for MIMO radar orthogonal waveform design. Numerical simulation validates the theoretical analysis.

Multiple pulse repetition frequency (multi-PRF) radar is widely utilized due to its advantages in range-Doppler ambiguity suppression and anti-jamming capabilities. Most existing research focuses on intra-frame multi-PRF mode, which lacks flexibility in PRF scheduling and robustness against clutter and dynamic targets. In contrast, inter-frame multi-PRF mode allows PRF variation across frames, enhancing ambiguity resolution and target detection performance in complex environments. However, research on detecting and tracking ambiguous targets under the inter-frame multi-PRF mode remains limited. To address this gap, we propose a multi-frame track-before-detect (MF-TBD) and fusion disambiguation method based on inter-frame multiPRF radar systems, referred to as IF-MF-TBD. First, an efficient method for constructing a pseudo-measurement plane is proposed to mitigate the computational complexity of ambiguity resolution. Then, to estimate the target's ambiguous state across different PRFs, intra-PRF multi-frame energy accumulation is performed within the pseudo-measurement plane, generating multiple sets of ambiguous plot-sequences. Finally, ambiguity resolution is achieved through plot-sequences association and fusion method, yielding unambiguous target tracking results. Simulation results demonstrate that the proposed IF-MF-TBD algorithm effectively enhances target detection and tracking performance in interframe multi-PRF radar systems.