Coherent Integration for Radar High-Speed Maneuvering Target Based on Frequency-Domain Second-Order Phase Difference

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 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.

Detection of high-speed maneuvering targets has attracted a great deal of attention recently. There are two main problems to be solved: improving detection ability under the condition of complicated range migration and Doppler frequency migration effects, and reducing computational load. Different from most existing fast algorithms which are at the cost of detection ability, this paper devises a computationally attractive method with excellent detection performance. First, the keystone transform is carried out to remove linear range migration. Thereafter, a fast discrete chirp-Fourier transform (FDCFT) based on radix-4 decomposition is proposed to compensate the undersampled linear Doppler frequency migration and quadratic Doppler frequency migration. Because of exploiting inherent symmetry and periodicity as in the fast Fourier transform (FFT), the FDCFT can largely reduce the computational complexity without performance loss. The novelty of the proposed algorithm lies in combining linear transform with the concept of decimation-in-time FFT, which avoids the demanding multi-dimensional search and severe performance loss via introducing nonlinear transforms. It is shown that the proposed method has an approximately optimal detection performance but with relatively low computational cost.

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.

This study considers the coherent integration problem for detecting a manoeuvring target, involving range migration (RM) and Doppler frequency migration (DFM) within the coherent processing interval. An efficient coherent integration method based on keystone transform (KT) and Lv's distribution (LVD) is proposed. It can not only correct the RM effect by KT and fold factor phase compensation, but also remove the DFM effect and achieve the coherent accumulation via LVD. Compared with the moving target detection, Radon‐Fourier transform, and Radon‐fractional Fourier transform algorithms, the proposed method can obtain better detection ability under low signal‐to‐noise ratio environment. Finally, several simulations are provided to demonstrate the effectiveness.

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.

This paper addresses the coherent integration problem for detecting a maneuvering target with complex motions, involving range migration (i.e., range walk and range curvature) and Doppler frequency migration (DFM) within the coherent processing interval. A new method based on adjacent cross correlation function (ACCF) and fractional Fourier transform (FRFT) is proposed, where the ACCF operation is firstly employed to remove the range migration (RM) and reduce the order of DFM. After that, the FRFT is applied to achieve the coherent accumulation. Several simulation experiments are provided to demonstrate the effectiveness.

This letter considers the coherent integration problem for a maneuvering target, involving range migration (RM) and Doppler frequency migration (DFM) within one coherent pulse interval. A new coherent integration method, known as Radon-Lv's distribution (RLVD), is proposed. It can not only eliminate the RM effect via jointly searching in the target's motion parameters space, but also remove the DFM and achieve the coherent integration via Lv's distribution (LVD). Finally, several simulations are provided to demonstrate the effectiveness. The results show that for detection ability, the proposed method is superior to the moving target detection (MTD), Radon-Fourier transform (RFT), and Radon-fractional Fourier transform (RFRFT) under low signal-to-noise-ratio (SNR) environment.

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.

Robust TDOA/FDOA estimation from emitter signals for hybrid localization using UAVs

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 describes a correlation-based watermarking technique with the fast Fourier transforms (FFTs) for three-dimensional (3-D) mesh models. For generating a watermark with desirable properties, similar to a pseudonoise (PN) signal, an impulse signal on a two-dimensional (2-D) space is spread through the FFT, multiplications of a complex sinusoid signal, and the inverse FFT. This system easily incorporate a frequency selectivity property, because zero-valued components in the multiplication block prevent the energy of the impulse signal at appropriate frequencies. As a result, the proposed approach requires no additional transform, such as the discrete cosine transform and wavelet transform. Since the amount of information that can be stored in the watermark depends on the size of a spread space, the elimination of the subband transform increases a payload of the watermark in a previous paper. The watermark, i.e., spread impulse signal, is embedded into 3-D data aligned by the principle component analysis (PCA). In the detection procedure, after realigning the watermarked mesh model through the PCA, we map the 3-D data on the 2-D space via block segmentation and averaging operation. The 2-D data are processed by the inverse system, i.e., the FFT, the division of the complex sinusoid signal, and the inverse FFT. From the resulting 2-D signal, we detect the position of the maximum value as a signature.

Fast Fourier Transform (FFT)/Inverse Fast Fourier Transform (IFFT) are the key computation block in Orthogonal Frequency Division Multiplexing (OFDM) system. They dominate most of the areas and power dissipation in implementation therefore efficient low-power and high-throughput implementation of FFT processor is essential for successful deployment of OFDM based system. High-throughput and Low-power 128-point FFT Processor is designed using Radix-25 algorithm to reduce computation complexity and the feedforward pipeline architecture [called Multipath Delay Commutator (MDC)] with four data path for providing higher throughput. This architecture is more hardware-efficient than Multipath parallel feedback (MDF) design, which makes them attractive for the computation of FFT in most demanding applications. The proposed FFT processor uses improved Digit slice multiplier for complex multiplication. This proposed FFT processor is designed using Verilog and implemented using 180 nm CMOS Technology with supply voltage of 1.8v. The result shows significant reduction in power consumption in comparison with existing design and increasing throughput with area trade off.

The conventional multicarrier faster-than-Nyquist (MFTN) achieves the spectral efficiency (SE) gain by deep compression. However, deep compression leads to severe intersymbol interference (ISI) or intercarrier interference (ICI). We propose the MFTN based on efficient implementation and probabilistic amplitude shaping (PAS) to achieve the SE gain with low complexity. We use mild compression instead of conventional deep compression to achieve the compression gain. The MFTN transceiver with the mild compression can be efficiently implemented by fast Fourier transform (FFT)/inverse FFT (IFFT) and filtering operation. The linear pre-equalization (LPE) method eliminates the ISI for mild compression. The MFTN with efficient implementation employs PAS to achieve extra shaping gain. The theoretical results and simulation results show that our method can achieve better performance than the conventional FTN/MFTN with deep compression. The proposed method does not require a complex equalization algorithm and global turbo iteration so that the total complexity is reduced.