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In this article, we propose a phase-derived velocity measurement (PDVM) method for high-speed spatial targets based on the stepped-frequency chirp signal (SFCS). This method is capable of accurately measuring the velocity of high-speed targets and yields root-mean-squared error values at the level of centimeters per second; therefore, it has great potential for measuring the micromotion of targets and is of significant importance for target recognition. The traditional phase-derived measurement method is not applicable for high-speed targets. The main challenge that we have solved is how to extract the echo phase from the high-resolution range profile, which is corrupted by range migration, intrapulse motion, and range straddling under high-speed target conditions. To guide the implementation of the proposed method in radar systems, constraint conditions for the compensation accuracy are thoroughly derived and systematically justified under different radar parameter settings. The simulation results are presented to validate the high accuracy of the method under various circumstances. In addition, the small-amplitude micromotion measurement capability of the proposed method is verified, and reconstruction of the target micromotion trajectory is demonstrated.

Waveform diversity, which can be used to obtain synthetic bandwidth or mitigate range ambiguity, interference, and folded clutters, has attracted a great deal of attention in recent years. However, the range sidelobe modulation effect between agile pulses yields high range-Doppler sidelobes in pulse-Doppler (PD) radar applications, because of which traditional window functions or mismatched filters (MMFs) do not apply. In this article, a Doppler-tuned matched filter is used to equivalently obtain the PD result. Then, to mitigate the high range-Doppler sidelobes, a two-dimensional MMF (2-D MMF) is proposed, and the relevant signal-to-noise ratio (SNR) loss is deduced. A cyclic algorithm is also designed to calculate the 2-D MMF for suppressing sidelobes over desired range-Doppler regions with constrained SNR loss and mainlobe width. Several simulations and an experiment based on real measured data of an airborne platform are conducted to illustrate the effectiveness of the proposed 2-D MMF.

This paper proposes a phase-derived velocity measurement (PDVM) method for high-speed targets based on wideband direct sampling linear frequency modulated radar. First, a high-speed target echo model considering intrapulse Doppler modulation is developed. Then, a PDVM model considering acceleration is established. The key to realizing PDVM is resolving phase ambiguity. Under low signal-to-noise ratio (SNR) conditions, a joint processing method combining acceleration information and multiframe data to solve phase ambiguity is proposed, which can significantly reduce the SNR requirement for PDVM. In this paper, the small-amplitude micromotion measurement capability of the proposed method is verified by simulation. Moreover, the measured data of a Ku-band ground-based radar are used to verify the applicability of the PDVM method under low SNR conditions and its feasibility to be applied to complex multi-scattering point targets. Both the simulation and experimental results show that the proposed method is suitable for high-speed targets with radial motion, including acceleration and jerk, and that the PDVM precision can reach the order of magnitude of centimeters per second or millimeters per second.

The Doppler sensitivity issue is an urgent problem to be solved for the phase-coded radar although it can give the promise of improved range resolution and resistance against various kinds of distortion. Due to the ideal autocorrelation and cross-correlation properties, the complementary sequence is utilised in high-frequency surface wave radar and MIMO radar. However, the Doppler frequency shift affects the autocorrelation property of the complementary sequence. This study aims to solve this problem. Based on the signal model and mathematical derivation, a new algorithm is proposed and the simulation results indicate the effectiveness of this method. This study also puts forward the signal processing diagram and the method to obtain the new code.

A novel high-accuracy phase-derived velocity measurement (PDVM) method for fast-moving space targets is presented in this letter. First, a wideband linear frequency-modulated signal model that considers the effect of radial acceleration was developed. To obtain the unambiguous phase difference between two adjacent echo pulses, coarse velocity and acceleration measurements derived from range profile cross correlation were used to resolve the phase ambiguity. Then, the derived accurate and unambiguous phase difference and the phase error induced by the discrete Fourier transform were analyzed. The PDVM technique was applied after the phase error was compensated for, and all required parameters were calculated. Under low signal-to-noise ratio (SNR) conditions, a correction for the phase unwrapping error was developed. The simulation results showed that the proposed PDVM technique was highly accurate. The root-mean-square error of the PDVM results was less than 0.025 m/s when the SNR was greater than 15 dB.

Waveform diversity, which can be used to resolve range ambiguity and suppress range folded clutter in pulse-Doppler radar system, has attracted an increasing amount of attention in recent years. Especially for high pulse repetition frequency (PRF), the range folded clutter severely impacts the detection of small targets with long range and low speed. Using diverse waveforms, pulses of the transmitted sequence of radar are agile. It is possible to construct corresponding matched filters (MFs) to suppress the range folded clutter. However, the performance greatly depends on the cross-correlation among pulses of the transmitted sequence. In this paper, diverse nonlinear frequency modulation (NLFM) waveforms, the spectra of which are based on different window functions, are designed to construct a signal library, and positive and negative frequency modulation rate are both considered. Then, a Min-Max algorithm is proposed for sequentially selecting NLFM waveforms from the signal library to generate an optimal transmitted sequence. Pulse-to-pulse random initial phases are also added to each pulse of the sequence to further improve the irrelevance among pulses. Moreover, to eliminate the range sidelobe modulation (RSM) effect in Doppler processing, a cyclic algorithm for designing joint mismatched filters (JMMFs) with finite impulse response (FIR) is provided. Simulations show that the optimized pulse-agile sequence based on NLFM waveforms yields satisfactory performance on the ambiguity function, and range folded clutter can be effectively suppressed.

The target micro-motion features contain unique structural information and motion information, which can be utilized as an important basis for target recognition. At present, the main constraints of micro-motion feature extraction for high-speed targets include that the translational compensation is inaccurate, the scattering points are difficult to distinguish, the micro-motion amplitude is small, the data rate is not high enough, and so forth. The phase-derived velocity measurement (PDVM) method based on wideband radar has phase-magnitude velocity measurement precision, which can accurately reconstruct the target motion while ensuring high data rate, and meet the micro-motion measurement requirements of high-speed targets. In this paper, a PDVM method for high-speed targets based on wideband direct sampling LFM radar is proposed. The high-precision velocity measurement performance and micro-motion measurement capability of the proposed method are verified by simulation.

Background Bee venom acupuncture has been used in treating patients with shoulder adhesive capsulitis, yet the effectiveness and safety remains unclear. Therefore, this systematic review will aim to assess the effectiveness and safety of bee venom acupuncture for shoulder adhesive capsulitis. Methods Electronic databases including EMBASE, PUBMED, the Cochrane Central Register of Controlled Trials, China National Knowledge Infrastructure, Chinese Scientific Journal Database, Wanfang Database, and Chinese Biomedical Literature Database will be searched for relevant randomized controlled trials from their inception to the search data without language and publication status. Randomized controlled trials involving bee venom acupuncture for treating shoulder adhesive capsulitis will be included. The primary outcome will be pain visual analogue scale, and secondary outcomes include active and passive range of motions, shoulder pain and disability index. Meta-analysis will be conducted using Review Manager software (V.5.3). The results will be presented as risk ratio for dichotomous data, and standardized or weighted mean difference for continuous data. Results The results will be disseminated through a peer-reviewed journal publication. Conclusion These systematic review findings will provide an evidence of bee venom acupuncture for shoulder adhesive capsulitis, and help to inform clinical practitioners and policy-makers in the decision-making. Ethics and dissemination Ethics approval and patient consent are not required as this study is a systematic review based on published articles.

The linear stepped frequency and linear frequency shift keying (FSK) signal has been widely used in radar systems. However, such linear modulation signals suffer from the range–Doppler coupling that degrades radar multi-target resolution. Moreover, the fixed frequency-hopping or frequency-coded sequence can be easily predicted by the interception receiver in the electronic countermeasures (ECM) environments, which limits radar anti-jamming performance. In addition, the single FSK modulation reduces the radar low probability of intercept (LPI) performance, for it cannot achieve a large time–bandwidth product. To solve such problems, we propose a novel chaos-based stepped frequency (CSF) synthesized wideband signal in this paper. The signal introduces chaotic frequency hopping between the coherent stepped frequency pulses, and adopts a chaotic frequency shift keying (CFSK) and phase shift keying (PSK) composited coded modulation in a subpulse, called CSF-CFSK/PSK. Correspondingly, the processing method for the signal has been proposed. According to our theoretical analyses and the simulations, the proposed signal and processing method achieve better multi-target resolution and LPI performance. Furthermore, flexible modulation is able to increase the robustness against identification of the interception receiver and improve the anti-jamming performance of the radar.

A novel ISAR (inverse synthetic aperture radar) motion compensation approach in conjunction with the phase-derived velocity measurement (PDVM) technique to extract micro-motion feature is presented in this paper. In order to obtain high quality ISAR image, the accurate velocity information provided by PDVM is utilized for target motion compensation. By analyzing proper amount of adjacent Doppler cells around the prominent scatterer in the ISAR image, the impact of other scatterers is effectively reduced for micro-motion extraction. Experiments based on radar measured data are performed to show the effectiveness of the proposed method.

Development of radar technology needs to address the two-dimensional high resolution of range and velocity simultaneously for high-speed targets. Taking advantage of the superior coherent performance of synthetic wideband pulse Doppler radar, this paper elaborates the principles of phase-derived range and velocity measurements. Moreover, this paper explores the key technologies of unwrapping phase ambiguity, and discusses the phase unwrapping strategy at a low signal-to-noise ratio (SNR). The proposed method can be applied to the conditions of low SNR and has comparatively strong practicality in engineering. Both the ejection ball and civil aircraft experiments have validated the correctness and feasibility of the proposed method. In particular, the experimental results reveal that the accuracy of phase-derived range and velocity measurement has reached a level of submillimeter or millimeter and centimeter/second or submillimeter/second, respectively.