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Finding codes for the desired autocorrelation function (ACF) based on phase-coded modulation waveforms has always been a popular research topic, and the relevant literature is abundant. However, the optimized ACF may not be obtained in band-limited hardware due to the extended spectral sidelobes generated by instantaneous phase changes. Polyphase-coded FM (PCFM) waveforms based on continuous phase modulation (CPM), which uses a shape filter to smooth phase jumps, can provide effective spectral containment. However, for PCFM waveforms using the existing optimized phase codes, the original desired property of the ACF, e.g., a low integrated sidelobe level (ISL) or weighted ISL (WISL), will not be obtained because of the smoothness among all phases. Hence, PCFM waveforms based on CPM should be redesigned and optimized. Moreover, designing pulse-agile waveforms with different phase codes to mitigate range ambiguity has also attracted increased attention in recent years. However, different waveforms will yield range sidelobe modulation (RSM) in Doppler processing, which degrades the attendant Doppler coherency, leading to high sidelobes in the Doppler dimension. In this article, optimization algorithms for designing diverse PCFM waveforms and relevant joint mismatched filters (JMMFs) are proposed. A CPM-based cyclic algorithm (CPM-CA) using the method of alternating projection for optimizing the PCFM waveform with a desired ACF is proposed in the first step. The design of multiple diverse PCFM waveforms with similar ACFs and a small RSM effect is also considered. Then, to further optimize the ISL/WISL and reduce the RSM effect, a novel method for designing JMMFs using a cyclic algorithm (JMMF-CA) is proposed. Simulations and an experiment based on a real radar system indicate that the optimized PCFM waveforms and JMMFs using CPM-CA and JMMF-CA can yield a desired ISL/WISL while achieving a small RSM effect with a low loss of signal-to-noise ratio and satisfactory Doppler robustness.

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.

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.

To deal with the problem of aerodynamic and stealth integrated optimization of DSI inlet, a multi-objective optimization study on aerodynamic and stealth of the DSI inlet is carry out which based on the deformation of the three-dimensional compression bump surface. The FFD parametric method is used to parameterize the bump surface; CFD calculation based on RANS equations is used to analyze the aerodynamic performance of the DSI inlet, large element physical optical method and uniform theory of diffraction are used to calculate RCS of the DSI inlet; And ASMOPSO algorithm with the Kriging surrogate model which based on the expect hyper-volume improvement infill criterion is adopted for integrated optimization design. The results of DSI inlet aerodynamic and stealth integrated optimization exhibit considerable improvement.

This paper presents an efficient multi-objective optimization method, focusing on aerodynamic optimization of a diverterless supersonic inlet (DSI) in transonic and supersonic flight conditions. The DSI inlet, through scrutinizing the Bump shape has potential to attain greater aerodynamic performance on exit plane of inlet. However, the high cost of computational fluid dynamic (CFD) simulations raises a significant challenge in the DSI optimization process. In order to obtain solution set in few numbers of objective function calls, a meta-model multi-objective particle swarm optimization (MOPSO) method is proposed based on a self-adaptive Kriging surrogate model, and applied to solve this kind of costly black-box optimization problem. The Kriging model is updated by using a dynamic expected hyper-volume improvement (EHVI) sample metric, which is developed by analyzing disadvantages of the original sample criterion. With the help of the dynamic sample metric, simulation results show that the surrogate-based MOPSO algorithm can obtain plenty enough non-dominated solutions and achieve high precision in the approximation of the Pareto front. In terms of DSI inlet optimization, the bump shape is parameterized by free form deformation (FFD) method, and the total pressure distortions of inlet exit plane are treated as two minimization objectives under transonic and supersonic flight conditions. A well distributed non-dominated solution set is generated by the proposed algorithm within the context of a small call number of cost evaluations, and optimized inlet configurated by the selected solution has better aerodynamic characteristics compared with the initial inlet.

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.

The multi-objective particle swarm optimization algorithm (MOPSO) has been applied and modified for optimal designs in various engineering fields. However, the intimal algorithm is still has the problems of low accuracy and poor diversity of solutions as it is easy to fall into local optimum in the later evolution stage. A new dynamic mutation operator has been established based on the α-stable distribution theory and incorporated with multi-objective particle swarm optimization algorithm(ASMOPSO). By using random Numbers which generated by the α-stable distribution, the population of PSO algorithm was mutated. And this mutate operation increases the diversity of the population. Because the stability coefficient in the ASMOPSO algorithm can change the range and amplitude of the mutation. This operation makes the new algorithm has the ability to balance the calculation accuracy and global optimization. Several benchmark functions test show that the ASMOPSO algorithm has fast global optimization ability. The proposed algorithm is applied to the multi-objective aerodynamic optimization design of RAE2822 transonic airfoil. The comparison results also show that ASMOPSO algorithm is more excellent than the basic MOPSO algorithm.

Micromotion features of a target contain unique structural information and motion information about the target, which can be used as an important basis for target recognition. One of the technical bottlenecks for micromotion feature extraction is achieving a fine characterization of the target motion state. With the high-precision range and velocity measurement, this paper uses the phase-derived method to reconstruct the motion state of the target and realize accurate translational compensation for the target. At the same time, the high range resolution of wideband radar is used to effectively extract target scattering points with micromotion from the perspective of the one-dimensional high range resolution profile and the two-dimensional inverse synthetic aperture radar (ISAR) image. On this basis, reliable micromotion feature extraction can be achieved by using the slow variability of the target motion and eliminating the translational or rotational information of the target. The performance of the high-precision range and velocity measurement and the feasibility of the micromotion feature extraction based on phase-derived range and velocity measurement are verified by simulation results. Then, the effectiveness of the proposed algorithm is further verified by carrying out a steel ball ejection experiment and a civil aviation aircraft experiment.

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 existing methods for motion compensation in inverse synthetic aperture radar (ISAR) imaging are generally limited to the low-order target motion model, and require iterative optimization with limited velocity estimate precision and heavy computational burdens. This paper proposes a high-precision method of phase-derived velocity measurement (PDVM) and applies it to motion compensation of ISAR imaging. The method applies PDVM based on range profiles cross correlation to the translational velocity estimation of targets, and converts the velocity measurement results to the corresponding range increment. The equivalent phase-derived range measurement precision can reach the order of magnitude of millimeter (mm) or even sub-mm, which can satisfy the precision requirements of both envelope alignment and phase adjustment. The key to realizing PDVM is resolving phase ambiguity. The traditional method for resolving ambiguity has very high requirements for the signal-to-noise ratio (SNR). This work resolves ambiguity by combining multiframe data, i.e., by resolving ambiguity of multiframe data simultaneously instead of resolving ambiguity of single-frame data independently and correcting the above ambiguity-resolving results using a minimum-entropy method. Therefore, phase ambiguity can be correctly resolved under a relatively low SNR. Experimental results of an ISAR imaging of an airplane show that the method proposed in this paper can obtain high-quality ISAR imagery, and can efficiently realize robust imaging under the conditions of low SNR.

The challenges of the most multi-objective particle swarm optimization (MOPSO) algorithms are to improve the selection pressure, equilibrate the convergence and diversity when tackling large-scale many-objective problems. To overcome these challenges, this paper proposes a novel PSO-based large-scale many-objective algorithm, named as LMPSO. In LMPSO, the Alpha-stable mutation is performed to enhance the diversity of swarm for avoiding premature convergence. And the parameters of PSO and Alpha-stable mutation are dynamically set following the Logistic function, which emphasize different convergence and diversity at different optimization stages. Moreover, LMPSO adopts a fitness to maintain the external archive, and the calculation of fitness is based on binary additive epsilon indicator. The binary indicator is also used to update the personal best of particles to avoid wrongly selecting dominance resistance solutions (DRSs). Aims for improving the selection pressure, the proposed algorithm employs a concept of dominance resistance error to identify the DRSs. To verify this idea, the DTLZ, ZDT, and LSMOP test suites with up to 1000 decision variables and 10-objective are used to qualify the performance of LMPSO. The simulations reveal the fact that the LMPSO significantly outruns the several chosen state-of-the-art algorithms when solving large-scale many-objective test instances.

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.