Velocity Ambiguity Research Articles

A novel energy-focused slow-time MIMO radar and signal processing scheme

In this paper, we propose a novel energy-focused slow-time MIMO radar and signal processing scheme, aimed at addressing key challenges in slow-time coding and signal processing technology. Conventional slow-time MIMO radar faces issues such as energy waste due to the omnidirectional transmit beampattern of orthogonal coding and the velocity ambiguity problem. To overcome these limitations, the proposed radar system utilizes a method based on Doppler frequency offset diversity (DFOD) for slow-time coding design. This method enables the adjustment of Doppler offset parameters to achieve a rectangular transmit beampattern with any mainlobe width within a single coherent processing interval (CPI), offering the advantage of low computational complexity. Through an analysis of the ambiguity function for DFOD-based coding, we evaluate both Doppler and angular resolution. To further improve Doppler frequency resolution, a slow-time coding design is introduced based on Pulse Random Permutation (PRP). Subsequently, a signal processing scheme based on matched filtering is presented. To tackle the high Doppler sidelobe issue associated with PRP-based coding, we propose a mismatch filter (MMF) design method utilizing convex optimization. Ultimately, the performance enhancement of the proposed slow-time MIMO radar is verified through simulation analysis in comparison to existing technologies.

A Hybrid Integration Method Based on SMC-PHD-TBD for Multiple High-Speed and Highly Maneuverable Targets in Ubiquitous Radar

Based on the characteristic of ubiquitous radar emitting low-gain wide beam, a method of long-time coherent integration (LTCI) is required to enhance target detection capability. However, high-speed and highly maneuverable targets can cause Doppler frequency migration (DFM), range migration (RM), and velocity ambiguity (VA), severely degrading the performance of LTCI. Additionally, the number of targets is unknown and variable, and the presence of clutter further complicates the target tracking problem. To address these challenges, we propose a hybrid integration method to achieve joint detection and estimation of multiple high-speed, and highly maneuverable targets. Firstly, we compensate for first-order RM using the keystone transform (KT) and generate corresponding sub-range-Doppler (SRD) planes with different folding factors to achieve VA compensation. These SRD planes are then stitched together to form an extended range-Doppler (ERD) plane, which covers a broader velocity range. Secondly, during the track-before-detect (TBD) process, tracking is performed directly on the ERD plane. We use the sequential Monte Carlo (SMC) approximation of the probability hypothesis density (PHD) to propagate multi-target states. Additionally, we propose an amplitude-based adaptive prior distribution method and a line spread model (LSM) observation model to compensate for DFM. Since the acceleration of the target is included in the particle state, using particles to search for DFM does not increase the computational load. To address the issue of misclassifying mirror targets as real targets in the SRD plane, we propose a particle space projection method. By stacking the SRD planes to create a folding range-Doppler (FRD) space, particles are projected along the folding factor dimension, and then, the particles are clustered to eliminate the influence of the mirror targets. Finally, through simulation experiments, the superiority of the LSM for targets with acceleration was demonstrated. In comparative experiments, the proposed method showed superior performance and robustness compared to traditional methods, achieving a balance between performance and computational efficiency. Furthermore, the proposed method’s capability to detect and track multiple high-speed and highly maneuverable targets was validated using actual data from a ubiquitous radar system.

A Waveform and Velocity Ambiguity Resolution Method for Corner Radar

Millimeter-wave radar is experiencing an increasing demand for higher resolution and elevation measurement, necessitating its evolution from 3D millimeter-wave radar systems to 4D millimeter-wave radar. Unlike front automotive radar, corner radar is particularly interested in close-range targets. This article proposes a composite waveform tailored for automotive corner radar, employing different waveform schemes for various distances. This allows millimeter-wave angle radar to achieve superior range resolution and velocity resolution in the close and medium ranges. However, enhancing velocity resolution inevitably results in a reduction in the maximum unambiguous velocity. Consequently, a velocity ambiguity resolution method based on target parameter matching for front and rear frames is proposed to address this issue. The feasibility of the composite waveform and method are verified through simulation. Finally, a radar designed with the ALPS PRO chip is employed to test the designed waveform and velocity ambiguity resolution method, yielding results that are largely consistent with the simulation outcomes. The findings indicate a notable enhancement in resolution for medium distances ranging from 60 to 100 m when employing the proposed waveform. Moreover, the velocity ambiguity resolution method effectively resolves velocity ambiguity, leading to enhanced accuracy in velocity measurements. This suggests that the composite waveform and algorithm are well suited for current automotive angle radar applications.

4D High-Resolution Imagery of Point Clouds for Automotive mmWave Radar

In the community of automotive millimeter wave radar, the recently developed concept of four-dimensional (4D) radar can provide high-resolution point clouds image with enhanced imaging performance. Currently, the density of point clouds for single-frame image is usually too sparse to satisfy the demands of target classification and recognition due to the limitation of Doppler and angle resolutions. To address the aforementioned issues, a novel algorithm is proposed for 4D high-resolution imagery generation of point clouds with extremely high Doppler and angle resolutions in this paper. For high Doppler resolution with high-dynamic, a novel velocity ambiguity resolution algorithm is proposed using a dual pulse repetition frequency (dual-PRF) waveform design embedded in an innovative time-division multiplexing & Doppler-division multiplexing MIMO (TDM-DDM-MIMO) framework. Meanwhile, an attractive complex-valued deep convolutional network (CV-DCN) of super-resolution direction-of-arrival (DOA) estimation is proposed only using single-frame data. To be specific, a spatial smoothing operator on array data is applied as input of the network, and a CV-DCN is designed to learn the transformation of the spatial spectrum from the end-to-end to effectively protect the spectrum extraction. Furthermore, experimental analysis is performed to confirm the effectiveness of the proposed super-resolution DOA estimation algorithm. Finally, the 4D high-resolution imagery of point clouds is obtained by experiments in the parking lot.

A Velocity Ambiguity Resolution Algorithm Based on Improved Hypothetical Phase Compensation for TDM-MIMO Radar Traffic Target Imaging

A Velocity Ambiguity Resolution Algorithm Based on Improved Hypothetical Phase Compensation for TDM-MIMO Radar Traffic Target Imaging

Correction to “Joint Velocity Ambiguity Resolution and Ego-Motion Estimation Method for mmWave Radar” [Aug 23 4753-4760

Correction to “Joint Velocity Ambiguity Resolution and Ego-Motion Estimation Method for mmWave Radar” [Aug 23 4753-4760

Underwater weak moving target detection method based on wideband Multi-pulse coherent integration

When active sonar detects a weak moving target in a noisy background, coherent integration can be used to improve the signal-to-noise ratio of echo. The active sonar often transmits wideband signals and the target velocity ambiguity often occurs, in this case, the conventional coherent integration method makes the echo energy disperse and coherent integration gain decrease due to non-constant ambiguity factors in the bandwidth. To solve this problem, an underwater weak moving target detection method using multi-pulse coherent integration based on the wideband keystone transform is proposed. To compensate the non-constant ambiguity factors, a phase compensation function is constructed by replacing a single ambiguity factor with a set of ambiguity factors in the wideband keystone transform. After the proposed method, a well-focused image can be obtained in the delay-Doppler domain, and the coherent integration peak is detected to estimate delay and Doppler of the weak moving target. Simulations and lake test results verify the effectiveness of the proposed method, and show that the coherent integration gain with the proposed method is ca. 7–8 dB higher than that with the conventional method. The simulation results of integrating thirty pulses show that when the detection probability is greater than 0.7, the root-mean-square error of delay estimation of the proposed method is about 1/8 of that of the conventional method, and the root-mean-square error of Doppler estimation is about 1/3 of that of the conventional method, indicating that the proposed method has better parameter estimation accuracy.

Inner-Frame Time Division Multiplexing Waveform Design of Integrated Sensing and Communication in 5G NR System.

The design of an integrated sensing and communication (ISAC) waveform compatible with the 5G new radio (NR) system is crucial in enabling ISAC by utilizing the hardware of existing base stations (BSs). In this paper, we design an inner-frame time division multiplexed sensing waveform in the frame structure of 5G NR to achieve ISAC. The designed waveform is computed by the simulated annealing algorithm on an optimization cost function of a constrained combination of the peak-to-sidelobe ratio (PSLR) and the integrated sidelobe ratio (ISLR) of the velocity ambiguity function. Specifically, the constraints are the 5G communication protocol and 5G NR frame structure. In addition, we conducted corresponding signal detection and estimation methods to illustrate the performance of the sensing waveform. Both theoretical analysis and simulation experiments show that the designed waveform can effectively achieve target detection and parameter estimation under low sensing cost conditions.

An Hybrid Integration Method-Based Track-before-Detect for High-Speed and High-Maneuvering Targets in Ubiquitous Radar

Due to the limited transmission gain of ubiquitous radar systems, it has become necessary to use a long-time coherent integration method for range-Doppler (RD) analysis. However, when the target exhibits high-speed and high-maneuver capabilities, it introduces challenges, such as range migration (RM), Doppler frequency migration (DFM), and velocity ambiguity (VA) in the RD domain, thus posing significant difficulties in target detection and tracking. Moreover, the presence of VA further complicates the problem. To address these complexities while maintaining integration efficiency, this study proposes a hybrid integration approach. First, methods called Keystone-transform (KT) and matched filtering processing (MFP) are proposed for compensating for range migration (RM) and velocity ambiguity (VA) in Radar Detection (RD) images. The KT approach is employed to compensate for RM, followed by the generation of matched filters with varying ambiguity numbers. Subsequently, MFP enables the production of multiple RD images covering different but contiguous Doppler frequency ranges. These RD images can be compiled into an extended RD (ERD) image that exhibits an expanded Doppler frequency range. Second, an improved particle-filter (IPF) algorithm is raised to perform incoherent integration among ERD images and to achieve track-before-detect (TBD) for a target. In the IPF, the target state vector is augmented with ambiguous numbers, which are estimated via maximum posterior probability estimation. Then, to compensate for the DFM, a line spread model (LSM) is proposed instead of the point spread model (PSM) used in traditional PF. To evaluate the efficacy of the proposed method, a radar simulator is devised, encompassing comprehensive radar signal processing. The findings demonstrate that the proposed approach achieves a harmonious equilibrium between integration efficiency and computational complexity when it comes to detecting and tracking high-speed and high-maneuvering targets with intricate maneuvers. Furthermore, the algorithm’s effectiveness is authenticated by exploiting ubiquitous radar data.

A Deep Learning–Based Velocity Dealiasing Algorithm Derived from the WSR-88D Open Radar Product Generator

Abstract Radial velocity estimates provided by Doppler weather radar are critical measurements used by operational forecasters for the detection and monitoring of life-impacting storms. The sampling methods used to produce these measurements are inherently susceptible to aliasing, which produces ambiguous velocity values in regions with high winds and needs to be corrected using a velocity dealiasing algorithm (VDA). In the United States, the Weather Surveillance Radar-1988 Doppler (WSR-88D) Open Radar Product Generator (ORPG) is a processing environment that provides a world-class VDA; however, this algorithm is complex and can be difficult to port to other radar systems outside the WSR-88D network. In this work, a deep neural network (DNN) is used to emulate the two-dimensional WSR-88D ORPG dealiasing algorithm. It is shown that a DNN, specifically a customized U-Net, is highly effective for building VDAs that are accurate, fast, and portable to multiple radar types. To train the DNN model, a large dataset is generated containing aligned samples of folded and dealiased velocity pairs. This dataset contains samples collected from WSR-88D Level-II and Level-III archives and uses the ORPG dealiasing algorithm output as a source of truth. Using this dataset, a U-Net is trained to produce the number of folds at each point of a velocity image. Several performance metrics are presented using WSR-88D data. The algorithm is also applied to other non-WSR-88D radar systems to demonstrate portability to other hardware/software interfaces. A discussion of the broad applicability of this method is presented, including how other Level-III algorithms may benefit from this approach. Significance Statement Accurate and timely estimates of wind within storms are critically important for a number of applications, including severe storm nowcasting, maritime operational planning, aviation forecasting, and public safety coordination. Velocity aliasing is a common artifact that requires data quality control. While velocity dealiasing algorithms (VDAs) have been developed for decades, they remain a computationally complex and challenging problem. This paper presents an application of deep neural networks (DNNs) to increase the computational efficiency and portability of VDAs. A DNN is trained to emulate an operational algorithm, and performance is quantified over a large dataset. This work gives a convincing example of the benefits that deep learning can provide for radar algorithms, and future work highlighting these opportunities is discussed.

Coherent Multi-Dwell Processing of Un-Synchronized Dwells for High Velocity Estimation and Super-Resolution in Radar

This paper describes a coherent multi-dwell processing (CMDP) method for high velocity estimation and super-resolution in search and track, while search (TWS) radar modes use an un-conventional signal processing algorithm that exploits multi-dwell transmissions. The existence of the multi-dwell waveform is necessary for visibility needs by un-folding the target’s velocity and range ambiguity and is proposed to be utilized for high velocity estimation and super-resolution. In this paper, the proposed scheme is shown to result in improved velocity estimation and doppler resolution performance for un-ambiguous targets in comparison to classical radar processing. The processing concept uses the same transmitted waveform (WF) and time duration without the need to increase the time on target (TOT) through sophisticated coherent concatenation of the received dwells with velocity compensation between the dwells. The phase compensation in receive mode is implemented for each target according to its characteristics, which means that target velocities are estimated in each dwell separately. The notable result of the CMDP is the linear doppler resolution improvement obtained with the given search resources and without knowing the target characteristics in advance or the dwell delay time. Other possible benefits of this process are the ability to achieve larger detection ranges and high-angle measurement precisions in search mode due to the higher signal-to-noise ratio (SNR) of the extended dwell and the ability to track more targets due to efficient time and resource management. An outstanding opportunity to exploit the CMDP is by combining missions in phased array (PA) radars, meeting the multi-objective needs of both high spatial scan rates for illuminating the target and high doppler estimation and resolution performance.

An Unambiguity and Anti-Range Eclipse Method for PD Radar Using Biphase Coded Signals

Target detection is an important research content in the radar field. At present, efforts are being made to optimize the precision of detection information. In this paper, we use the high pulse repetition frequency (HPRF) transmission method and orthogonal biphase coded signals in each pulse to avoid velocity ambiguity and range ambiguity of radar detection. In addition, We also apply Walsh matrix and genetic algorithm (GA) to generate satisfying orthogonal biphase coded signals with low auto-correlation sidelobe peak and cross-correlation peak, which make the results more accurate. In a radar receiver, data rearrangement of echo signals is performed, and then pulse compression and moving target detection (MTD) are utilized to get the final velocity and range information of a target without velocity ambiguity and range ambiguity. Besides, a small transmitting pulse time width is adopted to reduce the working blind area, and two different high pulse repetition frequencies (HPRFs) are adopted to solve the problem of range eclipse. Simulation results finally prove the effectiveness and feasibility of the proposed method.

SSB-Based Signal Processing for Passive Radar Using a 5G Network

This paper presents an alternative processing chain for the passive radar using fifth-generation (5 G) standard technology for broadband cellular networks as illuminators of opportunity. The proposition is to use a 5 G synchronization signal block's (SSB) periodically transmitted modulated pulse in 5G-based passive coherent location (PCL) system processing. Although the SSB periodicity limits the velocity ambiguity, the paper describes a solution to tackle this problem in a single target scenario. The method is advantageous when there is a lack of transmission in the telecommunication channel, and the 5 G SSB is the only existing signal. The paper proposes a signal processing pipeline for 5G-based PCL that is inspired by passive radars using non-cooperative pulse radar as an illumination source. The method has been validated using simulated and real-life 5 G data measurements. The results presented in the paper show the possibility of detecting a moving target with a lack of data transmission in the 5 G network, using only the SSB when the classical passive radar signal processing fails. The presented results prove the possibility for a significant increase of 5 G network-based PCL utilization in short-range applications.

An effective scheme of joint migration inversion in the pseudo‐time domain

AbstractTraditional full‐waveform inversion is a non‐linear and ill‐posed inversion problem. To reduce the non‐linearity of it, joint migration inversion (joint migration inversion) was proposed as an alternative. Joint migration inversion tries to minimize the mismatch between measured and modelled reflection data. One key feature of joint migration inversion is its parameterization: two separate parameters, reflectivity (for the amplitudes of reflected events) and propagation velocity (for the phase effects). This separation helps to reduce the non‐linearity of the inversion. During joint migration inversion, with the velocity being updated, the reflectors in the updated image are also shifting in depth accordingly, this phenomenon is called depth–velocity ambiguity. This interaction between the two parameters during inversion is desired to keep the image time consistent with the measured data but may lead to non‐robustness of joint migration inversion due to the presence of local minima. Therefore, we propose a more robust joint migration inversion scheme, which parameterizes the models with vertical time, termed pseudo‐time joint migration inversion. In pseudo‐time, the updates of velocity will not result in the associated vertical location changes of reflectors in the estimated image. Instead, the reflectors are mainly getting more focused. One limitation is that the depth‐pseudo‐time conversion process assumes a simple linear relationship between depth and pseudo‐time, which might cause some artefacts in the converted models when there exist strong lateral velocity variations. One subsequent round of depth joint migration inversion is recommended to resolve this issue. We demonstrate the effectiveness of our proposed method with a two‐dimensional synthetic example in an extreme scenario, where the initial velocity model is homogeneous, a realistic offshore two‐dimensional synthetic example, a two‐dimensional field example from the Vøring basin in Norway and a simple three‐dimensional synthetic example. In all examples, pseudo‐time joint migration inversion manages to recover more reasonable updates in the inverted velocity and invert more focused reflectors in the inverted image, compared to depth joint migration inversion.

Urban Traffic Imaging Using Millimeter-Wave Radar

Imaging technology enhances radar environment awareness. Imaging radar can provide richer target information for traffic management systems than conventional traffic detection radar. However, there is still a lack of research on millimeter-wave radar imaging technology for urban traffic surveillance. To solve the above problem, we propose an improved three-dimensional FFT imaging algorithm architecture for radar roadside imaging in urban traffic scenarios, enabling the concurrence of dynamic and static targets imaging. Firstly, by analyzing the target characteristics and background noise in urban traffic scenes, the Monte-Carlo-based constant false alarm detection algorithm (MC-CFAR) and the improved MC-CFAR algorithm are proposed, respectively, for moving vehicles and static environmental targets detection. Then, for the velocity ambiguity solution problem with multiple targets and large velocity ambiguity cycles, an improved Hypothetical Phase Compensation algorithm (HPC-SNR) is proposed and complimented. Further, the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm is used to remove outliers to obtain a clean radar point cloud image. Finally, traffic targets within the 50 m range are presented as two-dimensional (2D) point cloud imaging. In addition, we also try to estimate the vehicle type by target point cloud size, and its accuracy reaches more than 80% in the vehicle sparse condition. The proposed method is verified by actual traffic scenario data collected by a millimeter-wave radar system installed on the roadside. The work can support further intelligent transportation management and extend radar imaging applications.

Weak and Maneuvering Target Detection with Long Observation Time Based on Segment Fusion for Narrowband Radar.

Detecting high-speed and maneuvering targets is challenging in early warning radar applications. Modern early warning radar has many functions such as detection, tracking, imaging, and recognition which need a high signal-to-noise ratio (SNR). Thus, long-time coherent integration is a necessary method to realize high SNR requirements. However, high-speed and maneuverable motion cause range and Doppler migration, which brings about serious coherent integration loss. Traditional integration methods usually have the drawbacks of model mismatching and high computational complexity. This paper establishes a novel long coherent processing interval (CPI) integration algorithm that detects maneuvering and weak targets which have a low reflection cross-section (RCS) and low echo SNR. The range and Doppler migration problems are solved via a layer integration by blending the association in a tracking-before-detection (TBD) technique. Compact SNR gain is achieved with a target information transmission mechanism and an updated constant false alarm ratio (CFAR) threshold. The algorithm is applicable in multiple target scenarios by considering different velocity ambiguities and maneuvers. A simulation and real-measured experiments confirm the effectiveness of the algorithm.

WSR-88D Sidelobe Contamination: From a Conceptual Model to Diagnostic Strategies for Improving NWS Warning Performance

Abstract Providing timely warnings for severe and potentially tornadic convection is a critical component of the NWS mission, and owing to the associated large reflectivity gradients, sidelobe contamination is possible. This paper focuses on elevation sidelobe contamination appearing in the low-level inflow region of supercells. A qualitative conceptual model of the Weather Surveillance Radar-1988 Doppler (WSR-88D) antenna pattern interacting with supercells is introduced, along with Doppler power spectrum representations of the potential mix of returned power from the main lobe and the sidelobes. These tools inform the multiple ways elevation sidelobe contamination appears in the low levels, primarily below 3 km (10 kft) of radar data. The most common manifestation is somewhat noisy data similar to particulates or biota in clear air. Trained NWS forecasters are accustomed to mentally filtering out noisy clear-air returns as less important. Elevation sidelobe contamination can be mixed with the three-body scatter spike (TBSS) artifact, though the TBSS remains the more salient feature. The most consequential form is the apparent circulation, and when it is incorrectly interpreted as valid, contributes to the false alarm ratio (FAR) for NWS tornado warnings. Quantitative results on the effect of elevation sidelobe contamination on FAR are presented. Diagnostic techniques are emphasized, and with familiarization, can be used in real-time warning operations to identify the apparent circulation as either valid or an imposter. Identification of these contaminated velocity signatures offers a unique opportunity to reduce the NWS tornado warning FAR without also reducing the probability of detection (POD). Significance Statement The WSR-88D weather radars provide overall high-quality data for users. However, with some severe thunderstorms, an artifact called elevation sidelobe contamination can produce what looks like a rotation signature, but it may not be real. These ambiguous velocity signatures can contribute to tornado warnings based on rotation signatures that are false circulations. This paper specifically focuses on elevation sidelobe contamination due to its impact on tornado warning decisions. Diagnostic techniques, including several examples, are presented here to aid the reader in correctly identifying elevation sidelobe contamination and why it may occur. Correct identification of an apparent circulation as an imposter due to contamination is a unique opportunity to improve NWS tornado warning performance by reducing warning false alarms.

Doppler–Range Processing for Enhanced High-Speed Moving Target Detection Using LFMCW Automotive Radar

Range/Doppler migration and velocity ambiguity are two well-known problems encountered in high-speed moving target detection using a linear-frequency-modulated continuous-wave automotive radar. To mitigate the problems, we introduce a simple Doppler–range processing (DRP) algorithm by first performing Doppler processing via fast Fourier transform (FFT) across slow-time samples, followed by a simple interpolation step, and then range processing via FFT along Doppler migration lines over fast-time samples. The proposed DRP algorithm can achieve full range and full velocity resolutions, as well as full coherent integration gains. It attains a computational complexity comparable to that of the conventional 2-D-FFT-based range–Doppler processing approach, computationally much more efficient than existing approaches. The proposed DRP algorithm can automatically resolve the velocity ambiguity problems. We analyze its velocity ambiguity mitigation capability in relation to the radar bandwidth and the number of slow-time samples within a coherent processing interval. The effectiveness and the computational efficiency of the proposed algorithm are demonstrated by numerical examples.

Frequency Diverse Array Introduced Into SAR GMTI to Mitigate Blind Velocity and Doppler Ambiguity

In this letter, a frequency diverse array (FDA) is introduced into synthetic aperture radar ground moving target indication (SAR GMTI) to mitigate both the blind velocity and Doppler ambiguity problems. Due to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula> periodicity of the echo phases, notches will occur periodically in clutter cancelers at nonzero velocities, leading to the blind velocity problem. In the proposed scheme, the dependence of the measured blind velocity on the transmission frequency is considered, and a new clutter canceler unaffected by the blind velocity problem is constructed via the integration of multiple cancelers with diverse frequencies. Moreover, to resolve the Doppler ambiguity, along-track interferometry (ATI) based double interferometry is proposed to extend the maximum unambiguous radial velocity (RV). Additionally, search-based clustering is adopted to enhance the precision of RV estimation. Finally, a moving target can be brought into focus and correctly relocated using the estimated RV. Numerical results verify the effectiveness of the proposed method.

Novel Multiplexing Scheme for Resolving the Velocity Ambiguity Problem in MIMO FMCW Radar Using MPSK Code

For the high-resolution DoA (Direction of Arrival) estimation, various multiplexing schemes are considered for the multi-input multi-output (MIMO) fast chirp frequency-modulated continuous-wave (FMCW) radar. However, current schemes such as time-division multiplexing (TDM) and binary-phase modulation (BPM) may reduce the maximum detectable velocity, which causes the velocity ambiguity problem. As an extension of the BPM scheme to mitigate this issue, we propose a novel multiplexing scheme using M phase-shift keying (MPSK) code which duplicates shifted target peaks at unequal intervals over the velocity domain. The proposed scheme finds the true peaks to resolve the velocity ambiguity problem by the inversion of the circulant matrix with low additional computation. In addition, the successful implementation of the proposed scheme is conducted with 4 by 8 MIMO uniform linear array (ULA) antennas through the state-of-the-art FMCW radar. Finally, the proposed scheme is compared to the conventional TDM based MIMO scheme regarding signal to noise ratio (SNR) and phase calibration issues for moving targets. The proposed scheme is to estimate the accurate 4D information of targets while resolving the velocity ambiguity problem in the MIMO FMCW radar systems.