Multiple-input Multiple-output Radar Research Articles

A MIMO moving target detection radar with optimal transmit and receive weightage

Target detection using multiple-input multiple-output (MIMO) radar has recently gained popularity in radar research due to its ability to mitigate the target radar cross-section fading and substantial spatial diversity gain. Recently, an optimal MIMO radar detector, including optimal transmit and receive weightage, has been proposed for the detection of steady targets. A moving target differs the scenario from a steady target case due to its Doppler. Hence, the optimal detector of a steady target case does not work for the case of a moving target. Therefore, in this paper, we proposed a MIMO radar detector for the context of moving targets, including optimal transmit and receive weight schemes. For obtaining the proposed detector, knowledge about the target fading that can be applied to a moving target scenario is a prerequisite. Therefore, we proposed to use a training mechanism in which a few transmit pulses are introduced once in every coherent processing interval, and the corresponding target returns are used to estimate the target fading. However, in a moving target scenario, the target returns are Doppler-steered versions of the target fading. Therefore, it is proposed to compensate the Doppler for target fading estimation by matching a steering vector to the target returns. This type of use of online estimation of the target fading characteristics and applying it for moving target detection is the first of its kind in radar research. The proposed radar is shown to outperform the state-of-the-art MIMO radars addressed in the literature.

Target Parameter Estimation Algorithm Based on Real-Valued HOSVD for Bistatic FDA-MIMO Radar

Since there is a frequency offset between each adjacent antenna of FDA radar, there exists angle-range two-dimensional dependence in the transmitter. For bistatic FDA-multiple input multiple output (MIMO) radar, range-direction of departure (DOD)-direction of arrival (DOA) information is coupled in transmitting the steering vector. How to decouple the three information has become the focus of research. Aiming at the issue of target parameter estimation of bistatic FDA-MIMO radar, a real-valued parameter estimation algorithm based on high-order-singular value decomposition (HOSVD) is developed. Firstly, for decoupling DOD and range in transmitter, it is necessary to divide the transmitter into subarrays. Then, the forward–backward averaging and unitary transformation techniques are utilized to convert complex-valued data into real-valued data. The signal subspace is obtained by HOSVD, and the two-dimensional spatial spectral function is constructed. Secondly, the dimension of spatial spectrum is reduced by the Lagrange algorithm, so that it is only related to DOA, and the DOA estimation is obtained. Then the frequency increment between subarrays is used to decouple the DOD and range information, and eliminate the phase ambiguity at the same time. Finally, the DOD and range estimation automatically matched with DOA estimation are obtained. The proposed algorithm uses the multidimensional structure of high-dimensional data to promote performance. Meanwhile, the proposed real-valued tensor-based method can effectively cut down the computing time. Simulation results verify the high efficiency of the developed method.

Data-Independent Phase-Only Beamforming of FDA-MIMO Radar for Swarm Interference Suppression

This paper proposes two data-independent phase-only beamforming algorithms for frequency diverse array multiple-input multiple-output radar against swarm interference. The proposed strategy can form a deep null at the interference area to achieve swarm interference suppression by tuning the phase of the weight vector, which can effectively reduce the hardware cost of the receiver. Specifically, the first algorithm imposes constant modulus constraint and sidelobe level constraint, and the phase-only weight vector is solved. The second algorithm performs a constant modulus decomposition of the weight vector to obtain two phase-only weight vectors, and uses two parallel phase shifters to synthesize one beamforming weight. Both methods can obtain the phase-only weight to realize suppression for swarm interference. Simulation results demonstrate that our strategy shows superiority in beam shape, output signal-to-interference-noise ratio, and phase shifter quantization performance, and has the potential for use in many applications, such as radar countermeasures and electronic defense.

Joint DOA, range and polarization estimation based on geometric algebra for near-field non-circular source with a symmetric MIMO array

Multiple-input multiple-output (MIMO) radar is a new type of radar with excellent performance in target detection and parameter estimations. The MIMO radar equipped with electromagnetic vector sensors (EMVSs) can record multi-dimensional information of the electromagnetic (EM) signal. Traditional methods based on long vector model cannot preserve orthogonality between the outputs of each component of the EMVS and have high computational complexity. In this paper, a novel geometric algebra (GA)-based localization method is proposed for direction of arrival (DOA), range, and polarization estimation of near-field (NF) non-circular (NC) sources for a symmetric MIMO array. First, the proposed method converts the output of an EMVS into a multi-vector through a GA matrix transformation. Then, the DOA and range parameters can be estimated by searching the one-dimensional (1-D) spectrum based on the GA-based NC rank reduction (GANC-RARE) algorithm. Finally, the polarization can be estimated by employing estimated DOAs and ranges based on the modified GA-based NC multiple signal classification (MGANC-MUSIC) algorithm. The computational complexity analysis demonstrates that our solution improves memory spaces of the covariance matrix and reduces computation efforts of the eigenvalue decomposition (EVD). The simulation results show the superiority and reliability of our proposed method in model error and coherent noise environment.

MIMO radar beampattern design by using Phased-Costas waveforms with PAR constraints employing a generalized ambiguity function

Multiple-input multiple-output (MIMO) radars have attracted interest due to some important advantages over Phased-array radars. The diversity that comes with multiple waveforms is used to maximize the power in the vicinity of targets and minimize the cross correlation of waveforms reflected from multiple targets for predefined angles. In this study, a novel approach is presented to overcome the limitations of current beamformer design techniques in terms of bandwidth, auto/cross (spatial) correlations, range-doppler resolutions, peak-to-average ratio (PAR) and mean squared error (MSE) for desired beamforming pattern. A generalized ambiguity function formulation is presented which employs all the beamformer design parameters in a mathematically tractable simple manner suitable for constrained optimization. We present Phased-Costas coded waveforms to generate desired beampatterns while minimizing range-doppler sidelobes and target cross-correlations with limited bandwidth. Beamformer design problem is casted as a constrained optimization which includes nonconvex PAR constraints. The resulting NP hard problem with nonconvex objective function is converted to a bi-convex form and the PAR constraints are converted as convex constraints. The final problem is efficiently solved by using Alternating Direction Method of Multipliers (ADMM) technique in polynomial time. The beamformer solution is shown to achieve PAR=1 with very little degradation compared to the unconstrained problem making the ultimate choice for MIMO beamforming applications. Several good features of the designed beamformer are shown through simulations and compared to the known methods.

Performance Boosting for Two-Step Localization Methods in Distributed MIMO Radar via a Robust Post-Processing Scheme

In radar target localization using time delay (TD) measurements, reliable TD extraction is an important prerequisite for conventional two-step localization methods. In the distributed multiple-input multiple-output (MIMO) radar, the low-quality TD measurements (i.e., outliers) always occur due to the target scattering fluctuations in various transmitter-receiver paths, which results in serious performance degradation to the generic two-step localization methods. To this end, we propose a simple yet effective performance boosting scheme in this letter. It constructs a robust estimator based on the Huber loss function and solves this problem iteratively by using the majorization-minimization (MM) technique. This proposal is a general post-processing module, and thus it can be combined with any existing two-step algorithms to achieve performance improvement in the presence of outliers. The simulations verify the effectiveness of the proposed scheme by comparing with the derived theoretical lower bound. In addition, the parameter robustness and the computational burden are also evaluated.

Vital Sign Tracking Using Modified Constant Modulus Algorithm Adaptive Array

This paper proposes a modified constant modulus algorithm (CMA)-based beamforming method for a multiple-input multiple-output radar to track and detect vital signs via blind processing. Our method consists of two key functions: (1) the beamforming weight and DC offset are jointly updated to remove the semi-constant clutter and maintain the constant amplitude, which is the original function of CMA, and (2) the weight is updated by considering the phase variance owing to the typical respiratory response to make the weight converge to the vital signs. The proposed method was experimentally evaluated by comparing its heart rate estimation accuracy with that of the conventional CMA-based and maximal-ratio combining (MRC)-based beamforming methods. The experimental results showed that the proposed beamforming method with and without the phase variance constraint achieved the median errors of 3.45 and 4.06 bpm from the reference electrocardiogram, respectively, whereas the conventional CMA-based and MRC-based beamforming methods achieved the median errors of 21.1 and 9.79 bpm, thereby demonstrating the effectiveness of the proposed method.

Energy-Guided Multitarget Detection and Localization for Distributed MIMO Radar: Analysis and Solution

This article investigates the multitarget detection and localization problem for distributed multiple-input multiple-output radar. We first derive the optimal approach of this issue in the high-dimensional space according to the generalized likelihood ratio test (GLRT) and the maximum likelihood estimation. Moreover, the theoretical multitarget localization accuracy under the considered discrete time signal model is analyzed by invoking the Cram$\acute{\text{e}}$r–Rao lower bound and the sampling lower bound. To deal with the high complexity problem of the optimal solution, an energy-guided framework including two modules is proposed to detect and locate multiple targets. In the first module, the energy accumulation approach based on the GLRT is employed for multitarget detection, and a fast energy accumulation strategy in terms of the far-field case is developed to improve the computational efficiency. In the second module, an innovative iterative similarity evaluation method is designed to determine the positions of multiple targets by exploiting the relationship between the energy accumulation characteristics and the multitarget existence conditions. The effectiveness of the proposed framework is verified via extensive simulations in both far-field and near-field cases.

Statistical Method Based Waveform Optimization in Collocated MIMO Radar Systems

Multiple-input multiple-output (MIMO) radar has acquired considerable attention as it offers an additional degree of freedom which results in performance gains when contrasted with the regular single antenna element radar system. Waveform optimization in MIMO radar is essential as it can offer tremendous improvements in target detection which are quantified in terms of reductions in the symbol error rate and improvements in target detection probability. In this work, we foster a strategy for the optimization of transmitter and receiver waveform in a collocated MIMO radar by only considering the second order statistics, thus relaxing the information of the instantaneous target states. Our contributions are primarily two-fold. First, we find a closed-form expression of the outage probability of an unknown target under clutter environment. For this prospect, we model the signal-to-interference-plus-noise ratio in a canonical quadratic structure, and then utilize the modern residue theory approach to characterize the distribution function. Secondly, we propose constrained and unconstrained optimization problems for the reduction in outage probability using algorithmic techniques such as interior-point, sequential-quadratic programming, and the active-set method for the optimization of the transmitter and receiver waveform. We also provide simulated re-enactments to validate our hypothetical deductions.

MIMO Radar Transmit Waveform Design for Beampattern Matching via Complex Circle Optimization

In this paper, we study the multiple-input multiple-output (MIMO) radar transmit waveform design method for beampattern matching. The purpose is to design the beampattern to approximate the actual one and minimize the cross-correlation sidelobes under the constant modulus constraint (CMC). Due to the CMC, the problem is non-convex, and the existing methods solve it with relaxation, resulting in performance degradation. Different from these methods, we notice that the CMC is the product of complex circles (CC). Based on this physical characteristic, the direct beampattern matching without relaxation (DBMWR) method is proposed. To be specific, we first formulate the original problem as an unconstrained quartic problem over the CC and then solve it by the proposed method without relaxation. Simulation results show that the proposed method can achieve a balance in terms of accuracy and computation complexity compared with other methods.

Forward-Looking Super-Resolution Imaging of MIMO Radar via Sparse and Double Low-Rank Constraints

Multiple-input multiple-output (MIMO) radar uses waveform diversity technology to form a virtual aperture to improve the azimuth resolution of forward-looking imaging. However, the super-resolution imaging capability of MIMO radar is limited, and the resolution can only be doubled compared with the real aperture. In the radar forward-looking image, compared with the whole imaging scene, the target only occupies a small part. This sparsity of the target distribution provides the feasibility of applying the compressed sensing (CS) method to MIMO radar to further improve the forward-looking imaging resolution. At the same time, the forward-looking imaging method for a MIMO radar based on CS has the ability to perform single snapshot imaging, which avoids the problem of a motion supplement. However, the strong noise in the radar echo poses a challenge to the imaging method based on CS. Inspired by the low-rank properties of the received radar echoes and the generated images, and considering the existing information about sparse target distribution, a forward-looking super-resolution imaging model of a MIMO radar that combines sparse and double low-rank constraints is established to overcome strong noise and achieve robust forward-looking super-resolution imaging. In order to solve the multiple optimization problem, a forward-looking image reconstruction method based on the augmented Lagrangian multiplier (ALM) is proposed within the framework of the alternating direction multiplier method (ADMM). Finally, the results of the simulation and the measurement data show that the proposed method is quite effective at improving the azimuth resolution and robustness of forward-looking radar imaging compared with other existing methods.

An ADMM-qSPICE-Based Sparse DOA Estimation Method for MIMO Radar

In recent years, sparse direction-of-arrival (DOA) estimation for multiple-input multiple-output (MIMO) radar has attracted extensive attention and been extensively studied, especially the method based on the classic least absolute shrinkage and selection operator (LASSO) estimator. The alternating-direction method of multipliers (ADMM) is an effective method for solving this problem at the cost of introducing an additional user parameter. To avoid introducing an additional user parameter, this paper adopts an equivalent transformation in the form of the generalized SParse Iterative Covariance-based Estimation (qSPICE) cost function to obtain a mean squared minimized form of the cost function. Then, the problem is transformed into a sparse optimization problem in the form of a weighted LASSO. Next, this unconstrained optimization problem is decomposed into three subproblems, which are solved separately to reduce the dimension of each problem and thus reduce the overall computational complexity based on ADMM. Simulation results and measured data indicate that the proposed method significantly outperforms the traditional super-resolution DOA estimation method and ADMM-LASSO method and slightly outperforms qSPICE in terms of resolution and sidelobe suppression capability. In addition, the proposed method has a much lower computational complexity and substantially fewer iterations than qSPICE.

3-D Positioning Method for Anonymous UAV Based on Bistatic Polarized MIMO Radar

The Angle-of-Arrival (AoA)-based approach is an appealing solution for unmanned aerial vehicle (UAV) positioning, and has received significant interest recently. In this article, we propose a novel framework for UAV three-dimensional (3-D) positioning, the core of which is to measure the two-dimensional (2-D) Angle-of-Departure (2D-AoD) and 2D-AoA via a bistatic multiple-input multiple-output (MIMO) radar. Unlike the existing positioning architectures, the MIMO radar is equipped with polarized array antennas. An estimator based on the parallel factor (PARAFAC) decomposition is developed. It first obtains the direction matrices via performing the PARAFAC decomposition of the array data. Thereafter, the rotational invariance characteristic is utilized to form a normalized polarization response vector, from which the 2D-AoD, 2D-AoA, and polarization status of the UAVs are achieved via incorporating the vector cross-product method and the least squares (LSs) technique. Finally, the 3-D positions of the UAVs are easily calculated via the location relationship between the 2D-AoD, 2D-AoA, and the coordinates of transmitting/receiving (Tx/Rx) array. The proposed framework is computationally friendly, and is capable of positioning anonymous UAV. Moreover, it is insensitive to the geometry of the Tx/Rx array, indicating that the proposed framework supports configurable Tx/Rx antennas. Simulation results are provided to verify our theoretical advantages.

$\ell _{0}$-Norm Minimization Based Robust Matrix Completion Approach for MIMO Radar Target Localization

In this paper, we propose a robust matrix completion approach based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula> -norm minimization for target localization in sub-Nyquist sampled multiple-input multiple-output (MIMO) radar. Owing to the low-rank property of the noise-free MIMO radar transmit matrix, our approach is able to recover the missing data and resist impulsive noise from the receive matrix. We adopt proximal block coordinate descent and adaptive penalty parameter adjustment by complex Laplacian kernel and normalized median absolute deviation. We analyze the resultant algorithm convergence and computational complexity, and demonstrate through simulations that it outperforms existing methods in terms of pseudospectrum, mean square error, and target detection probability in non-Gaussian impulsive noise, even for the full sampling schemes. While in the presence of Gaussian noise, our approach performs comparably with other sub-Nyquist methods.

Real-Time Through-Wall Multihuman Localization and Behavior Recognition Based on MIMO Radar

Human localization and behavior recognition (HLBR) is an important research topic in wireless sensing and computer vision. Most studies mainly use cameras and millimeter-wave radars, which can achieve fine-grained human localization; however, they cannot solve the problem of wall occlusion. Although methods that use Wi-Fi can penetrate walls, they cannot detect the precise localization of people due to their narrow bandwidth limitation. The above problems limit the application of HLBR in real life. This paper proposes a real-time, through-wall, multi-human localization and behavior recognition system, RTWLBR. In this system, we design a multiple-input multiple-output (MIMO) radar in the 1-2 GHz frequency range. An ultrawide band (UWB) positioning device and a camera are attached to the self-developed, through-wall radar system to capture the simultaneous localization, behavior information, and radar reflection heatmap of people behind a wall, where location information and behavior information are jointly embedded and encoded as a confidence matrix, which serves as a supervision signal for neural network training. A multi-feature fusion network based on a 3D convolutional neural network (3D CNN) is designed to learn human localization and behavior information from radar heatmaps. A joint heatmap compression autoencoder network is utilized to assist network training to reduce quantization error and running costs. The experimental results show that the RTWLBR method can perform real-time localization and behavior recognition of target humans behind a 24 cm brick wall.

Optimization of Mismatched Filters With Asymmetric Side-Lobe Shape for Short-Range MIMO Radars

This paper presents the design of signal compression and separation filters with asymmetric responses for multiple-input multiple-output (MIMO) radars that use pulses longer than the maximum return time of the reflected signal. Such radars suffer from direct penetration of the transmitted signal to the receiver, appearing as a very strong stationary reflection in the zero range. After pulse compression, the far-side lobes of this crosstalk may compete with the reflections of distant weak targets and limit the maximum radar range. Hence, in addition to the maximum suppression of the direct transmitted signal penetration to the receiver, the far-side lobe reduction of this crosstalk with positive time lags is desirable. Asymmetric response filters allow optimization to be focused on the region where the maximum suppression of crosstalk between the transmitted signal and the receiver is desired. Extreme suppression was achieved by applying lower demand in other areas and other parameters. In this paper, the problem is described in more detail along with the mathematical apparatus by which asymmetric filter outputs can be achieved.

Joint DOD and DOA Estimation of Coherent Targets for Coprime MIMO Radar

Recently, coprime arrays have attracted lots of interest due to their ability of providing enhanced degrees-of-freedom and reduced mutual coupling effect compared to conventional uniform linear arrays. Benefitting from these excellent properties, coprime multiple-input multiple-output (MIMO) radar has been recently suggested for improving parameter identifiability and target detection. In this paper, we address the problem of joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation of coherent targets in coprime MIMO radar. First of all, we establish an extended virtual uniform rectangular array (URA) by performing array interpolation on the transmit and receive arrays of coprime MIMO radar. Subsequently, we derive a low-rank block Hankel matrix that is constructed using the correlation information of the virtual URA expected outputs, and utilize the matched filter outputs to recover the block Hankel matrix by solving a low-rank structured matrix completion problem. Finally, we estimate the DODs and DOAs of coherent targets by applying the modified matrix pencil method on the recovered low-rank matrix. We also derive the Cramér-Rao bounds with closed-form expressions for DOD and DOA estimation of coherent targets using coprime MIMO radar. The proposed algorithm can identify multiple coherent targets and achieve parameter automatic pairing. Numerical results demonstrate the superiority of the proposed algorithm over several existing approaches when handling coherent targets.

Beam Scheduling for Early Warning With Distributed MIMO Radars

Distributed multiple-input multiple-output (MIMO) radars achieve long-range detection by steering and focusing the narrow beams of all transmit and receive antennas on a single point. This paper proposes a beam scheduling scheme based on the joint optimization of three components: arrangement of focal points, beam dwell time allocation of each focal point, and scanning order of focal points. The purpose is to enable distributed MIMO radars to provide early warning of incursions entering a broad surveillance region. To this end, a mathematical model is first developed to evaluate radar detection capability in a cell under test (CUT) over a scheduling period. By integrating all the CUTs within the region, the detection time required to reach a specified performance in terms of cumulative detection probability is then derived. On this basis, a beam scheduling strategy is devised, considering the maximum speed and minimum average radar cross-section constraints of targets to be detected. The main mechanism of the strategy is to minimize the detection time without sacrificing performance. To address the optimization problem of beam scheduling, we propose a two-stage method using a detection capability threshold as an extra optimization variable. In our method, the first stage is used to obtain optimal schemes for different given thresholds, and in the next stage, the optimal threshold is determined from these schemes. The simulation results show that the proposed algorithm is effective.

Weak Signal Detection With Low-Bit Quantization in Colocated MIMO Radar

This paper addresses the weak signal detection problem in a massive colocated multiple-input multiple-output (MIMO) radar. To cope with the sheer amount of data produced by the large-scale antennas, a low-bit quantizer is introduced in the sampling process to enable both for hardware limitations and a high detection performance. The generalized likelihood ratio test (GLRT) detector is proposed for the quantized data, with the batch gradient descent algorithm being introduced to form an estimate of the unknown parameters. Furthermore, as a low-complexity alternative to the GLRT detector, we propose a multi-bit Rao detector, yielding a closed-form test statistic, whose theoretical distribution is also presented. Finally, we refine the design of the quantizer by optimizing the quantization thresholds, which are obtained using the particle swarm optimization algorithm. Results from simulation and experimental data demonstrate the performance of the detectors using both unquantized and quantized data. They corroborate the theoretical analyses and show that the performance with 3-bit quantization yields a performance that approaches the cases without quantization, while reducing the overall complexity of the system substantially.

DDMA-MIMO Observations With the MU Radar: Validation by Measuring a Beam Broadening Effect

The phased-array radar, basically developed with the defense systems, has mainly utilized for the atmospheric radar and the wind profiling radar in the field of meteorological remote sensing, and recently it has also applied to the weather radar for research purposes. As a further development of phased-array technology, the “Multiple-Input Multiple-Output (MIMO) technique,” which has been developed in the field of communication systems, has been applied to radars. With the MIMO radar, it is possible to create a virtual antenna aperture plane beyond the actual antenna and to reduce the actual antenna size compared to that of the conventional antenna while maintaining the angular resolution. This effect is expected to reduce costs, which is one of the major hurdles in expanding phased array radars instead of parabolic antenna systems. In order to confirm the effect, an experimental observation was performed using the MU radar which is a VHF-band phased array atmospheric radar with multi-channel receivers. The MIMO technique requires orthogonal waveforms on each transmitter to identify the transmitted signals with multiple receivers, and various methods are known to realize orthogonality. In this paper, we focus on the “ Doppler Division Multiple Access (DDMA)” MIMO technique, with which slightly different frequencies are selected as transmit waveforms to separate in each receiver in the Doppler frequency domain. The observation results by measuring a beam broadening effect with the MU radar indicate that it will be a key technique for the atmospheric radar in the near future.