Bistatic Multiple-input Multiple-output Research Articles

Reduced-complexity multiple parameters estimation via toeplitz matrix triple iteration reconstruction with bistatic MIMO radar

In this advanced exploration, we focus on multiple parameters estimation in bistatic Multiple-Input Multiple-Output (MIMO) radar systems, a crucial technique for target localization and imaging. Our research innovatively addresses the joint estimation of the Direction of Departure (DOD), Direction of Arrival (DOA), and Doppler frequency for incoherent targets. We propose a novel approach that significantly reduces computational complexity by utilizing the Temporal-Spatial Nested Sampling Model (TSNSM). Our methodology begins with a multi-linear mapping mechanism to efficiently eliminate unnecessary virtual Degrees of Freedom (DOFs) and reorganize the remaining ones. We then employ the Toeplitz matrix triple iteration reconstruction method, surpassing the traditional Temporal-Spatial Smoothing Window (TSSW) approach, to mitigate the single snapshot effect and reduce computational demands. We further refine the high-dimensional ESPRIT algorithm for joint estimation of DOD, DOA, and Doppler frequency, eliminating the need for additional parameter pairing. Moreover, we meticulously derive the Cramér-Rao Bound (CRB) for the TSNSM. This signal model allows for a second expansion of DOFs in time and space domains, achieving high precision in target angle and Doppler frequency estimation with low computational complexity. Our adaptable algorithm is validated through simulations and is suitable for sparse array MIMO radars with various structures, ensuring higher precision in parameter estimation with less complexity burden.

Angle estimation based on Vandermonde constrained CP tensor decomposition for bistatic MIMO radar under spatially colored noise

We address the problem of Vandermonde constrained CANDECOMP/PARAFAC (CP) tensor decomposition in application to angle estimation for bistatic multiple-input multiple output (MIMO) radar under spatially colored noise. By exploiting the temporally uncorrelated characteristic of colored noise, a new denoising scheme based on the temporally smoothed cross-correlation approach is presented. Then, after rearranging the smoothed cross-correlation matrix into a fourth-order tensor, a Vandermonde constrained CP tensor decomposition model is formulated, which fully exploits the multidimensional structure of the array measurement and the Vandermonde structure of the factor matrices. To solve this model, an efficient constrained alternating least squares (ALS) algorithm is developed to decompose the Vandermonde factor matrices. Finally, joint estimates of direction of departure (DOD) and direction of arrival (DOA) are obtained by the generators of the Vandermonde factor matrices. Compared with the state-of-the-art approaches, the proposed method can achieve better angle estimation performance by jointly using the temporally smoothed cross-correlation denoising operation and enforcing the Vandermonde structure information in the tensor decomposition. Numerical simulation results verify the effectiveness and improvement of our algorithm.

Bistatic MIMO radar height estimation method based on adaptive beam-space RML data fusion

This paper focuses on the beam-space target height estimation for bistatic multiple-input multiple-output (MIMO) radars, which is greatly affected by the multipath effect in low-elevation areas. The beam-space technique compresses the data and reduces computation, making it an ideal solution for this problem. However, there is a lack of research on beam-space target height estimation for bistatic MIMO radar, which this paper aims to address. In order to obtain the target height parameters accurately, we propose bistatic MIMO radar height estimation method based on adaptive beam-space refined maximum likelihood (RML) data fusion. First, we analyze and simplify the signal model, and obtain rough estimation of direction of departure (DOD) and direction of arrival (DOA) using digital beamforming (DBF) scanning technique; then, we convert target signals from the element space to the beam-space, separates the transmitter and the receiver signals, and obtain two target height estimations using the beam-space RML algorithm; finally, the minimum mean square error (MSE) criterion is used to fuse the two height estimations of the transmitter and the receiver. On this basis, we also analyze the application and advantages of RML algorithm in complex terrain through the measured data. In addition, the computational complexity of the proposed algorithm and the comparison algorithm is also given. Through some simulation results, it is not difficult to find that the proposed algorithm has good estimation accuracy and robustness.

Computationally efficient angle estimation of bistatic MIMO radar based on multimodal optimization

AbstractIn this letter, a computationally efficient multiple signal classification (MUSIC)‐based evolutionary algorithm for angle estimation of bistatic multiple‐input multiple‐output (MIMO) radar is proposed. The existing MUSIC algorithms require a computationally cumbersome two‐dimensional (2D) peak searching and the performance is highly related to the grid that set, which leads to a conflict between the computational efficiency and estimation performance. To address this difficulty, a multimodal quantum‐inspired salp swarm algorithm, integrating kmeans clustering technique, is proposed to substitute the 2D peak searching to obtain multiple maxima of the MUSIC algorithm. The resulting computationally efficient algorithm obviously reduces the computational complexity of the MUSIC algorithm, avoids grid errors, and further exploits the potential of the MUSIC algorithm. Numerical simulations in various scenarios are carried out to verify the superiority of the method.

PSWF-based decoupled atomic norm minimization for DOD and DOA estimation in MIMO radar with arbitrary linear arrays

Decoupled atomic norm minimization (D-ANM) is a computationally-efficient gridless two-dimensional parameter estimation method via dividing the two-level Toeplitz matrix into two one-level matrices, and can be applied to the one-snapshot direction-of-departure (DOD) and direction-of-arrival (DOA) estimation in bistatic multiple-input multiple-output (MIMO) radar with uniform linear arrays (ULAs). Nevertheless, in actual applications, the transmitting and receiving arrays are not always ULAs, which leads to the Toeplitz structure not satisfied and the regular D-ANM algorithm not available. In this work, the one-snapshot DOD and DOA estimation in bistatic MIMO radar with arbitrary linear arrays (ALAs) is investigated. The Prolate spheroidal wave functions (PSWFs) are utilized to express such a D-ANM problem followed by a semi-definite programming (SDP) solution. The PSWF-based method can extend the application of D-ANM from ULAs to ALAs, and avoid the grid partition of the conventional sparse representation methods. The numerical experiments are conducted to verify the proposed method.

Angle Estimation for Bistatic MIMO Radar Using One-Bit Sampling Via Atomic Norm Minimization

In this article, we focus on the bistatic multiple-input multiple-output (MIMO) radar that performs one-bit quantization of received echo data. Based on the one-bit bistatic MIMO radar, we devise an effective algorithm for joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation. By exploiting the signal sparsity, we first formulate a decoupled atomic norm minimization problem to reconstruct two noise-free covariance matrices from one-bit quantized data. Subsequently, we apply the MUSIC algorithm on two reconstructed matrices to estimate the DODs and DOAs of targets, respectively. Furthermore, an additional procedure is proposed to achieve pairing of the estimated DODs and DOAs. The proposed algorithm can achieve satisfactory estimation performance only using single-pulse data. Numerical results demonstrate the effectiveness of the proposed algorithm.

Frequency Error Compensation of Unsynchronized Bistatic CW- MIMO Radar for Multiple Human-Body Localization.

This article presents and experimentally evaluates a frequency error elimination technique suitable for unsynchronized bistatic Multiple-Input Multiple-Output (MIMO) radar for human-body detection. First, a mathematical expression of human-body localization using bistatic MIMO radar is presented. Then the direct path is used to eliminate the phase error created by the frequency difference between the transmitter and receiver. A new Doppler-shifted component of the MIMO channel without phase error is derived, and the locations of the multiple targets are calculated by the 2-dimensional MUltiple SIgnal Classification (MUSIC) method. Next, the results of simulations that examine frequency error versus power ratios are discussed to illustrate the effectiveness of the proposed method. An experiment is carried out in an indoor multipath-rich environment. To emulate the unsynchronized condition, the transmitter and receiver use independent Signal Generators (SGs). One to six targets are tested. The experiments demonstrate that our unsynchronized radar system can identify the locations of multiple targets with high accuracy.

Localization and tracking of multiple fast moving targets in bistatic MIMO radar

In this paper, we propose a maximum likelihood (ML)-based scheme to accurately localize and track multiple fast-moving targets in multiple-input multiple-output (MIMO) radar systems. For the problem of tracking, the motion of the target will cause a spread spectrum effect, which broadens the beam width and skews the beam steering, rendering accurately localizing and tracking the fast moving targets extremely challenging. To tackle this problem, we use a locally linear model to approximate the real motion states of the target and define a vector to describe its motion state. As such, the motion states of targets at adjacent times can be accurately inferred within a short term based on this approximation model. To incorporate the effect of target motion when performing tracking, we estimate the motion state vector at a reference time from a batch of snapshots by using an ML estimator, instead of estimating the time-varying angular parameters directly as usual. Then the motion state vectors at other times can be inferred based on the estimated one by using the locally linear approximation model. The Cramér-Rao lower bound (CRLB) of the estimated parameters are also derived for performance evaluation. Numerical results validate the performance improvement of the proposed scheme compared to the benchmarks.

A PARAFAC estimator for MIMO radar under direction-dependent mutual coupling

Among the various research branches in multiple-input multiple-output (MIMO) radar, Direction finding is an interesting topic and has attracted extensive concerns. However, many previous strategies are only effective to deal with scenarios without model error, such as well-calibrated sensor array, which is unrealistic in practice. This paper revisits the direction finding issue in a bistatic MIMO radar, in which the direction-dependent mutual coupling (MC) effect in both the transmitting array and the receiving array are considered. An estimator based on parallel factor (PARAFAC) decomposition is introduced. Benefit from the fact that the multidimensional structure of the tensor measurement can be explored, the proposed PARAFAC estimator can offer closed-form solution to direction finding without additional pairing calculation, so it is much more accurate and efficient than the state-of-the-art spectrum search method and the rotational invariance algorithm. The improved PARAFAC approach is mathematically analyzed in detail, Several computer trials are carried out to show the theoretical advantages.

On Parameter Identifiability of Diversity-Smoothing-Based MIMO Radar

Diversity smoothing has been widely used for angle estimation with multiple input multiple output (MIMO) radar in the presence of coherent or correlated targets, and the parameter identifiability is an interesting issue. Previous works have shown sufficient conditions for some special cases, such as the coherent targets with conventional MIMO radar, and the array size are derived as a function of the target number and target structure. In this article, we further introduce the interelement spacings to build a complete parameter identifiability scheme. For monostatic MIMO radars, the antenna numbers and interelement spacings of transmit and receive arrays are derived as functions of the target number and the target structure. The optimization models are built to calculate the maximum number of detectable targets for a given target structure. Additionally, the conditions for the bistatic MIMO radar are derived from two-dimension viewpoint. It is shown that the new results improve upon previous spatial smoothing or diversity smoothing methods and recover them in special cases. Simulation results are presented that corroborate our theoretical findings.

Efficient Gridless Angle Estimation for Bistatic MIMO Radar With Planar Arrays

Direction finding in bistatic multiple-input multiple-output (MIMO) radar system is an important issue in target localization. Existing works focus on linear array which can only find 1-D angle information. In this paper, we focus on bistatic MIMO radar where both the transmitter and receiver are equipped with uniform planar arrays (UPAs) which can find full angle information of targets. To overcome the gridding effect, we use atomic norm minimization (ANM) to formulate a gridless model which is equivalent to a semidefinite programming (SDP). By solving the SDP we can obtain the angle estimates without discretizing the 4-D angle space. An alternating direction method of multipliers (ADMM) based implementation is also derived to reduce the computational complexity of the proposed method. Simulation results show that our proposed method can break through the gridding limitation to achieve a high estimation accuracy while enjoying low computational complexity.

Bayesian Robust Tensor Factorization for Angle Estimation in Bistatic MIMO Radar With Unknown Spatially Colored Noise

In this paper, we propose a robust tensor-based scheme for joint direction-of-departure (DOD) and direction-of-arrival (DOA) estimation in bistatic multiple-input multiple-output (MIMO) radar with unknown spatially colored noise. To eliminate the colored noise, the proposed algorithm first denoises the received signal from the temporal cross-correlation approach and constructs a third-order complex tensor model. Then, a real-valued compressed tensor model is developed by utilizing the characteristic of radar antenna arrays. Finally, Bayesian tensor factorization is derived to fit the constructed real-valued model and approximate factor matrices, from which DOD and DOA can be extracted. We also derive Cramér-Rao bound (CRB) results for angle estimation. The proposed algorithm is suitable for both uniform linear array (ULA) and uniform planar array (UPA) manifolds. Compared with existing angle estimation methods, the proposed one has better estimation accuracy and more stable performance. In addition, the proposed algorithm works well even if the number of targets is unknown. Simulation results demonstrate the effectiveness and improvement of the proposed angle estimation algorithm.

Dynamic subspace angle estimation method for bistatic MIMO radar with system imperfections

The development of high-resolution methods that can withstand unpleasant radar conditions for target localization is challenging. In this paper, a novel dynamic subspace method to address the problem of angle estimation of the bistatic Multiple-input multiple-output (MIMO) radar with system imperfections brought about by the coexistence of mutual coupling and coherent signals with large power differences is proposed. The proposed dynamic subspace angle estimation method comprises two subspace approaches; the dynamic subspace resampling with coupling calibration approach and the dynamic subspace superresolution with coupling calibration approach. The implementation of both approaches is such that they apply a linear transformation technique by way of exploiting the topology of the array structure to attain signal decoupling. In addition, the proposed approaches devise the decimation of the signal samples and the formulation of a beamforming framework to induce decorrelation and achieve signal resolution. Finally, a 1D pairwise spectral estimator which exploits matrix inversion mechanism coupled with a grid refining technique is introduced to resolve the target angle with obvious power differences.In contrast with the existing methods, the proposed method has an extra advantage of its applicability to colored noise scenarios due to its inherent noise suppression ability. This, therefore, augments its high suitability to imperfect systems. Evidence of the proposed algorithm's validity and effectiveness over existing methods is demonstrated in terms of numerical simulations under varying conditions.

A beamspace maximum likelihood algorithm for target height estimation for a bistatic MIMO radar

This paper discusses beamspace target height estimation for bistatic multiple-input multiple-output (MIMO) radars. Beamspace super-resolution algorithms for target height estimation have attracted significant attention due to low data transmission, storage, and computation. However, current literature has not yet considered beamspace target height estimation for a bistatic MIMO radar. Although target height estimation algorithms can be directly applied to a bistatic MIMO radar after minor modifications, such a direct application does not afford optimum performance. Therefore, we develop a three-dimensional beamspace maximum likelihood data fusion (3D-BMLF) algorithm appropriate for the target height estimation algorithm of a bistatic MIMO radar. The 3D-BMLF algorithm first converts target signals from the element space to the 3D beamspace, separates the transmitter and the receiver signals, and obtains two closed-form solutions of target height using the beamspace ML algorithm. Finally, the proposed method fuses the two closed-form solutions by minimizing the mean square error (MSE) of estimation. As a result, the 3D-BMLF algorithm has a very low computational burden and good estimation accuracy. Our computational complexity analysis and simulation results demonstrate the suitability of the 3D-BMLF algorithm for engineering applications.

A Four Cumulant-Based Direction Finding Method for Bistatic MIMO Radar with Mutual Coupling

The mutual coupling effects of the transmitter and receiver are known to degrade the performance of direction finding for a bistatic Multiple Input Multiple Output (MIMO) radar system. A four cumulant-combinatorial matrix-based algorithm is proposed to estimate jointly the Direction Of Departure (DOD)and Direction Of Arrival (DOA) of targets under the coexistences of unknown mutual coupling and Gaussian colored noise. Firstly, the multiple groups of four cumulant matrices both on transmitter and receiver are constructed by using the Kronecker product and the banded symmetric Toeplitz characteristics of the mutual coupling matrices. The block four-cumulant matrix is further constructed by combining the transmitter and receiver four cunmulant matrices. Then the new matrix is combined to extract the transmit and receive shift invariance matrices by using the transmitter and receiver four cumulant matrices. The results illustrate that: The proposed method can estimate the DOD and DOA of the targets efficiently in the presence of the strong mutual coupling effect, and parameters are paired automatically without extra pairing operation. The parameter estimation performance of the proposed method is better than those of the existing methods under the strong mutual coupling effect conditions.

Angle Estimation for MIMO Radar in the Presence of Gain-Phase Errors with One Instrumental Tx/Rx Sensor: A Theoretical and Numerical Study

Ideal transmitting and receiving (Tx/Rx) array response is always desirable in multiple-input multiple-output (MIMO) radar. In practice, nevertheless, Tx/Rx arrays may be susceptible to unknown gain-phase errors (GPE) and yield seriously decreased positioning accuracy. This paper focuses on the direction-of-departure (DOD) and direction-of-arrival (DOA) problem in bistatic MIMO radar with unknown gain-phase errors (GPE). A novel parallel factor (PARAFAC) estimator is proposed. The factor matrices containing DOD and DOA are firstly obtained via PARAFAC decomposition. One DOD-DOA pair estimation is then accomplished from the spectrum searching. Thereafter, the remainder DOD and DOA are achieved by the least squares technique with the previous estimated angle pair. The proposed estimator is analyzed in detail. It only requires one instrumental Tx/Rx sensor, and it outperforms the state-of-the-art algorithms. Numerical simulations verify the theoretical advantages.

Improved 2D-MUSIC estimation for low intercept coprime MIMO radar

In electronic warfare, airborne multiple input multiple output (MIMO) radar must not only accurately detect the Angle of moving target, but also ensure the low interception performance of radar. In order to solve this problem, a low interception bistatic MIMO radar with improved coprime array is proposed in this paper. By expanding the coprime array of the bistatic MIMO radar, the array spacing is further expanded to form a sparse array, which reduces the hardware and software cost and improves the anti-jamming capability. In addition, based on the two-dimensional MUSIC algorithm to detect the Angle of the maneuvering target, Taylor expansion method is added to realize the Angle estimation under low SNR. The research results show that, compared with the joint DOD and DOA estimation in a bistatic MIMO radar, the improved method in this paper increases the estimation accuracy, reduces the computational cost of the algorithm, applies to low SNR environment, and ensures low interception performance.

Direction Finding in Bistatic MIMO Radar With Direction-Dependent Mutual Coupling

Mutual coupling (MC) effect exists extensively in sensor array, and it will adversely affect the direction finding in multiple-input multiple-output (MIMO) radar. In the previous works, the MC effects in MIMO radar are always modeled with direction-independent MC matrices, which may not be guaranteed in practice. In this letter, we investigate into the issue of target localization and sensor calibration in bistatic MIMO radar in the presence of direction-dependent MC. A multiple signal classification (MUSIC)-like methodology is proposed. It links angle estimation to a quadratic optimization problem, which is solved via Lagrange multiplier method. The proposed method is suitable for arbitrary sensor geometry. Numerical simulations are provided to validate the effectiveness of the proposed method.

Angle Estimation and Mutual Coupling Self‐Calibration in Bistatic MIMO System with Arbitrary Geometry

Ideal array responses are often desirable to a multiple‐input multiple‐output (MIMO) system. Unfortunately, it may not be guaranteed in practice as the mutual coupling (MC) effects always exist. Current works concerning MC in the MIMO system only account for the uniform array geometry scenario. In this paper, we generalize the issue of angle estimation and MC self‐calibration in a bistatic MIMO system in the case of arbitrary sensor geometry. The MC effects corresponding to the transmit array and the receive array are modeled by two MC matrices with several distinct entities. Angle estimation is then recast to a linear constrained quadratic problem. Inspired by the MC transformation property, a multiple signal classification‐ (MUSIC‐) like strategy is proposed, which can estimate the direction‐of‐departure (DOD) and direction‐of‐arrival (DOA) via two individual spectrum searches. Thereafter, the MC coefficients are obtained by exploiting the orthogonality between the signal subspace and the noise subspace. The proposed method is suitable for arbitrary sensor geometry. Detailed analyses with respect to computational complexity, identifiability, and Cramer‐Rao bounds (CRBs) are provided. Simulation results validate the effectiveness of the proposed method.

Joint DOD and DOA estimation using tensor reconstruction based sparse representation approach for bistatic MIMO radar with unknown noise effect

Achieving a fair balance between accuracy and computational complexity of limited measurement signals by algorithms for the bistatic multiple-input multiple-output (MIMO) radar under unknown noise effect has been a seemingly difficult task for most covariance methods. In this paper, the aim is to present an efficient method to achieve an improved estimation of the joint direction of departure (DOD) and direction of arrival (DOA) for the bistatic MIMO radar with an unknown ‘Toeplitz’ colored noise effect. First, by taking advantage of the static property of the noise effect, a tensor reconstruction-based imaginary Hermitian matrix is developed to eliminate the unknown noise effect. Then the 2D angle estimation problem is then reduced to a 1D sparse recovery problem where the target sparsity is exploited. Further, we formulate a reverse 1D pairwise Simultaneous Orthogonal Matching Pursuit and sparse Bayesian learning algorithms to reconstruct the sparse signal and estimate the joint DOD-DOA of the target. In contrast with the existing tensor-based methods, the proposed approach not only is robust to the influence of Toeplitz colored noise, resolves targets with limited measurement data but also ensures superior performance with lower computational complexity. Numerical simulation conducted under varying conditions verifies the effectiveness of the proposed approach.