Gain-phase Errors Research Articles

Robust adaptive beamforming with partly calibrated arrays in the presence of gain-phase errors

The performance of the beamformer, especially the beamformer based on the interference plus noise covariance matrix (INCM) reconstruction which needs accurate array manifold knowledge, will degrade dramatically in the presence of gain-phase errors. To solve this problem, we propose a robust adaptive beamforming method based on partly calibrated arrays (PCA). The main idea of this method is to estimate the gain-phase errors more accurately using the higher signal-to-noise ratio (SNR) signal sources and the PCA. After that, we calibrate the interference signal steering vector (SV) and reconstruct the more accurate INCM based on the estimation results. Finally, the SV of the desired signal is estimated by the intersection of two special subspaces. On the basis of the above research, the optimal weight vector is obtained. Numerical simulation results demonstrate the superior performance of the proposed beamformer relative to other existing beamformers in the presence of gain-phase errors.

Method for DOA Estimation of Coprime Arrays Through Joint Auxiliary Arrays with Atomic Norm Minimization in the Presence of Gain-Phase Errors

Method for DOA Estimation of Coprime Arrays Through Joint Auxiliary Arrays with Atomic Norm Minimization in the Presence of Gain-Phase Errors

Low-Complexity DOA Estimation for Coherently Distributed Sources With Gain-Phase Errors in Massive MIMO Systems

Low-Complexity DOA Estimation for Coherently Distributed Sources With Gain-Phase Errors in Massive MIMO Systems

A High Degree of Freedom Radiation Near-Field Source Localization Algorithm with Gain–Phase Error

The limitation of the number of estimable sources in the localization of radiation near-field sources with gain–phase error is examined in this paper. When only the reference element has no gain–phase error, a new method based on an accurate model is proposed to enhance the maximum number of estimable sources. Based on the location parameter details of the auxiliary source, the method first derives the gain–phase error estimate matrix. Second, the source steering vector including errors is estimated using the total least square estimating signal parameter via rotational invariance techniques (TLS-ESPRIT), and the time-shifted data matrix is built utilizing the space–time combination idea, thus increasing the degree of freedom of the array. Then, the source steering vector containing the error is modified by the error compensation matrix constructed according to the moment of gain–phase error estimation. Finally, the estimated values of the source position parameters are obtained by using the closed formula of the gain phase of the modified source steering vector and the source position parameters. The experimental results show that the maximum estimable source number of the proposed algorithm is significantly improved compared with the previous results when only the reference array element has no gain–phase error. When the array number is 5 and 9, the maximum estimable source number of the algorithm is 9 and 17, respectively.

Traffic Target Location Estimation Based on Tensor Decomposition in Intelligent Transportation System

As the safety problems and economic losses caused by traffic accidents are becoming more and more serious, intelligent transportation system (ITS) came into being. After the outbreak of COVID-19, how to achieve effective traffic scheduling and macro command under less contact has attracted more attention. Therefore, the location estimation of traffic objectives is a key issue. In the developed framework, for the target parameter estimation in traffic, frequency diversity array multiple-input multiple-output (FDA-MIMO) radar is introduced into ITS, and tensor decomposition is used to process transportation big data (TBD) to improve the real-time performance of target location estimation. Unfortunately, spatial colored noise and array gain-phase error will affect the performance of FDA-MIMO radar in ITS. An algorithm that can solve the angle-range estimation problem of FDA-MIMO radar in the co-existence of array gain-phase error and spatial colored noise is proposed. Firstly, the four-dimensional tensor is constructed by using the temporal un-correlation of colored noise. Therefore, the influence of colored noise in ITS is removed. Secondly, the direction matrix containing target information is obtained by parallel factor (PARAFAC) decomposition. For the array gain-phase error, the optimization problem is constructed, and the Lagrange multiplier is employed to calculate the optimal solution. The effect of gain-phase error is eliminated by utilizing the optimal solution and the direction matrices. Finally, the location information of motor vehicle is achieved by calculating the solution of least square (LS) fitting. The developed scheme can achieve the location information of motor vehicles in the co-existence of array gain-phase error and spatial colored noise. Comprehensive numerical experiments illustrate that the developed scheme in ITS can efficiently obtain the location information of motor vehicles.

Robust Sparse Bayesian Two-Dimensional Direction-of-Arrival Estimation with Gain-Phase Errors

To reduce the influence of gain-phase errors and improve the performance of direction-of-arrival (DOA) estimation, a robust sparse Bayesian two-dimensional (2D) DOA estimation method with gain-phase errors is proposed for L-shaped sensor arrays. The proposed method introduces an auxiliary angle to transform the 2D DOA estimation problem into two 1D angle estimation problems. A sparse representation model with gain-phase errors is constructed using the diagonal element vector of the cross-correlation covariance matrix of two submatrices of the L-shaped sensor array. The expectation maximization algorithm derives unknown parameter expression, which is used for iterative operations to obtain off-grid and signal precision. Using these parameters, a new spatial spectral function is constructed to estimate the auxiliary angle. The obtained auxiliary angle is substituted into a sparse representation model with gain and phase errors, and then the sparse Bayesian learning method is used to estimate the elevation angle of the incident signal. Finally, according to the relationship of the three angles, the azimuth angle can be estimated. The simulation results show that the proposed method can effectively realize the automatic matching of the azimuth and elevation angles of the incident signal, and improves the accuracy of DOA estimation and angular resolution.

Direction-of-arrival estimation for a nested array with gain-phase error and impulse noise

To solve direction-finding problems for nested arrays under conditions of impulse noise and gain–phase errors, this paper proposes a direction-of-arrival (DOA) estimation method. First, a correntropy with an adaptive kernel length combined with an infinite norm of a variable weight value is proposed to suppress impulse noise. Then, the auxiliary array elements are used to realize the initial calibration of the amplitude and phase errors. On this basis, a DOA estimation method without a spectral peak search is proposed; this method is robust for arrays that still have residual gain–phase errors after calibration. Our method overcomes the difficulties of DOA estimation for nested arrays under conditions of gain–phase errors and impulse noise. Compared with traditional methods, the proposed method does not require prior knowledge, does not require a spectral peak search and has high superiority and robustness; a series of experiments have verified its superiority. In addition, a Cramér‒Rao bound (CRB) for angle estimation under conditions of gain–phase errors and impulse noise is proposed in this paper.

Performance analysis of two-dimensional DOA estimation for uniform circular array

Perturbation analysis of direction of arrival (DOA) estimation has been studied mostly on one-dimensional arrays rather than planar arrays, which remains room for exploration. For uniform circular arrays with various model errors, we establish the corresponding system model. Then a performance analysis of the two-dimensional MUSIC algorithm is proposed by first-order error analysis and verified by simulation. The results show that the root-mean-squared error of DOA estimation is proportional to the standard deviation of the model errors, including gain-phase errors, sensor position errors, and mutual coupling effect.

Robust Low-Sidelobe Transmit Beamforming under Peak-to-Average-Power Ratio Constraint.

Transmit beamforming (TBF) provides the capability of focusing illuminating power in the desired directions while reducing the emitting power in undesired directions. It is significantly important in low-altitude and slow-speed small (LSS) radar, which usually suffers from heavy clutter and rapidly changing interference on the near-ground side. Due to nonideal factors such as an inaccurate target direction and array gain-phase error, the robustness of TBF is also necessary to consider in practical applications. In this paper, we provide a robust TBF method that enables sidelobe control in preset regions and possesses high transmit efficiency in virtue of the peak-to-average-power ratio (PAPR) constraint on transmit weights. To achieve robustness, a norm upper bound is introduced to limit the fluctuation of transmit weights, and the steering vector mismatch is also considered by using a spherical uncertainty set surrounding the nominal steering vector. As the proposed robust TBF is nonconvex because of the nonconvexity of both the objective function and constraints, we translate it into a series of convex subproblems via several kinds of convex relaxation schemes. In particular, based on the special structure of the objective function and constraints, the translation of the nonconvex problem into a tractable SOCP problem is realized by using the combination of the triangle inequality and Cauchy-Schwartz inequality. Numerical results demonstrate the improvement in the efficiency and robustness of the proposed TBF method in comparison with traditional TBF methods.

Direction-of-Arrival Estimation in Non-uniform Linear Array with Gain-Phase Error Compensation

Direction-of-Arrival Estimation in Non-uniform Linear Array with Gain-Phase Error Compensation

A New Gain-Phase Error Pre-Calibration Method for Uniform Linear Arrays.

In this paper, we consider the gain-phase error calibration problem for uniform linear arrays (ULAs). Based on the adaptive antenna nulling technique, a new gain-phase error pre-calibration method is proposed, requiring only one calibration source with known direction of arrival (DOA). In the proposed method, a ULA with M array elements is divided into M-1 sub-arrays, and the gain-phase error of each sub-array can be uniquely extracted one by one. Furthermore, in order to obtain the accurate gain-phase error in each sub-array, we formulate an errors-in-variables (EIV) model and present a weighted total least-squares (WTLS) algorithm by exploiting the structure of the received data on sub-arrays. In addition, the solution to the proposed WTLS algorithm is exactly analyzed in the statistical sense, and the spatial location of the calibration source is also discussed. Simulation results demonstrate the efficiency and feasibility of our proposed method in both large-scale and small-scale ULAs and the superiority to some state-of-the-art gain-phase error calibration approaches.

Source Direction Finding and Direct Localization Exploiting UAV Array With Unknown Gain-Phase Errors

An unmanned aerial vehicle (UAV) array is composed of multiple UAVs carrying array elements, which can sense signals synchronously through a global positioning system (GPS) trigger. However, gain-phase errors caused by synchronization errors and the inconsistent complex gains of receiving array channels result in array manifold perturbation, which makes the performance of traditional localization methods degrade or even fail. In this article, two efficient algorithms for source direction finding and direct localization using a UAV array are, respectively, presented. First, the array manifold changes with the movement of UAVs, which contributes to multiposition fusion, thus avoiding the infinite solutions of underdetermined equations. Then, the quadratic optimization problem can be constructed by using the orthogonal relation between noise subspaces and contaminated steering vectors obtained from multiple observations. Thereafter, we can construct the cost function and obtain the spectral function, from which the source directions and positions can be all estimated by grid search. Meanwhile, the gain-phase error values can be solved successively. Moreover, in order to avoid the influence of heteroscedasticity of different observation positions in direct localization, we carry out a blind weighting operation. Simulation results demonstrate the effectiveness and superiority of the proposed algorithms.

Flexible Null Broadening Robust Beamforming Based on JADE

In order to flexibly and completely suppress dynamic interference, a flexible and robust beamforming based on JADE is proposed in this paper. In addition, it is insensitive to the gain–phase errors of the array. Firstly, the actual steering vector with gain–phase errors is separated from the received snapshot data by the joint approximate diagonalization of eigenmatrix (JADE) algorithm. Secondly, the direction of arrival (DOA) of interference can be estimated from the separated actual steering vector by the correlation coefficient method. Thus, the actual interference steering vector with gain–phase errors can be selected by the correlation coefficient with the nominal steering vector constructed by the estimated DOA. Then, the interference covariance matrix can be reconstructed by the actual interference steering vector, and the interference power estimated by the Capon power spectral. Finally, according to the prior information of the interference, only the dynamic interference covariance matrix is tapered by the novel covariance matrix trap (CMT), which can flexibly broaden and deepen the null. Simulation results show that the depth of the proposed beamformer is more than 10 dB deeper than that of the traditional algorithm in the non-stationary interference. In addition, it can save at least 2 degrees of freedom compared to the traditional method.

Joint Angle and Gain-Phase Error Estimation for Nested Bistatic MIMO Radar via Tensor Decomposition

To suppress the performance degradation in nested bistatic multiple-input multiple-output radar caused by gain-phase error, we propose a tensor-based angle and gain-phase error estimation algorithm. First, we construct a three-way tensor model using the virtual aperture of the nested array, which is derived from the distribution characteristics of gain-phase error. Then, we employ the position distribution of calibration and virtual sensors for angle and gain-phase error estimation. The results indicate that the proposed algorithm has better performance compared to the state-of-the-art methods. Numerical simulations verify the theoretical analysis and superiority of the proposed algorithm.

Gain-Phase Error-Calibrated Piezoelectric Sensor Array-Based Impact Localization on Stiffened Curved Composite Structures.

Stiffened structure-induced gain-phase errors degrade the performance of the high-resolution two-dimensional multiple signal classification (2D-MUSIC) algorithm, which makes it impossible to ensure the high accuracy of impact localization results. To eliminate the localization bias caused by these errors, a calibrated 2D-MUSIC-based impact localization method is first introduced. Firstly, time-frequency characteristics of the non-stationary impact signals are evaluated by experiment to obtain a clear first wave packet or a wave packet that purely corresponds to a single mode through continuous wavelet transform (CWT). Then, the uniform linear array covariance matrix with gain-phase errors is calibrated to be constructed as a Toeplitz structural matrix. By reconstructing covariance matrix R, 2D-MUSIC-based impact localization is calibrated for stiffened curved composite structures. Experimental research on the stiffened curved composite panel is carried out, and these impact localization results demonstrate the validity and effectiveness of the calibrated 2D-MUSIC-based method.

Online Gain-Phase Self-Calibration Method of MIMO Array Based on Statistical Characteristics of Target Angle Distribution

As a hot research topic, the gain-phase error self-calibration in MIMO radar systems has been investigated for many years. In this paper, we proposed a novel array error self-calibration method, termed online errors self-calibration based on feature learning (OES-FL). This method regards the statistical characteristics of the detected targets’ DOA as a prior knowledge and does not require the calibrated antenna subarray or external reference source to correct the array disturbances in real time. First, we analyse the monostatic MIMO signal model suffering gain-phase error. Then, we exploit the statistical characteristics of DOA of many targets for correcting gain-phase error of antenna array. Next, the gain-phase error estimation scheme based on LMS and the DOA deviation estimation method based on LSTM are proposed, respectively. Using real-life radar data collected at the integrated transportation hubs to generate simulation data, the proposed approach is shown to be effective in correcting gain-phase errors and, therefore, provides a promising model for online error self-calibration in monostatic MIMO radars.

Low-Complexity 2D DOA Estimation and Self-Calibration for Uniform Rectangle Array with Gain-Phase Error

Most subspace-based algorithms need exact array manifold for direction of arrival (DOA) estimation, while, in practical applications, the gain-phases of different array elements are usually inconsistent, degrading their estimation performance. In this paper, a novel low-complexity 2D DOA and gain-phase error estimation algorithm is proposed by adding auxiliary array elements in a uniform rectangular array (URA). Firstly, the URA is modeled as the Kronecker product of two uniform linear arrays (ULAs) to decouple the 2D DOA estimation. Then, several well-calibrated auxiliary array elements are added in the two ULAs, based on which the rotation invariant factor of the URA destroyed by the gain-phase error is reconstructed by solving constrained optimization problems. Lastly, ESPRIT is used to estimate the 2-D DOA and the gain-phase error coefficients. The closed-form expressions of the estimation CRBs are also derived, providing insight into the impact of gain-phase error on DOA estimation. Simulation results are used to validate the effectiveness of the proposed algorithm and the correctness of the theoretical analysis.

Central Direction-of-Arrival Estimation of Coherently Distributed Sources for Antenna Arrays With Gain-Phase Errors

Central Direction-of-Arrival Estimation of Coherently Distributed Sources for Antenna Arrays With Gain-Phase Errors

Tensor-Based Target Parameter Estimation Algorithm for FDA-MIMO Radar with Array Gain-Phase Error

As a new radar system, FDA-MIMO radar has recently developed rapidly, as it has broad prospects in angle-range estimation. Unfortunately, the performance of existing algorithms for FDA-MIMO radar is greatly degrading or even failing under the condition of array gain-phase error. This paper proposes an innovative solution to the joint angle and range estimation of FDA-MIMO radar under the condition of array gain-phase error and an estimation algorithm is developed. Moreover, the corresponding Cramér-Rao bound (CRB) is derived to evaluate the algorithm. The parallel factor (PARAFAC) decomposition technique can be utilized to calculate transmitter and receiver direction matrices. Taking advantage of receiver direction matrix, the angle estimation can be obtained. The range estimation can be estimated by transmitter direction matrix and angle estimation. To eliminate the error accumulation effect of array gain-phase error, the gain error and phase error are obtained separately. In this algorithm, the impact of gain-phase error on parameter estimation is removed and so is the error accumulation effect. Therefore, the proposed algorithm can provide excellent performance of angle-range and gain-phase error estimation. Numerical experiments prove the validity and advantages of the proposed method.

FEM simulation based adaptive sensors array error compensation method for impact monitoring on stiffened composite structures

To eliminate the sensor array based impact localization bias on stiffened composite structures, a finite element method (FEM) simulation based adaptive sensors array errors compensation method for impact monitoring is introduced. Firstly, detailed analysis and comparison discussion about Lamb wave propagation errors between the simple and stiffened plate are provided using FEM simulation, and the gain-phase errors obtained are structured as a array error matrix. Secondly, array error matrix is substituted into the steering vector of standard two-dimensional Multiple Signal Classification (2D-MUSIC) algorithm to compensate the stiffener effect. And then initial estimates of impact could be estimated by the compensated 2D-MUSIC algorithm. Finally substituting these initial estimates, the cost function is minimized by adaptive iterative to calculate the reasonable location of the impact source. The experiments on a carbon fiber composite stiffened plate demonstrate the validity and effectiveness of the proposed method.