Most of the existing direction of arrival(DOA)estimation algorithms are applied under the assumption that the array manifold is ideal.In practical engineering applications,the existence of non-ideal conditions such as...Most of the existing direction of arrival(DOA)estimation algorithms are applied under the assumption that the array manifold is ideal.In practical engineering applications,the existence of non-ideal conditions such as mutual coupling between array elements,array amplitude and phase errors,and array element position errors leads to defects in the array manifold,which makes the performance of the algorithm decline rapidly or even fail.In order to solve the problem of DOA estimation in the presence of amplitude and phase errors and array element position errors,this paper introduces the first-order Taylor expansion equivalent model of the received signal under the uniform linear array from the Bayesian point of view.In the solution,the amplitude and phase error parameters and the array element position error parameters are regarded as random variables obeying the Gaussian distribution.At the same time,the expectation-maximization algorithm is used to update the probability distribution parameters,and then the two error parameters are solved alternately to obtain more accurate DOA estimation results.Finally,the effectiveness of the proposed algorithm is verified by simulation and experiment.展开更多
A new direction-of-arrival （DOA） estimation algorithm for wideband sources is introduced, The new method obtains the output of the virtual arrays in the signal bandwidth using cubic spline function interpolation tec...A new direction-of-arrival （DOA） estimation algorithm for wideband sources is introduced, The new method obtains the output of the virtual arrays in the signal bandwidth using cubic spline function interpolation techniques. The narrowband high- resolution algorithm is then used to get the DOA estimation. This technique does not require any preliminary knowledge of DOA angles. Simulation results demonstrate the effectiveness of the method.展开更多
A novel identification method for point source,coherently distributed（CD） source and incoherently distributed（ICD） source is proposed.The differences among the point source,CD source and ICD source are studied.Acc...A novel identification method for point source,coherently distributed（CD） source and incoherently distributed（ICD） source is proposed.The differences among the point source,CD source and ICD source are studied.According to the different characters of covariance matrix and general steering vector of the array received source,a second order blind identification method is used to separate the sources,the mixing matrix could be obtained.From the mixing matrix,the type of the source is identified by using an amplitude criterion.And the direction of arrival for the array received source is estimated by using the matching pursuit algorithm from the vectors of the mixing matrix.Computer simulations validate the efficiency of the method.展开更多
A two-dimensional direction-of-arrival （DOA） and polarization estimation algorithm for coherent sources using a linear vector-sensor array is presented. Two matrices are first constructed by the receiving data. The ...A two-dimensional direction-of-arrival （DOA） and polarization estimation algorithm for coherent sources using a linear vector-sensor array is presented. Two matrices are first constructed by the receiving data. The ranks of the two matrices are only related to the DOAs of the sources and independent of their coherency. Then the source’s elevation is resolved via the matrix pencil （MP） method, and the singular value decomposition （SVD） is used to reduce the noise effect. Finally, the source’s steering vector is estimated, and the analytics solutions of the source’s azimuth and polarization parameter can be directly computed by using a vector cross-product estimator. Moreover, the proposed algorithm can achieve the unambiguous direction estimates, even if the space between adjacent sensors is larger than a half-wavelength. Theoretical and numerical simulations show the effectiveness of the proposed algorithm.展开更多
A direction-of-arrival （DOA） estimation algorithm based on direct data domain （D3） approach is presented. This method can accuracy estimate DOA using one snapshot modified data, called the temporal and spatial two...A direction-of-arrival （DOA） estimation algorithm based on direct data domain （D3） approach is presented. This method can accuracy estimate DOA using one snapshot modified data, called the temporal and spatial two-dimensional vector reconstruction （TSR） method. The key idea is to apply the D3 approach which can extract the signal of given frequency but null out other frequency signals in temporal domain. Then the spatial vector reconstruction processing is used to estimate the angle of the spatial coherent signal source based on extract signal data. Compared with the common temporal and spatial processing approach, the TSR method has a lower computational load, higher real-time performance, robustness and angular accuracy of DOA. The proposed algorithm can be directly applied to the phased array radar of coherent pulses. Simulation results demonstrate the performance of the proposed technique.展开更多
In order to resolve direction finding problems in the impulse noise,a direction of arrival(DOA)estimation method is proposed.The proposed DOA estimation method can restrain the impulse noise by using infinite norm exp...In order to resolve direction finding problems in the impulse noise,a direction of arrival(DOA)estimation method is proposed.The proposed DOA estimation method can restrain the impulse noise by using infinite norm exponential kernel covariance matrix and obtain excellent performance via the maximumlikelihood(ML)algorithm.In order to obtain the global optimal solutions of this method,a quantum electromagnetic field optimization(QEFO)algorithm is designed.In view of the QEFO algorithm,the proposed method can resolve the difficulties of DOA estimation in the impulse noise.Comparing with some traditional DOA estimation methods,the proposed DOA estimation method shows high superiority and robustness for determining the DOA of independent and coherent sources,which has been verified via the Monte-Carlo experiments of different schemes,especially in the case of snapshot deficiency,low generalized signal to noise ratio(GSNR)and strong impulse noise.Beyond that,the Cramer-Rao bound(CRB)of angle estimation in the impulse noise and the proof of the convergence of the QEFO algorithm are provided in this paper.展开更多
The nonuniform L-shaped spatially spread loop and dipole（SSLD） array whose inter-element spacing is greater than half a wavelength is studied. A joint parameter estimation algorithm of direction of arrival（DOA）, f...The nonuniform L-shaped spatially spread loop and dipole（SSLD） array whose inter-element spacing is greater than half a wavelength is studied. A joint parameter estimation algorithm of direction of arrival（DOA）, frequency and polarization is presented for plane-wave signals. The direct sampling and the corresponding delayed sampling data are used to construct the data correlation matrix. On the basis of the subspace theory and the least square method, the frequency and the steering vector of the whole array are obtained. According to the relationship of the array manifold vector between electric dipoles and magnetic loops,the polarization parameters are given. The unambiguous phase estimates are acquired by applying virtual baseline array transformation to the spatial steering vectors, and they are used as coarse references to disambiguate the cyclic phase ambiguities in phase differences between two adjacent array elements on the array,then the high accuracy DOA estimates are obtained. Closed-form solutions for each parameter are obtained. This method has advantages of lower calculation complexity and no parameter matching. The experiment results verify the effectiveness and feasibility of the presented algorithm.展开更多
针对互耦效应和脉冲噪声并存环境下的波达方向(direction of arrival,DOA)估计问题,提出一种结合M估计与稀疏重构的算法。首先,为了消除互耦效应的影响,依据互耦矩阵的托普利兹结构进行恒等变形,得到了不含未知互耦系数的字典。随后,为...针对互耦效应和脉冲噪声并存环境下的波达方向(direction of arrival,DOA)估计问题,提出一种结合M估计与稀疏重构的算法。首先,为了消除互耦效应的影响,依据互耦矩阵的托普利兹结构进行恒等变形,得到了不含未知互耦系数的字典。随后,为了使算法能适应高斯噪声和不同强度的脉冲噪声,将位置得分函数表示为高斯位置得分函数和一系列非线性函数的线性组合,利用噪声样本估计线性组合系数从而建立损失函数。最后,采用迭代硬阈值算法进行稀疏重构,并通过改进信号更新策略提高正确收敛的概率。仿真结果表明,所提算法能有效抑制互耦效应和脉冲(高斯)噪声的干扰,同时相较已有算法在低信噪比、强脉冲特性下的性能有显著提升。展开更多
This paper develops a deep estimator framework of deep convolution networks(DCNs)for super-resolution direction of arrival(DOA)estimation.In addition to the scenario of correlated signals,the quantization errors of th...This paper develops a deep estimator framework of deep convolution networks(DCNs)for super-resolution direction of arrival(DOA)estimation.In addition to the scenario of correlated signals,the quantization errors of the DCN are the major challenge.In our deep estimator framework,one DCN is used for spectrum estimation with quantization errors,and the remaining two DCNs are used to estimate quantization errors.We propose training our estimator using the spatial sampled covariance matrix directly as our deep estimator’s input without any feature extraction operation.Then,we reconstruct the original spatial spectrum from the spectrum estimate and quantization errors estimate.Also,the feasibility of the proposed deep estimator is analyzed in detail in this paper.Once the deep estimator is appropriately trained,it can recover the correlated signals’spatial spectrum fast and accurately.Simulation results show that our estimator performs well in both resolution and estimation error compared with the state-of-the-art algorithms.展开更多
This paper examines the direction of arrival(DOA)estimation for polarized signals impinging on a sparse vector sensor array which is based on the maximum interelement spacing constraint(MISC).The vector array effectiv...This paper examines the direction of arrival(DOA)estimation for polarized signals impinging on a sparse vector sensor array which is based on the maximum interelement spacing constraint(MISC).The vector array effectively utilizes the polarization domain information of incident signals,and the quaternion model is adopted for signals polarization characteristic maintenance and computational burden reduction.The features of MISC arrays are crucial to the mutual coupling effects reduction and higher degrees of freedom(DOFs).The quaternion data model based on vector MISC arrays is established,which extends the scalar MISC array into the vector MISC array.Based on the model,a quaternion multiple signal classification(MUSIC)algorithm based on vector MISC arrays is proposed for DOA estimation.The algorithm combines the advantages of the quaternion model and the vector MISC array to enhance the DOA estimation performance.Analytical simulations are performed to certify the capability of the algorithm.展开更多
It is always a challenging issue for radar systems to estimate the height of a low-angle target in the multipath propagation environment.The highly deterministic maximum likelihood estimator has a high accuracy,but th...It is always a challenging issue for radar systems to estimate the height of a low-angle target in the multipath propagation environment.The highly deterministic maximum likelihood estimator has a high accuracy,but the errors of the ground reflection coefficient and the reflecting surface height have serious influence on the method.In this paper,a robust es-timation method with less computation burden is proposed based on the compound reflection coefficient multipath model for low-angle targets.The compound reflection coefficient is es-timated from the received data of the array and then a one-di-mension generalized steering vector is constructed to estimate the target height.The algorithm is robust to the reflecting sur-face height error and the ground reflection coefficient error.Fi-nally,the experiment and simulation results demonstrate the validity of the proposed method.展开更多
针对现有二维波达方向(direction of arrival,DOA)估计方法对阵列接收信息利用不充分导致估计性能下降的问题,提出了一种平行互质阵列下对虚拟阵列插值的二维DOA估计方法。该方法通过对平行互质阵列扩展后的虚拟阵列进行插值,利用内插...针对现有二维波达方向(direction of arrival,DOA)估计方法对阵列接收信息利用不充分导致估计性能下降的问题,提出了一种平行互质阵列下对虚拟阵列插值的二维DOA估计方法。该方法通过对平行互质阵列扩展后的虚拟阵列进行插值,利用内插虚拟阵列的协方差矩阵与虚拟测量值之间的关系,提出一个关于等效虚拟测量向量的最小化问题,通过凸优化工具箱重构插值后的虚拟阵列协方差矩阵,结合酉变换和总体最小二乘方法进行DOA估计。仿真结果和湖上试验表明,该方法充分利用了非匀虚拟阵列中的所有虚拟阵元,提高了自由度和估计精度,具有有效性。展开更多
For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based ...For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.展开更多
To enhance direction of arrival(DOA)estimation accuracy,this paper proposes a low-cost method for calibrating farfield steering vectors of large aperture millimeter wave radar(mmWR).To this end,we first derive the ste...To enhance direction of arrival(DOA)estimation accuracy,this paper proposes a low-cost method for calibrating farfield steering vectors of large aperture millimeter wave radar(mmWR).To this end,we first derive the steering vectors with amplitude and phase errors,assuming that mmWR works in the time-sharing mode.Then,approximate relationship between the near-field calibration steering vector and the far-field calibration steering vector is analyzed,which is used to accomplish the mapping between the two of them.Finally,simulation results verify that the proposed method can effectively improve the angle measurement accuracy of mmWR with existing amplitude and phase errors.展开更多
传统的基于稀疏恢复的波达方向(direction of arrival,DOA)估计算法使用密集的采样网格,导致计算量显著增加,且对邻近入射信号的估计精度不高。针对这一问题,提出一种快速高精度DOA估计算法。该算法首先使用网格进化方法降低网格点总数...传统的基于稀疏恢复的波达方向(direction of arrival,DOA)估计算法使用密集的采样网格,导致计算量显著增加,且对邻近入射信号的估计精度不高。针对这一问题,提出一种快速高精度DOA估计算法。该算法首先使用网格进化方法降低网格点总数。然后,对噪声方差和信号功率进行二次估计,进而使用离网求根稀疏贝叶斯学习(off-grid root sparse Bayesian learning,OGRSBL)技术来实现入射角的精确估计。仿真表明,相比传统稀疏贝叶斯学习类算法,所提算法计算效率高,同时对紧邻信号有着更好的估计能力。展开更多
文摘Most of the existing direction of arrival(DOA)estimation algorithms are applied under the assumption that the array manifold is ideal.In practical engineering applications,the existence of non-ideal conditions such as mutual coupling between array elements,array amplitude and phase errors,and array element position errors leads to defects in the array manifold,which makes the performance of the algorithm decline rapidly or even fail.In order to solve the problem of DOA estimation in the presence of amplitude and phase errors and array element position errors,this paper introduces the first-order Taylor expansion equivalent model of the received signal under the uniform linear array from the Bayesian point of view.In the solution,the amplitude and phase error parameters and the array element position error parameters are regarded as random variables obeying the Gaussian distribution.At the same time,the expectation-maximization algorithm is used to update the probability distribution parameters,and then the two error parameters are solved alternately to obtain more accurate DOA estimation results.Finally,the effectiveness of the proposed algorithm is verified by simulation and experiment.
文摘A new direction-of-arrival （DOA） estimation algorithm for wideband sources is introduced, The new method obtains the output of the virtual arrays in the signal bandwidth using cubic spline function interpolation techniques. The narrowband high- resolution algorithm is then used to get the DOA estimation. This technique does not require any preliminary knowledge of DOA angles. Simulation results demonstrate the effectiveness of the method.
文摘A novel identification method for point source,coherently distributed（CD） source and incoherently distributed（ICD） source is proposed.The differences among the point source,CD source and ICD source are studied.According to the different characters of covariance matrix and general steering vector of the array received source,a second order blind identification method is used to separate the sources,the mixing matrix could be obtained.From the mixing matrix,the type of the source is identified by using an amplitude criterion.And the direction of arrival for the array received source is estimated by using the matching pursuit algorithm from the vectors of the mixing matrix.Computer simulations validate the efficiency of the method.
基金supported by the Program for Changjiang Scholars and Innovative Research Team in University (IRT0645)
文摘A two-dimensional direction-of-arrival （DOA） and polarization estimation algorithm for coherent sources using a linear vector-sensor array is presented. Two matrices are first constructed by the receiving data. The ranks of the two matrices are only related to the DOAs of the sources and independent of their coherency. Then the source’s elevation is resolved via the matrix pencil （MP） method, and the singular value decomposition （SVD） is used to reduce the noise effect. Finally, the source’s steering vector is estimated, and the analytics solutions of the source’s azimuth and polarization parameter can be directly computed by using a vector cross-product estimator. Moreover, the proposed algorithm can achieve the unambiguous direction estimates, even if the space between adjacent sensors is larger than a half-wavelength. Theoretical and numerical simulations show the effectiveness of the proposed algorithm.
文摘A direction-of-arrival （DOA） estimation algorithm based on direct data domain （D3） approach is presented. This method can accuracy estimate DOA using one snapshot modified data, called the temporal and spatial two-dimensional vector reconstruction （TSR） method. The key idea is to apply the D3 approach which can extract the signal of given frequency but null out other frequency signals in temporal domain. Then the spatial vector reconstruction processing is used to estimate the angle of the spatial coherent signal source based on extract signal data. Compared with the common temporal and spatial processing approach, the TSR method has a lower computational load, higher real-time performance, robustness and angular accuracy of DOA. The proposed algorithm can be directly applied to the phased array radar of coherent pulses. Simulation results demonstrate the performance of the proposed technique.
基金supported by the National Natural Science Foundation of China(61571149)the Natural Science Foundation of Heilongjiang Province(LH2020F017)+1 种基金the Initiation Fund for Postdoctoral Research in Heilongjiang Province(LBH-Q19098)the Heilongjiang Province Key Laboratory of High Accuracy Satellite Navigation and Marine Application Laboratory(HKL-2020-Y01).
文摘In order to resolve direction finding problems in the impulse noise,a direction of arrival(DOA)estimation method is proposed.The proposed DOA estimation method can restrain the impulse noise by using infinite norm exponential kernel covariance matrix and obtain excellent performance via the maximumlikelihood(ML)algorithm.In order to obtain the global optimal solutions of this method,a quantum electromagnetic field optimization(QEFO)algorithm is designed.In view of the QEFO algorithm,the proposed method can resolve the difficulties of DOA estimation in the impulse noise.Comparing with some traditional DOA estimation methods,the proposed DOA estimation method shows high superiority and robustness for determining the DOA of independent and coherent sources,which has been verified via the Monte-Carlo experiments of different schemes,especially in the case of snapshot deficiency,low generalized signal to noise ratio(GSNR)and strong impulse noise.Beyond that,the Cramer-Rao bound(CRB)of angle estimation in the impulse noise and the proof of the convergence of the QEFO algorithm are provided in this paper.
基金supported by the National Natural Science Foundation of China(6120129561231017)the Fundamental Research Funds for the Central Universities(K5051307017)
文摘The nonuniform L-shaped spatially spread loop and dipole（SSLD） array whose inter-element spacing is greater than half a wavelength is studied. A joint parameter estimation algorithm of direction of arrival（DOA）, frequency and polarization is presented for plane-wave signals. The direct sampling and the corresponding delayed sampling data are used to construct the data correlation matrix. On the basis of the subspace theory and the least square method, the frequency and the steering vector of the whole array are obtained. According to the relationship of the array manifold vector between electric dipoles and magnetic loops,the polarization parameters are given. The unambiguous phase estimates are acquired by applying virtual baseline array transformation to the spatial steering vectors, and they are used as coarse references to disambiguate the cyclic phase ambiguities in phase differences between two adjacent array elements on the array,then the high accuracy DOA estimates are obtained. Closed-form solutions for each parameter are obtained. This method has advantages of lower calculation complexity and no parameter matching. The experiment results verify the effectiveness and feasibility of the presented algorithm.
文摘针对互耦效应和脉冲噪声并存环境下的波达方向(direction of arrival,DOA)估计问题,提出一种结合M估计与稀疏重构的算法。首先,为了消除互耦效应的影响,依据互耦矩阵的托普利兹结构进行恒等变形,得到了不含未知互耦系数的字典。随后,为了使算法能适应高斯噪声和不同强度的脉冲噪声,将位置得分函数表示为高斯位置得分函数和一系列非线性函数的线性组合,利用噪声样本估计线性组合系数从而建立损失函数。最后,采用迭代硬阈值算法进行稀疏重构,并通过改进信号更新策略提高正确收敛的概率。仿真结果表明,所提算法能有效抑制互耦效应和脉冲(高斯)噪声的干扰,同时相较已有算法在低信噪比、强脉冲特性下的性能有显著提升。
文摘This paper develops a deep estimator framework of deep convolution networks(DCNs)for super-resolution direction of arrival(DOA)estimation.In addition to the scenario of correlated signals,the quantization errors of the DCN are the major challenge.In our deep estimator framework,one DCN is used for spectrum estimation with quantization errors,and the remaining two DCNs are used to estimate quantization errors.We propose training our estimator using the spatial sampled covariance matrix directly as our deep estimator’s input without any feature extraction operation.Then,we reconstruct the original spatial spectrum from the spectrum estimate and quantization errors estimate.Also,the feasibility of the proposed deep estimator is analyzed in detail in this paper.Once the deep estimator is appropriately trained,it can recover the correlated signals’spatial spectrum fast and accurately.Simulation results show that our estimator performs well in both resolution and estimation error compared with the state-of-the-art algorithms.
基金supported by the National Natural Science Foundation of China(62031015).
文摘This paper examines the direction of arrival(DOA)estimation for polarized signals impinging on a sparse vector sensor array which is based on the maximum interelement spacing constraint(MISC).The vector array effectively utilizes the polarization domain information of incident signals,and the quaternion model is adopted for signals polarization characteristic maintenance and computational burden reduction.The features of MISC arrays are crucial to the mutual coupling effects reduction and higher degrees of freedom(DOFs).The quaternion data model based on vector MISC arrays is established,which extends the scalar MISC array into the vector MISC array.Based on the model,a quaternion multiple signal classification(MUSIC)algorithm based on vector MISC arrays is proposed for DOA estimation.The algorithm combines the advantages of the quaternion model and the vector MISC array to enhance the DOA estimation performance.Analytical simulations are performed to certify the capability of the algorithm.
基金supported by the National Natural Science Foundation of China(61771367)the Science and Technology on Communication Networks Laboratory(6142104190204).
文摘It is always a challenging issue for radar systems to estimate the height of a low-angle target in the multipath propagation environment.The highly deterministic maximum likelihood estimator has a high accuracy,but the errors of the ground reflection coefficient and the reflecting surface height have serious influence on the method.In this paper,a robust es-timation method with less computation burden is proposed based on the compound reflection coefficient multipath model for low-angle targets.The compound reflection coefficient is es-timated from the received data of the array and then a one-di-mension generalized steering vector is constructed to estimate the target height.The algorithm is robust to the reflecting sur-face height error and the ground reflection coefficient error.Fi-nally,the experiment and simulation results demonstrate the validity of the proposed method.
文摘针对现有二维波达方向(direction of arrival,DOA)估计方法对阵列接收信息利用不充分导致估计性能下降的问题,提出了一种平行互质阵列下对虚拟阵列插值的二维DOA估计方法。该方法通过对平行互质阵列扩展后的虚拟阵列进行插值,利用内插虚拟阵列的协方差矩阵与虚拟测量值之间的关系,提出一个关于等效虚拟测量向量的最小化问题,通过凸优化工具箱重构插值后的虚拟阵列协方差矩阵,结合酉变换和总体最小二乘方法进行DOA估计。仿真结果和湖上试验表明,该方法充分利用了非匀虚拟阵列中的所有虚拟阵元,提高了自由度和估计精度,具有有效性。
基金supported by the National Natural Science Foundation of China(6150117661201399)+1 种基金the Education Department of Heilongjiang Province Science and Technology Research Projects(12541638)the Developing Key Laboratory of Sensing Technology and Systems in Cold Region of Heilongjiang Province and Ministry of Education,(Heilongjiang University),P.R.China(P201408)
文摘For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.
文摘To enhance direction of arrival(DOA)estimation accuracy,this paper proposes a low-cost method for calibrating farfield steering vectors of large aperture millimeter wave radar(mmWR).To this end,we first derive the steering vectors with amplitude and phase errors,assuming that mmWR works in the time-sharing mode.Then,approximate relationship between the near-field calibration steering vector and the far-field calibration steering vector is analyzed,which is used to accomplish the mapping between the two of them.Finally,simulation results verify that the proposed method can effectively improve the angle measurement accuracy of mmWR with existing amplitude and phase errors.
