A space-time joint domain beamforming method in a fast moving target scene

Abstract

The application relates to the field of radar array signal processing, in particular to a space-time joint domain beam forming method in a fast moving target scene. First, a sensor array is constructed, and initialization parameters including array configuration parameters, target echo signals and incident angles and Doppler frequency shifts of interference signals are set to establish a space-time two-dimensional steering vector model; then, in combination with the model, beam amplitude response constraint conditions are determined according to the incident angles and Doppler frequency shift ranges of the target echo signals, and a space-time two-dimensional robust beam forming model is constructed based on a minimum output power criterion; a covariance matrix of low sample echo data is obtained, the covariance matrix is reconstructed after eigenvalue decomposition and eigenvalue compensation; finally, a space-time adaptive processing model is constructed based on the reconstructed matrix, an initial weight vector is obtained through relaxation of non-convex constraints, and the initial weight vector is iteratively optimized through phase compensation until the conditions are met, so that the final weight vector is obtained, and the robustness and accuracy of beam forming in the low sample data can be improved in the fast moving target scene.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar array signal processing, and more particularly to a space-time joint domain beam forming method in a fast moving target scene. BACKGROUND

[0002] In the field of modern radar signal processing, adaptive arrays have formed a deep technical accumulation due to their excellent signal detection and estimation performance in complex electromagnetic environments, and continue to expand in depth in the direction of high-dimensional perception, intelligent anti-jamming and other frontiers. The design of adaptive array processors is usually based on a specific criterion, such as the minimum output power, maximum entropy or maximum signal-to-interference-plus-noise ratio (SINR) criterion. Among them, the Capon beam forming method uses the minimum output power criterion to set linear constraints in a specific angle direction, thereby realizing the robust response to the expected direction signal, and has been widely used in radar systems.

[0003] However, in the fast moving target scene, the performance of the adaptive beam former faces severe challenges. On the one hand, the radar echo signal angle of the target changes rapidly, which easily leads to deviation in the modeling of the steering vector of the echo signal; on the other hand, the sample data amount in the same range gate is small, which makes the array covariance matrix of the echo signal inaccurate, and further affects the accurate calculation of the beam former weight vector. Therefore, in the fast moving target scene, designing a robust adaptive beam former has become an important problem to be solved for array antenna radar.

[0004] To solve the problem of steering vector deviation caused by rapid angle change or large angle estimation error, there are mainly two ideas in the existing technology. One idea is not to correct the steering vector itself, but to directly introduce multi-point constraints, derivative constraints and other limiting conditions in the adaptive beam former model, aiming to form a wide beam in a certain angle region to maintain the gain of the expected angle direction from falling sharply. The other idea is to use optimization theory to construct a suitable objective function and corresponding constraint conditions, correct the steering vector, and then calculate the beam former weight vector.

[0005] When the array antenna radar performs fast time sampling in a single pulse repetition period, that is, sampling the echo signal in the duration of a single transmitting pulse or Chirp, the change of the echo signal in the distance dimension can be captured. However, when the target moves fast, the sample point data in the same distance gate will become less. To solve this problem, the current main solution is to start from the eigenvalue decomposition of the sample covariance matrix, to improve the second-order statistical characteristics of the received data by correcting the small eigenvalues corresponding to the noise, so as to prevent the beam pattern distortion caused by the small number of radar data samples. For example, the diagonal loading algorithm increases a small constant on the main diagonal elements of the sample covariance matrix to reduce the condition number of the eigenvalues, avoids the ill-conditioned matrix caused by the inverse operation in the process of calculating the beamformer weight vector, and improves the robustness of the Capon beamformer to a certain extent.

[0006] However, the prior art still has obvious defects. In the case of fast moving target, to solve the problem of deviation of the steering vector caused by the fast change of the target signal angle, it is usually considered to increase the expected response constraint in the specified direction or angle region on the basis of minimizing the output signal-to-interference-and-noise ratio. However, in the case that the spatial steering vector error is large and the angle of the interference signal is close to the angle of the target signal, the beam pattern of such method will have distortion problems such as side lobe rising and main lobe splitting, that is, it cannot maintain good gain in the direction of the expected signal angle, and the nulling effect in the interference direction is also poor. On the other hand, to solve the problem of insufficient sample point data in the same distance gate caused by the fast moving target, the diagonal loading method is usually used to reconstruct the sample covariance matrix, and the selection of the diagonal loading parameter is usually related to the noise power and other parameters, but the noise power is not easy to accurately obtain in the actual work of the array antenna radar.

[0007] Based on the above-mentioned defects of the prior art, in the case of fast moving target and close interference angle to the expected target echo signal, how to design a robust beamformer that can effectively solve the problems of steering vector deviation and insufficient sample data becomes a technical problem to be solved. SUMMARY

[0008] Therefore, the present application provides a space-time joint domain beamforming method in a fast moving target scene, which improves the robustness and accuracy of beamforming in a low sample data condition in a fast moving target scene by constructing a space-time two-dimensional robust model, optimizing the covariance matrix and iteratively solving the weight vector.

[0009] The technical scheme provided by the present application is as follows:

[0010] A space-time joint domain beamforming method in a fast moving target scene, comprising:

[0011] construct a sensor array and set initialization parameters, and establish a space-time two-dimensional steering vector model; the initialization parameters include array configuration parameters, and incident angle and Doppler shift parameters of each of expected target echo signals and interference signals;

[0012] In combination with the space-time two-dimensional steering vector model, a beam amplitude response constraint condition is determined by setting a parameter range of the target echo signal; the parameter range includes an angle range and a Doppler shift range of the expected echo signal reaching the array antenna, and the beam amplitude response constraint condition is used to limit the amplitude response of the beam within the angle range and the Doppler shift range to be within a preset upper and lower boundary interval;

[0013] A space-time two-dimensional robust beam forming model is constructed based on a minimum output power criterion and the beam amplitude response constraint condition, and is used to solve a beam former weight vector;

[0014] A covariance matrix of low-sample echo data is obtained and is subjected to eigenvalue decomposition;

[0015] Eigenvalue compensation is performed on an eigenvalue diagonal matrix composed of eigenvalues, and the covariance matrix is reconstructed based on the compensated eigenvalue diagonal matrix;

[0016] An initial beam former weight vector is obtained by relaxing a non-convex constraint in the space-time two-dimensional robust beam forming model based on a space-time adaptive processing model constructed based on the reconstructed covariance matrix, and the optimization weight vector is iterated through phase compensation until an error or an iteration number condition is met, and a final beam former weight vector is obtained.

[0017] In one possible implementation, the sensor array is an isotropic uniform linear sensor array, and the array configuration parameters include the number of antenna elements , the number of time domain delays , the interval distance of adjacent antenna elements , the wavelength of radar echo signals , and the pulse repetition frequency .

[0018] In one possible implementation, the space-time two-dimensional steering vector model is generated by Kronecker product operation of a space domain steering vector corresponding to an angle and a time domain steering vector corresponding to a Doppler shift, and the received data is described as a superposition form of target signals, interference signals, and noise on the space-time two-dimensional steering vector.

[0019] In one possible implementation, the space-time two-dimensional robust beam forming model is constructed based on the minimum output power criterion and the beam amplitude response constraint condition, and is represented as:

[0020]

[0021] wherein, denotes taking the minimum value of the objective function, denotes the beamformer weight vector to be solved, denotes the conjugate transpose, is the covariance matrix of array sample data, denotes the space-time steering vector of the expected target echo, denotes the incident angle of the expected target echo signal, is the Doppler shift; denotes the angle range of the expected echo signal reaching the receiving array antenna, denotes the Doppler shift range, denotes the lower bound of the amplitude response, denotes the upper bound of the amplitude response.

[0022] In one possible implementation, the covariance matrix of the low-sample echo data is obtained and eigenvalue decomposition is performed, comprising:

[0023] Eigenvalue decomposition is performed on the covariance matrix to obtain eigenvalues and eigenvectors;

[0024] A feature vector matrix and an eigenvalue diagonal matrix are constructed based on the eigenvectors and eigenvalues; wherein the eigenvalue diagonal matrix contains eigenvalues sorted by size.

[0025] In one possible implementation, the eigenvalue diagonal matrix is subjected to eigenvalue compensation to reconstruct the covariance matrix, comprising:

[0026] Based on the eigenvalues of the original covariance matrix, the condition number of the covariance matrix is determined; wherein the condition number of the covariance matrix is determined by the ratio of the maximum value to the minimum value in the eigenvalues;

[0027] The reciprocal of the condition number of the covariance matrix is taken as an eigenvalue compensation factor, and each eigenvalue in the original covariance matrix is subjected to compensation processing, and the maximum value of the original eigenvalue and the compensated eigenvalue is taken to construct a new eigenvalue diagonal matrix, denoted as:

[0028]

[0029] wherein, is the eigenvalue of the original covariance matrix , and , denotes the maximum value operation, is the eigenvalue compensation factor;

[0030] Based on the feature vector matrix and the new eigenvalue diagonal matrix, the covariance matrix is reconstructed, denoted as: .

[0031] In one possible implementation, the non-convex constraint in the space-time two-dimensional robust beamforming model is relaxed to obtain an initial beamformer weight vector, including:

[0032] The phase corresponding to the direction pattern function of the expected echo signal is expressed as:

[0033]

[0034] In the formula, is the phase of is a phase taking operation, and the non-convex constraint is expressed as ;

[0035] The non-convex constraint condition is relaxed as:

[0036]

[0037] The optimization problem of the initial beamformer weight vector is expressed as:

[0038]

[0039] In the formula, min represents taking the minimum value of the objective function, represents an initial value of the set beamformer weight vector, represents a conjugate transpose, is a reconstructed covariance matrix, represents a space-time steering vector of the expected target echo, represents an incident angle of the expected target echo signal, is a Doppler shift; represents an angle range of the expected echo signal to the receiving array antenna, represents a Doppler shift range, represents a lower bound of the amplitude response, represents an upper bound of the amplitude response.

[0040] In one possible implementation, the beamformer weight vector is optimized through phase compensation iteration, including:

[0041] Based on the beamformer weight vector of the current iteration, the phase value corresponding to the direction pattern function of the expected echo signal is calculated and expressed as:

[0042]

[0043] In the formula, represents the first​ iteration This represents the incident angle of the desired target echo signal. For Doppler frequency shift, Indicates the current number Beamformer weight vector for the next iteration This indicates the conjugate transpose. This represents the spacetime steering vector of the desired target echo. Indicates the total number of iterations;

[0044] Substituting the phase value into the space-time two-dimensional beamforming model, an optimization problem including phase compensation is constructed and solved to obtain the updated beamformer weight vector, expressed as:

[0045]

[0046] In the formula, This represents the currently updated beamformer weight vector. This indicates the conjugate transpose. It is the reconstructed covariance matrix; This indicates the angular range from which the expected echo signal will arrive at the receiving array antenna. Indicates the range of Doppler frequency shift; This represents the lower bound of the amplitude response. This represents the upper bound of the amplitude response.

[0047] One possible implementation involves iterating the optimized weight vector through phase compensation, which further includes:

[0048] Set iteration error threshold The error between the updated beamformer weight vector and the beamformer weight vector of the previous iteration is calculated and expressed as:

[0049]

[0050] In the formula, This represents the currently updated beamformer weight vector. This indicates the conjugate transpose. It is the reconstructed covariance matrix;

[0051] Determine whether the error is less than or equal to the iteration error threshold. Or the number of iterations reaches the total number of iterations. ;

[0052] If the error is less than or equal to the iteration error threshold If the number of iterations reaches the total number of iterations, then the currently updated beamformer weight vector will be used as the final result.

[0053] Compared with the prior art, the technical scheme of the application has the following beneficial effects:

[0054] The application is aimed at a fast-moving target scene, and by constructing a space-time two-dimensional steering vector model and a robust beam forming model, combining with target echo signal parameter range setting constraints, target signals can be accurately focused. In the face of the problem of few samples in the same range gate, the eigenvalue compensation is used to reconstruct the covariance matrix, the matrix estimation deviation is effectively corrected, and a reliable foundation is provided for the beam former weight vector calculation. Then, the initial beam former weight vector is obtained by relaxing the non-convex constraint, and the non-convex constraint solving problem is solved through phase compensation iteration optimization, so as to finally improve the calculation accuracy of the beam former weight vector, so that the radar can realize more robust and accurate beam forming in the fast-moving target scene, and the detection and tracking performance of the target is enhanced. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 A flowchart of a space-time joint area beam forming method in a fast-moving target scene is provided for the first embodiment of the application.

[0056] Figure 2 A flowchart of a space-time joint area beam forming method in a fast-moving target scene is provided for the second embodiment of the application.

[0057] Figure 3 A schematic diagram of array antenna radar receiving signals in a fast-moving target environment is provided for the second embodiment of the application.

[0058] Figure 4 A flowchart of a method for constructing a space-time two-dimensional robust beam forming model is provided for the second embodiment of the application.

[0059] Figure 5 A two-dimensional STAP beam pattern is provided for the third embodiment of the application.

[0060] Figure 6 A two-dimensional STAP beam pattern in the space domain perspective is provided for the third embodiment of the application.

[0061] Figure 7 A two-dimensional STAP beam pattern in the frequency domain perspective is provided for the third embodiment of the application. DETAILED DESCRIPTION

[0062] The technical solutions in the embodiments of the application will be described below in detail with the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, not all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the application.

[0063] The application focuses on the fast-moving target scene. For the radar using frequency modulated continuous wave (FMCW) system, when the angle of the jamming signal is close to the angle of the target signal, a space-time two-dimensional joint domain adaptive beamformer is designed by using space-time two-dimensional sampling. First, according to the approximate angle and frequency range of the expected target radar echo signal, the interval of the beam amplitude response constraint is confirmed. Then, a space-time adaptive processing (STAP) beamforming optimization model based on covariance matrix reconstruction is proposed. Finally, the phase compensation method is used to optimize and solve the beamformer weight vector.

[0064] Next, the space-time joint domain beamforming method in the fast-moving target scene provided by the application will be described in detail through specific embodiments.

[0065] Embodiment one

[0066] Reference Figure 1 A flow chart of a space-time joint domain beamforming method in a fast-moving target scene provided by the first embodiment of the application is shown in FIG. 1. Figure 1 The specific implementation steps of the above method include:

[0067] Step 101, construct a sensor array and initialize parameters, and establish a space-time two-dimensional steering vector model based on the above sensor array.

[0068] The sensor array uses an equidistant uniform linear array containing a plurality of isotropic sensors, and the established space-time two-dimensional steering vector model covers the array configuration parameters, the incident angles and Doppler frequency shifts of the expected target echo signal and the jamming signal. The space-time two-dimensional steering vector is generated by the Kronecker product operation of the corresponding angle space steering vector and the corresponding Doppler frequency time steering vector, and the received data is described as the superposition of the target signal, the jamming signal and the noise on the space-time two-dimensional steering vector.

[0069] Step 102, combine the above space-time two-dimensional steering vector model, determine the beam amplitude response constraint condition by setting the parameter range of the target echo signal, and construct a space-time two-dimensional robust beamforming model combined with the minimum output power criterion.

[0070] Specifically, the parameter range includes the angle range and the Doppler frequency shift range of the expected echo signal reaching the array antenna. The beam amplitude response constraint condition is used to limit the amplitude response of the beam within the above angle range and Doppler frequency shift range to be within the preset upper and lower boundary interval, so as to robustly control the expected target echo beam.

[0071] In the embodiment of the present application, the minimum output power criterion and the amplitude response constraint condition are adopted, and a space-time two-dimensional robust beamforming model is constructed in combination with the space-time two-dimensional steering vector model. The space-time two-dimensional robust beamforming model takes the beamformer weight vector as the solving object, and the objective function is to minimize the beam output power.

[0072] In step 103, the covariance matrix of the low-sample echo data is obtained, and eigenvalue decomposition is performed. The eigenvalue diagonal matrix composed of the eigenvalues is compensated for eigenvalues, and the covariance matrix is reconstructed based on the compensated eigenvalue diagonal matrix.

[0073] In the fast-moving target scene, due to the fast target motion speed, the amount of echo sample data that the receiving radar can obtain in the same range gate is small, which makes it difficult for the direct echo signal array covariance matrix to accurately reflect the real signal statistical characteristics, and estimation bias is likely to occur, thereby affecting the detection accuracy and tracking stability of the radar on the fast-moving target. Therefore, it is necessary to reconstruct and correct the covariance matrix.

[0074] As an implementable way, the present application first obtains the covariance matrix corresponding to the low-sample echo data, and decomposes it into eigenvectors and eigenvalues through eigenvalue decomposition. On this basis, in view of the problem that the eigenvalue estimation is not accurate due to insufficient samples, especially the eigenvalues corresponding to the noise subspace are prone to be small, an eigenvalue compensation method is used to correct the eigenvalue diagonal matrix, and an eigenvalue compensation factor is introduced to adjust the eigenvalue size. Subsequently, a new diagonal matrix is constructed using the corrected eigenvalues, and the original eigenvector matrix is combined to reconstruct the covariance matrix, so as to ensure that the beam can accurately point to the target in the fast-moving target scene.

[0075] In step 104, a space-time adaptive processing model is constructed based on the reconstructed covariance matrix, the non-convex constraint in the space-time two-dimensional robust beamforming model is relaxed to obtain an initial beamformer weight vector, the beamformer weight vector is iteratively optimized through phase compensation until the error or the number of iterations is satisfied, and the final beamformer weight vector is obtained.

[0076] Specifically, the present application considers that the non-convex constraint in the space-time two-dimensional robust beamforming model makes it difficult to be directly solved, so the non-convex constraint is first relaxed to obtain an initial beamformer weight vector, and then the weight vector is iteratively optimized through phase compensation. The iteration process is controlled by setting an error threshold and the number of iterations, and finally the beamformer weight vector that can solve the non-convex constraint problem is obtained, and accurate beamforming is realized.

[0077] Compared with the prior art, the technical scheme provided by the embodiment of the present application has the following beneficial effects:

[0078] The application can accurately focus target signals by constructing a space-time two-dimensional steering vector model and a robust beamforming model, combining with target echo signal parameter range setting constraints. The processing performance under low sample data is effectively improved by subspace division and reconstruction of the covariance matrix. For the non-convex constraint in the model, the relaxation processing and phase compensation iterative optimization method is adopted, which not only solves the non-convex constraint solving problem, but also improves the solving accuracy and efficiency of the beamformer weight vector, finally realizes more robust and accurate radar beamforming, and enhances the radar target detection and tracking capability.

[0079] Embodiment two

[0080] The embodiment two of the application is a further detailed description of the technical solutions provided by the application to ensure full disclosure of the technical solutions of the application. Referring to Figure 2 , a space-time joint domain beamforming method in a fast moving target scene is provided in the embodiment one of the application. As shown in Figure 2 , the specific implementation steps of the above method include:

[0081] Step 201, constructing an isotropic uniform linear sensor array and initializing and setting parameters of the array.

[0082] In the embodiment of the application, as shown in Figure 3 , the above isotropic sensor array is an equal-interval uniform linear array. The above setting parameters of the array include but are not limited to the number of antenna elements , the number of time domain delays , the interval distance of adjacent antenna elements , the wavelength of radar echo signal and the pulse repetition frequency . The interval distance of adjacent antenna elements .

[0083] Step 202, constructing a space-time two-dimensional steering vector model of array antenna radar receiving data based on the above isotropic sensor array.

[0084] When the expected target moves quickly within a single transmission pulse period, the number of samples captured by the frequency-modulated continuous wave radar in the same distance is reduced, the second-order statistical characteristics of the sample data are destroyed, and the beam pattern is distorted. At the same time, the expected signal angle received by the ground receiving radar appears in the to interval, which is easy to cause deviation in the modeling of the echo signal steering vector. Therefore, the application proposes to design a space-time two-dimensional joint domain robust beam filter in a fast moving target scene.

[0085] As an implementable manner, the application first establishes a space-time two-dimensional steering vector model. Assuming that the incident angle of the expected target echo signal is , the corresponding Doppler shift is ; the incident angle of the interference signal is , the corresponding Doppler shift is expressed as , then the data received by the array antenna at time can be expressed as:

[0086] (1)

[0087] wherein, denotes a transposition operation, and are the expected target echo signal and the interference signal respectively, denotes a Gaussian white noise, and are the space-time steering vectors of the expected target echo signal and the interference signal respectively.

[0088] The space-time steering vector is the Kronecker product of the space domain steering vector at the angle and the time domain steering vector at the Doppler shift , that is

[0089] (2)

[0090] In the formula, denotes the Kronecker product operation. and can be expressed as:

[0091] (3)

[0092] (4)

[0093] wherein, , .

[0094] Step 203, in combination with the above-mentioned space-time two-dimensional steering vector model, a space-time two-dimensional robust beamforming model is constructed.

[0095] In the embodiments of the present application, the minimum output power criterion and the amplitude response constraint condition are adopted, and a space-time two-dimensional robust beamforming model is constructed in combination with the space-time two-dimensional steering vector model. The space-time two-dimensional robust beamforming model takes the beamformer weight vector as the solving object, and the objective function is to minimize the beam output power. As shown in Figure 4 , the specific method for constructing the space-time two-dimensional robust beamforming model includes the following steps.

[0096] Step 2031, set the angle range and Doppler shift range of the expected echo signal reaching the array antenna, and determine the beam amplitude response constraint condition based thereon, which is used to limit the amplitude response of the beam in the above-mentioned angle range and Doppler shift range to be within the preset upper and lower boundary intervals.

[0097] Specifically, it is assumed that the angle range and Doppler shift range of the expected echo signal reaching the receiving array antenna are respectively denoted as and , the incident angle of the radar echo signal of the expected target is ( ), and the Doppler shift is represented as ( ).

[0098] In the fast-moving target scenario, the expected target echo signal changes rapidly in angle. In the present application, the amplitude response constraint condition is adopted to robustly control the expected target echo beam. First, the array pattern function is represented as:

[0099] (5)

[0100] In the formula, w represents the beamformer weight vector to be solved, represents the conjugate transpose.

[0101] Then, the amplitude response constraint condition adopted for the expected target echo signal is represented as:

[0102] (6)

[0103] wherein, is an absolute value operation. are real numbers, and respectively represent the lower bound and the upper bound of the amplitude response. The purpose is to constrain the pattern gain of the expected target echo signal within the interval, so that the signal gain is kept within the expected range.

[0104] Step 2032, based on the minimum output power criterion, the space-time two-dimensional robust beamforming model is constructed in combination with the above-mentioned amplitude response constraint condition.

[0105] ​In the embodiments of the present application, a minimum power criterion is used to construct a space-time two-dimensional robust beamformer, and the specific mathematical model is expressed as follows:

[0106] (7)

[0107] wherein, denotes the minimization of the objective function, denotes the constraint condition, is a covariance matrix of array sample data, and has a dimension of which is defined as follows:

[0108] (8)

[0109] wherein, denotes the mathematical expectation.

[0110] Further, the space-time two-dimensional beamforming model constructed above depends on an accurate covariance matrix to calculate the optimal weight vector. However, in the fast-moving target scene, the sample data captured by the receiving radar in the same distance unit is less, and the estimation accuracy of the covariance matrix of array sample data depends on the sample size. Therefore, the original covariance matrix in the fast-moving target scene may be inaccurate. To this end, the present application proposes a method of eigenvalue step length to correct and reconstruct the covariance matrix of low sample echo data. Wherein, the above low sample echo data refers to the case that the number of target echo signal samples received by the radar in the same distance unit in the fast-moving scene is less. As shown in the following formula (8), the method specifically includes the following steps: Figure 2

[0111] Step 204, obtaining a covariance matrix corresponding to the low sample echo data received by the array antenna radar, and performing eigenvalue decomposition on the covariance matrix, and constructing an eigenvector matrix and an eigenvalue diagonal matrix based on the eigenvectors and eigenvalues obtained by the decomposition. Wherein, the eigenvalue diagonal matrix contains eigenvalues sorted by size.

[0112] To avoid the problem that the beamformer weight vector calculation deviates due to the inaccuracy of the array covariance matrix of echo signals, the present application proposes a method of eigenvalue step length to correct the covariance matrix. First, the covariance matrix is decomposed into eigenvalues, expressed as:

[0113] (9)

[0114] wherein, is expressed as the eigenvector matrix of is the eigenvalue diagonal matrix of , and is specifically expressed as follows:​

[0115] (10)

[0116] wherein, is the eigenvalue of the covariance matrix, and the size order is .

[0117] According to the eigenvalue decomposition, the eigenvector matrix is obtained, and the eigenvector corresponding to the larger eigenvalue is selected to obtain the signal subspace, and the eigenvector corresponding to the smaller eigenvalue is selected to obtain the noise subspace.

[0118] The present application considers that when the number of samples is small, the smaller eigenvalue corresponding to the noise subspace may be too small, resulting in a pathological matrix due to the inverse operation in the process of solving the optimal weight vector of the antenna. In order to better characterize the covariance matrix of the received data under the condition of low sample sampling data, an eigenvalue compensation method is proposed to modify the covariance matrix, which includes the following steps.

[0119] Step 205, based on the eigenvalue of the original covariance matrix, determine the condition number of the covariance matrix.

[0120] The condition number of the covariance matrix is determined by the maximum and minimum values of the eigenvalues of the covariance matrix, and is expressed as:

[0121] (11)

[0122] wherein, represents the maximum value of the eigenvalue, represents the minimum value of the eigenvalue,

[0123] Step 206, take the reciprocal of the condition number of the covariance matrix as the eigenvalue compensation factor, compensate each eigenvalue in the original covariance matrix, and take the maximum value of the original eigenvalue and the compensated eigenvalue to construct a new eigenvalue diagonal matrix.

[0124] Specifically, the eigenvalue compensation factor is expressed as:

[0125] (12)

[0126] The new eigenvalue diagonal matrix is expressed as

[0127] (13)

[0128] wherein, ​​represents a maximum value operation.

[0129] Step 207, a new covariance matrix is reconstructed by using the above feature vector matrix and a new diagonal matrix, denoted as:

[0130] (14)

[0131] Step 208, based on the reconstructed covariance matrix, a space-time adaptive processing mathematical model is constructed to solve the beamformer weight vector.

[0132] The above space-time adaptive processing mathematical model can be expressed as:

[0133] (15)

[0134] The present application obtains a space-time two-dimensional beamforming model as described in formula (15) to solve the beamformer weight vector based on the above steps. However, the condition constraint in formula (15) is non-convex for the variable , that is, is non-convex, and cannot be solved by toolbox.

[0135] In view of the above problem, the present application proposes to use as the relaxed constraint of , and represents a real part operation. However, the beamformer weight vector solved in this way is a suboptimal solution. Therefore, the present application further proposes a phase compensation method, and the specific steps are as follows:

[0136] Step 209, the non-convex constraint condition in the above space-time two-dimensional beamforming model is relaxed, an initial optimization problem is constructed and solved to obtain an initial beamformer weight vector, and the total number of iterations is set.

[0137] Specifically, the phase corresponding to the directivity function of the expected echo signal is expressed as:

[0138] (16)

[0139] wherein is the phase of , and is a phase operation, then the non-convex constraint in the above formula (15) can be expressed as:

[0140] (17)

[0141] Therefore, the above formula (15) can be further represented as a space time adaptive processing based on covariance matrix reconstruction and phase compensation (STAP-CMR-PC) optimization model, represented as:

[0142] (18)

[0143] It can be seen from the above formula that the optimization problem has two variables and , and there is coupling between them, which cannot be directly solved by . If a feasible initial value is provided, then can be substituted into formula (16) to obtain , and then is substituted into formula (18) to update the beamformer weight vector , and so on, and is constantly updated until it converges to a certain value.

[0144] As a realizable way, the beamformer weight vector is initialized, and the total number of iterations is set.

[0145] Because for any complex number , it satisfies , the non-convex constraint condition is relaxed as:

[0146] (19)

[0147] Therefore, the optimization problem of the initial array weight is represented as:

[0148] (20)

[0149] Step 210, based on the beamformer weight vector of the current iteration, the phase value corresponding to the expected echo signal pattern function is calculated.

[0150] Specifically, the phase value of the th iteration is calculated and represented as:

[0151] (21)

[0152] In the formula, indicates the current Beamformer weight vector for the next iteration.

[0153] Step 211: Substitute the above phase values ​​into the space-time two-dimensional beamforming model, construct an optimization problem including phase compensation and solve it to obtain the updated beamformer weight vector.

[0154] Specifically, update The secondary beamformer weight vector is expressed as:

[0155] (twenty two)

[0156] Step 212: Set the iteration error threshold The error between the currently updated beamformer weight vector and the beamformer weight vector of the previous iteration is calculated and expressed as:

[0157] (twenty three)

[0158] In the formula, This represents the currently updated beamformer weight vector.

[0159] Step 213: Determine whether the above error is less than or equal to the preset threshold. Or the number of iterations reaches the total number of iterations. .

[0160] Step 214: If yes, use the currently updated beamformer weight vector as the final result. Otherwise, repeat the above steps to solve the problem caused by the non-convex constraint by iteratively optimizing the beamformer weight vector.

[0161] Compared with the prior art, the technical solution provided in Embodiment 2 of this application has the following beneficial effects:

[0162] The technical scheme of the application has remarkable beneficial effects: first, a "flat top" beam can be formed in a specific angle region, effectively covering the angle change range of the moving target, ensuring that the signal-to-interference-and-noise ratio of the beamformer output is not affected by the rapid movement of the target, and solving the problem that the main lobe cannot track the target in real time in the traditional space-time adaptive beamforming, resulting in reduced reception gain; second, the interference signal with an angle close to the target can be suppressed in the Doppler frequency domain, while ensuring that the beam main lobe does not distort in the space domain and the Doppler frequency domain, overcoming the main lobe distortion defect of the traditional amplitude response constraint space processing method; third, when reconstructing the covariance matrix, the noise power does not need to be estimated, but is directly decomposed by eigenvalues, simplifying the processing procedure and avoiding the influence of noise power estimation error; fourth, the phase compensation method is used to convert the non-convex constraint into a convex constraint, so that the beamformer weight vector can be directly solved without being extracted from the covariance matrix of the weight vector through a complex method, reducing error introduction and improving solving efficiency and accuracy.

[0163] Embodiment three

[0164] The embodiment three of the application is a test verification of the technical effects that can be achieved by the technical scheme of the application.

[0165] The uniform linear antenna array has 30 antenna array elements, the time domain delay stage number is 20, the frequency modulated continuous wave radar frequency is 77GHz, the distance between adjacent array elements is 1 / 2 of the wavelength of the radar echo signal, and the data sample snapshot number is 10. The simulation experiment of the embodiment three of the application considers one radar echo expected signal and one interference signal, the expected signal incidence angle is , the Doppler frequency shift of the expected signal is , the beam width is , the ripple within the beam width is , the corresponding amplitude response constraint upper limit value is , the amplitude response constraint lower limit value is , the signal-to-noise ratio is -10dB, the interference signal incidence angle is , the Doppler frequency shift of the interference signal is , and the noise type is Gaussian white noise.

[0166] Using the above simulation parameters, Figure 5 the two-dimensional STAP beam pattern (three-dimensional view) of the technology of the application is given, Figure 6 the two-dimensional STAP beam pattern (space domain view) of the technology of the application is given, Figure 7 and the two-dimensional STAP beam pattern (frequency domain view) of the technology of the application is given.

[0167] As can be seen from Figure 5 , the technology of the application can form a "flat top" beam in a specific angle region forms a "flat top" main lobe and forms a clear beam at a set Doppler frequency (f0) ), thus effectively ensuring the output signal-to-interference-and-noise ratio of the beamformer. It can be seen from Figure 5 and Figure 6 that when the angle of the interference signal is equal to the angle of the desired target echo signal (θ0 ), the present application can suppress the interference in the spatial domain while the main lobe of the beam does not distort in the spatial domain. It can be seen from Figure 5 and Figure 7 that the present application can form an effective main lobe at the Doppler frequency domain of the desired target echo (f0 ) and form a deep null (up to -120 dB) at the Doppler frequency of the interference (f1 ).

[0168] Although the embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and alterations can be made thereto without departing from the principles and spirit of the present application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A spatiotemporal joint domain beamforming method for a fast-moving target scenario, characterized in that, include: A sensor array is constructed and initialization parameters are set to establish a two-dimensional space-time steering vector model. The initialization parameters include array configuration parameters, the incident angle and Doppler frequency shift parameters of the desired target echo signal and the interference signal, respectively. Based on the aforementioned space-time two-dimensional steering vector model, beam amplitude response constraints are determined by setting the parameter range of the target echo signal. The parameter range includes the angular range and Doppler frequency shift range at which the desired echo signal reaches the array antenna. The beam amplitude response constraints are used to limit the amplitude response of the beam within the preset upper and lower bounds of the angular range and Doppler frequency shift range. A space-time two-dimensional robust beamforming model is constructed based on the minimum output power criterion and the beam amplitude response constraint to solve for the beamformer weight vector; the space-time two-dimensional robust beamforming model is expressed as: stL≤|w H a(θ0,f0)|≤B,θ0∈Θ s ,f0∈F s In the formula, min represents minimizing the objective function, w represents the beamformer weight vector to be solved, and (·) H Represents the conjugate transpose, R x This is the covariance matrix of the array sample data, where a(θ0,f0) represents the space-time steering vector of the desired target echo, θ0 represents the incident angle of the desired target echo signal, and f0 is the Doppler frequency shift; Θ s F represents the angular range from which the expected echo signal will arrive at the receiving array antenna. s L represents the lower bound of the amplitude response, and B represents the upper bound of the amplitude response. st represents the constraint condition; Obtain the covariance matrix of low-sample echo data and perform eigenvalue decomposition; Eigenvalue compensation is performed on the eigenvalue diagonal matrix composed of eigenvalues, and the covariance matrix is ​​reconstructed based on the compensated eigenvalue diagonal matrix; A space-time adaptive processing model is constructed based on the reconstructed covariance matrix. The non-convex constraints in the space-time two-dimensional robust beamforming model are relaxed to obtain the initial beamformer weight vector. The beamformer weight vector is iteratively optimized through phase compensation until the error or iteration number conditions are met, and the final beamformer weight vector is obtained.

2. The spatiotemporal joint domain beamforming method for a fast-moving target scenario according to claim 1, characterized in that, The sensor array is an isotropic, uniform, linear sensor array. The array configuration parameters include the number of antenna elements M, the number of time-domain delays N, the spacing d between adjacent antenna elements, the radar echo signal wavelength λ, and the pulse repetition frequency f. s .

3. The spatiotemporal joint domain beamforming method for a fast-moving target scenario according to claim 1, characterized in that, The space-time two-dimensional steering vector model is generated by the Kronecker product operation of the spatial steering vector at the corresponding angle and the temporal steering vector with the corresponding Doppler frequency shift. The received data is described as the superposition of the target signal, interference signal and noise on the space-time two-dimensional steering vector.

4. The spatiotemporal joint domain beamforming method for a fast-moving target scenario according to claim 1, characterized in that, Obtain the covariance matrix of low-sample echo data and perform eigenvalue decomposition, including: The covariance matrix is ​​decomposed into eigenvalues ​​to obtain eigenvalues ​​and eigenvectors. An eigenvector matrix and an eigenvalue diagonal matrix are constructed based on the eigenvectors and eigenvalues; wherein the eigenvalue diagonal matrix contains eigenvalues ​​sorted by size.

5. The spatiotemporal joint domain beamforming method for a fast-moving target scenario according to claim 1, characterized in that, The covariance matrix is ​​reconstructed by eigenvalue compensation of the eigenvalue diagonal matrix, including: Based on the eigenvalues ​​of the original covariance matrix, the condition number of the covariance matrix is ​​determined; wherein the condition number of the covariance matrix is ​​determined by the ratio of the maximum value to the minimum value among the eigenvalues. The reciprocal of the condition number of the covariance matrix is ​​taken as the eigenvalue compensation factor. This factor is used to compensate for each eigenvalue in the original covariance matrix. The maximum value between the original eigenvalue and the compensated eigenvalue is then used to construct a new eigenvalue diagonal matrix, represented as follows: In the formula, λ1,λ2,...,λ MN The original covariance matrix R x The eigenvalues ​​of λ1, λ2, ..., λ2 are given. MN max{·} represents the maximum value operation, and μ is the eigenvalue compensation factor; Based on the eigenvector matrix U and the new eigenvalue diagonal matrix, the covariance matrix is ​​reconstructed as follows:

6. The spatiotemporal joint domain beamforming method for a fast-moving target scenario according to claim 1, characterized in that, The initial beamformer weight vector is obtained by relaxing the non-convex constraints in the space-time two-dimensional robust beamforming model, including: The phase corresponding to the pattern function of the desired echo signal is represented as: φ(θ0,f0)=∠{w H a(θ0,f0)} In the formula, φ(θ0,f0) is w H The phase of a(θ0,f0), ∠{·} is the phase-taking operation, and the non-convex constraint L≤|w H a(θ0,f0)| is represented as The nonconvex constraint condition |w H a(θ0,f0)|≥L relaxes to: Re{w H a(θ0,f0)}≥L The optimization problem of the initial beamformer weight vector is then expressed as: In the formula, min represents the minimum value of the objective function, w0 represents the initial value of the beamformer weight vector, and (·) H This indicates the conjugate transpose. This is the reconstructed covariance matrix, where a(θ0,f0) represents the space-time steering vector of the desired target echo, θ0 represents the incident angle of the desired target echo signal, and f0 is the Doppler frequency shift; Θ s F represents the angular range from which the expected echo signal will arrive at the receiving array antenna. s Represents the Doppler frequency shift range, L represents the lower bound of the amplitude response, and B represents the upper bound of the amplitude response; Re{·} represents the real part operation.

7. The spatiotemporal joint domain beamforming method for a fast-moving target scenario according to claim 1, characterized in that, Iterative optimization of the beamformer weight vector through phase compensation includes: Based on the beamformer weight vector of the current iteration, the phase value corresponding to the desired echo signal pattern function is calculated, and expressed as: f k (θ0,f0)=∠{w k H a(θ0,f0)},k=0,1,…,K In the formula, k represents the k-th iteration, θ0 represents the incident angle of the desired target echo signal, f0 is the Doppler frequency shift, and w k Let (·) represent the beamformer weight vector for the current k-th iteration. H denoted as conjugate transpose, a(θ0,f0) represents the space-time steering vector of the desired target echo, K represents the total number of iterations; ∠{·} is the phase taking operation; Substituting the phase value into the space-time two-dimensional beamforming model, an optimization problem including phase compensation is constructed and solved to obtain the updated beamformer weight vector, expressed as: In the formula, w k+1 This represents the currently updated beamformer weight vector, (·). H This indicates the conjugate transpose. It is the reconstructed covariance matrix; Θ s F represents the angular range from which the expected echo signal will arrive at the receiving array antenna. s L represents the Doppler frequency shift range; B represents the lower bound of the amplitude response and B represents the upper bound of the amplitude response.

8. The spatiotemporal joint domain beamforming method for a fast-moving target scenario according to claim 1, characterized in that, Iterative optimization of beamformer weight vectors through phase compensation also includes: Set an iteration error threshold γ, calculate the error between the updated beamformer weight vector and the beamformer weight vector of the previous iteration, and express it as: In the formula, w k+1 This represents the currently updated beamformer weight vector, (·). H This indicates the conjugate transpose. It is the reconstructed covariance matrix; Determine whether the error is less than or equal to the iteration error threshold γ or whether the number of iterations reaches the total number of iterations K; If the error is less than or equal to the iteration error threshold γ or the number of iterations reaches the total number of iterations, then the currently updated beamformer weight vector is taken as the final result.

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