MIMO radar beamforming method with multiple non-convex region optimized direction vectors

Abstract

The application discloses a MIMO radar beam forming method for optimizing direction vectors of multiple non-certain areas, which comprises the following steps: constructing a MIMO radar signal model and a constraint area of multiple non-certain areas; constraining the beam response of the multiple non-certain areas, minimizing the output power of an array, and constructing an optimization model of a constrained direction vector based on the multiple non-certain areas; converting the optimization model into a relaxed semi-definite problem of the multiple non-certain areas for optimization, and then iteratively optimizing and solving; and adopting a characteristic decomposition rank-one regression method to extract the weight vector of a beam former under inaccurate direction vector estimation. The MIMO radar beam formed by the application has better performance in the case of serious direction vector error, can obtain maximum gain of a target signal received by the MIMO radar, effectively suppresses interference and noise signals, and is convenient for subsequent target detection.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of radar, and more particularly to the technical field of radar signal processing, and relates to a MIMO radar beam forming method for optimizing direction vectors of multiple non-accurate regions. BACKGROUND

[0002] Beam forming of MIMO radar refers to solving the optimal weight vector of the target signal received by the MIMO radar, so as to maximize the output gain of the target signal, suppress unnecessary interference and noise signals, and more accurately obtain target information. In order to solve the performance loss problem caused by inaccurate direction vector estimation of MIMO radar, many beam forming methods have been proposed, and these methods have certain robustness to direction vector estimation error. In the case of direction vector error, there are currently two algorithms to realize the MIMO radar beam forming method. The first algorithm is a MIMO radar beam forming method based on linearly constrained minimum variance algorithm. This method ensures that the target signal passes through the spatial filter without distortion while minimizing the interference and noise output power of the array as much as possible, and additionally imposes a linear constraint of distortion-free response to constrain the response of multiple directions near the target signal without distortion. Its optimal solution can be obtained by Lagrange multiplier technique. The linearly constrained minimum variance algorithm can solve the problem that the adaptive directivity pattern will form a null in the expected direction when the direction vector of the target signal has an error, and by constraining the main lobe of the beam to be wide and flat, the sensitivity to the direction vector estimation error is eliminated. The second algorithm is a MIMO radar beam forming method based on worst performance optimization algorithm. This method models the true target signal direction vector as the sum of an estimated direction vector and an unknown error direction vector, where the error direction vector is described by a non-accurate set. In order to ensure that the expected direction vector has a distortion-free response, this method minimizes the output power of the entire array while conservatively constraining all possible direction vectors in the non-accurate set to pass through the beam former, and solves the optimal weight vector by second-order cone optimization. Although the existing MIMO radar robust beam forming method has certain robustness, when the direction vector estimation of the MIMO radar system is inaccurate in a complex electromagnetic environment, the performance will be severely lost when the error is large.

[0003] A MIMO radar beamforming method based on linearly constrained minimum variance algorithm is proposed in the patent document "MIMO radar space-time-distance three-dimensional joint adaptive detection method based on LCMV criterion" (Patent application number: CN 202311271041.X, Patent publication number: CN 117406176 A). The implementation steps of this method are as follows: first, the received MIMO radar element-pulse-distance three-dimensional echo data is disassembled into multiple "space-time-waveform" three-dimensional data matrices according to the waveform length; then, each three-dimensional data matrix is converted into a two-dimensional data matrix as the input of joint adaptive processing; then, a joint adaptive filter is constructed based on the LCMV criterion, and the two-dimensional data matrix is subjected to joint adaptive filtering processing; finally, the output result of the joint adaptive filtering processing is used as the detection statistic, and the threshold detection is implemented. However, this method still has the following shortcomings: in a complex environment, for the traditional linearly constrained minimum variance algorithm, due to the simultaneous application of multiple constraints, the corresponding number of system degrees of freedom is lost, resulting in a certain degree of decline in the noise and interference suppression ability of the radar system.

[0004] Gao et al. in their published paper "A robust beamforming for mimo radar against virtual array steering vector mismatch" (Electronics Letters, 2023, 5, 59-9) proposed a MIMO radar beamforming method based on worst performance optimization algorithm. The implementation steps of this method are as follows: the error of any transmitter or receiver is modeled as a virtual array direction vector error, which describes the error of the transmitter, receiver and both ends of the transmitter-receiver. The objective function of the MIMO radar robust beamformer is constructed by the infinite norm of the output data, and then the objective function is solved by linear optimization method. Although this method can solve the problem that the beamforming algorithm is sensitive to the direction vector estimation error, this method still has the following two shortcomings: first, the size of the non-certain set needs to be set artificially, and too large or too small size will seriously affect the beamforming performance. Second, a single non-certain set cannot accurately cover the area where the direction vector of the real target signal may exist, resulting in a decline in the ability of the beamformer to suppress interference and noise. SUMMARY

[0005] The purpose of the present application is to solve the problems of the prior art, and to provide a MIMO radar beam forming method for optimizing the direction vector of multiple non-uncertain regions, so as to solve the problem of the linear constraint minimum variance algorithm in the prior art in a complex environment, which causes a certain degree of decline in the noise and interference suppression capability of the radar system due to the loss of a corresponding number of system degrees of freedom caused by the application of multiple constraints, and the inaccurate estimation of the direction vector of the MIMO radar system in a complex electromagnetic environment, resulting in a large error.

[0006] To achieve the above-mentioned purpose, the technical idea of the present application is to establish a multiple non-uncertain region MIMO radar signal model, then construct an optimization model for constraining the direction vector based on multiple non-uncertain regions, and convert the original optimization model into a relaxed semi-definite problem for optimizing multiple non-uncertain regions, and then iteratively optimize and solve it, and finally extract the weight vector of the beam former under inaccurate direction vector estimation by using the characteristic decomposition rank-one regression method. Since the present application constructs an optimization model for constraining the direction vector based on multiple non-uncertain regions, unlike the single non-uncertain set which is difficult to accurately cover the area where the direction vector of the real target signal may exist, the constraint area of multiple non-uncertain regions is more flexible and reasonable, and is no longer limited to a single non-uncertain region, but only constrains the necessary area and discards the unreasonable area, which not only covers the real target signal direction vector, but also avoids the problem of too conservative constraints caused by the too large size of the single non-uncertain set in order to include all possible direction vectors, which weakens the ability to suppress interference. Therefore, the present application has better performance in the case of serious direction vector error, and can realize effective and robust MIMO radar beam forming, so that the target signal of the MIMO radar obtains the maximum gain, and effectively suppresses the interference and noise signals.

[0007] To achieve the above-mentioned purpose, the technical solution adopted by the present application comprises the following steps:

[0008] Step 1: constructing a multiple non-uncertain region MIMO radar signal model and a constraint region;

[0009] Step 2: constraining the beam response of multiple non-uncertain regions, minimizing the output power of the array, and constructing an optimization model for constraining the direction vector based on multiple non-uncertain regions;

[0010] Step 3: converting the optimization model into a relaxed semi-definite problem for optimizing multiple non-uncertain regions, and then iteratively optimizing and solving it;

[0011] Step 4: extracting the weight vector of the beam former under inaccurate direction vector estimation by using the characteristic decomposition rank-one regression method.

[0012] Further, the multiple non-uncertain region MIMO radar signal model is as follows:

[0013]

[0014] Where x(t) represents the echo signal at time t, α0 represents the target complex amplitude, and α k Let a represent the complex amplitude of the k-th interfering signal, k = 1, 2, ..., K, where K represents the number of interfering signals. t (θ0) and a r (θ0) represent the transmit direction vector and receive direction vector of the target space angle, respectively, a t (θ k ) and a r (θ k () represents the transmit direction vector and receive direction vector of the k-th interference signal angle, respectively. This represents the Kronecker product operation. This indicates that the mean is 0 and the variance is 0. Gaussian white noise.

[0015] The expressions for the transmit direction vector and the receive direction vector are as follows:

[0016]

[0017] Where θ represents the angle of the direction vector, λ represents the wavelength of the MIMO radar system, d represents the spacing between radar elements, and M t and M r These represent the number of transmit antennas and receive antennas for the MIMO radar, respectively. T M represents the transpose operation. t =M r .

[0018] Furthermore, the constrained region is:

[0019] E n ={a n |a n =b n +r n ,||r n ||≤ε n}

[0020] Among them, E n Let a represent the nth constraint region. n and b n Let r represent the true target signal direction vector and the estimated direction vector corresponding to the nth constraint region, respectively. n b n The error vector corresponding to the nth unknown region, ||·|| represents the Euclidean modulus, ε n Let n represent the radius of the nth unknown region, where n = 1, ..., N, and N represents the total number of unknown regions.

[0021] Further, the optimization model based on multiple non-convex region constraints direction vector is as follows:

[0022]

[0023] wherein w represents the weight vector of MIMO radar beamformer, represents taking minimization operation on the target function (·) with w as optimization variable, (·) H represents conjugate transpose operation, represents received data covariance matrix, |·| represents taking absolute value operation;

[0024] The expression of the received data covariance matrix is as follows:

[0025]

[0026] wherein L represents the number of sample snapshot data, x(i) represents the i-th received signal snapshot data.

[0027] Further, the step of converting the optimization model into multiple non-convex region optimization relaxation semi-definite problem is as follows:

[0028] Firstly, the original target function is transformed to high-dimensional subspace according to the following formula:

[0029]

[0030] wherein tr(·) represents trace operation;

[0031] Secondly, the rank-one constraint is discarded to relax the semi-definite problem, and the relaxed optimization problem model is as follows:

[0032]

[0033] wherein W l represents the weight vector obtained by solving the above formula through semi-definite optimization after the l-th iteration, W l-1 represents the weight vector obtained through the (l-1)-th iteration.

[0034] Further, the step of iterative optimization solution is as follows:

[0035] Firstly, the initial value W0 of iteration is selected according to the following formula:

[0036]

[0037] wherein a0 represents the target signal in (θ p -Δθ, θ pA direction θ is selected within the interval +Δθ) r The estimated direction vector, i.e. θ p Δθ represents the estimated target angle, and Δθ represents the angle estimation error.

[0038] The second step is to iteratively solve for W in the relaxed optimization problem model:

[0039] The third step involves comprehensively considering both the algorithm's accuracy and execution time, aiming to achieve a relative balance between the two, and selecting the error tolerance factor ξ and the maximum number of iterations L. max Determine the current iteration value W. l Compared with the previous iteration value W l-1 Is the magnitude of the difference less than the error tolerance factor ξ, or does the number of iterations exceed the maximum number of iterations L? max If yes, proceed to step four; otherwise, proceed to step two.

[0040] The fourth step is to take the result of the current iteration as the optimal solution.

[0041] Furthermore, the eigenvalue decomposition rank-one regression method refers to, according to the following formula, performing... Perform eigenvalue decomposition:

[0042]

[0043] in, To find the optimal solution to W obtained by iteratively solving the optimization problem. rank(·) denotes the rank of a matrix, where λ1, λ2, ..., λ m They are respectively The eigenvalues ​​satisfy λ1≥λ2≥…λ m >0, w1,w2,…,w m Representing λ1, λ2, ..., λ respectively m The corresponding feature vectors.

[0044] Furthermore, the weight vector of the MIMO radar beamformer that extracts optimized direction vectors for multiple unknown regions is obtained by the following formula:

[0045]

[0046] in, The optimal weight vector represents the optimized direction vector of a MIMO radar beamformer for multiple unknown regions.

[0047] Compared with the prior art, the present invention has the following advantages:

[0048] Firstly, the application can reduce the demand of data, has faster operation speed, overcomes the shortcomings of the prior art MIMO radar beam forming method, i.e., the loss of system freedom degree, the decline of the noise and interference suppression capability of the radar system, effectively improves the robustness of the beam former, more accurately improves the gain of the target signal in the MIMO radar beam forming and suppresses the interference and noise, and is more convenient for engineering implementation.

[0049] Secondly, the application has more flexible and reasonable constraint regions, overcomes the shortcomings of the prior art MIMO radar beam forming method based on the worst performance optimization algorithm, i.e., the single non-accurate set is difficult to accurately cover the possible region of the direction vector of the real target signal, causes the performance loss of the radar system beam forming, suppresses the sidelobe generated by the strong target, avoids the shielding of the adjacent weak target, effectively suppresses the clutter, effectively reduces the sensitivity of the MIMO radar beam forming to the direction vector error, and greatly improves the performance of the beam former. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 The flow chart of the embodiment of the application.

[0051] Figure 2 The result chart of the simulation experiment of the application. Figure 2 (a) is the antenna directional diagram of the simulation experiment 1 of the application, Figure 2 (b) is the chart of the change of the output SINR with the input SNR of the simulation experiment 2 of the application, Figure 2 (c) is the chart of the change of the output SINR with the sample number of the simulation experiment 3 of the application. DETAILED DESCRIPTION

[0052] The application will be further described in detail below in combination with the drawings and embodiments.

[0053] The MIMO radar transmitting and receiving arrays of the embodiment of the application are both uniform linear arrays, the number of array elements is 8, and the array element spacing is half wavelength.

[0054] Reference Figure 1 The implementation steps of the embodiment of the application will be further described in detail.

[0055] Step 1, establishing a plurality of non-accurate region MIMO radar signal model.

[0056] In MIMO radar system, in order to carry out target detection, obtain accurate target position, need to the target transmission signal, to the received echo signal processing, including matching filter, beam forming etc., can make target signal obtain maximum gain, and effectively suppress interference and noise signal, so as to better detect target. Therefore, the weight vector w of the beam former is solved, and the beam former is kept robust to the direction vector error.

[0057] The embodiment of the application models the received signal of MIMO radar, and aims to calculate the received data covariance matrix, which is used in the iterative solution of the weight vector w in the optimization problem based on multiple non-certainty region constraints on the direction vector.

[0058] The multiple non-certainty region MIMO radar received signal model established by the embodiment of the application comprises a MIMO radar received signal model and multiple non-certainty constraint region representations, which are described below.

[0059] In MIMO radar system, the target is located at the spatial angle θ0, and K interference signals are respectively located at the spatial angles θ k (k=1,2,...,K), θ i , i=0, 1,..., K. In the embodiment of the application, θ0=5°, K=2, θ1=-20°, and θ2=30°.

[0060] The transmit direction vector and the receive direction vector are respectively represented as:

[0061]

[0062] Wherein, λ represents the wavelength of the MIMO radar system, d represents the interval between the array elements, M t and M r respectively represent the number of MIMO radar transmitting antennas and receiving antennas. In the embodiment of the application, λ=0.03m,

[0063] M t =M r =8.

[0064] After the entire MIMO radar received echo signal is matched filtered, the output signal is obtained as:

[0065]

[0066] Wherein, α0 represents the target complex amplitude, α k represents the complex amplitude of the kth interference signal, represents the complex amplitude of the kth interference signal, Gaussian white noise. In the embodiment of the present application, the value of α0is the product of the true value of signal-to-noise ratio SNR and a complex random matrix, α k The value of α0is the product of the true value of signal-to-noise ratio SNR and a complex random matrix, SNR = 25 dB (in simulation experiment 1 and simulation experiment 3), INR = 30 dB,

[0067] After the output signal is processed by vectorization, the final output signal is obtained as follows:

[0068]

[0069]

[0070] wherein vec(·) represents the vectorization operation of a matrix, denotes the Kronecker product operation, i = 0, 1, …, K represents the virtual direction vector of the MIMO radar. is the output of the noise after matched filtering.

[0071] The received data covariance matrix is:

[0072]

[0073] wherein L represents the number of sample snapshot data, and x(i) represents the i-th received signal snapshot data. In simulation experiment 1 and simulation experiment 2 of the embodiment of the present application, L = 2000.

[0074] In order to filter out the signals that are not of interest and improve the output target signal power, the MIMO radar final output signal needs to be processed by beamforming. How to establish an optimization problem model and then solve the weight vector w of the MIMO radar adaptive beamformer is the core of the MIMO radar beamforming method of multiple non-certain area optimization direction vectors.

[0075] The output signal of the beamformer can be expressed as:

[0076] y(t) = w H x(t)

[0077] wherein w represents the weight vector of the beamformer, and (·) H denotes the conjugate transpose operation.

[0078] Adaptive solution of beamformer weight vector w will use the estimated target direction vector b(θ0). Embodiments of the present invention design three non-certainty regions in MIMO radar receiving array to cover all possible direction vectors of real target signal, and accurately make target signal obtain maximum gain. Unlike single non-certainty set which is difficult to accurately cover the area where the possible direction vectors of real target signal exist, multiple non-certainty regions in embodiments of the present invention only constrain necessary area and discard unreasonable area, which not only can cover the direction vector of real target signal, but also avoid the situation that single non-certainty set is too large in size to cause too conservative constraint and weaken the performance of beamformer in order to include all possible direction vectors.

[0079] In each non-certainty region, the direction vector a n of real target signal is modeled as the sum of estimated direction vector b n and error direction vector r n , and error direction vector r n is a random vector with zero mean and covariance matrix R. Mathematical representation of this non-certainty region is as follows:

[0080]

[0081] wherein ε n represents the radius of the nth non-certainty region, and ||·|| represents Euclidean norm.

[0082] Therefore, the constraint region of MIMO radar signal with multiple non-certainty regions can be represented as:

[0083] E n = {a n |a n = b n + r n ,||r n ||≤ ε n}, n = 1, …, N

[0084] wherein b n represents the estimated nth direction vector, r n represents the error vector of the non-certainty region corresponding to b n , and N represents the total number of non-certainty regions. In embodiments of the present invention, N = 3, i.e. three non-certainty regions are used to constrain direction vector.

[0085] Step 2, construction of optimization model based on multiple non-certainty region constraint direction vector.

[0086] Based on the representation of constraint region of multiple non-certainty regions in embodiments of the present invention, the beamforming optimization model based on multiple non-certainty region constraint direction vector can be constructed as follows according to the principle of maximum output signal-to-interference-and-noise ratio of MIMO radar system:

[0087]

[0088] s.t.|w H (b n +r n )|≥1,for all r n ∈E n

[0089] where, denotes the received data covariance matrix.The constraint condition indicates that the direction vector is constrained by multiple non-certain regions, and the direction vector can pass through the beamformer without distortion by multiple non-certain regions while minimizing the overall array output power.

[0090] The semi-infinite constraint of the above formula is converted into a single constraint, and the above formula can be transformed into the following optimization model by the rotation invariance of the weight vector w:

[0091]

[0092] s.t.w H b n -ε n ||w||≥1

[0093] The above formula can be equivalent to the following optimization model of constraining the direction vector by multiple non-certain regions:

[0094]

[0095] Step 3, relaxation semi-definite iterative solution of the MIMO radar multiple non-certain region optimization model.

[0096] Since the absolute value operation in the above constraint condition cannot be directly discarded, the problem cannot be converted into a second-order cone optimization problem for solving. In addition, adding additional constraint conditions will consume more system degrees of freedom and weaken the performance of the system in suppressing interference. In order to solve these problems, the embodiment of the application further proposes a relaxation semi-definite iterative optimization solution for solving the solution of the beamforming optimization model on the basis of the idea of using multiple non-certain regions to iteratively optimize the target direction vector, and proposes to extract the beamformer weight vector w by using the idea of characteristic decomposition rank-one regression, so that the optimization solving process is more accurate.

[0097] By substituting the weight vector w as follows, the original objective function can be transformed into a high-dimensional subspace:

[0098]

[0099] wherein tr(·) denotes the trace operation. The matrix W is defined as is a Hermitian semi-definite matrix, that is and the rank of the matrix W is one.

[0100] Taking square of the constraint condition of the optimization model of the plurality of non-certain area constraint direction vectors obtained in step 2 on both sides of the inequality, the following formula is obtained:

[0101]

[0102] Accordingly, the optimization problem of the plurality of non-certain area constraint direction vectors of the MIMO radar is converted into the following semi-definite problem:

[0103]

[0104] Since and the existence of the rank-one constraint rank{W}=1, the above formula is nonlinear and non-convex. Therefore, the embodiment of the present application discards the rank-one constraint, relaxes the semi-definite problem, and solves W through an iterative method:

[0105]

[0106] wherein, W l represents the weight vector obtained by solving the above formula through semi-definite optimization after the lth iteration, W l-1 represents the weight vector obtained after the (l-1)th iteration. The initial value W0 of the iteration is selected as follows:

[0107]

[0108] wherein, a0 represents the direction vector of an arbitrary order estimation of the target signal, a0 is a direction vector in an arbitrary direction in the interval (θ p -Δθ, θ p +Δθ), θ p represents the estimated target angle, and Δθ represents the angle estimation error. In the embodiment of the present application, θ p =8° and Δθ=3°.

[0109] Specifically, the detailed iterative steps of the relaxed semi-definite iterative solution of the plurality of non-certain area optimization model of the MIMO radar are as follows:

[0110] Step 1, given the error tolerance factor ξ and the maximum iteration step number L max , calculate the initial iteration value W0;

[0111] Step 2, solve W l through the above optimization problem by iteration;

[0112] Step 3, if |||W l -W l-1 |||≤ξ or l>L maxIf yes, go to step 4, otherwise, let l:=l+1 and go to step 2;

[0113] Step 4, take the current iteration result as the optimal solution, i.e. Stop iteration.

[0114] In the embodiment of the application, ξ=10 -8 , L max =100.

[0115] Step 4, eigenvalue decomposition rank-one regression extraction of the beamformer weight vector.

[0116] According to the optimal solution determined in the last step the optimal weight vector needs to be extracted from it Since the rank-one constraint is discarded in the relaxation process in the last step, the obtained solution may not satisfy the rank-one constraint. Therefore, the embodiment of the application adopts the idea of eigenvalue decomposition rank-one regression to extract the optimal weight vector

[0117] First, eigenvalue decomposition of is as follows

[0118]

[0119] wherein, λ1,λ2,…,λ m are eigenvalues of and satisfy λ1≥λ2≥…λ m >0, w1,w2,…,w m respectively represent eigenvectors corresponding to λ1,λ2,…,λ m .

[0120] The weight vector of the MIMO radar beamformer of the plurality of non-uncertain area optimization direction vectors can be extracted as:

[0121]

[0122] At this time, the extracted weight vector is the optimal weight vector of the MIMO radar beamformer of the plurality of non-uncertain area optimization direction vectors.

[0123] The effect of the application can be further proved by the following simulation experiment.

[0124] 1. Simulation experiment conditions.

[0125] The software platform of the simulation experiment of the application is: Windows 10 operating system and Matlab R2021a.

[0126] 2. Simulation content and result analysis.

[0127] The simulation experiment of the application has three.

[0128] 2.1 The simulation experiment 1 is the simulation of the MIMO radar receiving antenna directional diagram.

[0129] The target signal direction of the simulation experiment 1 of the application is 5°, the error angle is 3°, that is, the estimated direction is 8°, and the two interference directions are-20° and 30° respectively.

[0130] The simulation experiment 1 of the application is to obtain the normalized gain value of the antenna directional diagram corresponding to the angle from-90° to 90° by using the method of the application and four prior arts respectively, and then draw the corresponding relationship between the obtained gain value and the angle into five curves as shown in Figure 2 (a).

[0131] In the simulation experiment 1, the four prior arts used are:

[0132] Prior art 1 refers to a minimum variance distortionless response beam forming method proposed by Capon J in the paper “High-resolution frequency-wavenumber spectrum analysis” (Proceedings of the IEEE, 1969, 57(8): 1408-1418).

[0133] Prior art 2 refers to a linearly constrained minimum variance beam forming method proposed by Forst O L in the paper “An algorithm for linearly constrained adaptive processing” (Proc. IEEE, 1972, 60(8): 926-935.).

[0134] Prior art 3 refers to a robust beam forming method based on eigen subspace projection proposed by Lee C C et al. in the paper “Eigenspace-based adaptive array beamforming with robust capabilities” (IEEE Transactions on Antennas and Propagation, 1997, 45(12): 1711-1716.).

[0135] The prior art 4 refers to the MIMO radar beam forming method based on the worst performance optimization algorithm proposed by Gao et al. in the published paper "A robust beamforming for mimoradar against virtual array steering vector mismatch" (Electronics Letters, 2023, 5, 59-9).

[0136] 2.2 Simulation experiment 2 is a simulation of the relationship between the output signal-to-interference-and-noise ratio and the input signal-to-noise ratio of MIMO radar beam forming.

[0137] The target signal direction, error angle size and interference direction used in simulation experiment 2 of the present application are the same as those in simulation experiment 1.

[0138] In simulation experiment 2 of the present application, the method of the present application and four prior arts are used to obtain the output signal-to-interference-and-noise ratio values when the input signal-to-noise ratio is from -10 dB to 30 dB, and then the relationship between the obtained output signal-to-interference-and-noise ratio and the input signal-to-noise ratio is plotted as five curves as shown in Figure 2 (b).

[0139] In simulation experiment 2, the four prior arts used are the same as those in simulation experiment 1.

[0140] 2.3 Simulation experiment 3 is a simulation of the change of the output signal-to-interference-and-noise ratio of MIMO radar beam forming with the sample number.

[0141] The target signal direction, error angle size and interference direction used in simulation experiment 3 of the present application are the same as those in simulation experiment 1.

[0142] In simulation experiment 3 of the present application, the method of the present application and four prior arts are used to obtain the output signal-to-interference-and-noise ratio values when the sample snapshot number is from 0 to 600, and then the relationship between the obtained output signal-to-interference-and-noise ratio and the sample snapshot number is plotted as five curves as shown in Figure 2 (c).

[0143] In simulation experiment 3, the four prior arts used are the same as those in simulation experiment 1.

[0144] The effects of the present application will be further described below in combination with the simulation graphs. Figure 2

[0145] Figure 2 ​The abscissa of (a) represents the angle in the MIMO radar space, in degree (°), and the ordinate represents the normalized gain value of the MIMO radar to the target at the corresponding angle, in dB. In order to more intuitively show the results, the target signal angle and the angle of the interference signal are drawn with straight lines. The curve marked with a green solid line represents the antenna pattern gain curve simulated by using the prior art 1, the curve marked with a yellow dashed line represents the antenna pattern gain curve simulated by using the prior art 2, the curve marked with a purple dashed line represents the antenna pattern gain curve simulated by using the prior art 3, the curve marked with a blue dashed line represents the antenna pattern gain curve simulated by using the prior art 4, and the curve marked with a red solid line represents the antenna pattern gain curve simulated by using the method proposed in the present application.

[0146] From Figure 2 As can be seen from (a), the present application can most accurately estimate the target angle, and has the maximum gain to the target signal, and can form nulls in two interference directions. The prior art 1 method and the prior art 2 method even form nulls in the main lobe.

[0147] Figure 2 The abscissa of (b) represents the signal-to-noise ratio of the MIMO radar system, in dB, and the ordinate represents the output signal-to-interference-and-noise ratio, in dB. The curve marked with a green dot represents the output signal-to-interference-and-noise ratio versus input signal-to-noise ratio relationship curve simulated by using the prior art 1, the curve marked with a yellow plus sign represents the output signal-to-interference-and-noise ratio versus input signal-to-noise ratio relationship curve simulated by using the prior art 2, the curve marked with a purple hexagram represents the output signal-to-interference-and-noise ratio versus input signal-to-noise ratio relationship curve simulated by using the prior art 3, the curve marked with a blue circle represents the output signal-to-interference-and-noise ratio versus input signal-to-noise ratio relationship curve simulated by using the prior art 4, and the curve marked with a red diamond represents the output signal-to-interference-and-noise ratio versus input signal-to-noise ratio relationship curve simulated by using the method proposed in the present application.

[0148] From Figure 2 As can be seen from (b), as the input signal-to-noise ratio increases, the prior art 1 method suppresses the target signal as interference, thereby causing a significant performance decline. Among the other methods, the robustness of the prior art 2 and prior art 4 methods is slightly better than that of the prior art 1 method, but the performance loss is also very serious. The prior art 3 method and the method proposed in the present application exhibit good robustness to the direction vector error. However, the proposed method has the best performance at high input signal-to-noise ratio (i.e., SNR≥15).

[0149] Figure 2The abscissa of (c) represents the sample snapshot number, and the ordinate represents the output signal-to-interference-and-noise ratio in dB. The curve marked with a green plus sign represents the output signal-to-interference-and-noise ratio curve obtained by simulation using the prior art 1, the curve marked with a yellow circle represents the output signal-to-interference-and-noise ratio curve obtained by simulation using the prior art 2, the curve marked with a purple hexagonal star represents the output signal-to-interference-and-noise ratio curve obtained by simulation using the prior art 3, the curve marked with a blue diamond represents the output signal-to-interference-and-noise ratio curve obtained by simulation using the prior art 4, and the curve marked with a red dot represents the output signal-to-interference-and-noise ratio curve obtained by simulation using the method proposed in the present application.

[0150] From Figure 2 As can be seen from (c), the prior art 1 method is very sensitive to the sample number, and the performance significantly deteriorates as the sample number increases. The prior art 2 and prior art 4 methods have certain robustness to the sample number. However, the prior art 3 method and the method proposed in the present application exhibit stronger robustness to the sample number. In terms of convergence speed, except that the prior art 1 method is slower, the convergence speeds of the other methods are roughly the same.

Claims

1. A MIMO radar beamforming method for optimizing direction vectors in multiple unknown regions, characterized in that, By constraining the beam response of multiple uncertain regions and minimizing the array's output power, this method utilizes multiple uncertain regions for iterative optimization to accurately cover the uncertain regions of the direction vector when modeling the MIMO radar beamforming optimization problem. The steps of this method include the following: Step 1: Construct multiple MIMO radar signal models and constrained regions for unknown areas; Step 2: Constrain the beam response of multiple unknown regions, minimize the array output power, and construct an optimization model based on the constrained direction vectors of multiple unknown regions; Step 3: Transform the optimization model into a relaxed semidefinite problem involving optimization of multiple unknown regions, and then perform iterative optimization to solve it. Step 4: Use the eigenvalue decomposition and rank-one regression method to extract the weight vector of the beamformer when the direction vector estimation is inaccurate; The eigenvalue decomposition rank-one regression method refers to, according to the following formula, performing... Perform eigenvalue decomposition: ， in, This represents the result obtained by iteratively solving the optimization problem. The optimal solution. , This indicates finding the rank of a matrix. They are respectively eigenvalues, and satisfying , Respectively represent and Corresponding feature vectors; The weight vector is obtained by the following formula: ， in, The optimal weight vector represents the optimized direction vector of a MIMO radar beamformer for multiple unknown regions.

2. The beamforming method according to claim 1, characterized in that, The multiple MIMO radar signal models for unknown regions mentioned in step 1 are as follows: ， in, Indicates the first Echo signal at each moment Indicates the target complexity. Indicates the first The complex amplitude of an interference signal, , Indicates the number of interfering signals. and These represent the transmit direction vector and receive direction vector, respectively, representing the target space angle. and They represent the first The transmit direction vector and receive direction vector of each interference signal angle. This represents the Kronecker product operation. This indicates that the mean is 0 and the variance is 0. Gaussian white noise; The expressions for the transmit direction vector and the receive direction vector are as follows: ， ， in, Angle representing the direction vector, Indicates the wavelength of the MIMO radar system. Indicates the spacing between radar array elements. and These represent the number of transmit antennas and receive antennas of the MIMO radar, respectively. This indicates the transpose operation. .

3. The beamforming method according to claim 2, characterized in that, The constrained region mentioned in step 1 refers to the region within which the true target signal direction vector is located. Modeled as estimated direction vector With error direction vector The sum of, and the error direction vector This uncertain region can be mathematically represented as follows: ,in, Indicates the first The radius of a non-known region Let Euclidean mode be represented; therefore, the constrained region for constructing multiple uncertain MIMO radar signals is represented as: ,in, Indicates the first A constrained region, and Respectively represent the first The true target signal direction vector and the estimated direction vector corresponding to each constrained region. express The corresponding number Error vector of an unknown region Represents the Euclidean model. Indicates the first The radius of a non-known region , This represents the total number of regions that are not known.

4. The beamforming method according to claim 3, characterized in that, The optimization model based on multiple unknown region constraint direction vectors described in step 2 is as follows: ， in, This represents the weight vector of the MIMO radar beamformer. Indicates To optimize the variables, the objective function is adjusted. Perform the minimize operation. This indicates the conjugate transpose operation. This represents the covariance matrix of the received data. This indicates the absolute value operation; The received data covariance matrix The expression is: ， in, This indicates the number of sample snapshots. This represents the snapshot data of the i-th received signal.

5. The beamforming method according to claim 4, characterized in that, The steps described in step 3 for transforming the optimization model into a relaxed semidefinite problem involving optimization of multiple unknown regions are as follows: The first step is to convert the original objective function according to the following formula. Transform to a higher-dimensional subspace: ， in, This indicates the trace operation; The second step is to relax the semidefinite problem by discarding the rank-one constraint, resulting in the relaxed optimization problem model: ， in, Indicates after the first After several iterations, the weight vector obtained from the above equation is solved by semidefinite optimization. Indicates after the first The weight vector obtained in the next iteration.

6. The beamforming method according to claim 5, characterized in that, The iterative optimization solution steps described in step 3 are as follows: The first step is to select the initial value for the iteration according to the following formula. : ， in, Indicates the target signal at A direction selected within the interval The estimated direction vector, i.e. , Indicates the estimated target angle. This indicates the angle estimation error; The second step is to process the relaxed optimization problem model... Perform iterative solution: The third step involves comprehensively considering both the algorithm's accuracy and execution time, aiming to achieve a relative balance between the two, and selecting an error tolerance factor. and maximum number of iterations Determine the current iteration value Compared with the previous iteration value Is the modulus of the difference less than the error tolerance factor? Or the number of iterations exceeds the maximum number of iterations. If yes, proceed to step four; otherwise, proceed to step two. The fourth step is to take the result of the current iteration as the optimal solution.

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