MIMO radar beam forming method for optimizing direction vectors in multiple unascertained areas

Abstract

The invention discloses an MIMO (Multiple Input Multiple Output) radar beam forming method for optimizing direction vectors in multiple unascertained areas. The method comprises the following steps of: constructing MIMO radar signal models and constraint areas in the multiple unascertained areas; constraining beam responses of the plurality of unascertained areas, minimizing the output power of the array, and constructing an optimization model based on constraint direction vectors of the plurality of unascertained areas; the optimization model is converted into a relaxation semi-definite problem of optimization of a plurality of unascertained regions, and iterative optimization solution is carried out; and extracting a weight vector of the beam former under inaccurate direction vector estimation by adopting a characteristic decomposition rank-one regression method. The MIMO radar beam formed by the method is better in performance under the condition of serious direction vector error, the target signal received by the MIMO radar can obtain the maximum gain, interference and noise signals are effectively suppressed, and subsequent target detection is facilitated.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and further relates to a MIMO radar beamforming method for optimizing direction vectors in multiple uncertain regions in the field of radar signal processing technology. The present invention obtains the maximum gain of the target signal of the MIMO radar, which can be used to effectively suppress interference and noise signals. Background Art

[0002] The beamforming of MIMO radar refers to solving the optimal weight vector for the MIMO radar to receive the target signal, thereby maximizing the output gain of the target signal, suppressing unnecessary interference and noise signals, and obtaining target information more accurately. In order to solve the performance loss problem caused by inaccurate directional vector estimation of MIMO radar, many beamforming methods have been proposed, and these methods are robust to the directional vector estimation error. In the case of directional vector errors, there are currently two algorithms to implement MIMO radar beamforming. The first algorithm is a MIMO radar beamforming method based on the linear constrained minimum variance algorithm. This method minimizes the interference and noise output power of the array as much as possible while ensuring that the signal in the target direction passes through the spatial filter without distortion. In addition, additional linear constraints on distortion-free response are imposed to constrain the response in multiple directions near the target signal to be undistorted. The optimal solution can be obtained through the Lagrange multiplier technology. The linear constrained minimum variance algorithm can solve the problem that when there is an error in the directional vector of the target signal, the adaptive directional pattern will form a null in the desired direction. By constraining the main lobe of the beam, it is widened and flattened, eliminating the sensitivity to the directional vector estimation error. The second algorithm is a MIMO radar beamforming method based on the 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 an uncertain set. In order to ensure that the desired direction vector has a distortion-free response, this method minimizes the output power of the entire array while constraining all possible direction vectors in this uncertain set to pass through the beamformer in a conservative way, and solves the optimal weight vector through second-order cone optimization. Although the existing MIMO radar robust beamforming method has a certain degree of robustness, in a complex electromagnetic environment, the MIMO radar system estimates the direction vector inaccurately, resulting in large errors, and the performance will be severely lost.

[0003] The patent document "MIMO radar space-time-range three-dimensional joint adaptive detection method based on LCMV criterion" (patent application number: CN 202311271041.X, patent publication number: CN 117406176 A) proposes a MIMO radar beamforming method based on the linear constrained minimum variance algorithm. The implementation steps of this method are: first, the received MIMO radar element-pulse-range 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 the 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 result of the joint adaptive filtering processing output is used as the detection statistic to implement the threshold detection. However, the method still has the disadvantage that in a complex environment, for the traditional linear constrained minimum variance algorithm, due to the application of multiple constraints, a corresponding number of system degrees of freedom will be lost, which makes the radar system's ability to suppress noise and interference decrease to a certain extent.

[0004] Gao et al. proposed a MIMO radar beamforming method based on the worst performance optimization algorithm in their paper “Arobust beamforming for mimo radar against virtual array steering vector mismatch” (Electronics Letters, 2023, 5, 59-9). The implementation steps of this method are to model the error of any transmitter or receiver as a virtual array direction vector error, which simultaneously describes the errors at both ends of transmission, reception, and transmission-reception. 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 a linear optimization method. Although this method can solve the problem that the beamforming algorithm is sensitive to the direction vector estimation error, the method still has the following two shortcomings: First, the size of the uncertain set needs to be set manually. If the size is set too large or too small, it will seriously affect the beamforming performance. Second, it is difficult for a single uncertain set to accurately cover the area where the direction vector of the real target signal may exist, resulting in a decrease in the ability of beamforming to suppress interference and noise. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a MIMO radar beamforming method for optimizing direction vectors in multiple uncertain regions, so as to solve the problem that the linear constrained minimum variance algorithm in the prior art in a complex environment will lose a corresponding number of system degrees of freedom due to the application of multiple constraints, so that the radar system's ability to suppress noise and interference is reduced to a certain extent, and in a complex electromagnetic environment, the MIMO radar system estimates the direction vector inaccurately, resulting in large errors.

[0006] To achieve the above purpose, the technical idea of ​​the present invention is to establish multiple MIMO radar signal models in uncertain regions, then construct an optimization model based on multiple uncertain regions to constrain direction vectors, and transform the original optimization model into a relaxed semi-definite problem of multiple uncertain regions, and then perform iterative optimization and solution, and finally adopt the idea of ​​eigendecomposition rank-one regression to extract the beamformer weight vector under inaccurate direction vector estimation. Since the present invention constructs an optimization model based on multiple uncertain regions to constrain direction vectors, it is different from a single uncertain set that is difficult to accurately cover the area where the direction vector of the real target signal may exist. The constraint area of ​​multiple uncertain regions is more flexible and reasonable, and is no longer restricted to a single uncertain region. Only necessary areas are constrained and unreasonable areas are abandoned. Not only can the real target signal direction vector be covered, but also the problem that the size of a single uncertain set is too large to include all possible direction vectors, resulting in overly conservative constraints and weakened interference suppression capabilities is avoided. Therefore, the present invention has better performance in the case of severe direction vector errors, can achieve effective and robust MIMO radar beamforming, so that the target signal of the MIMO radar obtains maximum gain, and effectively suppresses interference and noise signals.

[0007] In order to achieve the above object, the technical solution adopted by the invention includes the following steps:

[0008] Step 1, construct multiple unascertained area MIMO radar signal models and constraint areas;

[0009] Step 2, constraining the beam responses of multiple uncertain regions, minimizing the output power of the array, and constructing an optimization model based on the constrained direction vectors of multiple uncertain regions;

[0010] Step 3, convert the optimization model into a relaxed semi-definite problem of multiple undetermined region optimization, and then perform iterative optimization to solve it;

[0011] Step 4: Take the eigendecomposition rank-one regression method to extract the weight vector of the beamformer when the direction vector estimation is inaccurate.

[0012] Furthermore, the multiple unascertained area MIMO radar signal models are as follows:

[0013]

[0014] Among them, x(t) represents the echo signal at the tth moment, α0 represents the target complex amplitude, and α k represents the complex amplitude of the kth interference signal, k = 1, 2, ..., K, K represents the number of interference signals, a t (θ0) and a r (θ0) represents the transmitting direction vector and receiving direction vector of the target space angle, a t (θ k ) and a r (θ k ) represent the transmitting direction vector and receiving direction vector of the kth interference signal angle respectively, represents the Kronecker product operation, It means the mean is 0 and the variance is Gaussian white noise.

[0015] The expressions of the transmitting direction vector and the receiving direction vector are respectively:

[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 array elements, and M t and M r denote the number of transmitting antennas and receiving antennas of MIMO radar, respectively, (·) T represents the transpose operation, M t =M r .

[0018] Furthermore, the constraint area is:

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

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

[0021] Furthermore, the optimization model based on multiple unascertained region constraint direction vectors is as follows:

[0022]

[0023] Where w represents the weight vector of the MIMO radar beamformer, It means that w is the optimization variable and the objective function (·) is minimized. H represents the conjugate transpose operation, represents the covariance matrix of received data, |·| represents the absolute value operation;

[0024] The received data covariance matrix The expression is:

[0025]

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

[0027] Furthermore, the steps of converting the optimization model into a relaxed semidefinite problem of multiple undetermined region optimization are as follows:

[0028] The first step is to convert the original objective function into Transform to a higher-dimensional subspace:

[0029]

[0030] Among them, tr(·) represents the trace operation;

[0031] In the second step, the rank-one constraint is discarded to relax the semidefinite problem, and the relaxed optimization problem model is obtained as follows:

[0032]

[0033] Among them, W l represents the weight vector obtained by semidefinite optimization after the lth iteration, W l-1 Represents the weight vector obtained after the l-1th iteration.

[0034] Furthermore, the steps of iterative optimization solution are as follows:

[0035] The first step is to select the initial value W0 of the iteration according to the following formula:

[0036]

[0037] Among them, a0 represents the target signal at (θ p -Δθ,θ p+Δθ) in a direction θ r The estimated direction vector is θ p represents the estimated target angle, and Δθ represents the angle estimation error.

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

[0039] The third step is to comprehensively consider the accuracy and execution time of the algorithm, and select the error tolerance factor ξ and the maximum number of iterations L in order to achieve a relative balance between the two. max . Determine the current iteration value W l With the previous iteration value W l-1 Is the modulus of the difference less than the error tolerance factor ξ or the number of iterations exceeds the maximum number of iterations L? max , if yes, execute step 4, otherwise, execute step 2;

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

[0041] Furthermore, the characteristic decomposition rank-one regression method refers to, according to the following formula, Perform eigendecomposition:

[0042]

[0043] in, is the optimal solution of W obtained by iteratively solving the optimization problem, rank(·) means to find the rank of the matrix, λ1,λ2,…,λ m They are , and satisfies λ1≥λ2≥…λ m >0,w1,w2,…,w m Respectively represent λ1,λ2,…,λ m The corresponding feature vector.

[0044] Furthermore, the weight vector of the MIMO radar beamformer for extracting multiple unascertained region optimization direction vectors is obtained by the following formula:

[0045]

[0046] in, Represents the optimal weight vector of a MIMO radar beamformer for multiple undetermined region-optimized direction vectors.

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

[0048] First, since the present invention constrains the beam responses of multiple uncertain areas and minimizes the output power of the array, it can reduce the data demand and has a faster computing speed, overcoming the shortcomings of the existing MIMO radar beamforming method, which reduces the radar system's ability to suppress noise and interference due to the loss of system freedom. The present invention can effectively improve the robustness of the beamformer, enable it to more accurately improve the gain of the target signal in the formed MIMO radar beam and suppress interference and noise, and is more convenient for engineering implementation.

[0049] Second, because the present invention uses multiple uncertain areas to iteratively optimize to accurately cover the uncertain areas of the direction vector when modeling the MIMO radar beamforming optimization problem, it has a more flexible and reasonable constraint area, and overcomes the disadvantage that a single uncertain set of the MIMO radar beamforming method based on the worst performance optimization algorithm is difficult to accurately cover the area where the direction vector of the real target signal may exist, resulting in a loss of radar system beamforming performance. The present invention suppresses the side lobes generated by strong targets, avoids the occlusion of adjacent weak targets, can effectively suppress clutter, and effectively reduces the sensitivity of MIMO radar beamforming to direction vector errors, thereby greatly improving the performance of the beamformer. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of an embodiment of the present invention.

[0051] Figure 2 It is the result diagram of the simulation experiment of the present invention, wherein, Figure 2 (a) is the antenna pattern of the simulation experiment 1 of the present invention, Figure 2 (b) is a graph showing the variation of output SINR with input SNR in simulation experiment 2 of the present invention. Figure 2 (c) is a graph showing the output SINR of simulation experiment 3 of the present invention changing with the number of samples. DETAILED DESCRIPTION

[0052] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

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

[0054] Reference Figure 1 , the implementation steps of the embodiment of the present invention are further described in detail.

[0055] Step 1: Establish multiple undetermined regional MIMO radar signal models.

[0056] In MIMO radar systems, in order to detect targets and obtain accurate target positions, it is necessary to process the target transmission signal and the received echo signal, including matched filtering and beamforming, so that the target signal can obtain the maximum gain and effectively suppress interference and noise signals, thereby better detecting the target. Therefore, it is critical to solve the weight vector w of the beamformer so that the beamformer remains robust to the direction vector error.

[0057] The embodiment of the present invention models the received signal of the MIMO radar, with the purpose of calculating the received data covariance matrix, which is used in iteratively solving the weight vector w in the optimization problem based on multiple uncertain regional constraint direction vectors.

[0058] The multiple unascertained area MIMO radar reception signal models established in the embodiment of the present invention include a MIMO radar reception signal model and multiple unascertained constrained area representations, which are described in detail below.

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

[0060] The transmitting direction vector and the receiving direction vector are expressed as:

[0061]

[0062] Where λ represents the wavelength of the MIMO radar system, d represents the spacing between array elements, and M t and M r Respectively represent the number of MIMO radar transmitting antennas and receiving antennas. In the embodiment of the present invention, λ=0.03m,

[0063] M t =M r =8.

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

[0065]

[0066] Among them, α0 represents the target complex amplitude, α k represents the complex amplitude of the kth interference signal, It means the mean is 0 and the variance is In the embodiment of the present invention, the value of α0 is the product of the true value of the signal-to-noise ratio SNR and a complex random matrix. k The value of is the product of the true value of the interference-to-noise ratio INR and a complex random matrix, SNR = 25dB (in simulation experiments 1 and 3), INR = 30dB,

[0067] After vectorizing the output signal, the final output signal is:

[0068]

[0069]

[0070] Among them, vec(·) represents the vectorization operation of the matrix, represents 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] Then 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 experiments 1 and 2 of the embodiment of the present invention, L=2000.

[0074] In order to filter out signals of no interest and increase the output target signal power, the final output signal of the MIMO radar needs to be beamformed. 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 for optimizing direction vectors in multiple uncertain regions.

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

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

[0077] Where w represents the weight vector of the beamformer, (·) H Represents the conjugate transpose operation.

[0078] The estimated target direction vector b(θ0) is used to adaptively solve the beamformer weight vector w. In the embodiment of the present invention, three uncertain regions are designed in the MIMO radar receiving array to cover all possible direction vectors of the real target signal and accurately maximize the target signal gain. Unlike a single uncertain set that is difficult to accurately cover the area where the direction vector of the real target signal may exist, in the embodiment of the present invention, multiple uncertain regions only constrain necessary areas and discard unreasonable areas, which can not only cover the real target signal direction vector, but also avoid the single uncertain set being too large in size to include all possible direction vectors, resulting in overly conservative constraints and weakening the performance of the beamformer.

[0079] In each uncertain region, the true target signal direction vector a is n Modeled as an estimated direction vector b n and the error direction vector r n The sum of the error direction vector r n This undetermined region can be mathematically represented as:

[0080]

[0081] Among them, ε n represents the radius of the nth undetermined region, and ||·|| represents the Euclidean modulus.

[0082] Therefore, the constrained regions for constructing multiple unascertained regional MIMO radar signals can be expressed as:

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

[0084] Among them, b n represents the estimated nth direction vector, r n Indicates b n The error vector of the corresponding uncertain region, N represents the total number of the uncertain regions. In the embodiment of the present invention, N=3, that is, 3 uncertain regions are used to constrain the direction vector.

[0085] Step 2: construct an optimization model based on multiple uncertain regional constraint direction vectors.

[0086] Based on the characterization of the constraint areas of multiple unascertained areas in the embodiment of the present invention, according to the maximum output signal-to-interference-noise ratio principle of the MIMO radar system, a beamforming optimization model based on the constraint direction vectors of multiple unascertained areas can be constructed as follows:

[0087]

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

[0089] in, Represents the covariance matrix of the received data. The constraint condition represents that the direction vector is constrained by multiple uncertain regions, and the direction vector can pass through the beamformer without distortion while minimizing the output power of the entire array.

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

[0091]

[0092] swt H b n -ε n ||w||≥1

[0093] The above formula can be equivalent to the following optimization model for multiple uncertain regional constraint direction vectors:

[0094]

[0095] Step 3: Relaxed semidefinite iterative solution of the optimization model of multiple uncertain regions of MIMO radar.

[0096] Since the absolute value operation in the above constraints cannot be directly discarded, it is impossible to convert the problem into a second-order cone optimization problem for solution. In addition, adding additional constraints will also consume more system degrees of freedom and weaken the system's interference suppression performance. In order to solve these problems, the embodiment of the present invention further proposes a solution to the beamforming optimization model by relaxed semi-definite iterative optimization based on the idea of ​​using multiple uncertain regions to iteratively optimize the target direction vector, and proposes to extract the beamformer weight vector w by adopting the idea of ​​eigendecomposition rank-one regression, so that the optimization solution process is more accurate.

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

[0098]

[0099] Where tr(·) represents the trace operation. The matrix W is defined as is a Hermitian positive semidefinite matrix, that is And the rank of the matrix W is one.

[0100] The constraint conditions in the optimization model of multiple uncertain regional constraint direction vectors obtained in step 2 are squared on both sides of the inequality to obtain the following formula:

[0101]

[0102] Based on this, the optimization problem of multiple undetermined regional constraint direction vectors of MIMO radar is transformed into the following semi-definite problem:

[0103]

[0104] because As well as the existence of the rank-one constraint rank{W}=1, the above formula is nonlinear and non-convex. Therefore, the embodiment of the present invention discards the rank-one constraint to relax the semidefinite problem and solves W by an iterative method:

[0105]

[0106] Among them, W l represents the weight vector obtained by semidefinite optimization after the lth iteration, W l-1 represents the weight vector obtained after the l-1th iteration. The initial value W0 of the iteration is selected as follows:

[0107]

[0108] Among them, a0 represents the direction vector of the target signal estimated at any time, and a0 is in (θ p -Δθ,θ p +Δθ) interval, take a direction vector of any direction, θ p represents the estimated target angle, and Δθ represents the angle estimation error. p =8°, Δθ=3°.

[0109] Specifically, the detailed iterative steps of the relaxed semidefinite iterative solution of the optimization model of multiple undetermined regions of the MIMO radar are:

[0110] Step 1: Given the error tolerance factor ξ and the maximum number of iterations L max , calculate the initial value of iteration W0;

[0111] Step 2: Through the above optimization problem, W l Perform iterative solution;

[0112] Step 3, if |||W l -W l-1 |||≤ξor l>L max, then execute step 4, otherwise, set l:=l+1 and then execute step 2;

[0113] Step 4: Take the current iteration result as the optimal solution, that is Stop iteration.

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

[0115] Step 4: Extract the beamformer weight vector by eigendecomposition rank-one regression.

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

[0117] First The characteristic decomposition of

[0118]

[0119] in, λ1,λ2,…,λ m for The eigenvalues ​​of and satisfy λ1≥λ2≥…λ m >0,w1,w2,…,w m Respectively represent λ1,λ2,…,λ m The corresponding feature vector.

[0120] The weight vector of the MIMO radar beamformer with multiple undetermined region optimization direction vectors can be extracted as:

[0121]

[0122] The weight vector extracted at this time is the optimal weight vector of the MIMO radar beamforming of multiple uncertain region optimization direction vectors.

[0123] The effect of the present invention can be further demonstrated through the following simulation experiments.

[0124] 1. Simulation experimental conditions.

[0125] The software platforms for the simulation experiment of the present invention are: Windows 10 operating system and Matlab R2021a.

[0126] 2. Analysis of simulation content and results.

[0127] There are three simulation experiments of the present invention.

[0128] 2.1 Simulation Experiment 1 is a simulation of the MIMO radar receiving antenna pattern.

[0129] The target signal direction set in the simulation experiment 1 of the present invention is 5°, and 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 present invention adopts the method of the present invention and four prior arts to obtain the normalized gain values ​​of the antenna pattern corresponding to the angle from -90° to 90°, and then plots the corresponding relationship between the obtained gain value and the angle as shown in the figure: Figure 2 (a) shows the five curves.

[0131] In simulation experiment 1, the four existing technologies used are:

[0132] Prior art 1 refers to a minimum variance distortion-free response beamforming method proposed by Capon J in his 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 beamforming method proposed by Forst OL in his paper “An algorithm for linearly constrained adaptive processing” (Proc. IEEE, 1972, 60(8): 926-935).

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

[0135] Prior art 4 refers to that Gao et al. proposed a MIMO radar beamforming method based on the worst performance optimization algorithm in their 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 simulates the relationship between the output signal-to-interference-noise ratio and the input signal-to-noise ratio of MIMO radar beamforming.

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

[0138] Simulation experiment 2 of the present invention adopts the method of the present invention and four prior arts to obtain the output signal-to-noise ratio values ​​when the input signal-to-noise ratio ranges from -10dB to 30dB, and then plots the relationship between the obtained output signal-to-noise ratio and the input signal-to-noise ratio as shown in the figure. Figure 2 (b) The five curves shown.

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

[0140] 2.3 Simulation Experiment 3 is a simulation of the signal-to-interference-noise ratio of MIMO radar beamforming output changing with the number of samples.

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

[0142] Simulation experiment 3 of the present invention adopts the method of the present invention and four prior arts to obtain the output signal-to-interference-noise ratio values ​​when the number of sample snapshots ranges from 0 to 600, and then plots the relationship between the obtained output signal-to-interference-noise ratio and the number of sample snapshots as shown in the figure: Figure 2 (c) shows the five curves.

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

[0144] Combine the following Figure 2 The simulation diagram of the present invention is further described.

[0145] Figure 2The horizontal axis of (a) represents the angle in the MIMO radar airspace, in degrees (°), and the vertical axis represents the normalized gain value of the MIMO radar to the target at the corresponding angle, in dB. In order to display the results more intuitively, the target signal angle and the interference signal angle are plotted with straight lines. Among them, the curve marked with a green solid line represents the antenna pattern gain curve simulated by prior art 1, the curve marked with a yellow dotted line represents the antenna pattern gain curve simulated by prior art 2, the curve marked with a purple dotted line represents the antenna pattern gain curve simulated by prior art 3, the curve marked with a blue dotted line represents the antenna pattern gain curve simulated by prior art 4, and the curve marked with a red solid line represents the antenna pattern gain curve simulated by the method proposed in the present invention.

[0146] from Figure 2 It can be seen from (a) that the present invention can estimate the target angle most accurately, has the largest gain on the target signal, and can form nulls in two interference directions, while the prior art method 1 and the prior art method 2 even form nulls in the main lobe.

[0147] Figure 2 The horizontal axis of (b) represents the signal-to-noise ratio of the MIMO radar system, in dB, and the vertical axis represents the output signal-to-noise ratio, in dB. The curve marked with green dots represents the output signal-to-noise ratio and input signal-to-noise ratio relationship curve obtained by simulating the prior art 1, the curve marked with a yellow plus sign represents the output signal-to-noise ratio and input signal-to-noise ratio relationship curve obtained by simulating the prior art 2, the curve marked with a purple hexagonal star represents the output signal-to-noise ratio and input signal-to-noise ratio relationship curve obtained by simulating the prior art 3, the curve marked with a blue circle represents the output signal-to-noise ratio and input signal-to-noise ratio relationship curve obtained by simulating the prior art 4, and the curve marked with a red diamond represents the output signal-to-noise ratio and input signal-to-noise ratio relationship curve obtained by simulating the method proposed in the present invention.

[0148] from Figure 2 As can be seen in (b), as the input signal-to-noise ratio increases, the prior art 1 method suppresses the target signal as interference, resulting in a significant decrease in its performance. 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 serious. The prior art 3 method and the method proposed in the present invention show good robustness to the direction vector error. However, the proposed method performs best when the input signal-to-noise ratio is high (i.e., SNR≥15).

[0149] Figure 2The horizontal axis of (c) represents the number of sample snapshots, and the vertical axis represents the output signal to noise ratio, in dB. The curve marked with a green plus sign represents the output signal to noise ratio obtained by simulating the prior art 1 with the number of samples, the curve marked with a yellow circle represents the output signal to noise ratio obtained by simulating the prior art 2 with the number of samples, the curve marked with a purple six-pointed star represents the output signal to noise ratio obtained by simulating the prior art 3 with the number of samples, the curve marked with a blue diamond represents the output signal to noise ratio obtained by simulating the prior art 4 with the number of samples, and the curve marked with a red dot represents the output signal to noise ratio obtained by simulating the method proposed in the present invention with the number of samples.

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

Claims

1. A MIMO radar beamforming method for optimizing direction vectors in multiple undetermined regions, characterized in that: The beam responses of multiple undefined regions are constrained to minimize the output power of the array. When modeling the MIMO radar beamforming optimization problem, multiple undefined regions are used for iterative optimization to accurately cover the undefined regions of the direction vector. The steps of the estimation method include the following: Step 1, construct multiple unascertained area MIMO radar signal models and constraint areas; Step 2, constraining the beam responses of multiple uncertain regions, minimizing the output power of the array, and constructing an optimization model based on the constrained direction vectors of multiple uncertain regions; Step 3, convert the optimization model into a relaxed semi-definite problem of multiple undetermined region optimization, and then perform iterative optimization to solve it; Step 4: Take the eigendecomposition rank-one regression method to extract the weight vector of the beamformer when the direction vector estimation is inaccurate.

2. The beamforming method according to claim 1, characterized in that: The multiple unascertained regional MIMO radar signal models described in step 1 are as follows: Among them, x(t) represents the echo signal at the tth moment, α0 represents the target complex amplitude, and α k represents the complex amplitude of the kth interference signal, k = 1, 2, ..., K, K represents the number of interference signals, a t (θ0) and a r (θ0) represents the transmitting direction vector and receiving direction vector of the target space angle, a t (θ k ) and a r (θ k ) represent the transmitting direction vector and receiving direction vector of the kth interference signal angle respectively, represents the Kronecker product operation, It means the mean is 0 and the variance is Gaussian white noise; The expressions of the transmitting direction vector and the receiving direction vector are respectively: Where θ represents the angle of the direction vector, λ represents the wavelength of the MIMO radar system, d represents the spacing between radar array elements, and M t and M r denote the number of transmitting antennas and receiving antennas of MIMO radar, respectively, (·) T represents the transpose operation, M t =M r .

3. The beamforming method according to claim 2, characterized in that: The constraint area described in step 1 is: E n ={a n |a n =b n +r n ,||r n ||≤ε n } Among them, E n represents the nth constraint area, a n and b n denote the true target signal direction vector and the estimated direction vector corresponding to the nth constraint area, r n Indicates b n The error vector of the corresponding nth uncertain region, ‖·‖ represents the Euclidean modulus, ε n represents the radius of the nth uncertain region, n=1,…,N, and N represents the total number of uncertain regions.

4. The beamforming method according to claim 3, characterized in that: The optimization model based on multiple undetermined region constraint direction vectors described in step 2 is as follows: Where w represents the weight vector of the MIMO radar beamformer, It means that w is the optimization variable and the objective function (·) is minimized. H represents the conjugate transpose operation, represents the covariance matrix of received data, |·| represents the absolute value operation; The received data covariance matrix The expression is: Wherein, L represents the number of sample snapshot data, and x(i) represents the i-th received signal snapshot data.

5. The beamforming method according to claim 4, characterized in that: The steps for converting the optimization model into a relaxed semidefinite problem of multiple undetermined region optimization described in step 3 are as follows: The first step is to convert the original objective function into Transform to a higher-dimensional subspace: Among them, tr(·) represents the trace operation; In the second step, the rank-one constraint is discarded to relax the semidefinite problem, and the relaxed optimization problem model is obtained as follows: Among them, W l represents the weight vector obtained by semidefinite optimization after the lth iteration, W l-1 Represents the weight vector obtained after the l-1th iteration.

6. The beamforming method according to claim 5, characterized in that: The steps of iterative optimization solution described in step 3 are as follows: The first step is to select the initial value W0 of the iteration according to the following formula: Among them, a0 represents the target signal at (θ p -Δθ,θ p +Δθ) in a direction θ r The estimated direction vector is θ p represents the estimated target angle, Δθ represents the angle estimation error; The second step is to iteratively solve W in the relaxed optimization problem model: The third step is to comprehensively consider the accuracy and execution time of the algorithm, and select the error tolerance factor ξ and the maximum number of iterations L in order to achieve a relative balance between the two. max ; Determine the current iteration value W l The value W of the previous iteration l-1 Is the modulus of the difference less than the error tolerance factor ξ or the number of iterations exceeds the maximum number of iterations L? max , if yes, execute step 4, otherwise, execute step 2; The fourth step is to take the current iterative result as the optimal solution.

7. The beamforming method according to claim 6, characterized in that: The method of feature decomposition rank-one regression in step 4 refers to, according to the following formula, Perform eigendecomposition: in, is the optimal solution of W obtained by iteratively solving the optimization problem, rank(·) means to find the rank of the matrix, λ1,λ2,…,λ m They are , and satisfies λ1≥λ2≥…λ m >0,w1,w2,…,w m Respectively represent λ1,λ2,…,λ m The corresponding feature vector.

8. The beamforming method according to claim 7, characterized in that: The weight vector of the MIMO radar beamformer for extracting multiple unascertained region optimization direction vectors in step 4 is obtained by the following formula: in, Represents the optimal weight vector of a MIMO radar beamformer for multiple undetermined region-optimized direction vectors.

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