A planar array FDA-MIMO radar main lobe interference suppression method

Abstract

The application discloses a planar array FDA-MIMO radar main lobe interference suppression method, and the Capon technology is used to estimate target signal power to dynamically adjust a DL loading factor; based on eigenvalue distribution of a sample covariance matrix, an adaptive subspace dimension selection strategy is introduced to balance robustness and main lobe suppression performance under different mismatch conditions; the beamformer can adjust the projection subspace and the diagonal loading coefficient according to actual conditions, and can solve the mismatch problem of the steering vector caused by the distance-angle error, the array element position error, the frequency offset and the coherent local scattering, effectively suppress the main lobe interference while improving the beam robustness, obtain better SINR performance, and has wide application value and promotion prospect.

Description

Technical Field

[0001] This invention belongs to the field of radar technology and mainly relates to a method for suppressing main lobe interference in a planar array FDA-MIMO radar. Background Technology

[0002] With the rapid development of electronic countermeasures technology, modern radar systems face increasingly complex jamming threats. Deceptive jamming, in particular, uses digital radio frequency storage technology to scale, delay, modulate, and retransmit intercepted radar signals to generate false targets. Dense jamming is then superimposed on these false targets, severely impacting target detection performance. Especially when the jamming signal falls within the radar's main lobe, traditional sidelobe suppression methods are ineffective, making main lobe jamming suppression a key challenge in radar anti-jamming research.

[0003] Frequency Diverse Array (FDA) radar, as a promising technology, introduces small frequency increments between transmit elements, providing additional degrees of freedom in the range dimension, making beam pattern design more flexible and aiding in interference suppression. Furthermore, integrating a Multiple Input Multiple Output (MIMO) architecture into the FDA system to form FDA-MIMO radar not only achieves higher spatial resolution but also possesses multi-dimensional beam control capabilities, thus showing potential advantages in main lobe interference scenarios. However, existing FDA-MIMO beamforming technology for main lobe interference suppression still has several limitations: (1) Guide vector mismatch problem: The beam pointing vector depends on both angle and distance. Mismatch caused by distance-angle coupling will significantly reduce beamforming performance. (2) Insufficient suppression of main lobe interference: Under strong main lobe interference, traditional side lobe suppression and fixed diagonal loading methods are difficult to effectively suppress interference signals; (3) Fixed parameter limitation: Most diagonal loading strategies rely on fixed or empirical parameters and lack the ability to adapt to dynamic environments and interference conditions. (4) Limitations of existing subspace constraint methods: Traditional subspace constraints are mostly for phased array designs that depend only on angles, and are difficult to cope with the spatial nonstationarity and non-shift invariance of FDA-MIMO. These characteristics make traditional DL and subspace methods ineffective when directly applied to FDA-MIMO architecture.

[0004] Therefore, researching a beamforming method that can effectively tolerate steering vector mismatch, enhance main lobe interference suppression, and has adaptive capabilities has significant theoretical and engineering application value. Summary of the Invention

[0005] To overcome the problem of steering vector mismatch in traditional beamforming methods under conditions of range-angle error, element position deviation, frequency offset mismatch, and coherent scattering, this invention provides a main lobe interference suppression method for planar array FDA-MIMO radar. This invention effectively improves beamforming robustness by introducing an adaptive mechanism in subspace construction and loading factor adjustment, achieving efficient suppression of main lobe interference in complex electromagnetic interference environments, thereby significantly enhancing the radar system's anti-interference capability. Unlike traditional methods that rely on fixed or empirically tuned DL factors, this invention dynamically adjusts the DL loading factor by estimating the target signal power using Capon technology. This power calculation considers the range-angle dependence and spatial non-stationarity of the FDA-MIMO radar beam steering vector. Furthermore, based on the eigenvalue distribution of the sample covariance matrix, an adaptive subspace dimension selection strategy is introduced to balance robustness and main lobe suppression performance under different mismatch conditions. By jointly optimizing the subspace and diagonal loading factor in FDA-MIMO scenarios, the proposed method achieves effective main lobe interference suppression and superior SINR performance even in the presence of main lobe interference and steering vector mismatch.

[0006] A method for suppressing main lobe interference in a planar array FDA-MIMO radar includes the following steps: Step 1: Construct a frequency diversity array for the antenna elements of the FDA-MIMO radar transmitter; Assuming the FDA-MIMO radar transmitter is... It consists of several transmitting elements, which are evenly arranged. The transmitting array elements form a frequency diversity array on a two-dimensional plane; the element spacing between the transmitting array elements is... The radar's transmitting and receiving elements are co-located. and These represent the row and column indices of any two different array elements in the transmitting array; For receiving array element number OK The column's receiver element index; where the frequency step size between each transmitter element is... Frequency step size Much smaller than the reference operating carrier frequency of the transmitting array element ;No. m OK n The frequency of the signal transmitted by the array's transmitting elements is ;No. m OK n The signal transmitted by the array of transmitting elements Any two different launch array elements and The corresponding baseband pulse signals satisfy the orthogonality condition; Step 2: Configure the transmitter to set the transmission signal frequency for each transmitting element. After determining the spacing between array elements, a signal is transmitted towards the target to be detected; based on the echo signal received by the receiver, the interfering received signal, and the Gaussian noise, the total received signal is determined. ; Step 3: Based on the acquired total received signal To minimize the output power while maintaining the undistorted gain of the target direction, the initial beamforming weights based on minimum variance distortionless response (MVDR) are obtained. Step 4: Based on the initial beamforming weights, in the subspace with dimension... S The minimum variance distortionless response problem is resolved within the subspace to obtain the subspace-constrained beamforming weight vector.

[0007] Furthermore, the step of obtaining the subspace-constrained beamforming weight vector is as follows: Let the subspace basis matrix be , S If the subspace dimension is given, then the beamforming weight vector... for:

[0008] in, It is a low-dimensional weighted vector within the subspace, used to describe the potential mismatch effect of the steering vector; To obtain the low-dimensional weight vector in the optimal subspace The beamforming problem is transformed into a constrained optimization problem:

[0009] Among them, superscript It is the conjugate transpose operation. For a limited number of snapshots K The sample covariance matrix, The subspace dimension is S The subspace basis matrix, As a diagonal loading factor, Let be the identity matrix, and arg(.) be the phase angle of the complex number. For the transmit-receive joint steering vector, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane represents the angle between the target to be detected and the horizontal plane in the vertical plane; The goal of transforming the beamforming problem into a constrained optimization problem is to minimize the weighted output power while keeping the gain in the direction of the target undistorted. By solving the constrained optimization problem, the subspace beamforming weight vector in closed-form solution is obtained. :

[0010] in It is the projection matrix, defined as:

[0011] Among them, superscript It is the conjugate transpose operation. The subspace dimension is S The subspace basis matrix, This is a diagonal loading factor used to enhance the stability of the covariance matrix. It is the identity matrix. For a limited number of snapshots K The sample covariance matrix.

[0012] Furthermore, in the step of obtaining the subspace-constrained beamforming weight vector, the diagonal loading factor is... Make corrections to obtain the estimated value of the diagonal loading factor. The process is as follows: Diagonal loading factor estimate for:

[0013] in: The noise power is an estimate derived from the sample covariance matrix. The minimum eigenvalue is obtained, that is... , For a limited number of snapshots K The sample covariance matrix, This is an estimate of the diagonal loading factor; For the corresponding point, the transmit-receive joint steering vector, It indicates its energy, reflecting the array's nominal gain; The estimated signal power of the target to be detected is obtained by searching for the maximum local power within the entire search area, representing the maximum signal energy of the target to be detected; the estimated signal power of the target to be detected. Based on Capon's spectral estimation method, the local power at a single point is first calculated. :

[0014] in For a single point Local power estimates; superscript H This indicates the conjugate transpose. For a limited number of snapshots K The sample covariance matrix, The distance is r azimuth angle is Pitch angle is The transmit / receive steering vector below; Subsequently, throughout the entire search area Within the range, the maximum local power at a single point is selected as the estimated power value of the target signal to be detected. :

[0015] Based on diagonal loading estimation The reconstructed covariance matrix for: (28) in, For a limited number of snapshots K The sample covariance matrix, It is the identity matrix. This is an estimate of the adaptive diagonal loading factor; Based on this, the reconstructed covariance matrix is ​​used. Calculate the diagonal loading estimate Optimal beamforming weight vector

[0016]

[0017] The overall received signal x is compared with the optimal beamforming weight vector. Multiply and sum to obtain the output signal after suppressing the main lobe interference. :

[0018] in for Rights protection vector, The output signal is x, and the total received signal is x. (Superscript) H This indicates the conjugate transpose.

[0019] Furthermore, for subspaces with dimension of S Optimize to obtain the optimal subspace dimension; For a subspace of dimension S subspace basis matrix The corresponding beamforming weight vector is Interference plus noise residual power Defined as:

[0020] Among them, superscript H This indicates the conjugate transpose. For a limited number of snapshots K The sample covariance matrix, This is the estimated value of the desired signal power; The dimension is S Beamforming weight vector in the subspace, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane; Traversing the dimension of candidate subspaces ,in ),in Represents finding a matrix Rank, calculate residual power for each candidate dimension And select the subspace dimension corresponding to the minimum residual power as the optimal subspace dimension:

[0021] in, This represents the dimension of the optimal subspace. Residual power; Based on optimal subspace dimension The covariance matrix of the subsumed and reconstructed The projection matrix in the optimal subspace for:

[0022] in For dimension is The optimal subspace basis matrix, The reconstructed covariance matrix; Based on this, the final optimal beamforming weight vector is calculated. :

[0023] in, It is the optimal subspace The projection matrix below, This is the combined transmission and reception steering vector of the target signal to be detected.

[0024] Using the corresponding subspace-constrained beamforming weight vector The weighted filtering of the overall signal vector x received by the radar yields the final output signal: The total received signal x and the weight vector Multiplying and summing the results yields the output signal y after suppressing the main lobe interference, expressed by the formula:

[0025] in for Weight vector, y is the output signal, x is the overall received signal, superscript H This indicates the conjugate transpose.

[0026] Furthermore, based on the echo signal received by the receiver, the interfering received signal, and the Gaussian noise, the steps to determine the overall received signal are as follows: The received echo signal undergoes mixing processing of the reference operating carrier frequency, digital mixing processing of the frequency step, and matched filtering processing to obtain a received signal in vector form, which is a snapshot signal composed of the two-dimensional spatial-temporal steering vector of the target to be detected. :

[0027] in , express Complex space of dimension 1 The number of receiving array elements in the transmitter-receiver unit. r 0 represents the distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The pitch angle of the target to be detected relative to the frequency diversity array plane is used to describe the angle between the target to be detected and the horizontal plane in the vertical plane. For Kronecker product, Let be the echo complexity coefficient of the target to be detected, where For signal propagation delay The subsequent reception time, sin c For the Singer function, For reference operating carrier frequency, At the speed of light, For the launch guidance vector, To receive the guide vector, and They are respectively:

[0028]

[0029] in The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The pitch angle of the target to be detected relative to the frequency diversity array plane is used to describe the angle between the target to be detected and the horizontal plane in the vertical plane. For the first m OK n The signal frequency transmitted by the array elements is indicated by the superscript. T It is the transpose operator. e It is a natural constant. It is the transmission delay of the target signal to be detected. The reception delay of the target signal to be detected is expressed as:

[0030]

[0031] in The element spacing between the transmitting elements. It is the element spacing between the receiving elements, let's say the spacing between the transmitting and receiving elements. ; in , For frequency step size, For wavelength, , ; Assuming the environment contains Q The main lobe interference from a pseudo-random distribution, the th q The first interfering signal propagates to the receiver's first... m OK n Interference signals received by the array's receiving elements for:

[0032] in , For the first The distance between each interference source and the transmitting array element The azimuth angle of the interference source relative to the normal of the frequency diversity array. The pitch angle of the interference source relative to the frequency diversity array is used to describe the angle between the identified target (other than the target to be detected) and the horizontal plane in the vertical plane. For the first q The echo recovery coefficient of the interference; This is the transmission steering vector for the interference signal. This is the receiving steering vector for the interference signal; and They are respectively:

[0033]

[0034] in For the first The distance between each interference source and the transmitting array element The azimuth angle of the interference source relative to the normal of the frequency diversity array. The pitch angle of the interference source relative to the frequency diversity array is used to describe the angle between the identified target (other than the target to be detected) and the horizontal plane in the vertical plane. For the first m OK n The signal frequency transmitted by the array's transmitting elements, indicated by the superscript. T It is the transpose operator. e It is a natural constant. It is the transmission delay of the interference signal. It is the delay in receiving interference signals. and They are represented as follows:

[0035]

[0036] in The element spacing between the transmitting elements. This refers to the element spacing between the receiving elements. Assume the element spacing between the transmitting elements and the receiving elements are equal, and both are... ,Right now ;in , For frequency step size, For wavelength, , ; Total received signal for:

[0037] in The snapshot signal of the target to be detected. For the received interference signal, It is Gaussian noise.

[0038] Furthermore, the step of obtaining the initial beamforming weights based on the minimum variance distortionless response (MVDR) is as follows: The radar signal processing module receives the total signal. Construct beamforming weight vector ,in And calculate the output signal y as:

[0039] Among them, superscript It is the conjugate transpose operation; To evaluate output performance, the signal-to-interference-plus-noise ratio (SINR) is introduced:

[0040] in, Indicates the desired signal power; The noise covariance matrix is ​​the interference plus noise. For the combined transmit-receive steering vector:

[0041] in, For the launch guidance vector, To receive the guide vector, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane represents the angle between the target to be detected and the horizontal plane in the vertical plane; Through constraints And minimize the weighted output power to obtain the initial weights for beamforming. :

[0042] in, For a limited number of snapshots K The sample covariance matrix; superscript -1 For the inverse operator, superscript It is the conjugate transpose operation. For the transmit-receive joint steering vector, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The pitch angle of the target to be detected relative to the frequency diversity array plane represents the angle between the target to be detected and the horizontal plane in the vertical plane.

[0043] The beneficial effects of this invention are: (1) Introducing a subspace constraint mechanism into the FDA-MIMO radar effectively alleviates the problem of guide vector mismatch caused by range-angle coupling and improves the robustness of beamforming; (2) Design an adaptive diagonal loading factor that can be adaptively adjusted according to interference and noise environment, avoiding the performance limitations caused by fixed loading parameters; (3) Even in complex scenarios with strong main lobe interference, it can still maintain a high output signal-to-interference-plus-noise ratio. Compared with existing technologies, the SINR is improved by 7dB and the gain is 33%, thereby achieving effective suppression of main lobe interference. (4) This invention relies on matrix operations and eigenvalue decomposition, without relying on complex iterative optimization processes; it solves low-dimensional matrices under the constraint of optimal subspace, which greatly reduces the computational complexity compared to full-dimensional processing. The algorithm has a simple structure, high parallelizability, and is easy to implement on hardware platforms, and has good engineering application value. (5) The present invention can take into account both robustness and practicality, and provides a better solution for target detection of FDA-MIMO radar in complex interference environment. Attached Figure Description

[0044] Figure 1 This is a diagram illustrating the main lobe interference suppression process of a planar FDA-MIMO radar. Figure 2 is a transmit-receive model of a planar FDA-MIMO radar; Figure 3 These are the results of suppressing main lobe interference by the planar FDA-MIMO radar in the embodiments under angle and range errors, where (a) is the optimal beam; (b) is FDA-MIMO DL Fixed; (c) is FDA-MIMO DL Eigen; (d) is FDA-MIMO WCP; (e) is FDA-MIMO RDL; and (f) is the FDA-MIMO ASDL of the present invention. Figure 4 shows the relationship between the output SINR and the input SNR of a planar FDA-MIMO radar under ideal conditions, i.e., without array error. Figure 5 This is the curve showing the relationship between the output SINR and input SNR of a planar FDA-MIMO radar when random range-angle errors exist; Figure 6 This is the curve showing the relationship between the output SINR and the input SNR of a planar FDA-MIMO radar under random frequency offset error conditions. Figure 7 It is the curve showing the relationship between the output SINR and the input SNR when there is random error in the array cell position; Figure 8 It is the curve showing the relationship between output SINR and input SNR in the presence of coherent scattering. Detailed Implementation

[0045] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0046] The technical solution adopted in this invention includes the following steps: Step 1: Construct the frequency diversity array of the FDA-MIMO radar transmitter antenna array elements; Unlike phased arrays where the electromagnetic wave carrier frequency emitted by each antenna element is the same, frequency diversity arrays introduce a small frequency variation on the transmission frequency of each transmitting element. Therefore, the center frequencies of different antenna elements are different, which is equivalent to introducing a transmission frequency difference for each transmitting element. The frequency diversity method is used to configure the antenna elements and spacing of the radar transmitter so that the antenna elements of the transmitter form a frequency diversity array. Assuming the FDA-MIMO radar transmitter is... It consists of several transmitting elements, which are evenly arranged. The transmitting array elements form a frequency diversity array on a two-dimensional plane; the element spacing between the transmitting array elements is... The radar's transmitting and receiving elements are co-located. and These represent the row and column indices of any two different array elements in the transmitting array; For receiving array element number OK The column's receiver element index; where the frequency step size between each transmitting element in the transmitted signal is... Frequency step size Much smaller than the reference operating carrier frequency of the transmitting array element Frequency step size The range is in the MHz to GHz range. The range is on the GHz scale; No. m OK n The frequency of the signal transmitted by the array's transmitting elements for: (1) in For reference operating carrier frequency; This is the frequency step size; No. m OK n The signal transmitted by the array of transmitting elements for: (2) in It is a baseband pulse with unit energy. Indicates the time within a radar pulse. The duration of the pulse; The imaginary unit; By assigning mutually orthogonal baseband pulse signals to different array elements This enables spatial and waveform diversity of multi-element transmitted signals; any two different transmitted elements... and The corresponding baseband pulse signals satisfy the orthogonality condition: (3) in, It is a baseband pulse signal with unit energy. t Indicates the time within a radar pulse. Represents the conjugate operator. and These represent the row and column indices of any two different array elements in the transmission array, used to distinguish the transmission signals corresponding to different transmission arrays; Step 2: Configure the transmission signal frequency of each transmitting element in the transmitter. After determining the spacing between array elements, a signal is transmitted to the target to be detected; the overall received signal is determined based on the echo signal received by the receiver, the interference received signal, and the Gaussian noise. The received echo signal undergoes mixing processing at the reference operating carrier frequency, digital mixing processing of the frequency step, and matched filtering processing to obtain a received signal in vector form, which is a snapshot signal composed of the two-dimensional guide vector of the target in space and time. : (4) in , express Complex space of dimension 1 The number of receiving array elements in the transmitter-receiver unit. r 0 represents the distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The pitch angle of the target to be detected relative to the frequency diversity array plane is used to describe the angle between the target to be detected and the horizontal plane in the vertical plane. For Kronecker product, Let be the echo complexity coefficient of the target to be detected, where For signal propagation delay The subsequent reception time, sin c For the Singer function, For reference operating carrier frequency, At the speed of light, For the launch guidance vector, To receive the guide vector, and They are respectively: (5) (6) in The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The pitch angle of the target to be detected relative to the frequency diversity array plane is used to describe the angle between the target to be detected and the horizontal plane in the vertical plane. For the first m OK n The signal frequency transmitted by the array elements is indicated by the superscript. T It is the transpose operator. e It is a natural constant. It is the transmission delay of the target signal to be detected. The reception delay of the target signal to be detected is expressed as: (7) (8) in The element spacing between the transmitting elements. It is the element spacing between the receiving elements, let's say the spacing between the transmitting and receiving elements. ; in , For frequency step size, For wavelength, , ; Assuming the environment contains Q The main lobe interference from a pseudo-random distribution, the th q The first interfering signal propagates to the receiver's first... m OK n The receiver array element of the column is represented as: (9) in For the received interference signal, For the first The distance between each interference source and the transmitting array element The azimuth angle of the interference source relative to the normal of the frequency diversity array. The pitch angle of the interference source relative to the frequency diversity array is used to describe the angle between the identified target (other than the target to be detected) and the horizontal plane in the vertical plane. For the first q The echo recovery coefficient of the interference; This is the transmission steering vector for the interference signal. This is the receiving steering vector for the interference signal; and They are respectively: (10) (11) in For the first The distance between each interference source and the transmitting array element The azimuth angle of the interference source relative to the normal of the frequency diversity array. The pitch angle of the interference source relative to the frequency diversity array is used to describe the angle between the identified target (other than the target to be detected) and the horizontal plane in the vertical plane. For the first m OK n The signal frequency transmitted by the array's transmitting elements, indicated by the superscript. T It is the transpose operator. e It is a natural constant. It is the transmission delay of the interference signal. It is the delay in receiving interference signals. and They are represented as follows: (12) (13) in The element spacing between the transmitting elements. This refers to the element spacing between the receiving elements. Assume the element spacing between the transmitting elements and the receiving elements are equal, and both are... ,Right now ;in , For frequency step size, For wavelength, , ; Total received signal for: (14) in The snapshot signal of the target to be detected. For the received interference signal, It is Gaussian noise; Step 3, based on the acquired total radar received signal To minimize the output power while keeping the gain of the target under test undistorted, the initial beamforming weights based on minimum variance distortionless response (MVDR) are obtained. The radar signal processing module receives the total signal. Construct beamforming weight vector And calculate the output signal y as: (15) Among them, superscript It is the conjugate transpose operation; To evaluate output performance, the signal-to-interference-plus-noise ratio (SINR) is introduced: (16) in, Indicates the desired signal power; The noise covariance matrix is ​​the interference plus noise. For the transmit-receive joint steering vector: (17) in, For the launch guidance vector, To receive the guide vector, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane represents the angle between the target to be detected and the horizontal plane in the vertical plane; Through constraints And minimize the weighted output power to obtain the initial weights for beamforming. : (18) in, For a limited number of snapshots K The sample covariance matrix; superscript -1 For the inverse operator, superscript It is the conjugate transpose operation. For the transmit-receive joint steering vector, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane represents the angle between the target to be detected and the horizontal plane in the vertical plane; Step 4: When there is direction mismatch, range mismatch or main lobe interference, the beamforming initial weights obtained by directly using the calculation formula (18) in step 3 will have performance degradation. In order to improve robustness, this invention restricts the beamforming initial weights to a low-dimensional candidate subspace. Based on the beamforming initial weights, the minimum variance distortionless response problem is solved again in the low-dimensional candidate subspace to obtain the subspace-constrained beamforming weight vector. Let the subspace basis matrix be , S If the subspace dimension is given, then the beamforming weight vector... for: (19) in, It is a low-dimensional weighted vector within the subspace, used to describe the potential mismatch effect of the steering vector; To obtain the low-dimensional weight vector in the optimal subspace The beamforming problem is transformed into a constrained optimization problem: (20) Among them, superscript It is the conjugate transpose operation. For a limited number of snapshots K The sample covariance matrix, The subspace dimension is S The subspace basis matrix, Diagonal loading factor, Let be the identity matrix, and arg(.) be the phase angle of the complex number. For the transmit-receive joint steering vector, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane represents the angle between the target to be detected and the horizontal plane in the vertical plane; The goal of transforming the beamforming problem into a constrained optimization problem is to minimize the weighted output power while keeping the gain in the direction of the target undistorted. By solving the constrained optimization problem (20), the subspace beamforming weight vector in closed-form solution is obtained. : (twenty one) in It is the projection matrix, defined as: (twenty two) Among them, superscript It is the conjugate transpose operation. The subspace dimension is S The subspace basis matrix, This is a diagonal loading factor used to enhance the stability of the covariance matrix. It is the identity matrix. For a limited number of snapshots K The sample covariance matrix; Step 5: Although subspace constraints can reduce the mismatch dimension, the covariance matrix still exhibits singular or ill-conditioned conditions under limited snapshot numbers or low signal-to-noise ratios. To address the issue of singular or ill-conditioned covariance matrices, this invention further introduces diagonal loading correction based on subspace constraints and calculates the covariance matrix using an adaptive method. Diagonal loading factor estimate To enhance the robustness of beamforming; Diagonal loading factor estimate for: (twenty three) in: The noise power is an estimate derived from the sample covariance matrix. The minimum eigenvalue is obtained, that is... , For a limited number of snapshots K The sample covariance matrix, This is an estimate of the diagonal loading factor; For the corresponding point, the transmit-receive joint steering vector, It indicates its energy, reflecting the array's nominal gain; The estimated signal power of the target to be detected is obtained by searching for the maximum local power within the entire search area, representing the maximum signal energy in the direction of the target to be detected; the estimated signal power of the target to be detected. Based on Capon's spectral estimation method, the local power at a single point is first calculated. : (twenty four) in For a single point Local power estimates; superscript H This indicates the conjugate transpose. For a limited number of snapshots K The sample covariance matrix, The distance is r azimuth angle is Pitch angle is The transmit / receive steering vector below; Subsequently, throughout the entire search area Within the range, the maximum local power at a single point is selected as the estimated power value of the target signal to be detected. : (25) Step 6, Subspace Dimension SThe selection of the dimension has a significant impact on beamforming performance: if the dimension is too large, the subspace contains too much noise, which will lead to main lobe expansion and interference leakage; if the dimension is too small, the desired signal information will be lost, weakening the main lobe gain and resolution. In order to further improve the robustness under the conditions of main lobe interference and steering vector mismatch, this invention proposes an adaptive subspace dimension selection method based on the criterion of minimizing the residual power of interference plus noise. For a subspace of dimension S candidate subspace basis matrix The corresponding beamforming weight vector is Interference plus noise residual power Defined as: (26) Among them, superscript H This indicates the conjugate transpose. For a limited number of snapshots K The sample covariance matrix, This is the estimated value of the desired signal power; The dimension is S Beamforming weight vector in the subspace, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane; Traversing the dimension of candidate subspaces ,in ),in Represents finding a matrix Rank, calculate residual power for each candidate dimension And select the subspace dimension corresponding to the minimum residual power as the optimal subspace dimension: (27) in, This represents the dimension of the optimal subspace. Residual power; This method achieves optimal suppression of interference and noise while ensuring that the gain in the main lobe direction is not distorted, and adaptively determines the subspace dimension, thereby improving the robustness of beamforming. Step 7: Obtain the corresponding adaptive diagonal loading estimate from step 5. Below, the reconstructed covariance matrix for: (28) in, For a limited number of snapshots K The sample covariance matrix, It is the identity matrix. This is an estimate of the adaptive diagonal loading factor; Based on this, in formula (28) Replace the formula (18) The estimated value of diagonal loading was calculated. Optimal beamforming weight vector

[0047] (29) Optimal beamforming weight vector It is calculated in full-dimensional space and is mainly used to suppress interference and noise while maintaining the gain of the target direction without distortion; it uses the optimal beamforming weight vector. The weighted filtering of the overall signal vector x received by the radar yields the final output signal: The overall received signal x is compared with the optimal beamforming weight vector. Multiply and sum to obtain the output signal after suppressing the main lobe interference. This can be expressed as a formula: (30) in for Rights protection vector, The output signal is x, and the total received signal is x. (Superscript) H Indicates conjugate transpose; Compared to directly based on the sample covariance matrix The obtained results are diagonal loading estimates. The introduction of this effectively improves the ill-conditioned nature and estimation bias of the covariance matrix under conditions of limited snapshot number, low signal-to-noise ratio, or target mismatch; Furthermore, based on the optimal subspace dimension obtained in step 6 The covariance matrix of the subsumed and reconstructed The projection matrix in the optimal subspace Represented as: (31) in For dimension is The optimal subspace basis matrix, The reconstructed covariance matrix; Based on this, the final optimal beamforming weight vector is calculated. : (32) in, It is the optimal subspace The projection matrix below, This is the combined transmission and reception steering vector of the target signal to be detected.

[0048] Using the corresponding subspace-constrained beamforming weight vector The weighted filtering of the overall signal vector x received by the radar yields the final output signal: The total received signal x and the weight vector Multiplying and summing the results yields the output signal y after suppressing the main lobe interference, expressed by the formula: (33) in for Weight vector, y is the output signal, x is the overall received signal, superscript H This indicates the conjugate transpose.

[0049] Compared to the output signal obtained based on full-dimensional space in formula (30) The output signal y in formula (33) is the result obtained under the optimal subspace constraint. This is achieved by reconstructing the covariance matrix... Projected onto the optimal subspace It can effectively filter out noise subspace components and retain the signal subspace where the main energy of the target and interference is located, thereby further improving the stability of beamforming weight vector and interference suppression capability; Based on the above steps, a robust weight vector is finally obtained by combining subspace-constrained beamforming with adaptive diagonal loading. This vector is then used to perform weighted filtering on the overall signal of the receiving array, achieving a linear combination of the received signals from each array element. During this process, the signal in the direction of the target to be detected is effectively enhanced, while main lobe interference and noise in the undesired direction are suppressed, thus outputting a robust and reliable signal y, ensuring optimal performance of beamforming in both target detection and interference suppression. The main lobe interference suppression process proposed in this invention is as follows: Figure 1 As shown. Assume there exists a point target in the far field of space, after passing through... Each array element receives the signal; the received signal is first mixed, and then the signal from each receiving channel is processed... The process involves a matched filter. The matched filtering process consists of two steps: the first step involves matching each received channel with... The relevant digital mixing, i.e., multiplied by The second step is to perform matched filtering on each transmitted waveform. The sum of the signals from each receiving array element after matched filtering can form a column vector. The covariance matrix of the received signal is estimated, and then the adaptive optimal weights are calculated through an optimization problem to suppress main lobe interference.

[0050] The planar FDA-MIMO radar transmit and receive array distribution described in this invention is as follows: Figure 2As shown. The radar transmitting array adopts a planar array frequency diversity structure. Consider a co-located MIMO radar system where the transmitting and receiving elements are identical, where... Each transmitting array operates independently, emitting radar wave signals at a specific frequency. Each receiving element is used to receive the echo signal. Since each transmitting element introduces a fixed frequency less than the carrier frequency, this radar system contains... A transmitting array with different frequencies, the frequencies being respectively f 11 , f 12 , ..., f MN The radar receives echoes through multiple narrow beams, which can form a steering matrix for a frequency diversity array, thus obtaining the array's output.

[0051] The proposed method for suppressing main lobe interference in a planar frequency diversity array radar under steering vector mismatch conditions was used for simulation verification. The experimental results fully demonstrate the effectiveness of the proposed method. Assume the antenna array receives a narrowband signal from the far field, containing one useful signal and three interference sources. The actual incident angle of the useful signal is... The incident angles of the three interference sources are respectively... , and The pitch angles of the three interference sources are fixed at 1. Furthermore, it is assumed that the additive noise follows a zero-mean Gaussian random process. Considering the complex real-world environment, the experiment further assumes that the incident azimuth angle of the desired signal and the interference signal information cannot be accurately obtained.

[0052] To simulate array calibration error, it is assumed that each component of the steering vector of each incident signal is perturbed, where the angular sector of the desired signal is set to... θ s = [ θ s - , θ s + The distance range of the target signal to be detected is set to... R s =[ R s -1 km, R s + 1 km]. The corner sector of the interference signal is set to θ int = [ θ int - , θ int + The distance range of the interference signal is set to... R int = [ R int - 1 km, R int +1 km]. The angle and distance sectors mentioned above are all uniformly discretely sampled, where the distance interval Δ r = 0.2 km, angular interval is The integration interval is set to For detailed parameters, please refer to Table 1: Table 1 Parameter Table

[0053] Figure 3 This demonstrates the effectiveness of various beamforming methods in suppressing main lobe interference in planar FDA-MIMO radar under conditions of angular and range errors, using a linear frequency offset configuration. For example... Figure 3 As shown in (a), the optimal beamforming method can achieve high-precision focusing at the location of the target to be detected. In contrast, as... Figure 3 The traditional methods shown in (b)-3(e) struggle to form well-localized beammaps, leading to a significant increase in sidelobe energy and beam shift. In some cases, the target signal may even be incorrectly suppressed because it cannot be effectively distinguished from interfering signals. In contrast, Figure 3 (f) The ASDL method proposed in this invention achieves a highly focused beam pattern in both distance and angle dimensions, effectively suppressing main lobe interference and mitigating the impact of guide vector mismatch, thereby ensuring reliable detection of the target and significantly improving system performance.

[0054] Furthermore, Figure 4 This paper presents a comparative analysis of the output SINR versus input SNR of different beamforming methods under ideal conditions, i.e., when the array has no range-angle errors. The Optimal curve represents the theoretical performance upper limit when the interference and noise covariance matrices are known. The results show that the DL Eve algorithm exhibits the lowest SINR performance; while traditional methods, including RDL, WCP, DL Eigen, and DL Fixed strategies, have almost identical output SINR values ​​under ideal conditions, indicating that their main lobe interference suppression capabilities are comparable when there are no array errors. Notably, the ASDL method proposed in this invention demonstrates superior main lobe interference suppression capability, with an output SINR value approximately 10 dB higher than other methods, and approaching the optimal system performance.

[0055] like Figure 5As shown, under non-ideal conditions, i.e., when the array has range and angle errors, different beamforming methods exhibit significant differences in their suppression performance of main lobe interference in planar FDA-MIMO radar. The Optimal curve represents the theoretical upper limit of performance when the interference and noise covariance matrix is ​​known. Analysis of the output SINR versus input SNR curves reveals that the DL Eigen algorithm exhibits the lowest SINR performance. The ASDL method proposed in this invention can more effectively mitigate the impact of range-angle mismatch on beam performance, achieving precise interference suppression while accurately pointing the beam to the target location, thus bringing the system performance close to ideal. Compared to other traditional methods (such as RDL, WCP, DL Eigen, and DLFixed), the output SINR is improved by 7 dB, with a gain of approximately 33%. In contrast, traditional beamforming methods (such as RDL, WCP, DL Eigen, and DLFixed) suffer from insufficient gain in the desired signal direction due to errors in range and angle estimation, especially exhibiting problems such as decreased output SINR and degraded target detection performance under low input signal power.

[0056] like Figure 6 As shown, the impact of random frequency offset error on the output SINR as a function of input SNR is further analyzed. Experimental results show that even in the presence of frequency offset error, the ASDL method proposed in this invention can still maintain a high output SINR, which is significantly superior to WCP, RDL, DL Fixed, DL Eigen, and DL Eve methods. This indicates that frequency offset error will disrupt the array coherence of the FDA-MIMO planar array, thereby reducing beamforming efficiency. It is worth noting that the DL Eve method exhibits the worst anti-jamming performance under the same SNR conditions, showing its high sensitivity to interference and parameter changes. In contrast, the method of this invention, through joint optimization of adaptive subspace and diagonal loading, can maintain stable output SINR under uncertain conditions, demonstrating robustness to steering vector mismatch caused by frequency offset error, highlighting the practical application value of this method for main lobe interference suppression in actual radar systems.

[0057] Figure 7 This paper presents a comparison of the output SINR versus input SNR of different beamformers when array position errors are present, assuming the error is in the range [-0.1, 0.1]. λUniform distribution within the beam. Results show that the ASDL method proposed in this invention exhibits significant robustness in dealing with main lobe interference caused by position errors, outperforming traditional methods such as RDL, WCP, DL Eigen, DL Fixed, and DL Eve. These traditional methods are susceptible to array position errors, leading to deviations in beamforming weight vector calculation and resulting in performance degradation. In contrast, the ASDL method can effectively compensate for position errors, maintaining a stable high SINR output under different SNR conditions. Under this error condition, the ASDL method achieves a SINR improvement of approximately 15 dB compared to WCP, RDL, DL Fixed, and DL Eigen.

[0058] also, Figure 8 This paper presents a performance comparison of different beamforming algorithms under coherent local scattering conditions, showing the effect of output SINR on input SNR. The results demonstrate that the proposed ASDL method significantly outperforms other methods in interference suppression, with its output SINR being approximately 13 dB higher than the other four schemes (WCP, RDL, DL Fixed, and DL Eigen) and approximately 10 dB higher than DLEve. This fully demonstrates the effectiveness of the proposed method in addressing the steering vector model mismatch problem caused by coherent local scattering. Traditional beamforming methods suffer from decreased output SINR due to target steering vector mismatch, leading to weakened main lobe interference suppression capabilities. The ASDL method, through a robust beamforming strategy, effectively compensates for steering vector mismatch, achieving superior main lobe suppression. The comparison of output SINR under the four steering vector mismatch conditions shows that effectively designing robust beams is key to achieving main lobe interference suppression under mismatch conditions. The robust beam proposed in this invention enables FDA-MIMO radar to outperform existing methods in main lobe interference suppression, and the experimental results fully verify the effectiveness of the proposed method.

[0059] This invention proposes a planar FDA-MIMO radar main lobe interference suppression method based on subspace and diagonal loading. This method utilizes the range dimension degree of freedom introduced by the frequency diversity array to effectively distinguish the target being detected from the interference signal. A beamforming weight vector is constructed using the obtained radar received signal vector. To minimize the output power while maintaining the undistorted directional gain of the target being detected, initial beamforming weights based on minimum variance distortion-free response are obtained. A sample covariance matrix is ​​constructed and combined with the transmit-receive joint steering vector of the target being detected to form the beam output. When directional mismatch, range mismatch, or main lobe interference exists, the beamforming weight vector is restricted to a candidate subspace to obtain weights under subspace constraints. A diagonal loading correction is introduced into the subspace weights, and the loading factor is calculated adaptively. Based on the modified weight vector, the final beamforming output is completed. This invention can effectively suppress main lobe interference in the environment of guide vector mismatch, significantly improve the anti-interference capability of the radar system and the detection accuracy of the target, and has broad application prospects and practical value.

Claims

1. A method for suppressing main lobe interference in a planar array FDA-MIMO radar, characterized in that, Includes the following steps: Step 1: Construct a frequency diversity array for the antenna elements of the FDA-MIMO radar transmitter; Assuming the FDA-MIMO radar transmitter is... It consists of several transmitting elements, which are evenly arranged. The transmitting array elements form a frequency diversity array on a two-dimensional plane; the element spacing between the transmitting array elements is... ; The radar's transmitting and receiving array elements are co-located; and These represent the row and column indices of any two different array elements in the transmitting array; For receiving array element number OK The column's receiver element index; where the frequency step size between each transmitter element is... Frequency step size Much smaller than the reference operating carrier frequency of the transmitting array element ;No. m OK n The frequency of the signal transmitted by the array element is ;No. m OK n The array of transmitting elements transmits signals. ; Any two different launch array elements and The corresponding baseband pulse signals satisfy the orthogonality condition; Step 2: Configure the signal frequencies of each transmitting element in the transmitter. After adjusting the spacing between array elements, a signal is transmitted toward the target to be detected; Based on the echo signal received by the receiver, the interfering received signal, and the Gaussian noise, the total received signal is determined. ; Step 3: Based on the acquired total received signal To minimize the output power while keeping the gain of the target under test undistorted, the initial beamforming weights based on minimum variance distortionless response (MVDR) are obtained. Step 4: Based on the initial beamforming weights, in the subspace with dimension... S The minimum variance distortionless response problem is resolved within the subspace to obtain the subspace-constrained beamforming weight vector.

2. The method for suppressing main lobe interference in a planar array FDA-MIMO radar according to claim 1, characterized in that, The step of obtaining the subspace-constrained beamforming weight vector is as follows: Let the subspace basis matrix be , S If the subspace dimension is given, then the beamforming weight vector... for: in, It is a low-dimensional weighted vector within the subspace, used to describe the potential mismatch effect of the steering vector; The beamforming problem is transformed into a constrained optimization problem to obtain the low-dimensional weight vector in the optimal subspace. : Among them, superscript It is the conjugate transpose operation. For a limited number of snapshots K The sample covariance matrix, The subspace dimension is S The subspace basis matrix, Diagonal loading factor, Let be the identity matrix, and arg(.) be the phase angle of the complex number. For the transmit-receive joint steering vector, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane represents the angle between the target to be detected and the horizontal plane in the vertical plane; The goal of transforming the beamforming problem into a constrained optimization problem is to minimize the weighted output power while keeping the gain in the direction of the target undistorted. By solving the constrained optimization problem, the subspace beamforming weight vector in closed-form solution is obtained. : in It is the projection matrix, defined as: Among them, superscript It is the conjugate transpose operation. The subspace dimension is S The subspace basis matrix, This is a diagonal loading factor used to enhance the stability of the covariance matrix. It is the identity matrix. For a limited number of snapshots K The sample covariance matrix.

3. The method for suppressing main lobe interference in a planar array FDA-MIMO radar according to claim 2, characterized in that, In the step of obtaining the subspace-constrained beamforming weight vector, the diagonal loading factor is... Make corrections to obtain the estimated value of the diagonal loading factor. And calculate the reconstructed covariance matrix. Based on the diagonal loading factor estimate and the reconstructed covariance matrix To obtain the optimal beamforming weight vector The process of obtaining the output signal after suppressing the main lobe interference is as follows: Diagonal loading factor estimate for: in: The noise power is an estimate derived from the sample covariance matrix. The minimum eigenvalue is obtained, that is... , For a limited number of snapshots K The sample covariance matrix, This is an estimate of the diagonal loading factor; For the corresponding point, the transmit-receive joint steering vector, It indicates its energy, reflecting the array's nominal gain; The estimated signal power of the target to be detected is obtained by searching for the maximum local power within the entire search area, representing the maximum signal energy in the direction of the target to be detected; the estimated signal power of the target to be detected. Based on Capon's spectral estimation method, the local power at a single point is first calculated. : in For a single point Local power estimates; superscript H This indicates the conjugate transpose. For a limited number of snapshots K The sample covariance matrix, The distance is r azimuth angle is Pitch angle is The transmit / receive steering vector below; Subsequently, throughout the entire search area Within the range, the maximum local power at a single point is selected as the estimated power value of the target signal to be detected. : Based on diagonal loading estimation The reconstructed covariance matrix for: (28) in, For a limited number of snapshots K The sample covariance matrix, It is the identity matrix. This is an estimate of the adaptive diagonal loading factor; Based on this, the reconstructed covariance matrix is ​​used. Calculate the diagonal loading estimate Optimal beamforming weight vector The overall received signal x is compared with the optimal beamforming weight vector. Multiply and sum to obtain the output signal after suppressing the main lobe interference. : in for Rights protection vector, The output signal is x, and the total received signal is x. (Superscript) H This indicates the conjugate transpose.

4. The method for suppressing main lobe interference in a planar array FDA-MIMO radar according to claim 3, characterized in that, The dimension of the subspace is S Optimize to obtain the optimal subspace dimension; based on the optimal subspace dimension... and the reconstructed covariance matrix Obtain the projection matrix in the optimal subspace. This leads to the final optimal beamforming weight vector. Based on the final optimal beamforming weight vector Calculate the output signal y after suppressing the main lobe interference; For a subspace of dimension S subspace basis matrix The corresponding beamforming weight vector is Interference plus noise residual power Defined as: Among them, superscript H This indicates the conjugate transpose. For a limited number of snapshots K The sample covariance matrix, This is the estimated value of the desired signal power; The dimension is S Beamforming weight vector in the subspace, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane; Traversing the dimension of candidate subspaces ,in ),in Represents finding a matrix Rank, calculate residual power for each candidate dimension And select the subspace dimension corresponding to the minimum residual power as the optimal subspace dimension: in, This represents the dimension of the optimal subspace. Residual power; Based on optimal subspace dimension The covariance matrix of the subsumed and reconstructed The projection matrix in the optimal subspace for: in For dimension is The optimal subspace basis matrix, The reconstructed covariance matrix; Based on this, the final optimal beamforming weight vector is calculated. : in, It is the optimal subspace The projection matrix below, The transmit-receive joint steering vector of the target signal to be detected; Using the corresponding subspace-constrained beamforming weight vector The weighted filtering of the overall signal vector x received by the radar yields the final output signal: The total received signal x and the weight vector Multiplying and summing the results yields the output signal y after suppressing the main lobe interference, expressed by the formula: in for Weight vector, y is the output signal, x is the overall received signal, superscript H This indicates the conjugate transpose.

5. The method for suppressing main lobe interference in a planar array FDA-MIMO radar according to claim 1, characterized in that, The steps to determine the overall received signal based on the echo signal, interfering received signals, and Gaussian noise are as follows: The received echo signal undergoes mixing processing at the reference operating carrier frequency, digital mixing processing for the frequency step, and matched filtering processing to obtain a received signal in vector form, which is a snapshot signal composed of the two-dimensional guide vector of the target in space and time. : in , express Complex space of dimension 1 The number of receiving array elements in the transmitter-receiver unit. r 0 represents the distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The pitch angle of the target to be detected relative to the frequency diversity array plane is used to describe the angle between the target to be detected and the horizontal plane in the vertical plane. For Kronecker product, Let be the echo complexity coefficient of the target to be detected, where For signal propagation delay The subsequent reception time, sin c For the Singer function, For reference operating carrier frequency, At the speed of light, For the launch guidance vector, To receive the guide vector, and They are respectively: ； ； in The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The pitch angle of the target to be detected relative to the frequency diversity array plane is used to describe the angle between the target to be detected and the horizontal plane in the vertical plane. For the first m OK n The signal frequency transmitted by the array elements is indicated by the superscript. T It is the transpose operator. e It is a natural constant. It is the transmission delay of the target signal to be detected. The reception delay of the target signal to be detected is expressed as: in The element spacing between the transmitting elements. It is the element spacing between the receiving elements, let's say the spacing between the transmitting and receiving elements. ; in , For frequency step size, For wavelength, , ; Assuming the environment contains Q The main lobe interference from a pseudo-random distribution, the th q The interfering signal propagates to the receiver. m OK n Interference signals from array receiving elements for: in , For the first The distance between each interference source and the transmitting array element The azimuth angle of the interference source relative to the normal of the frequency diversity array. The pitch angle of the interference source relative to the frequency diversity array; used to describe the angle between the identified target (other than the target to be detected) and the horizontal plane in the vertical plane. For the first q The echo recovery coefficient of the interference; This is the transmission steering vector for the interference signal. This is the receiving steering vector for the interference signal; and They are respectively: ； ； in For the first The distance between each interference source and the transmitting array element The azimuth angle of the interference source relative to the normal of the frequency diversity array. The elevation angle of the interference source relative to the frequency diversity array; For the first m OK n The signal frequency transmitted by the array's transmitting elements, indicated by the superscript. T It is the transpose operator. e It is a natural constant. It is the transmission delay of the interference signal. It is the delay in receiving interference signals. and They are respectively: in The element spacing between the transmitting elements. This refers to the element spacing between the receiving elements. Assume the element spacing between the transmitting elements and the receiving elements are equal, and both are... ,Right now ;in , For frequency step size, For wavelength, , ; Total received signal for: in The snapshot signal of the target to be detected. For the received interference signal, It is Gaussian noise.

6. The method for suppressing main lobe interference in a planar array FDA-MIMO radar according to claim 1, characterized in that, The steps for obtaining the initial beamforming weights based on the minimum variance distortionless response (MVDR) are as follows: The radar signal processing module receives the total signal. Construct beamforming weight vector ,in And calculate the output signal y as: Among them, superscript It is the conjugate transpose operation; To evaluate output performance, the signal-to-interference-plus-noise ratio (SINR) is introduced: in, Indicates the desired signal power; The interference plus noise covariance matrix; For the combined transmit-receive steering vector: in, For the launch guidance vector, To receive the guide vector, The distance between the transmitting element and the target to be detected. Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The elevation angle of the target to be detected relative to the frequency diversity array plane represents the angle between the target to be detected and the horizontal plane in the vertical plane; Through constraints And minimize the weighted output power to obtain the initial weights for beamforming. : in, For a limited number of snapshots K The sample covariance matrix; superscript -1 For the inverse operator, superscript It is the conjugate transpose operation. For the transmit-receive joint steering vector, Let be the azimuth angle of the target to be detected relative to the normal of the frequency diversity array. The pitch angle of the target to be detected relative to the frequency diversity array plane represents the angle between the target to be detected and the horizontal plane in the vertical plane.

7. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements a planar array FDA-MIMO radar main lobe interference suppression method according to any one of claims 1-6.

8. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements a method for suppressing main lobe interference of a planar array FDA-MIMO radar according to any one of claims 1-6.

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