A polarization agile jamming suppression method based on polarization frequency control array radar

Abstract

This invention discloses a polarization-agile interference suppression method based on a polarization-frequency-controlled array radar, belonging to the field of radar anti-jamming and array signal processing technology. Under the PFDA-MIMO radar system, this invention achieves spatial position parameter estimation and globally optimal self-pairing for polarization-agile interference by utilizing the array spatial manifold rotation invariance and cyclic measure algorithms. Furthermore, it combines spatial decoupling to eliminate crosstalk between multiple interferences and uses the least squares criterion to obtain instantaneous polarization information under a single snapshot. It further reconstructs the instantaneous interference plus noise covariance matrix under a single snapshot, obtains the optimal weight vector, and performs joint space-polarization adaptive filtering. In the scenario of polarization-agile interference, it achieves high-fidelity target extraction and deep cancellation of interference energy, effectively improving the system's output signal-to-interference-plus-noise ratio and target detection capability.

Description

Technical Field

[0001] This invention belongs to the field of radar anti-jamming and array signal processing technology, specifically relating to a polarization-agile interference suppression method for polarization-controlled array radar. It is particularly suitable for dealing with complex electromagnetic interference environments exhibiting rapid polarization time-varying characteristics. Background Technology

[0002] Frequency Diverse Array (FDA) radar, by introducing small frequency increments between transmitting elements, makes the array steering vector simultaneously correlated with angle and range, thus possessing unique advantages in target detection, jamming suppression, and beam control. Further incorporating polarization diversity into the FDA MIMO system creates a Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radar system, enhancing the system's information acquisition capabilities across multiple dimensions of space, frequency, and polarization. In the FDA-MIMO system, frequency offsets between transmitting elements couple the phase of echoes from different elements with range, angle, and frequency offsets, easily leading to range periodic mapping during parameter estimation and consequently, secondary range ambiguity. In modern electronic warfare, active jamming technology is evolving towards greater intelligence and dexterity. Among them, polarization-agile jamming, as a novel type of jamming, can cause the polarization state of the jamming signal to change rapidly, randomly, or regularly between or even within pulses. This high-speed time-varying characteristic of the polarization state makes the jamming signal exhibit extremely strong non-stationarity in the polarization domain, rendering traditional suppression methods ineffective. Therefore, how to robustly suppress jamming in environments with rapidly changing polarization is a pressing technical challenge in the field of radar anti-jamming.

[0003] Existing anti-jamming techniques mostly achieve interference suppression from the perspectives of spatial, temporal, polarization, or multi-domain joint processing. Typical spatial-temporal methods usually rely on accumulating training samples over a long period of time, estimating the interference-noise covariance matrix in the received data based on this, and then employing Minimum Variance Distortionless Response (MVDR) beamforming to achieve interference suppression. In polarization domain processing, for fixed polarization interference, static polarization matched filters or polarization orthogonal filters can be constructed to enhance the desired polarization component or suppress the interfering polarization component. However, the above methods generally suffer from the following limitations.

[0004] If the interference polarization state changes between snapshots, a fixed polarization parameter model cannot accurately represent the real interference. Therefore, the polarization filter and steering vector constructed based on static assumptions will mismatch with the real interference, thus affecting the subsequent suppression effect. Simultaneously, polarization-agile interference exhibits typical time-varying and non-stationary characteristics; a single polarization-agile interference can be equivalent to two orthogonal linear polarization components with the same direction of arrival, causing rank expansion of the interference subspace. If the traditional long-term accumulation method is used for covariance estimation, the resulting covariance matrix is ​​a statistical average of multiple instantaneous interference states and cannot accurately correspond to the real interference characteristics under any snapshot. Based on this, adaptive beamforming is difficult to form optimal suppression weights that match the instantaneous interference, resulting in a decrease in the output signal-to-interference-plus-noise ratio. On the other hand, for PFDA-MIMO radar, its steering vector has a periodic response characteristic to range, which will produce secondary range ambiguity. If a target constraint or interference model is constructed without resolving the ambiguity, it will lead to a deviation in the range phase term, resulting in a mismatch in the joint steering vector, causing main lobe shift and a decrease in interference suppression performance. Summary of the Invention

[0005] The purpose of this invention is to propose a polarization-agile interference suppression method based on a polarization frequency-controlled array radar. This method utilizes the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm to estimate the two-dimensional spatial location parameters of the interference. It combines weighted minimum Euclidean distance and cyclic measure to complete self-pairing of multiple interference parameters. Based on the obtained high-precision spatial location information, the instantaneous polarization parameters of the polarization-agile interference under a single snapshot are extracted through spatial decoupling. Finally, based on the reconstructed space-polarization joint steering vector, a polarization-matched interference plus noise covariance matrix is ​​further constructed, and space-polarization joint adaptive filtering is performed to achieve robust suppression of polarization-agile interference.

[0006] The technical solution of this invention is as follows:

[0007] A method for suppressing polarization-agile interference based on a polarization frequency-controlled array radar, comprising the following steps:

[0008] Step S1: Receive the PFDA-MIMO radar echo signal from the frequency-controlled array, perform a rough range estimate by down-conversion matched filtering, and simultaneously use the ESPRIT algorithm based on rotation invariance to divide the transmitting and receiving arrays. Through the translation invariance of the array structure, the two-dimensional spatial parameters of the interference signal are converted into rotational relationships between signal subspaces for solution, resulting in a set of estimated two-dimensional spatial parameters for the target and multiple interference signals. The two-dimensional spatial parameters include azimuth and range.

[0009] Step S2: Introduce cyclic distance and define the generalized Euclidean distance between any two points; the estimated two-dimensional spatial parameters of the target and multiple interference signals constitute a two-dimensional spatial location candidate set. The two-dimensional spatial location candidate set is regarded as an undirected complete graph, with vertices as two-dimensional spatial parameters and edge weights as generalized Euclidean distances; perform self-pairing on each vertex to obtain the optimal partitioning scheme, and fuse the parameters of the paired vertices to obtain the two-dimensional spatial parameters of the paired interference signals and the two-dimensional spatial parameters of the unpaired target;

[0010] Step S3: Using the two-dimensional spatial parameter set obtained in step S2, perform spatial decoupling. By using the linear constraint minimum variance criterion, obtain the polarization state vector of each interference signal under a single snapshot. Then, solve the polarization parameters under a single snapshot using the least squares criterion to obtain the instantaneous polarization information of each interference signal under a single snapshot.

[0011] Step S4: Based on the two-dimensional spatial parameters and instantaneous polarization information of the paired interference signal, the interference steering vector under each snapshot is accurately reconstructed, and the instantaneous interference plus noise covariance matrix is ​​established accordingly; at the same time, an adaptive space-time-polarization joint filter is designed based on the minimum variance distortionless response (MVDR) criterion to minimize the interference noise output power while ensuring the distortionless output of the desired target signal.

[0012] The down-conversion matched filter performs a rough distance estimate as follows:

[0013] For a uniform linear PFDA-MIMO radar composed of orthogonal dipoles with M transmitting elements and N receiving elements, the spacing between the transmitting elements is... The spacing between the receiving array elements is , For wavelength, a small frequency offset is introduced for the transmitting array. , No. The signals corresponding to each transmitting element are:

[0014]

[0015] In the formula It is a natural constant. The imaginary unit, It is a time variable. The pulse repetition period, The center frequency of the carrier. For the first The carrier frequency of each transmitting element For the first The polarization vector of each transmitting element. For the first One baseband waveform;

[0016] Assuming there is one real target and [other target] in the environment where the PFDA-MIMO radar is located. There are several false targets, where the real target is located... The interference signal of the false target is located in , , and Indicates the azimuth angle of the target and the interference signal. and Let represent the distance between the target and the interference signal, then the th The signal received by each receiving element is represented as:

[0017]

[0018] in Represents the speed of light. Indicates the amplitude of the target signal. Indicates the first The amplitude of the false target Represents the polarization scattering matrix of the target. and They represent the first The transmit and receive polarization vectors of a dummy target; , These respectively represent the signal from the first... The launch array element is launched, passing through the real target, the first... After being reflected again from a false target, it reached the first... Path delay of each receiving array element;

[0019] For the The signal received by the receiving array element is down-converted and matched-filtered, wherein the target signal and the first element are... The output signals after matched filtering of the interference signals are respectively represented as follows: , :

[0020]

[0021]

[0022] in Indicates the first The complex amplitude of the interference signal, Represents the polarization scattering matrix of the decoy jammer; For the complex coefficients of the target signal, For the first Complex coefficients of a dummy target signal;

[0023] for The receiving array element, whose actual target received signal and the first receiving array element. A fake target receives a signal. The vectorized representations are as follows:

[0024]

[0025]

[0026] in Represents the Kronecker product. Represents the Hadamard product. A diagonal matrix representing the polarization vector of the target signal. For the first The diagonal matrix of the polarization vectors of a dummy target signal. , For angle receiving vector, For angular emission vectors, This is the range emission vector;

[0027] Assume the total number of snapshots is Then the matched filter is the first The received vector of a snapshot is represented as:

[0028]

[0029] in For the first The complex coefficients of a dummy target signal, Indicates the true target at the 1st The corresponding received response vector for each snapshot Indicates the first The false target signal in the first The corresponding received response vector for each snapshot It is a Gaussian white noise signal;

[0030] The rotation-invariant signal parameter estimation algorithm is as follows:

[0031] Define two overlapping receiver subarrays in the receiver array: Subarray 1 contains the previous... Each array element, including subarray 2. Each subarray has one array element; the two subarrays differ spatially by one array element. The translation amount; constructing the receiver array selection matrix for the two subarrays. and ;

[0032] The signal subspace corresponding to the large eigenvalues ​​obtained by decomposing the covariance matrix of the received data. There exists a non-singular linear transformation matrix. Make ,Right now ,in , This represents the transformation matrix obtained from the rotation-invariant relation of the receiving array. Represents the phase rotation matrix of the receiving array:

[0033]

[0034] in This represents the incident angle of the false target signal after the interference subspace has expanded;

[0035] The transmitter array contains There are array elements, and the spacing between the array elements is... The transmission array is divided into Given three polarization pairs, define two emission subarrays: subarray 3 consists of the first element of each emission polarization pair, and subarray 4 consists of the second element of each emission polarization pair; construct the emission array selection matrices for subarrays 3 and 4. , Establish rotation-invariant equations: ,in , This represents the transformation matrix obtained from the rotation-invariant relation of the transmitting array. Represents the phase rotation matrix of the transmitting array:

[0036]

[0037] in Indicates the location of the false target signal after the interference subspace expands;

[0038] Solve using least squares respectively , Assuming the solution is obtained The eigenvalues ​​are respectively and , The azimuth and distance are obtained as follows:

[0039]

[0040]

[0041] in At the maximum unambiguous distance The residual value within the modulus.

[0042] Step S2 is as follows:

[0043] After obtaining the estimated azimuth and distance using the ESPRIT algorithm, the output is... An unordered set of spatial location candidates Introducing cyclic distance, we can reconstruct any two estimated points. and Distance difference between:

[0044]

[0045] In the formula Indicates fuzzy distance, Indicates distance difference;

[0046] Further introduce angle normalization factor and distance normalization factor The class-generalized Euclidean distance between any two points in the candidate set is defined as:

[0047]

[0048] The two-dimensional spatial location candidate set output by the ESPRIT algorithm Viewed as an undirected complete graph The vertex set, where the vertex set Edge set The weights on the surface are the generalized Euclidean distances. Assume the vertex index corresponding to the target is Then the remainder The subset consisting of vertices is In the subset Seeking a partitioning scheme The local minimum cost function under this condition is defined by minimizing the sum of the edge weights of each pair within the partition; all candidate target points are traversed. Find the optimal outlier index for the global minimum of its paired cost function. At this time, make Partition scheme to obtain the minimum value That is The optimal pairing combination of polarization-agile interferences is obtained. Optimal pairing indexes for polarization agile interference Afterwards, The azimuth and distance of each index pair are fused separately to obtain... Two-dimensional spatial parameters of the interference signal, isolated point index For target signal.

[0049] Step S3 is as follows:

[0050] Based on the two-dimensional spatial parameters of the target signal obtained in step S2 and the two-dimensional spatial parameters of the interference signal Constructing the exclusion of the first The interference plus noise covariance matrix of each interference. :

[0051]

[0052] in Indicates the first An angle of interference and distance Related joint guidance matrix, For the target signal power, To interfere with signal power, Noise power;

[0053] Make the first The interference passes through, while simultaneously creating depth space nulls in other targets and interference directions. Based on the linear constraint minimum variance criterion, the interference is excluded. Spatial decoupling weight matrix of each disturbance :

[0054]

[0055] Receive data The weight vector matrix is ​​formed by this beam. Then, the first single snapshot output The polarization vector of the interference , column vector Rearranged as The least squares method is used to solve for the estimated th... The polarization scattering matrix of the interference This is expressed as the outer product of the jammer's receiving polarization vector and transmitting polarization vector:

[0056]

[0057] in Indicates the first The interference at the first The horizontally polarized scattering component captured in a quick snapshot. , express The interference at the first Cross-polarized scattering components captured in a quick snapshot No. The interference at the first The vertically polarized scattering component captured in a quick snapshot; and They represent the first The polarization phase angle and polarization phase difference of the emitted polarization vector of each interference. and They represent the first The polarization phase angle and polarization phase difference of the received polarization vector of each interference.

[0058] Step S4 is as follows:

[0059] Reconstruct the instantaneous spatial-polarization domain steering vector for each interference signal in a single snapshot:

[0060]

[0061] In the formula For the first A column vector of polarization information of each disturbance. This indicates vectorized operations. The amplitude of the interference signal, express The interference at the first The diagonal matrix of polarization vectors captured in a single snapshot;

[0062] Using the reconstructed instantaneous steering vector of the disturbance, the disturbance plus noise covariance matrix is ​​reconstructed in a single snapshot:

[0063]

[0064] In the formula The matrix formed by all the instantaneous steering vectors of the disturbances;

[0065] Filter design based on the minimum variance distortionless response criterion:

[0066]

[0067] in The joint steering vector of the target's spatial-polarization domain. This represents the reconstructed instantaneous disturbance plus noise covariance matrix;

[0068] The optimal weight vector can be obtained by solving the filter:

[0069]

[0070] The received signal is filtered using the aforementioned weight vector:

[0071]

[0072] In the formula This represents the filtered signal. This indicates that the array receives signals. Represents the weight vector.

[0073] In summary, the beneficial effects of the technical solution provided by this invention are as follows:

[0074] Leveraging the translation invariance of the PFDA-MIMO transmitter and receiver arrays, the ESPRIT algorithm is used to estimate the azimuth and range parameters of the target and interference. This avoids the high computational complexity of traditional two-dimensional spectral peak search, improving the efficiency and accuracy of range-angle joint localization in multi-interference scenarios. Addressing the rank expansion effect of polarization-agile interference and the secondary range ambiguity problem of the PFDA-MIMO system, weighted minimum range is used to automatically partition and pair the estimated parameters. This correctly associates two polarization components belonging to the same physical interference source. Furthermore, cyclic range metrics and periodic averaging are introduced in parameter pairing, ensuring reasonable matching and fusion of range parameters within the ambiguity period, thereby reducing the joint steering vector deviation caused by range phase term errors. Replacing the traditional long-term average statistical estimation method with snapshot-by-shot instantaneous estimation allows for more accurate tracking of the dynamic changes in interference polarization. By reconstructing the covariance matrix step by step, the model mismatch caused by the inaccurate representation of polarization agility features by the traditional sample covariance matrix can be effectively reduced. This allows the beamforming weights to be more accurately aligned with the current polarization direction of the interference to form a suppression null, thereby improving the output signal-to-interference-plus-noise ratio, interference suppression depth, and target echo retention capability under polarization agility interference environment. Attached Figure Description

[0075] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0076] Figure 1 This is a flowchart of a polarization agile interference suppression method based on a polarization frequency-controlled array radar provided in an embodiment of the present invention;

[0077] Figure 2 This is a scatter plot of two-dimensional spatial parameter estimation for the target and polarization agile interference in this embodiment of the invention;

[0078] Figure 3 This is a scatter plot of polarization parameter estimation for polarization agile interference according to an embodiment of the present invention. Wherein, (3-a) represents the polarization phase angle of the polarization agile interference (instantaneous jump). Estimate the scatter plot; (3-b) is the polarization phase difference of the polarization agile disturbance (instantaneous jump). Estimate the scatter plot; (3-c) is the polarization phase angle of the polarization agile interference (slow jump). Estimate the scatter plot; (3-d) is the polarization phase difference of the polarization agile interference (slow jump). Estimate the scatter plot;

[0079] Figure 4 These are the results after beamforming matched filtering in the embodiments of the invention. Among them, (4-a) is the result under the LFM dummy target polarization agile interference scenario; (4-b) is the result under the noise suppression polarization agile interference scenario. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0081] This embodiment takes a 16-element linear PFDA-MIMO radar as an example and provides a polarization-agile interference suppression method based on a polarization frequency-controlled array radar, such as... Figure 1 As shown, it includes the following steps:

[0082] S1. Receive the PFDA-MIMO radar echo signal, perform a rough range estimate using down-conversion and matched filtering, and simultaneously divide the transmitting and receiving arrays using the ESPRIT algorithm. Leveraging the translation invariance of the array structure, the two-dimensional spatial parameters (azimuth and range) of the interference signal are converted into rotational relationships between signal subspaces for solution, yielding the estimated two-dimensional spatial parameters. The specific steps are as follows:

[0083] For a uniform linear PFDA-MIMO radar composed of orthogonal dipoles with M transmitting elements and N receiving elements, the spacing between the transmitting elements is... The spacing between the receiving array elements is , For wavelength, a small frequency offset is introduced for the transmitting array. , No. The signals corresponding to each transmitting element are:

[0084]

[0085] In the formula It is a natural constant. The imaginary unit, It is a time variable. The pulse repetition period, The center frequency of the carrier. , for the first The carrier frequency of each transmitting element For the first The polarization vector of each transmitting element. For the first The complex amplitude components of each transmitting element in the horizontal polarization direction. For the first Complex amplitude components of each transmitting element in the vertical polarization direction For the first One baseband waveform, For the first Complex conjugate of each baseband waveform:

[0086]

[0087] Assuming there is one real target and [other target] in the environment where the PFDA-MIMO radar is located. There are several false targets, where the real target is located... The false target interference signal is located at , , and Indicates the azimuth angle of the target and the interference signal. and Let represent the distance between the target and the interference signal, then the th The signal received by each receiving element can be represented as:

[0088]

[0089] in Represents the speed of light. Indicates the amplitude of the target signal. Indicates the first The amplitude of the false target Represents the polarization scattering matrix of the target. and They represent the first The transmit and receive polarization vectors of a dummy target; , These respectively represent the signal from the first... The launch array element is launched, passing through the real target, the first... After being reflected again from a false target, it reached the first... Path delay of each receiving array element:

[0090]

[0091]

[0092]

[0093] in This represents the scattering coefficient of the horizontally transmitted and horizontally received polarized channels. This represents the scattering coefficient of the vertically transmitted and horizontally received polarized channels. This represents the scattering coefficient of the horizontally transmitting and vertically receiving polarized channels. This represents the scattering coefficient of the vertically transmitted and vertically received polarized channels.

[0094] For the The signal received by the receiving array element is down-converted and matched-filtered, wherein the target signal and the first element are... The output signals after matched filtering of the interference signals can be represented as follows: , :

[0095]

[0096]

[0097] in Indicates the first The complex amplitude of the interference signal, This represents the polarization scattering matrix of the decoy jammer. and They represent the first The transmit and receive polarization vectors of a dummy target.

[0098] for The receiving array element, whose actual target received signal and the first receiving array element. A fake target receives a signal. They can be vectorized as follows:

[0099]

[0100]

[0101] in Represents the Kronecker product. Represents the Hadamard product. A diagonal matrix representing the polarization vector of the target signal. For the first The diagonal matrix of the polarization vectors of a dummy target signal. , For the complex coefficients of the target signal, For the first The complex coefficients of a dummy target signal, , These are the target polarization information vector and the interference polarization vector, respectively. For angle receiving vector, For angular emission vectors, The range emission vector, Represents distance, where:

[0102]

[0103]

[0104]

[0105] For ease of description, using the vectorized representation described above, consider a real target and... There are several deceptive targets; assuming the total number of snapshots is... Then the matched filter is the first The receive vector of a snapshot can be represented as:

[0106]

[0107] in For the complex coefficients of the target signal, For the first Complex coefficients of the dummy target signal Indicates the true target at the 1st The corresponding received response vector for each snapshot Indicates the first The false target signal in the first The corresponding received response vector for each snapshot It is a Gaussian white noise signal.

[0108] Define two overlapping receiver subarrays in the receiver array: Subarray 1 contains the previous... Each array element, including subarray 2. Each subarray has one element. The two subarrays differ spatially by one element. The translation amount. Construct the receiver array selection matrix for the two subarrays. and .

[0109] The signal subspace corresponding to the large eigenvalues ​​obtained by decomposing the covariance matrix of the received data. There exists a non-singular linear transformation matrix. Make ,Right now ,in ,

[0110]

[0111] in This represents the transformation matrix obtained from the rotation-invariant relation of the receiving array. This represents the phase rotation matrix of the receiving array. This represents the incident angle of the false target signal after the interference subspace has expanded.

[0112] The transmitter array contains There are array elements, and the spacing between the array elements is... The transmission array is divided into Given three polarization pairs, define two emitter subarrays: subarray 3 consists of the first element of each emitter polarization pair, and subarray 4 consists of the second element of each emitter polarization pair. Construct the emitter array selection matrices for subarrays 3 and 4. , Establish rotation-invariant equations: ,in ,

[0113]

[0114] This represents the transformation matrix obtained from the rotation-invariant relation of the transmitting array. This represents the phase rotation matrix of the transmitting array. This indicates the location of the false target signal after the interference subspace expands.

[0115] Solve using least squares respectively ,

[0116]

[0117]

[0118] In the formula The transformation matrix represents the transformation obtained by considering the rotation-invariant relationship of the receiving array. The estimation results The transformation matrix represents the transformation obtained by considering the rotational invariance of the transmitting array. The estimation results Denotes the Frobenius norm. This represents the Moore-Penrose pseudo-inverse operation.

[0119] because and resemblance, and They are similar, therefore their eigenvalues ​​are the same. Assume the solution yields... The eigenvalues ​​are respectively and , The azimuth and distance are obtained as follows:

[0120]

[0121]

[0122] in At the maximum unambiguous distance The residual value within the modulus.

[0123] S2. For the two-dimensional signal subspace expansion characteristic of polarization agile interference, the number of its two-dimensional spatial parameters will expand to twice the number of actual physical signal sources. The difference in dimensional scale between angle and distance is eliminated by weighted minimum distance. To address the distance ambiguity of PFDA-MIMO, cyclic distance is introduced, and a generalized Euclidean distance between two points is defined. The estimated two-dimensional spatial parameters of the multiple interferences and targets are self-paired to obtain the optimal partitioning scheme. The obtained parameters are then fused (angle average and distance circumferential average) to obtain the paired two-dimensional spatial parameters of the target and interference. The specific steps are as follows:

[0124] After obtaining the hybrid eigenvalues ​​using the ESPRIT algorithm, due to the two-dimensional signal subspace expansion characteristic of polarization agile interference, the output will... An unordered set of spatial location candidates ,because and By introducing cyclic distances with different physical dimensions, we can reconstruct any two estimated points. and Distance difference between:

[0125]

[0126] In the formula Indicates fuzzy distance, This represents the distance difference.

[0127] Further introduce angle normalization factor and distance normalization factor The class-generalized Euclidean distance between any two points in the candidate set is defined as:

[0128]

[0129] The two-dimensional spatial location candidate set output by the ESPRIT algorithm Viewed as an undirected complete graph The vertex set, where the vertex set Edge set The weights on the surface are the generalized Euclidean distances. Assume the vertex index corresponding to the target is... Then the remainder The subset consisting of vertices is In the subset Seeking a partitioning scheme To minimize the sum of edge weights for each pair within the partition, we define a local minimum cost function under this condition. :

[0130]

[0131] Traverse all candidate target points Find the optimal outlier index for the global minimum of its paired cost function. At this time, make Partition scheme to obtain the minimum value That is The optimal pairing combination of polarization-agile interferences is obtained. Optimal pairing indexes for polarization agile interference Then, its parameters are fused; for those defined in Euclidean space The azimuth angle on the surface is the optimal unbiased estimate of the arithmetic mean of the two values:

[0132]

[0133] For a one-dimensional spherical manifold Baseband distance According to the definition of the Fréchet mean in Riemannian geometry:

[0134]

[0135] Using isomorphism mapping Map the distance onto the unit circle in the complex plane, calculate the argument of the vector sum in the complex plane, and then perform the inverse mapping. Projecting back into the distance domain, we can obtain the closed-form analytical solution to the above Fréchet optimization problem:

[0136]

[0137] The absolute distance can be recovered by combining the radar's fast time prior distance. At this point, the two-dimensional spatial parameters of the interference signal can be obtained. Remaining unpaired outlier index The two-dimensional spatial position is the two-dimensional spatial parameter of the target signal. .

[0138] S3. Using the obtained azimuth and range parameters of the target and interference, spatial decoupling is performed. The polarization state vector of each interference signal under a single snapshot is obtained using the Linearly Constrained Minimum Variance (LCMV) criterion. The polarization parameters (polarization angle and polarization phase angle) under a single snapshot are then solved using the least squares criterion to obtain the instantaneous polarization information of each interference signal under a single snapshot. The specific steps are as follows:

[0139] Two-dimensional spatial parameters of the target signal estimated based on step S2 and the two-dimensional spatial parameters of the interference signal Constructing the exclusion of the first The interference plus noise covariance matrix of each interference. :

[0140]

[0141] in Indicates the first An angle of interference and distance Related joint guidance matrix, For the target signal power, , To interfere with signal power, This represents noise power.

[0142] Make the first The interference passes through, while simultaneously creating depth space nulls in other targets and interference directions. According to the Linearly Constrained Minimum Variance (LCMV) criterion, the first interference can be excluded. Spatial decoupling weight matrix of each disturbance :

[0143]

[0144] Receive data The weight vector matrix is ​​formed by this beam. Then, the first single snapshot output The polarization vector of the interference , column vector Rearranged as Using the least squares method, we can obtain the estimated value for the th... The polarization scattering matrix of the interference It can be expressed as the outer product of the jammer's receiving polarization vector and transmitting polarization vector:

[0145]

[0146] in Indicates the first The interference at the first The horizontally polarized scattering component captured in a quick snapshot. , express The interference at the first Cross-polarized scattering components captured in a quick snapshot No. The interference at the first The vertically polarized scattering component captured in a quick snapshot.

[0147] No. Polarization phase angle of the emitted polarization vector of each interference Polarization phase difference , No. Polarization phase angle of the received polarization vector of each interference Polarization phase difference It can be represented as:

[0148]

[0149] S4. Based on the estimated azimuth angle, range, and instantaneous parameters (polarization angle and polarization phase angle) of the interference signal, the interference steering vector under each snapshot is accurately reconstructed, and an instantaneous interference plus noise covariance matrix is ​​established accordingly. Simultaneously, an adaptive space-time-polarization joint filter is designed based on the MVDR criterion to minimize the interference noise output power while ensuring distortion-free output of the desired target signal, thereby effectively suppressing polarization-agile interference. Details are as follows:

[0150] Using the two-dimensional spatial parameters and polarization parameters of the interference signal obtained in steps S2 and S3, the instantaneous spatial-polarization domain steering vector for each interference reconstruction snapshot is:

[0151]

[0152] In the formula For the first A column vector of polarization information of each disturbance. This indicates vectorized operations. The amplitude of the interference signal, express The interference at the first The diagonal matrix of polarization vectors captured in a snapshot. .

[0153] Using the reconstructed instantaneous steering vector of the disturbance, the disturbance plus noise covariance matrix is ​​reconstructed in a single snapshot:

[0154]

[0155] In the formula The matrix formed by all the instantaneous steering vectors of the disturbances. This represents noise power.

[0156] Filter design based on the Minimum Variance Distortionless Response (MVDR) criterion:

[0157]

[0158] in The joint steering vector of the target's spatial-polarization domain. This represents the reconstructed instantaneous disturbance plus noise covariance matrix.

[0159] The optimal weight vector can be obtained by solving the filter:

[0160]

[0161] In the formula The joint steering vector of the target space-polarization domain.

[0162] The received signal is filtered using the aforementioned weight vector:

[0163]

[0164] In the formula This represents the filtered signal. This indicates that the array receives signals. Represents the weight vector.

[0165] After the received signal is filtered, polarization agility interference can be robustly suppressed, and the system output signal-to-interference-plus-noise ratio and target echo retention capability can be improved.

[0166] To further verify the performance of the method proposed in this invention, experimental verification was conducted, with the experimental parameters set as shown in Table 1 below:

[0167] Table 1 Parameter Settings

[0168] parameter value parameter value Number of launch array elements 16 Pulse repetition period 10us Number of receiving array elements 16 Signal-to-noise ratio 10dB carrier frequency 10GHz Noise ratio 30 dB Frequency deviation 5MHz Target information (20°, 8km) bandwidth 4MHz False Target 1 (10°, 4.8km) Pulse width 4us False Target 2 (21.3°, 11km) Sampling rate 8MHz

[0169] Based on the parameter settings given in Table 1, simulation experiments were conducted. Pseudo-target 1 used intra-pulse polarization transient modulation, while pseudo-target 2 used intra-pulse polarization slow modulation. The rotational invariance principle of the ESPRIT algorithm was used to estimate the spatial two-dimensional parameters of the target and interference. Weighted minimum Euclidean distance and cyclic measure were used to perform parameter self-pairing for multiple interferences, and combined with coarse distance information to further obtain accurate spatial position parameters, as shown in Table 1. Figure 2 As shown; based on the obtained spatial location of the interference Spatial decoupling is performed using the least squares criterion to analyze the instantaneous polarization parameters under a single snapshot. The solution is performed, and the first 200 snapshots are displayed as follows: Figure 3 As shown; where Figure 3 -a、 Figure 3 -b represents the parameter estimation results of polarization phase angle and polarization phase difference under transient polarization parameter conditions, respectively; Figure 3 -c、 Figure 3-d represents the parameter estimation results of polarization phase angle and polarization phase difference under slowly varying polarization parameters, respectively. Based on the obtained spatial location of the interference signal and instantaneous polarization parameter information, the interference plus noise covariance matrix is ​​reconstructed. Adaptive filtering is performed to obtain the optimal filter weight vector. The received data is then filtered using the obtained weight vector, and the results are as follows: Figure 4 As shown. Among them. Figure 4 -a indicates the signal filtering result in the LFM dummy target scenario. Figure 4 -b indicates the signal filtering result under noise suppression interference scenario. The results show that the embodiments of the present invention can effectively suppress polarization agility interference.

[0170] It should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, appropriate adjustments, improvements, or equivalent substitutions can be made to the steps, parameters, structures, or processing methods in the above embodiments without departing from the principles and technical concept of the present invention. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

[0171] The above descriptions are merely some embodiments of the present invention. For those skilled in the art, any modifications, equivalent substitutions, combinations, simplifications, or improvements made within the technical concept, principles, and scope of protection of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for suppressing polarization-agile interference based on a polarization frequency-controlled array radar, characterized in that, Includes the following steps: Step S1: Receive the PFDA-MIMO radar echo signal from the frequency-controlled array, perform a rough range estimate by down-conversion matched filtering, and simultaneously use the ESPRIT algorithm based on rotation invariance to divide the transmitting and receiving arrays. Through the translation invariance of the array structure, the two-dimensional spatial parameters of the interference signal are converted into rotational relationships between signal subspaces for solution, resulting in a set of estimated two-dimensional spatial parameters for the target and multiple interference signals. The two-dimensional spatial parameters include azimuth and range. Step S2: Introduce cyclic distance and define the generalized Euclidean distance between any two points; the estimated two-dimensional spatial parameters of the target and multiple interference signals constitute a two-dimensional spatial location candidate set. The two-dimensional spatial location candidate set is regarded as an undirected complete graph, with vertices as two-dimensional spatial parameters and edge weights as generalized Euclidean distances; perform self-pairing on each vertex to obtain the optimal partitioning scheme, and fuse the parameters of the paired vertices to obtain the two-dimensional spatial parameters of the paired interference signals and the two-dimensional spatial parameters of the unpaired target; Step S3: Using the two-dimensional spatial parameter set obtained in step S2, perform spatial decoupling. By using the linear constraint minimum variance criterion, obtain the polarization state vector of each interference signal under a single snapshot. Then, solve the polarization parameters under a single snapshot using the least squares criterion to obtain the instantaneous polarization information of each interference signal under a single snapshot. Step S4: Based on the two-dimensional spatial parameters and instantaneous polarization information of the paired interference signal, the interference steering vector under each snapshot is accurately reconstructed, and the instantaneous interference plus noise covariance matrix is ​​established accordingly; at the same time, an adaptive space-time-polarization joint filter is designed based on the minimum variance distortionless response (MVDR) criterion to minimize the interference noise output power while ensuring the distortionless output of the desired target signal.

2. The polarization agility interference suppression method based on a polarization frequency-controlled array radar according to claim 1, characterized in that, The down-conversion matched filter performs a rough distance estimate as follows: For a uniform linear PFDA-MIMO radar composed of orthogonal dipoles with M transmitting elements and N receiving elements, the spacing between the transmitting elements is... The spacing between the receiving array elements is , For wavelength, a small frequency offset is introduced for the transmitting array. , No. The signals corresponding to each transmitting element are: In the formula It is a natural constant. The imaginary unit, It is a time variable. The pulse repetition period, The center frequency of the carrier. For the first The carrier frequency of each transmitting element For the first The polarization vector of each transmitting element. For the first One baseband waveform; Assuming there is one real target and [other target] in the environment where the PFDA-MIMO radar is located. There are several false targets, where the real target is located... The interference signal of the false target is located in , , and Indicates the azimuth angle of the target and the interference signal. and Let represent the distance between the target and the interference signal, then the th The signal received by each receiving element is represented as: in Represents the speed of light. Indicates the amplitude of the target signal. Indicates the first The amplitude of the false target Represents the polarization scattering matrix of the target. and They represent the first The transmit and receive polarization vectors of a dummy target; , These respectively represent the signal from the first... The launch array element is launched, passing through the real target, the first... After being reflected again from a false target, it reached the first... The path delay of each receiving array element; For the The signal received by the receiving array element is down-converted and matched-filtered, wherein the target signal and the first element are... The output signals after matched filtering of the interference signals are respectively represented as follows: , : in Indicates the first The complex amplitude of the interference signal, Represents the polarization scattering matrix of the decoy jammer; For the complex coefficients of the target signal, For the first Complex coefficients of a dummy target signal; for The receiving array element, whose actual target received signal and the first receiving array element. A fake target receives a signal. The vectorized representations are as follows: in Represents the Kronecker product. Represents the Hadamard product. A diagonal matrix representing the polarization vector of the target signal. For the first The diagonal matrix of the polarization vectors of a dummy target signal. , For angle receiving vector, For angular emission vectors, This is the range emission vector; Assume the total number of snapshots is Then the matched filter is the first The received vector of a snapshot is represented as: in For the first The complex coefficients of a dummy target signal, Indicates the true target at the 1st The corresponding received response vector for each snapshot Indicates the first The false target signal in the first The corresponding received response vector for each snapshot It is a Gaussian white noise signal.

3. The polarization agility interference suppression method based on a polarization frequency-controlled array radar according to claim 2, characterized in that, The rotation-invariant signal parameter estimation algorithm is as follows: Define two overlapping receiver subarrays in the receiver array: Subarray 1 contains the previous... Each array element, including subarray 2. Each subarray has one array element; the two subarrays differ spatially by one array element. The translation amount; constructing the receiver array selection matrix for the two subarrays. and ; The signal subspace corresponding to the large eigenvalues ​​obtained by decomposing the covariance matrix of the received data. There exists a non-singular linear transformation matrix. Make ,Right now ,in , This represents the transformation matrix obtained from the rotation-invariant relation of the receiving array. Represents the phase rotation matrix of the receiving array: in This represents the incident angle of the false target signal after the interference subspace has expanded; The transmitter array contains There are array elements, and the spacing between the array elements is... The transmission array is divided into Given three polarization pairs, define two emission subarrays: subarray 3 consists of the first element of each emission polarization pair, and subarray 4 consists of the second element of each emission polarization pair; construct the emission array selection matrices for subarrays 3 and 4. , Establish rotation-invariant equations: ,in , This represents the transformation matrix obtained from the rotation-invariant relation of the transmitting array. Represents the phase rotation matrix of the transmitting array: in Indicates the location of the false target signal after the interference subspace expands; Solve using least squares respectively , Assuming the solution is obtained The eigenvalues ​​are respectively and , The azimuth and distance are obtained as follows: in At the maximum unambiguous distance The residual value within the modulus.

4. The polarization agility interference suppression method based on a polarization frequency-controlled array radar according to claim 3, characterized in that, Step S2 is as follows: After obtaining the estimated azimuth and distance using the ESPRIT algorithm, the output is... An unordered set of spatial location candidates Introducing cyclic distance, we can reconstruct any two estimated points. and Distance difference between: In the formula Indicates fuzzy distance, Indicates distance difference; Further introduce angle normalization factor and distance normalization factor The class-generalized Euclidean distance between any two points in the candidate set is defined as: The two-dimensional spatial location candidate set output by the ESPRIT algorithm Viewed as an undirected complete graph The vertex set, where the vertex set Edge set The weights on the surface are the generalized Euclidean distances. Assume the vertex index corresponding to the target is Then the remainder The subset consisting of vertices is In the subset Seeking a partitioning scheme The local minimum cost function under this condition is defined by minimizing the sum of the edge weights of each pair within the partition; all candidate target points are traversed. Find the optimal outlier index for the global minimum of its paired cost function. At this time, make Partition scheme that achieves the minimum value That is The optimal homogeneous pairing combination of polarization agile interferences is obtained. Optimal pairing indexes for polarization agile interference Then, the azimuth and distance of the K index pairs are fused to obtain the two-dimensional spatial parameters of the K interference signals, and the isolated point index. For target signal.

5. The polarization agility interference suppression method based on a polarization frequency-controlled array radar according to claim 4, characterized in that, Step S3 is as follows: Based on the two-dimensional spatial parameters of the target signal obtained in step S2 and the two-dimensional spatial parameters of the interference signal Constructing the exclusion of the first The interference plus noise covariance matrix of each interference. : in Indicates the first An angle of interference and distance Related joint guidance matrix, For the target signal power, To interfere with signal power, Noise power; Make the first The interference passes through, while simultaneously creating depth space nulls in other targets and interference directions. Based on the linear constraint minimum variance criterion, the interference is excluded. Spatial decoupling weight matrix of each disturbance : Receive data The weight vector matrix is ​​formed by this beam. Then, the first single snapshot output The polarization vector of the interference , column vector Rearranged as The least squares method is used to solve for the estimated th... The polarization scattering matrix of the interference This is expressed as the outer product of the jammer's receiving polarization vector and transmitting polarization vector: in Indicates the first The interference at the first The horizontally polarized scattering component captured in a quick snapshot. , express The interference at the first Cross-polarized scattering components captured in a quick snapshot No. The interference at the first The vertically polarized scattering component captured in a quick snapshot; and They represent the first The polarization phase angle and polarization phase difference of the emitted polarization vector of each interference. and They represent the first The polarization phase angle and polarization phase difference of the received polarization vector of each interference.

6. The polarization agility interference suppression method based on a polarization frequency-controlled array radar according to claim 5, characterized in that, Step S4 is as follows: Reconstruct the instantaneous spatial-polarization domain steering vector for each interference signal in a single snapshot: In the formula For the first A column vector of polarization information of the interference. This indicates vectorized operations. The amplitude of the interference signal, express The interference at the first The diagonal matrix of polarization vectors captured in a single snapshot; Using the reconstructed instantaneous steering vector of the disturbance, the disturbance plus noise covariance matrix is ​​reconstructed in a single snapshot: In the formula The matrix formed by all the instantaneous steering vectors of the disturbances; Filter design based on the minimum variance distortionless response criterion: in The joint steering vector of the target's spatial-polarization domain. This represents the reconstructed instantaneous disturbance plus noise covariance matrix; The optimal weight vector can be obtained by solving the filter: The received signal is filtered using the aforementioned weight vector: In the formula This represents the filtered signal. This indicates that the array receives signals. Represents the weight vector.

7. A polarization-agile interference suppression method based on a polarization frequency-controlled array radar according to claim 6, characterized in that, The azimuth and distance of the K index pairs are fused to obtain the two-dimensional spatial parameters of the K interference signals, as follows: For those defined in Euclidean space The azimuth angle on the surface is the optimal unbiased estimate of the arithmetic mean of the two values: For a one-dimensional spherical manifold Baseband distance According to the definition of the Fréchet mean in Riemannian geometry: Using isomorphism mapping Map the distance onto the unit circle in the complex plane, calculate the argument of the vector sum in the complex plane, and then perform the inverse mapping. Projecting back into the distance domain, we obtain the closed-form analytical solution to the above Fréchet optimization problem: The absolute distance can be recovered by combining the radar's fast time prior distance. .

8. The polarization agility interference suppression method based on a polarization frequency-controlled array radar according to claim 7, characterized in that, The solution is obtained using least squares. , The formula is as follows: In the formula The transformation matrix represents the transformation obtained by considering the rotation-invariant relationship of the receiving array. The estimation results The transformation matrix represents the transformation obtained by considering the rotational invariance of the transmitting array. The estimation results Denotes the Frobenius norm. This represents the Moore-Penrose pseudo-inverse operation.

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