Dimension reduction robust adaptive beamforming method based on cyclic optimization of packets

Abstract

The application discloses a dimension-reduction robust adaptive beamforming method based on grouping cycle optimization, which comprises the following steps: 1, calculating a sampling covariance matrix based on array sampling snapshot data; 2, designing a linear constraint condition of a weight vector according to actual application requirements; 3, initializing the weight vector and related parameters; 4, grouping elements in the weight vector and correspondingly blocking the related parameters; 5, calculating a blocking matrix and a transformation matrix corresponding to each group; 6, optimizing elements in each group and updating the related parameters in sequence; 7, calculating an output variance and a relative change measure of two successive iterations; 8, making a threshold decision on whether iteration is terminated, if the relative change measure is less than a threshold value, iteration is terminated and an optimal weight vector is output, otherwise, steps 6-8 are repeated.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of adaptive interference suppression, and particularly relates to a dimensionality reduction robust adaptive beamforming method based on grouping cycle optimization. BACKGROUND

[0002] The adaptive digital beamforming (ADBF) technology realizes adaptive suppression of undesired signals in received data by optimizing the weighting values of each channel of the array, thereby effectively improving the signal-to-interference-and-noise ratio (SINR), and has been widely applied in the fields of radar, communication, sonar, etc. The common implementation methods of ADBF include the sample covariance matrix inversion method and the adaptive filtering method. The former is directly derived based on the maximum SINR criterion, and has reliable performance, but involves complex matrix inversion operation; the latter is based on low-complexity iteration / recursion implementation, but the convergence is difficult to guarantee in actual application scenarios. Although the sample covariance matrix inversion method is currently the most commonly used in radar systems, for large-scale phased arrays with a large number of antenna elements, effective dimensionality reduction processing must be taken to meet the real-time requirements of engineering applications. The commonly used dimensionality reduction methods include the beam-domain ADBF method and the subarray-level ADBF method. The former reduces the data dimension by forming multiple beams and realizes interference cancellation by using auxiliary beams, but in order to ensure its performance, it is necessary to estimate the interference direction, which inevitably brings additional hardware cost or computational cost; the latter reduces the data dimension by data synthesis of multiple antenna elements in the subarray to reduce the computational burden of the sample covariance matrix-based ADBF method. For large phased array radars with a long range, in order to meet the power requirements of the system, the receiving array has thousands or even tens of thousands of antenna elements, and in order to reduce the hardware and processing cost, the radar usually digitizes at the subarray level; however, in order to reduce the grating lobe effect caused by subarray-level digitization, the size of the subarray is usually limited, and the array still has hundreds of digital channels, so further dimensionality reduction processing must be considered when using the subarray-level ADBF technology.

[0003] The patent application filed by Xi'an University of Electronic Science and Technology, entitled "Cyclic Joint Adaptive Beamforming Method Based on Subarray Partitioning" (Patent Application No.: 201410140297.1, Publication No.: CN103885045B), discloses a cyclic joint adaptive beamforming method based on subarray partitioning. This method decomposes the weight vector of the entire array into the Kronecker product of the weight vectors of the inner and outer arrays through uniform subarray partitioning, and obtains the optimal weight vector based on cyclic optimization of the weight vectors of the two arrays. Compared with the traditional sampling covariance matrix inversion method, this method can reduce computational complexity to a certain extent and requires fewer training samples. However, it still requires two matrix inversions in each iteration, resulting in limited improvement in real-time performance for large-scale phased arrays. Moreover, this method actually requires the array to be an ideal array with uniform spatial arrangement; for irregular arrays or real arrays with non-ideal characteristics, this method is no longer applicable, or its performance will be significantly reduced. Summary of the Invention

[0004] The purpose of this invention is to overcome the real-time performance limitations of existing adaptive digital beamforming (ADBF) techniques when applied to large-scale phased arrays. This invention provides a dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization. This method combines digital subarray partitioning and grouped cyclic optimization, decomposing high-dimensional matrix inversion operations into multiple parallel-processable low-dimensional matrix inversion operations. The iterative process for solving the optimal weight vector involves only multiplication and addition operations, significantly reducing the computational complexity of large-scale phased array ADBF. It achieves excellent anti-interference performance without requiring estimation of the number and direction of interference, and requires far fewer training samples than traditional sampling covariance matrix inversion methods, making it more suitable for complex electromagnetic environments with highly dynamic interference states. It facilitates low sidelobe processing, further weakening unwanted signals such as clutter while suppressing strong directional interference. It is compatible with arrays with regular / irregular spatial arrangements and cell-level / subarray-level digitization.

[0005] To achieve the aforementioned objectives of the invention, the technical solution adopted to solve its technical problems is as follows:

[0006] A dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization includes the following steps:

[0007] Step 1: Calculate the sampling covariance matrix based on the array sampling snapshot data;

[0008] Step 2: Design linear constraints for the weight vectors based on actual application requirements;

[0009] Step 3: Initialize the weight vector and related parameters;

[0010] Step 4: Group the elements in the weight vector and divide the relevant parameters into blocks accordingly;

[0011] Step 5: Calculate the blocking matrix and transformation matrix for each group;

[0012] Step 6: Optimize each group of elements sequentially and update the relevant parameters;

[0013] Step 7: Calculate the output variance and the measure of relative change between two consecutive iterations;

[0014] Step 8: Determine whether the iteration should terminate based on a threshold. If the relative change metric is less than the threshold, terminate the iteration and output the optimal weight vector; otherwise, repeat steps 6 to 8.

[0015] Furthermore, step 1 includes the following:

[0016] Based on the sampled snapshot data X from the radar receiver array, estimate the sampling covariance matrix R: R = X X H / L, where X is an M×L dimensional matrix, each column of which represents the sampled data of all digital channels at a certain moment, M is the total number of digital channels in the phased array, and L is the number of time samples; the superscript H denotes the conjugate transpose operation of the matrix, denoted as The total number of antenna elements in the phased array:

[0017] If the array is digitized at the subarray level, then Where, N m The number of antenna elements contained in the m-th subarray;

[0018] If the array is digitized at the cell level, then obviously there is

[0019] Furthermore, step 2 includes the following:

[0020] Based on practical application requirements, design linear equality constraints C for the ADBF weight vector w, with a dimension of M×1. H w = v, where the size of C is M × Q, the size of v is Q × 1, and Q is the number of constraints.

[0021] Specifically, the design rules for the constraints described in step 2 are as follows:

[0022] a) Distortionless response: If only a signal in a certain direction of interest is required to pass through without distortion, then C = T H a, v = 1, where T is The transformation matrix of the subarray, where 'a' is the matrix corresponding to the direction of interest. The dimensional array steering vector; to minimize unwanted signals outside the main lobe, the resulting beam has low sidelobe characteristics. In this case, C can be rewritten as... in, Represents the Hadamard product. The dimension vector y is the amplitude weighted average at a specified sidelobe level;

[0023] b) Functional Extension: To further suppress interference in a specified direction or broaden the main lobe / null, additional constraints can be added to the distortion-free response. This involves adding corresponding columns and rows to C and v, respectively. If the array steering vector for suppressing interference in a specific direction is a′, then C = T. H [aa′]、 If a low-sidelobe beam is desired, then C can be rewritten similarly to the above.

[0024] The two design rules described above correspond to the minimum variance distortionless response beamformer and the linearly constrained minimum variance beamformer at the subarray level, respectively. The specific construction of the subarray transformation matrix T involved is explained below:

[0025] If the array is digitized at the subarray level, then T is constructed as follows: If the phased array... If an antenna element belongs to the m-th (m = 1, 2, ..., M) subarray, then the first antenna element of T... row, m-th column element for in, For the first The simulated weighted values ​​on each antenna element are indicated by the superscript "*" to represent the conjugate of the complex number; otherwise, the corresponding element is 0.

[0026] If the array is digitized at the cell level, then T is obviously the identity matrix of the corresponding size.

[0027] Furthermore, step 3 includes the following:

[0028] Initialize the ADBF weight vector w = C(C) to be optimized H C) -1 v, vector u = Rw, and output variance p = w H Rw = w H u, where (·) -1 Represents the matrix inversion operation; and uses... and Record the historical values ​​of w and p respectively, i.e. The symbol "←" indicates that the value on the right is assigned to the value on the left.

[0029] Furthermore, step 4 includes the following:

[0030] Divide the M elements constituting w into J groups, where the j-th group (j = 1, 2, ..., J) contains K elements. j K elements j K should be satisfiedj >Q and To reduce computational load, K j It should be slightly larger than Q, and the vector u, constraint matrix C, and sampling covariance matrix R should be divided into blocks according to the corresponding partitioning method.

[0031] Specifically, the block division rules for vectors and matrices described in step 4 are as follows:

[0032] Divide the vector w into blocks as follows:

[0033]

[0034] Among them, w j K is formed by the j-th group of elements j The 1×1 dimensional column vector, according to the corresponding partitioning method, divides the vector u, constraint matrix C, and sampling covariance matrix R into blocks by row or column as follows:

[0035] R = [R1 R2 … R] J ]

[0036] Among them, u j C j R j The dimensions are K j ×1、K j ×Q、M×K j ; and R j Further divided into:

[0037]

[0038] Among them, R ij The size is K i ×K j .

[0039] Furthermore, step 5 includes the following:

[0040] Calculate the transformation matrix for each group (j = 1, 2, ..., J). Among them, B j C j Corresponding K j ×(K j -Q) dimensional grouping blocking matrix, specifically composed of C j orthogonal complement matrix The previous K j -Column Q is given.

[0041] Specifically, the simplified calculation method for the grouping blocking matrix and transformation matrix in step 5 is as follows:

[0042] a) Given and All are full-rank Hermitian matrices, and the corresponding matrix inversion can be achieved based on fast algorithms such as Cholesky decomposition;

[0043] b) In calculating B for each group j and D j At this time, it can be accelerated through parallel processing;

[0044] c) If the subarrays corresponding to each group have translation invariance, that is, they have the same number of antenna elements and spatial arrangement, then the corresponding B j They are all the same, that is, B. j It only needs to be calculated once, thus significantly reducing the amount of computation;

[0045] d) When Q = 1, B j It can also be given directly by the following formula:

[0046]

[0047] Where c jk Represents vector C j The k-th element, since most of its elements are zero, is represented by the sparse matrix B. j Calculate D j The amount of computation required for the process can also be significantly reduced.

[0048] Furthermore, step 6 includes the following:

[0049] Using minimizing the output variance of beamforming as the criterion, the column vector w composed of each group of elements is optimized sequentially in the order of j = 1, 2, ..., J. j And update vector u, the corresponding optimization / update expression is: Δw j =-D j u j w j ←w j +Δw j u←u+R j Δw j .

[0050] Specifically, the principle of step 6 is described in detail below:

[0051] To achieve adaptive suppression of interference and noise, the following optimization problem is constructed with respect to the weighting vector w, minimizing the output variance of beamforming under the linear constraints designed in step 2:

[0052]

[0053] in, This means finding the w that minimizes the cost function Π under the constraint of Θ. Based on the partitioning method described in step 4, the above optimization problem can be rewritten as:

[0054]

[0055] In each iteration, the component w formed by the j-th group of elements is optimized sequentially. j (j = 1, 2, ..., J) to complete a global update of the variable w to be optimized; when optimizing a certain set of elements w j At that time, only the additional change Δw for this group j While fixing all other groups w i (i≠j), that is:

[0056]

[0057] in, This is the estimate of the j-th group of elements obtained in the previous iteration;

[0058] Therefore, the above optimization problem can be decomposed into the following: the change Δw of the j-th group of elements j Sub-optimization problem:

[0059]

[0060] in, To be with Δw j Irrelevant constant terms can be ignored in subsequent solutions without affecting the obtained optimal solution. Furthermore, the constraints in the above equation can be rewritten as follows: Given that the initial value of w given in step 3 satisfies C H w = v, as long as w is guaranteed during the iterative update process. That will satisfy The condition holds true for all conditions, thus guaranteeing that the constraints of this sub-optimization problem always hold true. Therefore, the sub-optimization problem can be further rewritten in the following equivalent form:

[0061]

[0062] The Lagrange multiplier method is applied to solve this sub-optimization problem, introducing a Q×1 dimensional multiplier vector λ. j Then the optimal solution satisfies:

[0063]

[0064] From the above equation, the expression for the optimal solution can be obtained as follows: Observing the definition of the intermediate parameter u given in step 3, we can see that... Therefore: Substitute it into the equality constraints achievable Substitute it into Δw j The expression can be obtained as follows:

[0065]

[0066] The terms within the square brackets on the right side of the equal sign can be simplified as follows:

[0067]

[0068] in, Representation matrix The orthogonal projection matrix, obviously, for K j ×Q-dimensional matrix C j If we find a K that is orthogonal to it in the column space j ×(K j -Q) Dimensional Grouping Blocking Matrix B j , making Then there is That is all Replace with matrix projection matrix Therefore:

[0069]

[0070] Combine step 5 with matrix D j From the definition, we can obtain Δw j =-D j u j ;

[0071] In summary, we can obtain Δw in step 6. j The optimal solution Δw j =-D j u j In the current iteration, w j The updated value can be obtained from the solution and change Δw obtained in the previous iteration. j The sum is given, i.e., w j ←w j +Δw j Additionally, according to the definition of u in step 3, u = Rw, after the weighted vector w is updated, u still needs to be adjusted, since only one set of elements w is updated each time. j In fact, the change in u is only R. j Δw j To save computational costs, its update expression is u←u+R j Δw j .

[0072] Furthermore, step 7 includes the following:

[0073] After completing a process for all groups wj After the optimized update of (j = 1, 2, ..., J), the current output variance p = w is calculated. H u, and the measure of the relative change in output variance between two consecutive iterations. Or a measure of the relative change in the weight vector.

[0074] Furthermore, step 8 includes the following:

[0075] The iteration termination condition is set as Δp < ε or Δw < ε, where ε is a threshold value that can be 10. -3 10 -4 If the condition is not met, then the currently obtained w and p are recorded as historical values, i.e. Repeat steps 6-8; if satisfied, terminate the iteration, using the currently obtained w as the final ADBF weight vector, and utilize its conjugate transpose w. H The optimal output w can be obtained by weighted summation of the array sampling snapshot data X. H X completes adaptive interference suppression.

[0076] By employing the above technical solutions, this invention has the following advantages and positive effects compared with the prior art:

[0077] (1) The proposed method decomposes the high-dimensional matrix inversion operation in the traditional sampling covariance matrix inversion-type ADBF method into multiple low-dimensional matrix inversion operations that can be processed in parallel. The iterative process of solving the optimal weight vector only involves multiplication and addition operations, which greatly reduces the computational cost of large-scale phased array ADBF and improves the ease of its engineering implementation.

[0078] (2) The proposed method can achieve excellent anti-interference performance without the need to estimate the number and direction of interference.

[0079] (3) The proposed method further decomposes the digital subarray partitioning and optimization process, and the sampling covariance matrix for inversion operation is also low. Therefore, the performance remains robust even with a small number of training samples, making it more suitable for practical arrays in engineering applications and complex electromagnetic environments with highly dynamic changes in interference states.

[0080] (4) The proposed method can easily perform low sidelobe processing, and while suppressing strong directional interference, it can further weaken unwanted signals such as clutter outside the main lobe.

[0081] (5) The proposed method has no special requirements for array spatial arrangement and array form: it is compatible with linear array, planar array and three-dimensional array, and is applicable to regular array with uniform array element arrangement and irregular array with arbitrary array element arrangement. It is also applicable to small and medium-sized phased arrays with array element-level digitization and large-scale phased arrays with subarray-level digitization.

[0082] (6) This method is applicable to adaptive interference suppression of narrowband phased array radar. It has low computational complexity, is easy to implement, does not require estimation of the number and direction of interference, has a very robust performance when the number of training samples is small, is compatible with low sidelobe processing, and can further weaken unwanted signals such as clutter outside the main lobe while suppressing interference. It is also applicable to various array spatial arrangements and array forms. Attached Figure Description

[0083] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0084] Figure 1 This is a flowchart of a dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization according to the present invention;

[0085] Figure 2 This is a schematic diagram illustrating the phased array beamforming principle in the application scenario of this invention;

[0086] Figure 3 This is a schematic diagram illustrating the principle of the dimension reduction adaptive beamforming method proposed in this invention;

[0087] Figure 4 To compare the radiation patterns of the proposed method with existing methods under the conditions of unit-level digital phased array and 20,000 sampling snapshots;

[0088] Figure 5 The method proposed in this invention is compared with existing methods under the conditions of unit-level digital phased array and sampling snapshot number of 2000.

[0089] Figure 6 The method proposed in this invention is compared with the existing methods under the conditions of unit-level digital phased array and sampling snapshot number of 200.

[0090] Figure 7 The output signal-to-interference-plus-noise ratio (SINR) changes during the iterative process of the proposed method under the conditions of a unit-level digital phased array and a sampling snapshot number of 20,000.

[0091] Figure 8 To compare the radiation patterns of the proposed method with existing methods under the conditions of subarray-level digital phased array and 20,000 sampling snapshots. Detailed Implementation

[0092] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0093] refer to Figure 1 The flowchart illustrates a dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization, comprising the following steps:

[0094] Step 1: Calculate the sampling covariance matrix based on the array sampling snapshot data;

[0095] Step 2: Design linear constraints for the weight vectors based on actual application requirements;

[0096] Step 3: Initialize the weight vector and related parameters;

[0097] Step 4: Group the elements in the weight vector and divide the relevant parameters into blocks accordingly;

[0098] Step 5: Calculate the blocking matrix and transformation matrix for each group;

[0099] Step 6: Optimize each group of elements sequentially and update the relevant parameters;

[0100] Step 7: Calculate the output variance and the measure of relative change between two consecutive iterations;

[0101] Step 8: Determine whether the iteration should terminate based on a threshold. If the relative change metric is less than the threshold, terminate the iteration and output the optimal weight vector; otherwise, repeat steps 6 to 8.

[0102] The specific explanations for each of the above steps are as follows:

[0103] Furthermore, step 1 includes the following:

[0104] Based on the sampled snapshot data X from the radar receiver array, estimate the sampling covariance matrix R: R = X X H / L, where X is an M×L dimensional matrix, each column of which represents the sampled data of all digital channels at a certain moment, M is the total number of digital channels in the phased array, and L is the number of time samples; the superscript H denotes the conjugate transpose operation of the matrix, denoted as The total number of antenna elements in the phased array:

[0105] If the array is digitized at the subarray level (e.g.) Figure 2 (as shown), then Where, N m The number of antenna elements contained in the m-th subarray;

[0106] If the array is digitized at the cell level, then obviously there is In fact, it is equivalent to the size N of all subarrays. m A subarray-level digital phased array, each with a value of 1.

[0107] Clearly, cell-level digitization can be considered a special case of subarray-level digitization, and Figure 2 It is then presented in a general format. Additionally, it should be noted that, for the sake of simplicity and ease of understanding, the diagrams are presented in a more concise and understandable manner. Figure 2 Arranging all antenna elements in a row does not imply spatial arrangement of the array; the model and method involved in this invention are not actually limited by array arrangement, and neither the individual subarrays nor the individual antenna elements within a subarray need to be arranged in a straight line.

[0108] With Taking a phased array with 100 antenna elements (rectangular arrangement, 100 elements in both the horizontal and vertical directions) as an example, if digitization is performed at the element level... If X has M = 10000 rows, to ensure the obtained ADBF weight vector has satisfactory interference suppression performance, L should also be no less than 10000. At this point, even just calculating R requires a considerable amount of computation; and if digitization is performed at the subarray level, with each N... m =For example, a subarray is composed of 16 antenna elements (4 elements in both the horizontal and vertical directions) (N) m It should generally not be too large (to avoid producing excessively high grid lobes), then Clearly, the dimension of R has been significantly reduced at this point, alleviating the computational burden. However, even with subarray-level digitization, directly using traditional ADBF methods that invert the sampling covariance matrix still results in computational complexity that is insufficient to meet the real-time requirements of many practical applications. Therefore, further dimensionality reduction must be considered when performing ADBF, which is the starting point of this invention.

[0109] Furthermore, step 2 includes the following:

[0110] Based on practical application requirements, design linear equality constraints C for the ADBF weight vector w, with a dimension of M×1. H w = v, where the size of C is M × Q, the size of v is Q × 1, and Q is the number of constraints.

[0111] Specifically, the design rules for the constraints described in step 2 are as follows:

[0112] a) Distortionless response: If only a signal in a certain direction of interest is required to pass through without distortion, then C = T H a, v = 1, where T is The transformation matrix of the subarray, where 'a' is the matrix corresponding to the direction of interest. The dimensional array steering vector, whose specific expression can be explicitly given based on known array arrangement and operating frequency, etc., is used to minimize unwanted signals (clutter and interference) other than the main lobe. To achieve this, it is often desirable for the formed beam to have low sidelobe characteristics. In this case, C can be rewritten as... in, Represents the Hadamard product. The dimension vector y represents the amplitude weighting at a specified sidelobe level. Commonly used design methods include Taylor weighting and Dolph-Chebyshev weighting.

[0113] b) Functional Extension: To further suppress interference in a specified direction or broaden the main lobe / null, additional constraints can be added to the distortion-free response, i.e., corresponding columns and rows can be added to C and v respectively. For example, to additionally suppress interference in a specific direction, with the corresponding array steering vector a′, then C = T H [aa′]、 Furthermore, if a low-sidelobe beam is desired, then C can be rewritten similarly to the above.

[0114] The two design rules described above correspond to the minimum variance distortionless response (MVDR) beamformer and the linearly constrained minimum variance (LCMV) beamformer at the subarray level, respectively. The specific construction of the subarray transformation matrix T involved is explained below:

[0115] If the array is digitized at the subarray level (e.g.) Figure 2 As shown), then T is constructed as follows: If the phased array of the first phase is... If an antenna element belongs to the m-th (m = 1, 2, ..., M) subarray, then the first antenna element of T... row, m-th column element for in, For the first The simulated weighted values ​​on each antenna element are indicated by the superscript "*" to represent the conjugate of the complex number; otherwise, the corresponding element is 0.

[0116] If the array is digitized at the cell level, then T is clearly the identity matrix of the corresponding size (as...). Figure 2 In the special case where all subarrays have a size of 1, the array can employ fully flexible digital weighting, while all analog weights... All are 1).

[0117] Furthermore, step 3 includes the following:

[0118] Initialize the ADBF weight vector w = C(C) to be optimized H C) -1v, vector u = Rw, and output variance p = w H Rw = w H u, where (·) -1 Represents the matrix inversion operation; and uses... and Record the historical values ​​of w and p respectively, i.e. The symbol "←" indicates that the value on the right is assigned to the value on the left.

[0119] Furthermore, step 4 includes the following:

[0120] Divide the M elements constituting w into J groups (e.g., ... Figure 3 As shown), the j-th group (J = 1, 2, ..., J) contains K. j K elements j K should be satisfied j >Q and To reduce computational load, K j It should be slightly larger than Q, and the vector u, constraint matrix C, and sampling covariance matrix R should be divided into blocks according to the corresponding partitioning method.

[0121] Specifically, the block division rules for vectors and matrices described in step 4 are as follows:

[0122] Divide the vector w into blocks as follows:

[0123]

[0124] Among them, w j K is formed by the j-th group of elements j The 1×1 dimensional column vector, according to the corresponding partitioning method, divides the vector u, constraint matrix C, and sampling covariance matrix R into blocks by row or column as follows:

[0125] R = [R1 R2 … R] J ]

[0126] Among them, u j C j R j The dimensions are K j ×1、K j ×Q、M×K j ; and R j Further divided into:

[0127]

[0128] Among them, R ij The size is K i ×K j .

[0129] Furthermore, step 5 includes the following:

[0130] Calculate the transformation matrix for each group (j = 1, 2, ..., J). Among them, B j C j Corresponding K j ×(K j -Q) dimensional grouping blocking matrix, specifically composed of C j orthogonal complement matrix The previous K j -Column Q is given.

[0131] Specifically, the simplified calculation method for the grouping blocking matrix and transformation matrix in step 5 is as follows:

[0132] a) Given and All are full-rank Hermitian matrices, and the corresponding matrix inversion can be achieved based on fast algorithms such as Cholesky decomposition;

[0133] b) In calculating B for each group j and D j At this time, it can be accelerated through parallel processing;

[0134] c) If the subarrays corresponding to each group have translation invariance, that is, they have the same number of antenna elements and spatial arrangement, then the corresponding B j They are all the same, that is, B. j It only needs to be calculated once, thus significantly reducing the amount of computation;

[0135] d) When Q = 1, B j It can also be given directly by the following formula:

[0136]

[0137] Where c jk Represents vector C j The k-th element, since most of its elements are zero, is represented by the sparse matrix B. j Calculate D j The amount of computation required for the process can also be significantly reduced.

[0138] In fact, even if the array spatial arrangement or digital subarray division is irregular, taking MVDR beamforming with only a single linear constraint (Q=1) as an example, C j Calculate the grouping blocking matrix B, where the number of columns is 1. j Inverse of the matrix required for time Simplifying to finding the reciprocal of a scalar, the computational complexity is almost negligible; if the chosen group size K... j If B is only slightly greater than the number of constraints Q, thenj The number of columns K j -Q will be very small, calculate the transformation matrix D. j Matrices that need to be inverted The dimensionality will also be very low, and the computational load will not be too high. Taking the aforementioned number of antenna elements as an example... Taking a phased array with M=625 digital channels as an example, if we let all K... j If both are 5, then J = M / K j =125, K j With Q=4, calculating all transformation matrices only requires 125 parallelizable 4×4 matrix inversions. Compared to directly inverting high-dimensional matrices (10000×10000 or 625×625), its real-time performance is significantly improved.

[0139] Furthermore, step 6 includes the following:

[0140] Using minimizing the output variance of beamforming as the criterion, the column vector w composed of each group of elements is optimized sequentially in the order of j = 1, 2, ..., J. j And update vector u, the corresponding optimization / update expression is: Δw j =-D j u j w j ←w j +Δw j u←u+R j Δw j .

[0141] Specifically, the principle of step 6 is described in detail below:

[0142] To achieve adaptive suppression of interference and noise, the following optimization problem is constructed with respect to the weighting vector w, minimizing the output variance of beamforming under the linear constraints designed in step 2:

[0143]

[0144] in, This means finding the w that minimizes the cost function Π under the constraint of Θ. Based on the partitioning method described in step 4, the above optimization problem can be rewritten as:

[0145]

[0146] like Figure 3 As shown, the idea of ​​"grouped iterative optimization" is to construct an iterative solution framework for optimization problems: in each iteration, the components w formed by the j-th group of elements are optimized sequentially. j (j = 1, 2, ..., J) to complete a global update of the variable w to be optimized; when optimizing a certain set of elements wj At that time, only the additional change Δw for this group j While fixing all other groups w i (i≠j), that is:

[0147]

[0148] in, This is the estimate of the j-th group of elements obtained in the previous iteration;

[0149] Therefore, the above optimization problem can be decomposed into the following: the change Δw of the j-th group of elements j Sub-optimization problem:

[0150]

[0151] in, To be with Δw j Irrelevant constant terms can be ignored in subsequent solutions without affecting the obtained optimal solution. Furthermore, the constraints in the above equation can be rewritten as follows: Given that the initial value of w given in step 3 satisfies C H w = v, as long as w is guaranteed during the iterative update process. That will satisfy The condition holds true for all conditions, thus guaranteeing that the constraints of this sub-optimization problem always hold true. Therefore, the sub-optimization problem can be further rewritten in the following equivalent form:

[0152]

[0153] The Lagrange multiplier method is applied to solve this sub-optimization problem, introducing a Q×1 dimensional multiplier vector λ. j Then the optimal solution satisfies:

[0154]

[0155] From the above equation, the expression for the optimal solution can be obtained as follows: Observing the definition of the intermediate parameter u given in step 3, we can see that... Therefore: Substitute it into the equality constraints achievable Substitute it into Δw j The expression can be obtained as follows:

[0156]

[0157] The terms within the square brackets on the right side of the equal sign can be simplified as follows:

[0158]

[0159] in, Representation matrix The orthogonal projection matrix, obviously, for K j ×Q-dimensional matrix C j If we find a K that is orthogonal to it in the column space j ×(K j -Q) Dimensional Grouping Blocking Matrix B j , making Then there is That is all Replace with matrix projection matrix Therefore:

[0160]

[0161] Combine step 5 with matrix D j From the definition, we can obtain Δw j =-D j u j ;

[0162] In summary, we can obtain Δw in step 6. j The optimal solution Δw j =-D j u j In the current iteration, w j The updated value can be obtained from the solution and change Δw obtained in the previous iteration. j The sum is given, i.e., w j ←w j +Δw j Additionally, according to the definition of u in step 3, u = Rw, after the weighted vector w is updated, u still needs to be adjusted, since only one set of elements w is updated each time. j In fact, the change in u is only R. j Δw j To save computational costs, its update expression is u←u+R j Δw j .

[0163] Furthermore, step 7 includes the following:

[0164] After completing a process for all groups w j After the optimized update of (j = 1, 2, ..., J), the current output variance p = w is calculated. H u, and the measure of the relative change in output variance between two consecutive iterations. Or a measure of the relative change in the weight vector.

[0165] Furthermore, step 8 includes the following:

[0166] The iteration termination condition is set as Δp < ε or Δw < ε, where ε is a threshold value that can be 10. -3 10 -4 If the condition is not met, then the currently obtained w and p are recorded as historical values, i.e. Repeat steps 6-8; if satisfied, terminate the iteration, using the currently obtained w as the final ADBF weight vector, and utilize its conjugate transpose w. H The optimal output w can be obtained by weighted summation of the array sampling snapshot data X. H X completes adaptive interference suppression.

[0167] As can be seen from the above implementation steps, only steps 3 and 5 involve matrix inversion operations, with corresponding matrix dimensions of Q×Q and (K)×Q respectively. j -Q)×(K j -Q), where the number of constraints Q is usually very small, or even 1, and the group size K j Alternatively, a value only slightly greater than Q can be selected to ensure K. j -Q is very small, meaning that this invention only involves low-dimensional matrix inversion operations and simple matrix multiplication and addition operations in the iterative process described in steps 6 to 8. The overall computational complexity is far lower than that of traditional ADBF methods that invert the sampling covariance matrix. In addition, this invention avoids the inversion operation of the high-dimensional sampling covariance matrix, and it no longer needs to collect a large amount of array snapshot data to calculate the sampling covariance matrix, thus ensuring its robustness when training samples are insufficient.

[0168] In summary, the dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization proposed in this invention is suitable for adaptive interference suppression of narrowband phased array radar. It has low computational complexity, is easy to implement, does not require estimation of the number and direction of interference, performs quite robustly under conditions such as a small number of training samples, is compatible with low sidelobe processing, and can further weaken unwanted signals such as clutter outside the main lobe while suppressing interference. It is also universal for various array spatial arrangements and array forms.

[0169] The effectiveness of the present invention has been verified through the following embodiments and simulation experiments.

[0170] The simulation conditions are as follows: the array spatial arrangement is a uniform linear array with an antenna element spacing of half a wavelength (note: the proposed method is not limited to this array form); the maximum amplitude fluctuation of each antenna element is 0.5dB, and the maximum phase fluctuation is 3°; the desired beam pointing is 10°; there is one interference with an interference ratio of 50dB every 5° in the range of -80° to 0° and 20° to 80°, for a total of 30 interferences; the design value of the highest sidelobe level is -35dB; the grouping size K of the proposed method is... j The iteration termination condition is 5, where the relative decrease in the dB value of the output variance p between two iterations is less than 10.-5 .

[0171] Figure 4 A unit-level digital phased array with 100 array elements is given. A comparison of radiation patterns of several adaptive beamforming (ADBF) methods with a sampling snapshot count of 20,000 is presented. The traditional ADBF method is compared to MVDR beamforming, which directly uses the inverse of the sampling covariance matrix. The beam-domain ADBF method is compared to ADBF, which forms an auxiliary beam in the interference direction and uses its main lobe to cancel the sidelobes of the main beam in the desired direction (also known as Gabriel beamforming or adaptive-adaptive beamforming). It can be seen that the proposed method is applicable to adaptive beamforming of cell-level digital phased arrays, achieving the desired low sidelobe effect similar to the compared methods, and forming nulls in 30 interference directions, effectively suppressing unwanted signals. Furthermore, Figure 5 and Figure 6 The radiation patterns are compared when the number of sampling snapshots is 2000 and 200, respectively. It can be seen that as the number of sampling snapshots decreases, although several methods can still accurately form nulls in the direction of interference, the sidelobes of the traditional ADBF method gradually rise, while the proposed method and beam-domain ADBF can maintain stable performance with fewer training samples. In addition, it should be noted that to ensure the performance of beam-domain ADBF, the number and direction of interference sources must be known or estimated, or more auxiliary beams must be used (leading to increased computation and decreased robustness under small sample conditions), while the proposed method avoids this defect. Figure 7 The output signal-to-interference-plus-noise ratio of the proposed method with the number of iterations is shown when the number of sampling snapshots is 20,000. It can be seen that the proposed method can converge in just a few iterations.

[0172] Figure 8 The number of array elements is given as A comparison of radiation patterns of several adaptive beamforming (ADBF) methods was conducted using a subarray-level digital phased array (M=100) with 5 antenna elements per subarray and 20,000 sampling snapshots. The comparison methods, subarray-level ADBF and subarray-level beam-domain ADBF, refer to the traditional ADBF method based on subarray-level digital sampling data and the beam-domain ADBF method, respectively, with a maximum phase ripple of 0.5° for each antenna element. The proposed method is applicable to adaptive beamforming of subarray-level digital phased arrays, achieving the desired low sidelobe effect while forming nulls in 30 interference directions. In contrast, subarray-level ADBF has higher sidelobes (related to the need for more training samples), and subarray-level beam-domain ADBF exhibits some beam pointing deviation, approaching one-third of the beamwidth in this experiment. This is because the auxiliary beams pointing in each interference direction at the subarray level have severe grating lobes.

[0173] In terms of computational complexity, Figure 8 Taking the corresponding experiment as an example, subarray-level ADBF requires a 100×100 dimensional matrix inversion, and subarray-level beam domain ADBF requires a 31×31 dimensional matrix inversion (where 31 corresponds to the number of interferences plus 1), while the proposed method only requires 20 4×4 dimensional matrix inversions (where 20 corresponds to the number of groups M / K). j 4 corresponds to group size K j =5 minus the number of constraints (1), since the computational complexity of inverting a Z×Z dimensional matrix is ​​O(Z). 3 If the computational complexity of the subarray-level ADBF, the subarray-level beam domain ADBF, and the proposed method are O(1000000), O(29791), and 20×O(64), respectively, it can be seen that the proposed method has significant advantages in real-time anti-interference applications of large-scale phased arrays.

[0174] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization, characterized in that, Includes the following steps: Step 1: Calculate the sampling covariance matrix R based on the radar receiver array's sampled snapshot data; Step 2: Design linear constraints for the weight vector w based on actual application requirements, including: designing linear equality constraints C for the weight vector w with dimension M×1 based on actual application requirements. H w = v, where the size of C is M×Q, the size of v is Q×1, and Q is the number of constraints; where M is the total number of digital channels of the phased array, and the superscript H indicates the conjugate transpose operation of the matrix; Step 3: Initialize the weight vector and related parameters, including: initializing the weight vector to be optimized w = C(C H C) -1 v, vector u = Rw, and output variance p = w H Rw = w H u, where (·) -1 Represents the matrix inversion operation; and uses... and Record the historical values ​​of w and p respectively, i.e. The symbol "←" indicates that the value on the right is assigned to the value on the left. Step 4: Group the elements in the weight vector and correspondingly divide the relevant parameters into blocks. Divide the M elements constituting w into J groups, where the j-th group contains K elements. j There are 1, 2, ..., J elements; The block division rules for the vectors and matrices are as follows: Divide the vector w into blocks as follows: Among them, w j K is formed by the j-th group of elements j The 1×1 dimensional column vector, according to the corresponding partitioning method, divides the vector u, constraint matrix C, and sampling covariance matrix R into blocks by row or column as follows: R=[R1 R2…R J ] Among them, u j C j R j The dimensions are K j ×1、K j ×Q、M×K j ; and R j Further divided into: Among them, R ij The size is K j ×K j ; Step 5: Calculate the blocking matrix B for each group. j and transformation matrix D j ; Step 6: Optimize each group of elements sequentially and update the relevant parameters, including: optimizing the column vector w formed by each group of elements sequentially in the order of j = 1, 2, ..., J, based on minimizing the output variance of beamforming. j And update vector u, the corresponding optimization / update expression is: Δw j =-D j u j w j ←w j +Δw j u←u+R j Δw j ; Step 7: Calculate the current output variance, and calculate the relative change measure Δp of the output variance between two consecutive iterations or the relative change measure Δw of the weight vector between two consecutive iterations; Step 8: Make a threshold decision on whether the iteration should be terminated. If Δp or Δw is less than the threshold, terminate the iteration and output the optimal weight vector; otherwise, repeat steps 6 to 8.

2. The dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization according to claim 1, characterized in that, Step 1 includes the following: Based on the sampled snapshot data X from the radar receiver array, estimate the sampling covariance matrix R: R = X X H / L, where X is an M×L dimensional matrix, each column of which represents the sampled data of all digital channels at a certain moment, and L is the number of time samples, denoted as . The total number of antenna elements in the phased array: If the array is digitized at the subarray level, then Where, N m The number of antenna elements contained in the m-th subarray; If the array is digitized at the cell level, then obviously there is 3. The dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization according to claim 2, characterized in that, The design rules for the constraints described in step 2 are as follows: a) Distortionless response: If only a signal in a certain direction of interest is required to pass through without distortion, then C = T H a, v = 1, where T is The transformation matrix of the subarray, where 'a' is the matrix corresponding to the direction of interest. 3D array guide vector; C rewritten as in, Represents the Hadamard product. The dimension vector y is the amplitude weighted average at a specified sidelobe level; b) Functional Extension: To further suppress interference in a specified direction, broaden the main lobe, or broaden the null, additional constraints are added to the distortion-free response. This involves adding corresponding columns and rows to C and v, respectively. If the array steering vector for suppressing interference in a specific direction is a′, then C = T. H [aa′]、 If a low-sidelobe beam is desired, then C is rewritten as The two design rules described above correspond to the minimum variance distortionless response beamformer and the linearly constrained minimum variance beamformer at the subarray level, respectively. The specific construction of the subarray transformation matrix T involved is explained below: If the array is digitized at the subarray level, then T is constructed as follows: If the phased array... Each antenna element belongs to the m-th subarray. m = 1, 2, ..., M; then the first _t_ is... row, m-th column element for in, For the first The simulated weighted values ​​on each antenna element are marked with an asterisk "*" to indicate that the complex number is taken as its conjugate; otherwise, the corresponding element is 0. If the array is digitized at the cell level, then T is obviously the identity matrix of the corresponding size.

4. The dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization according to claim 3, characterized in that, Step 4 includes the following: K j K should be satisfied j >Q and 5. The dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization according to claim 4, characterized in that, Step 5 includes the following: Calculate the transformation matrix for each group separately. Where j = 1, 2, ..., J, B j C j Corresponding K j ×(K j -Q) dimensional grouping blocking matrix, specifically composed of C j orthogonal complement matrix The previous K j -Column Q is given.

6. The dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization according to claim 5, characterized in that, The simplified calculation method for the grouping blocking matrix and transformation matrix mentioned in step 5 is as follows: a) Given and All are full-rank Hermitian matrices, and the corresponding matrix inversion is implemented based on the Cholesky decomposition fast algorithm. b) In calculating B for each group j and D j At that time, acceleration is achieved through parallel processing; c) If the subarrays corresponding to each group have translation invariance, that is, they have the same number of antenna elements and spatial arrangement, then the corresponding B j They are all the same, that is, B. j It only needs to be calculated once, thus significantly reducing the amount of computation; d) When Q = 1, B j It is also given directly by the following formula: Where c jk Represents vector C j The k-th element, since most of its elements are zero, is represented by the sparse matrix B. j Calculate D j The amount of computation required for the process is also significantly reduced.

7. The dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization according to claim 6, characterized in that, Step 7 includes the following: After completing a process for all groups w j After optimizing and updating j = 1, 2, ..., J, calculate the current output variance p = w H u, and the measure of the relative change in output variance between two consecutive iterations. Or a measure of the relative change in the weight vector.

8. The dimension-reduced robust adaptive beamforming method based on grouped cyclic optimization according to claim 7, characterized in that, Step 8 includes the following: The iteration termination condition is set as Δp < ε or Δw < ε, where ε is a threshold value of 10. -3 10 -4 If the condition is not met, then the currently obtained w and p are recorded as historical values, i.e. Repeat steps 6-8; if satisfied, terminate the iteration, using the currently obtained w as the final weight vector, and utilize its conjugate transpose w. H The optimal output w is obtained by weighted summation of the array sampling snapshot data X. H X completes adaptive interference suppression.

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