A robust adaptive beamforming method and system based on successive convex approximation

Abstract

This invention relates to the field of signal processing technology, and discloses a robust adaptive beamforming method and system based on continuous convex approximation, comprising the following specific steps: S1, establishing a model of the output signal to interference noise ratio of the signal to be processed; S2, establishing an uncertain set of the covariance matrix and the guiding vector of the desired signal based on the covariance matrix of the signal to be processed and the guiding vector of the desired signal; obtaining an optimization problem of maximizing the output signal to interference noise ratio model under the worst-case performance condition; S3, transforming the optimization problem into a quadratic matrix inequality problem; transforming the quadratic matrix inequality problem into a semidefinite programming problem through positive semidefinite relaxation and strong duality theorem; S4, solving for the rank-one solution of the optimal beam weight vector based on continuous convex approximation; realizing robust adaptive beamforming of the signal to be processed based on the rank-one solution. This invention solves the problem of low quality in existing adaptive beamforming technologies and has the characteristics of high performance and strong robustness.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and more specifically, to a robust adaptive beamforming method and system based on continuous convex approximation. Background Technology

[0002] Adaptive beamforming has been widely used in radar, sonar, communications, microphone array speech, audio processing, medical imaging, radio astronomy, and other fields. However, due to potential errors in prediction direction, imperfect array calibration, and antenna shape distortion in real-world scenarios, a mismatch may exist between the actual signal received by the base station and the ideal signal. For traditional adaptive beamformers, such as minimum variance distortionless response (MVDR) beamformers, performance will significantly degrade when there is a mismatch in the guidance vector. Therefore, robust adaptive beamforming technology has emerged.

[0003] In recent years, robust adaptive beamforming techniques based on worst-case performance optimization have attracted much attention. The diagonal loading method is a widely used approach, whose performance depends on the loading factor and can improve robustness to any mismatch type; however, the actual size of the loading factor is difficult to determine. Feature space-based methods are also powerful, but their performance degrades significantly with increasing interference and decreasing signal-to-noise ratio. This optimization algorithm employs a worst-case performance optimization beamforming method, which is robust to arbitrary guide vector mismatches. Therefore, when designing the optimal beamformer, constraints for various guide vector mismatches are incorporated to make the optimization problem more robust. The signal-to-interference plus-noise ratio is used as the performance evaluation criterion to maximize this ratio.

[0004] There is a robust beamforming design method based on channel estimation error network in the existing technology, which mainly solves the problem that the model is difficult to solve when both useful channel and interference channel have uncertainty. The specific process is as follows: (1) Initialize the beam vector correlation matrix Q1 of the user to be designed and construct the optimization objective equation with the highest rate; (2) Transform the objective equation into a step-by-step iterative subproblem; (3) Solve each subproblem; (4) Iterate (2)-(3) until the optimal correlation matrix Q1 is obtained; (5) Apply rank-1 decomposition to the optimal Q1 to obtain the optimal beam vector v1.

[0005] However, existing technologies still suffer from low quality in adaptive beamforming. Therefore, how to invent a robust adaptive beamforming system based on continuous convex approximation is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] To address the problem of low quality in existing adaptive beamforming technologies, this invention provides a robust adaptive beamforming method and system based on continuous convex approximation, which features high performance and robustness.

[0007] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows:

[0008] A robust adaptive beamforming method based on continuous convex approximation includes the following specific steps:

[0009] S1. Receive the signal to be processed and establish a model of the output signal to interference noise ratio of the signal to be processed.

[0010] S2. Based on the covariance matrix of the signal to be processed and the guiding vector of the desired signal, establish the uncertainty set of the covariance matrix and the guiding vector; substitute the uncertainty set into the output signal-to-interference-noise ratio model to obtain the optimization problem of maximizing the output signal-to-interference-noise ratio model under the worst performance condition.

[0011] S3. Transform the optimization problem into a quadratic matrix inequality problem; transform the quadratic matrix inequality problem into a semidefinite programming problem using positive semidefinite relaxation and strong duality theorem;

[0012] S4. Based on continuous convex approximation, the rank-one solution of the optimal beam weight vector is obtained; robust adaptive beamforming of the signal to be processed is realized based on the rank-one solution.

[0013] Preferably, in step S1, establishing the output signal to interference-to-noise ratio model specifically involves: assuming the beam to be processed has N sensor arrays, the signal to be processed is represented as y(t) = s(t) + i(t) + n(t), where s(t) represents the desired signal, i(t) represents interference, and n(t) represents noise; the output signal of the receiving beamformer is represented as x(t) = w H y(t), where w represents an N-dimensional complex weight coefficient vector, and H is the transpose matrix; construct the signal-to-interference-noise ratio (SINR) model:

[0014]

[0015] Where a is the desired signal guiding factor, R i+n The difference matrix is ​​a representation of the interference and noise. The power of the desired signal is represented by "||", which indicates the modulus.

[0016] Furthermore, if R i+n If it is not available, then use the sampling matrix of the signal to be processed. Replace R i+n The signal-to-interference-to-noise ratio model is expressed as:

[0017]

[0018] Furthermore, in step S2, the uncertain set of the covariance matrix and the guidance vector is established as follows: Let d(θ) be the guidance vector related to direction θ determined by the set structure of the antenna array corresponding to the signal to be processed, Θ be the angular sector of the signal to be processed, a0 be the ideal guidance vector of the desired signal, E be the regular matrix of the set of ellipsoids, and γ1 and γ2 be the lengths of the first and second half-axis of the set of ellipsoids in advance, respectively.

[0019] Let C = ∫ Θ d(θ)d H (θ)dθ, thus obtaining the guiding vector Δ1=min of the signal to be processed. θ∈Θ d H (θ)Cdθ;

[0020] Construct an uncertain set A = {a|a} of the guidance vectors H Ca≥Δ1,γ1≤(a-a0) H E(a-a0)≤γ2,||a||=N};

[0021] Constructing the uncertain set of the covariance matrix Where Δ represents the guidance vector matrix, |||| F Denotes the F-norm of a matrix. It represents positive semi-definite, and γ is the threshold value of the norm sphere set in advance.

[0022] Furthermore, in step S3, the optimization problem of maximizing the output signal-to-interference-noise ratio model under the worst-case performance condition is specifically as follows:

[0023]

[0024] Furthermore, in step S3, the optimization problem is transformed into a quadratic matrix inequality problem, specifically as follows:

[0025] S3101. Consider the uncertainty set B of the output signal versus interference-to-noise ratio model under the worst-case performance maximization condition: use make Transform the optimization problem into a minimization problem:

[0026]

[0027] in, I is an N-dimensional identity matrix;

[0028] S3102. Rewrite the minimization problem as a constrained problem:

[0029]

[0030] S3103, Let x = [a] H ,t] H The constraint problem can be expressed as a quadratic matrix inequality problem:

[0031]

[0032] in,

[0033] Furthermore, in step S3, the quadratic matrix inequality problem is transformed into a positive semidefinite programming problem using positive semidefinite relaxation and the strong duality theorem. The specific steps are as follows:

[0034] S3201. Relaxing the quadratic matrix inequality problem with positive semidefinite relaxation:

[0035]

[0036] Where (tr(A)) represents the trace of matrix A;

[0037] S3202. Using the strong duality theorem, we obtain the dual problem of the quadratic matrix inequality problem after semi-definite relaxation:

[0038]

[0039] Where R represents all real numbers, and y1, y2, y3, y4, and y5 are the introduced dual variables;

[0040] S303. Substitute the dual problem into the minimization problem and perform positive semidefinite relaxation to obtain the positive semidefinite programming problem:

[0041]

[0042] Furthermore, in step S4, based on continuous convex approximation, the rank-one solution of the optimal beam weight vector is obtained; specifically:

[0043] Solve a semidefinite programming problem and determine whether the optimal solution output by the semidefinite programming problem is a rank-1 solution;

[0044] The method for determining the rank of a matrix is ​​as follows: if W satisfies the equation λ1(W)≥tr(W), then the rank of the matrix is ​​considered to be 1; where λ1(W) represents the largest eigenvalue of matrix W. Its corresponding first-order differential is

[0045] If so, then for the rank-1 solution W * Perform rank-one decomposition: W * =w *w *H , where w * The optimal beam weight vector is used to minimize the problem.

[0046] If not, then use the continuous convex approximation method W. * Perform iterative rank reduction until a rank-1 solution is obtained.

[0047] In one specific implementation, in step S4, the continuous convex approximation method W is used. * Perform iterative rank reduction until a rank-1 solution is obtained, specifically as follows:

[0048] Based on the alternating optimization iteration of continuous convex approximation, it can be expressed as:

[0049]

[0050] Where matrix X represents the optimization variable solved in this iteration, and matrix X0 represents the solution obtained in the previous iteration. It is the first differential of the function f;

[0051] Combining λ1(W) and f(X), if W satisfies Then it is assumed that a rank-1 solution exists, where z0 is the eigenvector corresponding to the largest eigenvalue of the initial matrix W; for After relaxation, we obtain the bilinear constraint:

[0052]

[0053] in, To take the real part, To take the complex part;

[0054] Using the alternating optimization method, with a fixed matrix W, optimize z to solve the first alternating optimization problem:

[0055]

[0056] Where z k-1 W k-1 This is the optimal value obtained in the previous iteration of the optimization process;

[0057] Solving the alternation optimization problem yields z k According to z k Solve the second alternation optimization problem:

[0058]

[0059] The first and second alternating optimization problems are solved iteratively until ||z| is satisfied. k -z k-1 ||≤ξ, where ξ is the maximum allowed interval for termination set in advance;

[0060] The optimal solution W with rank 1 is obtained. * Perform rank-one decomposition on the optimal solution, W * =w * w *H , where w* is the optimal beam weight vector obtained by optimizing the output signal to interference noise ratio model under the worst performance condition.

[0061] A robust adaptive beamforming system based on continuous convex approximation includes a model building module, an optimization problem planning module, a semidefinite programming transformation module, and a beamforming solution module.

[0062] The model building module is used to receive the signal to be processed and establish a model of the output signal and interference noise ratio of the signal to be processed.

[0063] The optimization problem planning module is used to establish an uncertain set of the covariance matrix and the guiding vector of the desired signal based on the covariance matrix of the signal to be processed and the guiding vector of the desired signal; and to substitute the uncertain set into the output signal and interference noise ratio model to obtain the optimization problem of maximizing the output signal and interference noise ratio model under the worst performance condition.

[0064] The semidefinite programming transformation module is used to transform optimization problems into quadratic matrix inequality problems; and to transform quadratic matrix inequality problems into semidefinite programming problems through semidefinite relaxation and strong duality theorems.

[0065] The solution shaping module is used to obtain the rank-one solution of the optimal beam weight vector based on continuous convex approximation; and to realize robust adaptive beamforming of the signal to be processed based on the rank-one solution.

[0066] The beneficial effects of this invention are as follows:

[0067] This invention discloses a robust adaptive beamforming method based on maximizing the output signal-to-interference-plus-noise ratio (IRR) under worst-case performance. The invention establishes an output signal-to-interference-plus-noise ratio model for the signal to be processed. Based on the covariance matrix of the signal to be processed and the guiding vector of the desired signal, it establishes an uncertainty set for the covariance matrix and the guiding vector. Substituting this uncertainty set into the output signal-to-interference-plus-noise ratio model yields an optimization problem for maximizing the output signal-to-interference-plus-noise ratio under worst-case performance. Furthermore, the invention transforms the optimization problem into a quadratic matrix inequality problem. This problem is then transformed into a semidefinite programming problem using positive semidefinite relaxation and strong duality theorem. Based on continuous convex approximation, the rank-one solution for the optimal beam weight vector is obtained. This invention ensures high-quality adaptive beam weight vectors while significantly improving algorithm performance. Therefore, the proposed method solves the problem of low quality in existing adaptive beamforming technologies and exhibits high performance and robustness. Attached Figure Description

[0068] Figure 1 This is a flowchart of a robust adaptive beamforming method based on continuous convex approximation according to the present invention.

[0069] Figure 2 This is a schematic diagram of the specific process of a robust adaptive beamforming method based on continuous convex approximation according to the present invention in Embodiment 2.

[0070] Figure 3 This is a schematic diagram of the alternating optimization algorithm based on continuous convex approximation in the robust adaptive beamforming method based on continuous convex approximation of the present invention.

[0071] Figure 4 In Embodiment 2, the uncertainty set of the guidance vector γ1≤(a-a0) is given by the robust adaptive beamforming method based on continuous convex approximation of the present invention. H A schematic diagram illustrating the physical meaning of E(a-a0)≤γ2. Detailed Implementation

[0072] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0073] Example 1

[0074] like Figure 1 As shown, a robust adaptive beamforming method based on continuous convex approximation includes the following specific steps:

[0075] S1. Receive the signal to be processed and establish a model of the output signal to interference noise ratio of the signal to be processed.

[0076] S2. Based on the covariance matrix of the signal to be processed and the guiding vector of the desired signal, establish the uncertainty set of the covariance matrix and the guiding vector; substitute the uncertainty set into the output signal-to-interference-noise ratio model to obtain the optimization problem of maximizing the output signal-to-interference-noise ratio model under the worst performance condition.

[0077] S3. Transform the optimization problem into a quadratic matrix inequality problem; transform the quadratic matrix inequality problem into a semidefinite programming problem using positive semidefinite relaxation and strong duality theorem;

[0078] S4. Based on continuous convex approximation, the rank-one solution of the optimal beam weight vector is obtained; robust adaptive beamforming of the signal to be processed is realized based on the rank-one solution.

[0079] In this embodiment, based on continuous convex approximation, the rank-one solution of the optimal beam weight vector is obtained; specifically:

[0080] Solve a semidefinite programming problem and determine whether the optimal solution output by the semidefinite programming problem is a rank-1 solution;

[0081] The method for determining the rank of a matrix is ​​as follows: if W satisfies the equation λ1(W)≥tr(W), then the rank of the matrix is ​​considered to be 1; where λ1(W) represents the largest eigenvalue of matrix W. Its corresponding first-order differential is

[0082] If so, then for the rank-1 solution W * Perform rank-one decomposition: W * =w * w *H , where w * The optimal beam weight vector is used to minimize the problem.

[0083] If not, then use the continuous convex approximation method W. * Perform iterative rank reduction until a rank-1 solution is obtained.

[0084] In this embodiment, the present invention proposes a robust adaptive beamforming algorithm based on maximizing the worst-case signal-to-interference-plus-noise ratio. For modeling the mismatch set of the actual guidance vectors, a set of arrival directions characterized by a non-convex bilateral ellipsoidal uncertainty set and all linear combinations preventing the arrival angle of the desired signal from converging to the interfering guidance vector is considered. The algorithm then determines the maximum signal-to-interference-plus-noise ratio under worst-case performance and calculates the weight vector of the robust adaptive beam. In the proposed new algorithm, strong duality, semi-definite relaxation (SDR), and alternating optimization (AO) algorithms based on continuous convex approximation (SCA) are employed to solve for the optimal beamforming vector in a short time, improving the performance of the robust adaptive beamformer and making it more applicable in real-world situations.

[0085] Example 2

[0086] More specifically, such as Figure 2 As shown, in step S1, establishing the output signal to interference noise ratio model specifically involves: assuming the beam to be processed has N sensor arrays, the signal to be processed is represented as y(t) = s(t) + i(t) + n(t), where s(t) represents the desired signal, i(t) represents interference, and n(t) represents noise; the output signal of the receiving beamformer is represented as x(t) = w H y(t), where w represents an N-dimensional complex weight coefficient vector, and H is the transpose matrix; construct the signal-to-interference-noise ratio (SINR) model:

[0087]

[0088] Where a is the desired signal guiding factor, R i+n The difference matrix is ​​a representation of the interference and noise. The power of the desired signal is represented by "||", which indicates the modulus.

[0089] In one specific embodiment, if R i+n If it is not available, then use the sampling matrix of the signal to be processed. Replace R i+n The signal-to-interference-to-noise ratio model is expressed as:

[0090]

[0091] In a specific embodiment, in step S2, the uncertain set of covariance matrix and guidance vector is established as follows: let d(θ) be the guidance vector related to direction θ determined by the set structure of the antenna array corresponding to the signal to be processed, Θ be the angular sector of the signal to be processed, a0 be the ideal guidance vector of the desired signal, E be the regular matrix of the set of ellipsoids, and γ1 and γ2 be the lengths of the first and second half-axis of the set of ellipsoids in advance, respectively.

[0092] Let C = ∫ Θ d(θ)d H (θ)dθ, thus obtaining the guiding vector Δ1=min of the signal to be processed. 0∈Θ d H (θ)Cdθ;

[0093] Construct an uncertain set A = {a|a} of the guidance vectors H Ca≥Δ1,γ1≤(a-a0) H E(a-a0)≤γ2,||a||=N};

[0094] Constructing the uncertain set of the covariance matrix Where Δ represents the guidance vector matrix, |||| F Denotes the F-norm of a matrix. It represents positive semi-definite, and γ is the threshold value of the norm sphere set in advance.

[0095] In one specific embodiment, step S3, which optimizes the output signal-to-interference-noise ratio model under the worst-case performance condition, specifically involves:

[0096]

[0097] In one specific embodiment, in step S3, the optimization problem is transformed into a quadratic matrix inequality problem, specifically as follows:

[0098] S3101. Consider the uncertainty set B of the output signal versus interference-to-noise ratio model under the worst-case performance maximization condition: use make Transform the optimization problem into a minimization problem:

[0099]

[0100] in, I is an N-dimensional identity matrix;

[0101] S3102. Rewrite the minimization problem as a constrained problem:

[0102]

[0103] In this embodiment, the physical meaning of the uncertain set γ1≤(a-a0)HE(a-a0)≤γ2 of the guidance vector is as follows: Figure 4 As shown.

[0104] S3103, Let x = [a] H ,t] H The constraint problem can be expressed as a quadratic matrix inequality problem:

[0105]

[0106] in,

[0107] In one specific embodiment, step S3 transforms the quadratic matrix inequality problem into a positive semidefinite programming problem using positive semidefinite relaxation and the strong duality theorem. The specific steps are as follows:

[0108] S3201. Relaxing the quadratic matrix inequality problem with positive semidefinite relaxation:

[0109]

[0110] Where (tr(A)) represents the trace of matrix A;

[0111] S3202. Using the strong duality theorem, we obtain the dual problem of the quadratic matrix inequality problem after semi-definite relaxation:

[0112]

[0113] Where R represents all real numbers, and y1, y2, y3, y4, and y5 are the introduced dual variables;

[0114] S303. Substitute the dual problem into the minimization problem and perform positive semidefinite relaxation to obtain the positive semidefinite programming problem:

[0115]

[0116] In one specific embodiment, in step S4, based on continuous convex approximation, the rank-one solution of the optimal beam weight vector is obtained; specifically:

[0117] Solve a semidefinite programming problem and determine whether the optimal solution output by the semidefinite programming problem is a rank-1 solution;

[0118] The method for determining the rank of a matrix is ​​as follows: if W satisfies the equation λ1(W)≥tr(W), then the rank of the matrix is ​​considered to be 1; where λ1(W) represents the largest eigenvalue of matrix W. Its corresponding first-order differential is

[0119] If so, then for the rank-1 solution W * Perform rank-one decomposition: W * =w * w *H , where w * The optimal beam weight vector is used to minimize the problem.

[0120] If not, then use the continuous convex approximation method W. * Perform iterative rank reduction until a rank-1 solution is obtained.

[0121] In one specific embodiment, such as Figure 3 As shown, in step S4, the continuous convex approximation method W is used. * Perform iterative rank reduction until a rank-1 solution is obtained, specifically as follows:

[0122] Based on the alternating optimization iteration of continuous convex approximation, it can be expressed as:

[0123]

[0124] Where matrix X represents the optimization variable solved in this iteration, and matrix X0 represents the solution obtained in the previous iteration. It is the first differential of the function f;

[0125] Combining λ1(W) and f(X), if W satisfies Then it is assumed that a rank-1 solution exists, where z0 is the eigenvector corresponding to the largest eigenvalue of the initial matrix W; for After relaxation, we obtain the bilinear constraint:

[0126]

[0127] in, To take the real part, To take the complex part;

[0128] Using the alternating optimization method, with a fixed matrix W, optimize z to solve the first alternating optimization problem:

[0129]

[0130] Where z k-1 W k-1This is the optimal value obtained in the previous iteration of the optimization process;

[0131] Solving the alternation optimization problem yields z k According to z k Solve the second alternation optimization problem:

[0132]

[0133] The first and second alternating optimization problems are solved iteratively until ||z| is satisfied. k -z k-1 ||≤ξ, where ξ is the maximum allowed interval for termination set in advance;

[0134] The optimal solution W with rank 1 is obtained. * Perform rank-one decomposition on the optimal solution, W * =w * w *H , where w* is the optimal beam weight vector obtained by optimizing the output signal to interference noise ratio model under the worst performance condition.

[0135] In this embodiment, the Alternating Optimization (AO) algorithm based on Continuous Convex Approximation (SCA) comprises the following steps:

[0136] A1. Input parameters

[0137] A2, Solving the problem yields W k , z;

[0138] A3, let W k-1 =W k , z k =z k-1 ;

[0139] A4. Determine W k-1 Is the rank of 1?

[0140] If so, proceed to step A5;

[0141] If not, then based on the known W k-1 , z k- Find z k ; and based on the known z k , z k-1 , obtain W k Return to step S4;

[0142] A5, regarding W k-1 Perform rank-one decomposition and output the optimal solution w. * .

[0143] In this embodiment, the optimal solution is obtained by using the CVX toolkit based on the rank-one solution.

[0144] This invention discloses a robust adaptive beamforming method for maximizing the output signal-to-interference-plus-noise ratio (IRR) under worst-case performance. The invention establishes an output signal-to-interference-plus-noise ratio model for the signal to be processed. Based on the covariance matrix of the signal to be processed and the guidance vector of the desired signal, it establishes an uncertainty set for the covariance matrix and the guidance vector. Substituting this uncertainty set into the output signal-to-interference-plus-noise ratio model yields an optimization problem for maximizing the output signal-to-interference-plus-noise ratio under worst-case performance. Furthermore, the invention transforms the optimization problem into a quadratic matrix inequality problem. This problem is then transformed into a semidefinite programming problem using positive semidefinite relaxation and strong duality theorems. Based on continuous convex approximation, the rank-one solution for the optimal beam weight vector is obtained. This invention not only guarantees a high-quality adaptive beam weight vector but also significantly improves the algorithm's performance.

[0145] This invention uses a novel uncertain set to model the uncertainty of the guidance vector, which is more general and more generalizable than the general sphere set.

[0146] This invention uses non-convex sets to model the covariance matrix and guiding vector, enabling optimal system performance even under practical conditions. This makes the system more robust and more practically significant.

[0147] This invention uses the strong duality theorem and semidefinite relaxation (SDR) to transform a non-convex problem into a convex problem, which greatly reduces the difficulty of solving the optimization problem.

[0148] This invention uses an alternating optimization (AO) algorithm based on continuous convex approximation (SCA) to find the rank-one solution. After a finite number of iterations, the algorithm converges to the optimal solution. Compared with existing methods for finding the rank-one solution (Gaussian stochastic process), this invention reduces the algorithm complexity, improves the reliability of the system, and reduces the computation time of the system.

[0149] Therefore, the method proposed in this invention solves the problem of low quality in adaptive beamforming in the prior art, and has the characteristics of high performance and strong robustness.

[0150] Example 3

[0151] A robust adaptive beamforming system based on continuous convex approximation includes a model building module, an optimization problem planning module, a semidefinite programming transformation module, and a beamforming solution module.

[0152] The model building module is used to receive the signal to be processed and establish a model of the output signal and interference noise ratio of the signal to be processed.

[0153] The optimization problem planning module is used to establish an uncertain set of the covariance matrix and the guiding vector of the desired signal based on the covariance matrix of the signal to be processed and the guiding vector of the desired signal; and to substitute the uncertain set into the output signal and interference noise ratio model to obtain the optimization problem of maximizing the output signal and interference noise ratio model under the worst performance condition.

[0154] The semidefinite programming transformation module is used to transform optimization problems into quadratic matrix inequality problems; and to transform quadratic matrix inequality problems into semidefinite programming problems through semidefinite relaxation and strong duality theorems.

[0155] The solution shaping module is used to obtain the rank-one solution of the optimal beam weight vector based on continuous convex approximation; and to realize robust adaptive beamforming of the signal to be processed based on the rank-one solution.

[0156] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A robust adaptive beamforming method based on continuous convex approximation, characterized in that: The specific steps include the following: S1. Receive the signal to be processed and establish a model of the output signal to interference noise ratio of the signal to be processed. S2. Based on the covariance matrix of the signal to be processed and the guiding vector of the desired signal, establish the uncertainty set of the covariance matrix and the guiding vector; By substituting the uncertain set into the output signal-to-interference-to-noise ratio model, we obtain the optimization problem of maximizing the output signal-to-interference-to-noise ratio model under the worst-case performance condition. Specifically, the uncertain set of the covariance matrix and the guiding vector is established as follows: Let... The orientation is determined by the structure of the antenna array corresponding to the signal to be processed. Related guidance vectors, For the corner sector of the signal to be processed, The ideal guide vector for the desired signal, For the given ellipsoid set, the regular matrix, and These are the lengths of the first and second semi-axes of the pre-defined ellipsoid set, respectively. set up The guiding vector of the signal to be processed is obtained. ; Constructing an uncertain set of guidance vectors ; Constructing the uncertain set of the covariance matrix ,in, Represents the guidance vector matrix. Denotes the F-norm of a matrix. Indicates positive semidefinite. The threshold value for the pre-defined norm sphere; S3. Transform the optimization problem into a quadratic matrix inequality problem; transform the quadratic matrix inequality problem into a semidefinite programming problem using positive semidefinite relaxation and strong duality theorem; S4. Based on continuous convex approximation, the rank-one solution of the optimal beam weight vector is obtained; robust adaptive beamforming of the signal to be processed is realized based on the rank-one solution.

2. The robust adaptive beamforming method based on continuous convex approximation according to claim 1, characterized in that: In step S1, establishing the output signal to interference noise ratio model specifically involves: assuming the beam to be processed has N sensor arrays, and representing the signal to be processed as... ,in Indicates the desired signal. Indicates interference. Representing noise; the output signal of the receiving beamformer is represented as ,in This represents an N-dimensional complex weight coefficient vector. The superscript represents the transpose of the matrix; construct the signal-to-interference-to-noise ratio model. : （1） in The guide vector for the desired signal. The covariance matrix of the interference plus noise. The power of the desired signal, Indicates the modulus length.

3. The robust adaptive beamforming method based on continuous convex approximation according to claim 2, characterized in that: like If it is not available, then use the sampling matrix of the signal to be processed. replace The signal-to-interference-to-noise ratio model is expressed as: （2）。 4. The robust adaptive beamforming method based on continuous convex approximation according to claim 3, characterized in that: In step S3, the optimization problem of maximizing the output signal-to-interference-to-noise ratio model under the worst-case performance condition is specifically as follows: （3）。 5. The robust adaptive beamforming method based on continuous convex approximation according to claim 4, characterized in that: In step S3, the optimization problem is transformed into a quadratic matrix inequality problem, specifically: S3101. Consider the uncertainty set B of the output signal versus interference-to-noise ratio model under the worst-case performance maximization condition: ;use ,make The optimization problem is transformed into a minimization problem: （4） in, , It is an N-dimensional identity matrix; S3102. Rewrite the minimization problem as a constrained problem: （5） S3103, Order The constraint problem can be expressed as a quadratic matrix inequality problem: （6） in, .

6. The robust adaptive beamforming method based on continuous convex approximation according to claim 5, characterized in that: In step S3, the quadratic matrix inequality problem is transformed into a positive semidefinite programming problem using positive semidefinite relaxation and the strong duality theorem. The specific steps are as follows: S3201. Relaxing the quadratic matrix inequality problem with positive semidefinite relaxation: （7） in, Represented as the trace of matrix A; S3202. Using the strong duality theorem, we obtain the dual problem of the quadratic matrix inequality problem after semi-definite relaxation: （8） Where R represents all real numbers, and y1, y2, y3, y4, and y5 are the introduced dual variables; S303. Substitute the dual problem into the minimization problem and perform positive semidefinite relaxation to obtain the positive semidefinite programming problem: （9）。 7. The robust adaptive beamforming method based on continuous convex approximation according to claim 6, characterized in that: In step S4, based on continuous convex approximation, the rank-1 solution of the optimal beam weight vector is obtained; specifically: Solve a semidefinite programming problem and determine whether the optimal solution output by the semidefinite programming problem is a rank-1 solution; The method for determining the rank-one solution is: if W satisfies the equation If the rank of the matrix is ​​1, then the rank of the matrix is ​​considered to be 1; where, This represents the largest eigenvalue of matrix W. Its corresponding first differential is ; If so, then the solution for rank one is... Perform rank-one factorization: ,in The optimal beam weight vector is used to minimize the problem. If not, then use the continuous convex approximation method. Perform iterative rank reduction until a rank-1 solution is obtained.

8. The robust adaptive beamforming method based on continuous convex approximation according to claim 7, characterized in that: In step S4, a continuous convex approximation method is used. Perform iterative rank reduction until a rank-1 solution is obtained, specifically as follows: Based on the alternating optimization iteration of continuous convex approximation, it can be expressed as: （10） Where matrix X represents the optimization variable solved in this iteration, and matrix X0 represents the solution obtained in the previous iteration. For function The first differential; Combination and If W satisfies Then it is believed that there exists a rank-one solution, where Let W be the eigenvector corresponding to the largest eigenvalue of the initial matrix W; for After relaxation, we obtain the bilinear constraint: （11） in, To take the real part, To take the complex part; Using the alternating optimization method, with a fixed matrix W, optimize z to solve the first alternating optimization problem: （12） in , This is the optimal value obtained in the previous iteration of the optimization process; Solving the alternation optimization problem yields ,according to Solve the second alternation optimization problem: （13） The first and second alternating optimization problems are solved iteratively until the desired outcome is achieved. ,in The maximum allowed interval for termination is set in advance; The optimal solution with rank 1 was obtained. Perform rank-one decomposition on the optimal solution. ,in The optimal beam weight vector is obtained by optimizing the output signal-to-interference-to-noise ratio model under the worst-case performance condition.

9. A robust adaptive beamforming system based on continuous convex approximation, characterized in that: It includes a model building module, an optimization problem planning module, a semidefinite programming transformation module, and a solution shaping module: The model building module is used to receive the signal to be processed and establish a model of the output signal and interference noise ratio of the signal to be processed. The optimization problem planning module is used to establish an uncertain set of the covariance matrix and the guiding vector of the desired signal based on the covariance matrix of the signal to be processed and the guiding vector of the desired signal. By substituting the uncertain set into the output signal-to-interference-to-noise ratio model, we obtain the optimization problem of maximizing the output signal-to-interference-to-noise ratio model under the worst-case performance condition. Specifically, the uncertain set of the covariance matrix and the guiding vector is established as follows: Let... The orientation is determined by the structure of the antenna array corresponding to the signal to be processed. Related guidance vectors, For the corner sector of the signal to be processed, The ideal guide vector for the desired signal, For the given ellipsoid set, the regular matrix, and These are the lengths of the first and second semi-axes of the pre-defined ellipsoid set, respectively. set up The guiding vector of the signal to be processed is obtained. ; Constructing an uncertain set of guidance vectors ; Constructing the uncertain set of the covariance matrix ,in, Represents the guidance vector matrix. Denotes the F-norm of a matrix. Indicates positive semidefinite. The threshold value for the pre-defined norm sphere; The semidefinite programming transformation module is used to transform optimization problems into quadratic matrix inequality problems; and to transform quadratic matrix inequality problems into semidefinite programming problems through semidefinite relaxation and strong duality theorems. The solution shaping module is used to obtain the rank-one solution of the optimal beam weight vector based on continuous convex approximation; and to realize robust adaptive beamforming of the signal to be processed based on the rank-one solution.

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