CN112699526B - Robust adaptive beamforming method and system for non-convex quadratic matrix inequality - Google Patents

Abstract

The invention provides a robust self-adaptive beam forming method of a non-convex quadratic matrix inequality, which comprises the steps of constructing a maximized SINR model; replacing the covariance matrix of interference plus noise of the SINR model with a sampling covariance matrix, generating a new target optimization function and adding an error matrix to obtain a new target optimization problem; and solving the target optimization problem to obtain an optimal solution or a suboptimal solution, and outputting a final beam forming vector. The invention also provides a robust self-adaptive beam forming system, firstly modeling the robust self-adaptive beam forming problem as a maximized signal to noise ratio problem, converting the maximized problem into a quadratic matrix inequality problem through a strong dual principle of convex optimization, solving the quadratic matrix inequality problem by using a polynomial time method, realizing the optimal solution or suboptimal solution for rapidly solving the original problem, effectively improving the output signal to dry ratio and the overall performance of the array by using the output beam forming vector, and completing the solving of a polynomial time model.

Description

Robust adaptive beamforming method and system for non-convex quadratic matrix inequalities

Technical Field

The present invention relates to the technical field of array signal processing, and more specifically, to a robust adaptive beamforming method and system for non-convex quadratic matrix inequality.

Background Art

Adaptive beamforming is an important research branch in the field of adaptive array signal processing. Adaptive beamforming, also known as spatial adaptive filtering, mainly studies the automatic adjustment of the weight vector of the antenna array element, and can also suppress interference and noise, thereby improving the signal-to-noise ratio of the received signal. Due to the advantages of high signal-to-noise ratio output, robust adaptive beamforming technology is widely used in radar, voice, sonar, wireless communication, medical imaging and other fields. Robust adaptive beamforming technology provides a powerful method to significantly improve the array output signal-to-noise ratio and performance matrices such as main lobe width and sidelobe level. When it is difficult to obtain the required signal covariance matrix, the mismatch between the assumed and actual source covariance matrices will cause a sharp drop in performance, and robust adaptive beamforming technology is very effective for mismatches. Therefore, it is of great significance to study adaptive beamforming with robustness or robustness.

Many robust adaptive beamforming methods have been proposed for the signal model of the rank-one useful covariance matrix. In the early studies, the signal model of the rank-one useful signal covariance matrix was studied, and the signal source corresponding to the desired signal was from a point source. However, it is of practical significance to consider the general rank signal model because the signal source can often be incoherent scattering. In the signal-to-interference-plus-noise ratio (SINR) model of robust adaptive beamforming of the general rank signal model, such as the Chinese invention patent application with patent number CN108008364A, which was published on May 8, 2018, a joint optimization method for transmitting waveforms and receiving weights to improve MIMO-STAP detection performance, which describes the use of semi-positive regularization (SDP) to solve the model, but due to factors such as sampling errors, the input parameters in the model are uncertain, so the model cannot be solved in polynomial time. Later, an inner second-order cone programming (SOCP) approximation was proposed, which helps to significantly reduce the order of computational complexity, but cannot solve the original problem.

Summary of the invention

The present invention provides a robust adaptive beamforming method and system for non-convex quadratic matrix inequality in order to overcome the technical defect that the existing signal to interference plus noise ratio (SINR) model cannot be solved in polynomial time during the solution process.

In order to solve the above technical problems, the technical solution of the present invention is as follows:

A robust adaptive beamforming method for non-convex quadratic matrix inequalities, comprising the following steps:

S1: Establish the output maximization signal-to-noise ratio model of array antenna beamforming, namely SINR model;

S2: The covariance matrix of the interference plus noise of the SINR model is replaced by the sampling covariance matrix to generate a new target optimization function;

S3: Add the error matrix to the target optimization function to obtain a new target optimization problem;

S4: Make corresponding changes to the target optimization problem and solve it to obtain the optimal solution or suboptimal solution, and output the final waveform to form a vector.

In the above scheme, the robust adaptive beamforming problem is firstly modeled as a signal-to-noise ratio maximization problem, and the maximization problem is transformed into a quadratic matrix inequality problem through the strong duality principle of convex optimization; finally, a polynomial time method is proposed to solve the quadratic matrix inequality problem, which realizes the rapid solution of the optimal solution or suboptimal solution of the original problem. The output beamforming vector effectively improves the output signal-to-noise ratio and overall performance of the array, and completes the solution of the polynomial time model with short calculation time and high work efficiency.

Wherein, in the step S1, the SINR model is specifically expressed as:

Among them, w is the beamformer weight vector of the array antenna optimization design in the SINR model, _Rs is the covariance matrix of the desired signal, and Ri _+n is the covariance matrix of the interference plus noise.

The covariance matrix R _i+n of the interference plus noise is generally not available, so in step S2, the sampling covariance matrix Instead, it is specifically expressed as:

Where T represents the number of sampling times, y(t) represents the vector of the received signal, and y(t) ^H is the conjugate transpose of the received signal vector.

Wherein, in step S3, the covariance matrix R _s of the desired signal and the sampling matrix When obtaining parameters, corresponding errors will occur. Therefore, it is necessary to add corresponding error values Δ ₁ , Δ ₂ to the input parameters to obtain the optimization model:

in:

After decomposition and the inequality w ^H Δ ₁ w＝tr(Δ ₁ ww ^H )≤||Δ ₁ || ₂ ||ww ^H || ₂ ≤γ||w|| ² , where C represents the complex matrix, N represents the number of antennas in the array antenna, γ and ε are the maximum singular values of Δ ₁ and Δ ₂ respectively, and tr(·) represents the trace of the matrix; thus, a new target optimization problem is obtained, which is specifically expressed as:

Where I is the identity matrix.

Wherein, the step S4 is specifically as follows:

S41: Solve the following equation:

||Δ ₂ || ₂ ≤ε

The dual problem is:

Where Y, Z represent Lagrange multiplier vectors;

S42: Using the linear matrix inequality relaxation technique, namely LMI relaxation technique, let W = ww ^H , we have:

S43: The dual problem of optimization problem (2) is as follows:

Where a and A represent the Lagrange multiplier vectors respectively;

The complementary condition of formula (3) is calculated as follows:

tr[A(W+Z-Y)]＝0

Combination get:

S44: Assuming that the rank of W ^* is M, there exists a rank-one decomposition matrix:

Substituting in:

and

tr[(Mw _i w _i ^H )A ^* ]＝tr(W ^* A ^* )＝a ^* ,i＝1,...,M (6)

when If the two equality conditions of equations (5) and (6) are satisfied and the second constraint of equation (2) is also satisfied, is the optimal solution, executing step S46; if the second constraint of equation (2) is not satisfied, executing step S45 to find a suboptimal solution;

S45: There exists a rank-one decomposition w _i , and the objective function is:

subject to Mw _i w _i ^H +ZY≥0，i＝1,...,M

Y≥0, Z≥0

Substitute w _i into the objective function, and finally take the maximum value of the objective optimization problem as the suboptimal value, and the corresponding w _i as the suboptimal solution;

S46: Output the final waveform according to the obtained solution to form a vector, thereby forming a robust adaptive beam.

A robust adaptive beamforming system for non-convex quadratic matrix inequality includes a SINR model building module, an array replacement module, an error matrix adding module and an optimization problem solving module; wherein:

The SINR model building module is used to establish an output maximization signal-to-noise ratio model for array antenna beamforming, that is, an SINR model;

The array replacement module is used to replace the covariance matrix of the interference plus noise of the SINR model with the sampling covariance matrix to generate a new target optimization function;

The error matrix adding module is used to add an error matrix to the target optimization function to obtain the target optimization problem;

The optimization problem solving module makes corresponding changes to the target optimization problem and solves it to obtain an optimal solution or a suboptimal solution, and outputs the final waveform to form a vector.

Among them, in the SINR model, the SINR model is specifically expressed as:

Among them, w is the beamformer weight vector of the array antenna optimization design in the SINR model, _Rs is the covariance matrix of the desired signal, and Ri _+n is the covariance matrix of the interference plus noise.

The covariance matrix R _i+n of the interference plus noise is generally not available, so in the array replacement module, the sampling covariance matrix R i+n is used. Instead of the covariance matrix R _i+n of interference plus noise, it is specifically expressed as:

Where T represents the number of sampling times, y(t) represents the vector of the received signal, and y(t) ^H is the conjugate transpose of the received signal vector.

Among them, in the adding error matrix module, the covariance matrix _Rs of the expected signal and the sampling matrix When obtaining parameters, corresponding errors will occur. Therefore, it is necessary to add corresponding error values Δ ₁ , Δ ₂ to the input parameters to obtain the optimization model:

in:

After decomposition and the inequality w ^H Δ ₁ w＝tr(Δ ₁ ww ^H )≤||Δ ₁ || ₂ ||ww ^H || ₂ ≤γ||w|| ² , where C represents the complex matrix, N represents the number of antennas in the array antenna; γ and ε are the maximum singular values of Δ ₁ and Δ ₂ respectively, and tr(·) represents the trace of the matrix; thus, a new target optimization problem is obtained, which is specifically expressed as:

Among them, in the optimization problem solving module, the process of solving the optimization problem is specifically as follows:

Solve the following equation:

||Δ ₂ || ₂ ≤ε

The dual problem is:

Where Y, Z represent Lagrange multiplier vectors;

Using the linear matrix inequality relaxation technique, namely LMI relaxation technique, let W = ww ^H , we have:

The dual problem of optimization problem (2) is as follows:

Where a and A represent the Lagrange multiplier vector;

The complementary condition of formula (3) is calculated as follows:

tr[A(W+Z-Y)]＝0

Combination get:

Assuming that the rank of W ^* is M, there exists a rank-one decomposition matrix:

Substituting in:

and

tr[(Mw _i w _i ^H )A ^* ]＝tr(W ^* A ^* )＝a ^* ,i＝1,...,M (6)

when If the two equality conditions of equations (5) and (6) are satisfied and the second constraint of equation (2) is also satisfied, is the optimal solution; if the second constraint of equation (2) is not satisfied, find the suboptimal solution;

There exists a rank-one decomposition w _i , and the objective function is:

subject to Mw _i w _i ^H +ZY≥0，i＝1,...,M

Y≥0, Z≥0

Substitute w _i into the objective function, and finally take the maximum value of the objective optimization problem as the suboptimal value, and the corresponding w _i as the suboptimal solution;

The final waveform is outputted according to the obtained optimal solution or suboptimal solution to form a vector, thereby forming a robust adaptive beam.

Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

The present invention provides a robust adaptive beamforming method and system for non-convex quadratic matrix inequality. Firstly, the robust adaptive beamforming problem is modeled as a signal-to-noise ratio maximization problem. The maximization problem is converted into a quadratic matrix inequality problem through the strong duality principle of convex optimization. Finally, a polynomial time method is proposed to solve the quadratic matrix inequality problem, so that the optimal solution or suboptimal solution of the original problem can be quickly solved. The output beamforming vector effectively improves the output signal-to-noise ratio and the overall performance of the array, and the solution of the polynomial time model is completed, and the operation time is short and the work efficiency is high.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic flow chart of the method of the present invention;

FIG. 2 is a schematic diagram of the system structure of the present invention.

DETAILED DESCRIPTION

The drawings are for illustrative purposes only and are not to be construed as limiting the present patent;

In order to better illustrate the present embodiment, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product;

It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

Example 1

As shown in FIG1 , the robust adaptive beamforming method for non-convex quadratic matrix inequality includes the following steps:

S1: Establish the output maximization signal-to-noise ratio model of array antenna beamforming, namely SINR model;

S2: The covariance matrix of the interference plus noise of the SINR model is replaced by the sampling covariance matrix to generate a new target optimization function;

S3: Add the error matrix to the target optimization function to obtain a new target optimization problem;

S4: Make corresponding changes to the target optimization problem and solve it to obtain the optimal solution or suboptimal solution, and output the final waveform to form a vector.

In the specific implementation process, the robust adaptive beamforming problem is first modeled as a signal-to-noise ratio maximization problem, and the strong duality principle of convex optimization is used to transform the maximization problem into a quadratic matrix inequality problem; finally, a polynomial time method is proposed to solve the quadratic matrix inequality problem, which realizes the rapid solution to the optimal solution or suboptimal solution of the original problem. The output beamforming vector effectively improves the output signal-to-noise ratio and overall performance of the array, and completes the solution of the polynomial time model with short calculation time and high work efficiency.

More specifically, in step S1, the SINR model is specifically expressed as:

Among them, w is the beamformer weight vector of the array antenna optimization design in the SINR model, _Rs is the covariance matrix of the desired signal, and Ri _+n is the covariance matrix of the interference plus noise.

More specifically, the covariance matrix R _i+n of the interference plus noise is generally not available, so in step S2, the sampling covariance matrix R i+n is used. Instead, it is specifically expressed as:

Where T represents the number of sampling times, y(t) represents the vector of the received signal, and y(t) ^H is the conjugate transpose of the received signal vector.

More specifically, in step S3, the covariance matrix R _s of the desired signal and the sampling matrix When obtaining parameters, corresponding errors will occur. Therefore, it is necessary to add corresponding error values Δ ₁ , Δ ₂ to the input parameters to obtain the optimization model:

in:

After decomposition and the inequality w ^H Δ ₁ w＝tr(Δ ₁ ww ^H )≤||Δ ₁ || ₂ ||ww ^H || ₂ ≤γ||w|| ² , where C represents the complex matrix, N represents the number of antennas in the array antenna, γ and ε are the maximum singular values of Δ ₁ and Δ ₂ respectively, and tr(·) represents the trace of the matrix; thus, a new target optimization problem is obtained, which is specifically expressed as:

Where I is the identity matrix.

Wherein, the step S4 is specifically as follows:

S41: Solve the following equation:

||Δ ₂ || ₂ ≤ε

The dual problem is:

Where Y, Z represent Lagrange multiplier vectors;

S42: Using the linear matrix inequality relaxation technique, namely LMI relaxation technique, let W = ww ^H , we have:

S43: The dual problem of optimization problem (2) is as follows:

Where a and A represent the Lagrange multiplier vectors respectively;

The complementary condition of formula (3) is calculated as follows:

tr[A(W+Z-Y)]＝0

Combination get:

S44: Assuming that the rank of W ^* is M, there exists a rank-one decomposition matrix:

Substituting in:

and

tr[(Mw _i w _i ^H )A ^* ]＝tr(W ^* A ^* )＝a ^* ,i＝1,...,M (6)

when If the two equality conditions of equations (5) and (6) are satisfied and the second constraint of equation (2) is also satisfied, is the optimal solution, executing step S46; if the second constraint of equation (2) is not satisfied, executing step S45 to find a suboptimal solution;

S45: There exists a rank-one decomposition w _i , and the objective function is:

subject to Mw _i w _i ^H +ZY≥0，i＝1,...,M

Y≥0, Z≥0

Substitute w _i into the objective function, and finally take the maximum value of the objective optimization problem as the suboptimal value, and the corresponding w _i as the suboptimal solution;

S46: Output the final waveform according to the obtained solution to form a vector, thereby forming a robust adaptive beam.

In the specific implementation process, compared with the existing adaptive beamforming algorithms based on semi-definite programming (SDP) technology and second-order cone programming (SOCP) technology, this method adopts a robust adaptive beamforming algorithm constrained by non-convex quadratic matrix inequality, which can well solve the signal-to-noise ratio of the model. The algorithm has a short operation time and achieves the original goal of the model.

Example 2

More specifically, based on Example 1, as shown in FIG2 , a robust adaptive beamforming system for non-convex quadratic matrix inequality is provided, including an SINR model building module, an array replacement module, an error matrix adding module, and an optimization problem solving module; wherein:

The SINR model building module is used to establish an output maximization signal-to-noise ratio model for array antenna beamforming, that is, an SINR model;

The array replacement module is used to replace the covariance matrix of the interference plus noise of the SINR model with the sampling covariance matrix to generate a new target optimization function;

The error matrix adding module is used to add an error matrix to the target optimization function to obtain the target optimization problem;

The optimization problem solving module makes corresponding changes to the target optimization problem and solves it to obtain an optimal solution or a suboptimal solution, and outputs the final waveform to form a vector.

More specifically, in the SINR model, the SINR model is specifically expressed as:

Among them, w is the beamformer weight vector of the array antenna optimization design in the SINR model, _Rs is the covariance matrix of the desired signal, and Ri _+n is the covariance matrix of the interference plus noise.

More specifically, the covariance matrix R _i+n of the interference plus noise is generally not available, so in the array replacement module, the sampling covariance matrix R i+n is used. Instead of the covariance matrix R _i+n of interference plus noise, it is specifically expressed as:

Where T represents the number of sampling times, y(t) represents the vector of the received signal, and y(t) ^H is the conjugate transpose of the received signal vector.

More specifically, in the error matrix adding module, the covariance matrix _Rs of the desired signal and the sampling matrix When obtaining parameters, corresponding errors will occur. Therefore, it is necessary to add corresponding error values Δ ₁ , Δ ₂ to the input parameters to obtain the optimization model:

in:

After decomposition and the inequality w ^H Δ ₁ w＝tr(Δ ₁ ww ^H )≤||Δ ₁ || ₂ ||ww ^H || ₂ ≤γ||w|| ² , where C represents the complex matrix, N represents the number of antennas in the array antenna; γ and ε are the maximum singular values of Δ ₁ and Δ ₂ respectively, and tr(·) represents the trace of the matrix; thus, a new objective optimization problem is obtained, which is specifically expressed as:

Wherein, in the optimization problem solving module, the process of solving the optimization problem is specifically as follows:

Solve the following equation:

||Δ ₂ || ₂ ≤ε

The dual problem is:

Where Y, Z represent Lagrange multiplier vectors;

Using the linear matrix inequality relaxation technique, namely LMI relaxation technique, let W = ww ^H , we have:

The dual problem of optimization problem (2) is as follows:

Where a and A represent the Lagrange multiplier vector;

The complementary condition of formula (3) is calculated as follows:

tr[A(W+Z-Y)]＝0

Combination get:

Assuming that the rank of W ^* is M, there exists a rank-one decomposition matrix:

Substituting in:

and

tr[(Mw _i w _i ^H )A ^* ]＝tr(W ^* A ^* )＝a ^* ,i＝1,...,M (6)

when If the two equality conditions of equations (5) and (6) are satisfied and the second constraint of equation (2) is also satisfied, is the optimal solution; if the second constraint of equation (2) is not satisfied, find the suboptimal solution;

There exists a rank-one decomposition w _i , and the objective function is:

subject to Mw _i w _i ^H +ZY≥0，i＝1,...,M

Y≥0, Z≥0

Substitute w _i into the objective function, and finally take the maximum value of the objective optimization problem as the suboptimal value, and the corresponding w _i as the suboptimal solution;

The final waveform is outputted according to the obtained optimal solution or suboptimal solution to form a vector, thereby forming a robust adaptive beam.

In a specific implementation process, the present invention provides a robust adaptive beamforming system for non-convex quadratic matrix inequality, which models the robust adaptive beamforming problem as a signal-to-noise ratio maximization problem in an SINR model construction module; then in an array replacement module and an error matrix addition module, the maximization problem is converted into a quadratic matrix inequality problem by the strong duality principle of convex optimization; finally, a polynomial time method is used in an optimization problem solving module to solve the quadratic matrix inequality problem, thereby realizing rapid solution to the optimal solution or suboptimal solution of the original problem, and the output beamforming vector effectively improves the output signal-to-noise ratio and overall performance of the array, completes the solution of the polynomial time model, and has short operation time and high work efficiency.

Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims (4)

1. A robust adaptive beamforming method for non-convex quadratic matrix inequality, characterized by comprising the following steps: S1: Establish the output maximization signal-to-noise ratio model of array antenna beamforming, namely SINR model; In step S1, the SINR model is specifically expressed as: Wherein, w is the beamformer weight vector of the array antenna optimization design in the SINR model, _Rs is the covariance matrix of the desired signal, and Rj _+n is the covariance matrix of the interference plus noise; S2: The covariance matrix of the interference plus noise of the SINR model is replaced by the sampling covariance matrix to generate a new target optimization function; S3: Add the error matrix to the target optimization function to obtain a new target optimization problem; The covariance matrix _Rs of the expected signal and the sampling matrix When obtaining parameters, corresponding errors will occur. Therefore, it is necessary to add corresponding error values Δ ₁ , Δ ₂ to the input parameters to obtain the optimization model: in: w ^H Δ ₁ w＝tr(Δ ₁ ww ^H )≤||Δ ₁ || ₂ ||ww ^H || ₂ ≤γ||w|| ² ; where C represents the complex matrix, N represents the number of antennas in the array antenna, γ and ε are the maximum singular values of Δ ₁ and Δ ₂ respectively, and tr(·) represents the trace of the matrix; thus, a new objective optimization problem is obtained, which is specifically expressed as: Where I is the identity matrix; S4: Make corresponding changes to the target optimization problem and solve it to obtain the optimal solution or suboptimal solution, and output the final waveform to form a vector; The step S4 is specifically as follows: S41: Solve the following equation: ||Δ ₂ || ₂ ≤ε The dual problem is: Where Y, Z represent Lagrange multiplier vectors; S42: Using the linear matrix inequality relaxation technique, namely LMI relaxation technique, let W = ww ^H , we have: S43: The dual problem of optimization problem (2) is as follows: Where a and A represent the Lagrange multiplier vectors respectively; The complementary condition of formula (3) is calculated as follows: tr[A(W+Z-Y)]＝0 Combination get: S44: Assume the rank of W ^* to be M, there exists a rank-one decomposition matrix: Substituting in: and when If the two equality conditions of equations (5) and (6) are satisfied and the second constraint of equation (2) is also satisfied, is the optimal solution, executing step S46; if the second constraint of formula (2) is not satisfied, executing step S45 to solve the suboptimal solution; S45: There exists a rank-one decomposition w _i , and the objective function is: subject to Mw _i w _i ^H +ZY≥0，i＝1,...,M Y≥0, Z≥0 Substitute w _i into the objective function, and finally take the maximum value of the objective optimization problem as the suboptimal value, and the corresponding w _i as the suboptimal solution; S46: Output the final waveform according to the obtained solution to form a vector, thereby forming a robust adaptive beam. 2. The robust adaptive beamforming method for non-convex quadratic matrix inequality according to claim 1, characterized in that the covariance matrix R _j+n of the interference plus noise is generally not available, so in the step S2, the sampling matrix Instead of the covariance matrix R _j+n of interference plus noise, it is specifically expressed as: Wherein, T represents the number of sampling times, y(t) represents the vector of the received signal, and y ^H (t) is the conjugate transpose of the received signal vector. 3. A robust adaptive beamforming system for non-convex quadratic matrix inequality, characterized by comprising an SINR model building module, an array replacement module, an error matrix addition module and an optimization problem solving module; wherein: The SINR model building module is used to establish an output maximization signal-to-noise ratio model for array antenna beamforming, that is, an SINR model; In the SINR model, the SINR model is specifically expressed as: Wherein, w is the beamformer weight vector of the array antenna optimization design in the SINR model, _Rs is the covariance matrix of the desired signal, and Rj _+n is the covariance matrix of the interference plus noise; The array replacement module is used to replace the covariance matrix of the interference plus noise of the SINR model with a sampling matrix to generate a new target optimization function; The error matrix adding module is used to add an error matrix to the target optimization function to obtain the target optimization problem; In the error matrix adding module, the covariance matrix _Rs of the desired signal and the sampling matrix When obtaining parameters, corresponding errors will occur. Therefore, it is necessary to add corresponding error values Δ ₁ , Δ ₂ to the input parameters to obtain the optimization model: in: w ^H Δ ₁ w＝tr(Δ ₁ ww ^H )≤||Δ ₁ || ₂ ||ww ^H || ₂ ≤γ||w|| ² ; where C represents the complex matrix, N represents the number of antennas in the array antenna; γ and ε are the maximum singular values of Δ ₁ and Δ ₂ , respectively, and tr(·) represents the trace of the matrix; thus, a new objective optimization problem is obtained, which is specifically expressed as: Where I is the identity matrix; The optimization problem solving module makes corresponding changes to the target optimization problem and solves it to obtain an optimal solution or a suboptimal solution, and outputs the final waveform to form a vector; In the optimization problem solving module, the process of solving the optimization problem is specifically as follows: Solve the following equation: ||Δ ₂ || ₂ ≤ε The dual problem is: Where Y, Z represent Lagrange multiplier vectors; Using the linear matrix inequality relaxation technique, namely LMI relaxation technique, let W = ww ^H , we have: The dual problem of optimization problem (2) is as follows: Where a and A represent the Lagrange multiplier vector; The complementary condition of formula (3) is calculated as follows: tr[A(W+Z-Y)]＝0 Combination get: Assuming the rank of W ^* is M, there exists a rank-one decomposition matrix: Substituting in: and tr[(Mw _i w _i ^H )A ^* ]＝tr(W ^* A ^* )＝a ^* ,i＝1,...,M (6) when If the two equality conditions of equations (5) and (6) are satisfied and the second constraint of equation (2) is also satisfied, is the optimal solution; if the second constraint of formula (2) is not satisfied, find the suboptimal solution; There exists a rank-one decomposition w _i , and the objective function is: subjecttoMw _i w _i ^H +ZY≥0，i＝1,...,M Y≥0, Z≥0 Substitute w _i into the objective function, and finally take the maximum value of the objective optimization problem as the suboptimal value, and the corresponding w _i as the suboptimal solution; The final waveform is outputted according to the obtained optimal solution or suboptimal solution to form a vector, thereby forming a robust adaptive beam. 4. The robust adaptive beamforming system for non-convex quadratic matrix inequality according to claim 3, characterized in that the covariance matrix R _j+n of the interference plus noise is generally not available, so in the array replacement module, a sampling matrix is used Instead of the covariance matrix R _j+n of interference plus noise, it is specifically expressed as: Wherein, T represents the number of sampling times, y(t) represents the vector of the received signal, and y ^H (t) is the conjugate transpose of the received signal vector.