Conformal array transmit beamforming method based on pre-weighted orthogonal projection decomposition

Abstract

This invention relates to radar communication technology and discloses a conformal array transmit beamforming method based on pre-weighted orthogonal projection decomposition. The invention constructs an optimization problem by providing the expressions for the main polarization and cross-polarization steering vectors, constraining the main beam pointing and polarization, and obtaining an initial weight vector for pre-weighting. Combining the initial weight vector, a transmit weight vector is obtained based on a minimum variance distortion-free response algorithm, and orthogonal projection decomposition is performed on the weight vector. Beamforming of the conformal array transmit beam pattern is achieved by adjusting real numbers. This invention effectively reduces the peak sidelobe level of the transmit pattern, creates a concave shape within a set angle range, and constrains the polarization and cross-polarization, ensuring that the conformal array transmit beam pattern meets various performance requirements while maintaining the main beam aligned with the desired transmit direction.

Description

Technical Field

[0001] This invention pertains to radar communication technology, and particularly relates to a conformal array transmit beamforming technology based on pre-weighted orthogonal projection decomposition. Background Technology

[0002] Compared to traditional arrays, conformal arrays are characterized by their conformity to the carrier, allowing them to be attached to the carrier and offering advantages such as ease of installation and a large array angle scanning range. They are widely used in radar, communications, and other fields. However, compared to traditional scalar arrays, conformal arrays suffer from carrier shielding effects and inconsistent radiation polarization. This can lead to high sidelobe levels and severe cross-polarization in the transmitted beam pattern, resulting in poor scanning characteristics. Therefore, beamforming of conformal arrays—that is, designing weight vectors to ensure the transmitted beam pattern meets performance requirements—is of great research significance.

[0003] Intelligent optimization algorithms, such as genetic algorithms, particle swarm optimization, and hybrid algorithms, are widely used in conformal array beamforming. However, these algorithms, which search the global system using random methods to find the optimal solution, suffer from time consumption, susceptibility to local optima, and inability to meet certain performance requirements, hindering their widespread adoption. Alternating projection algorithms construct two sets and alternately project them to obtain the intersection point, which serves as the beamforming weight vector. This effectively reduces sidelobe levels (see: H. Steyskal, "Pattern synthesis for a conformalwing array," Proceedings, IEEE Aerospace Conference, Big Sky, MT, USA, 2002, pp. 2-2). However, this method can lead to main beam pointing offset in some applications and neglects constraints on polarization parameters. Transforming the performance requirements of conformal arrays into a convex optimization problem and using a toolkit to obtain the optimal solution for the weight vector to achieve beamforming is a widely used and effective method for beamforming of conformal arrays. It can change the optimization problem according to different transmission pattern performance requirements, making the algorithm widely applicable. However, this method has a large computational load and is time-consuming when solving for the optimal weights. At the same time, the relevant parameters of the optimization problem are difficult to determine (see: B. Fuchs and J. J. Fuchs, "Optimal Polarization Synthesis of Arbitrary Arrays With FocusedPower Pattern," in IEEE Transactions on Antennas and Propagation, vol. 59, no. 12, pp. 4512-4519, Dec. 2011).

[0004] Based on the above points, how to design weight vectors to shape the transmit beam of a conformal array so that the transmit beam pattern meets performance requirements while effectively constraining polarization can be applied to different scenarios, and has great research potential and application value. Summary of the Invention

[0005] The applicant analyzed the advantages and disadvantages of existing classical conformal array transmit beamforming algorithms. Existing methods fail to meet the radiation pattern performance requirements and constrain polarization while being simple and efficient for application in different scenarios. The technical problem this invention aims to solve is to propose a convenient and efficient method for solving the weight vector to achieve the conformal array transmit beam pattern performance requirements and constrain polarization.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is a conformal array transmit beamforming method based on pre-weighted orthogonal projection decomposition, wherein the total number of array elements of the conformal array in the rectangular coordinate system is... The array elements are rectangular microstrip antennas, placed at horizontal and vertical intervals. The nth array element is located at the azimuth angle. and pitch angle The element radiation pattern in the direction is , , ,in For azimuth angle variables, The elevation angle is a variable; the conformal array transmit beam direction is... The polarization parameters are ,in It is the polarization angle. The phase difference is; the conformal array spatial steering vector is ,exist and The steering vectors in the directions are respectively and ;

[0007] The specific steps for transmitting beamforming are as follows:

[0008] Step 1) Using polarization parameters Indicates the main polarization direction :

[0009] ;

[0010] Step 2) Determine the cross-polarization parameters , representing the cross-polarization steering vector :

[0011] ;

[0012] Step 3) Constrain the downward polarization of the main beam to obtain the weight vector. initial value ,in This is the initial spatial correlation matrix related to the cross-polarization pointing downwards from the main beam;

[0013] Step 4) Determine the adjustment points other than the main beam pointing to obtain the weight vector. for , The spatial correlation matrix is ​​based on the adjustment points. , Adjusting the point power for the launch pattern It is the conjugate transpose; To adjust the beam direction, The steering vector represents the adjustment point of the conformal array emission pattern. By adjusting the components, it can be... Set it to either the main polarization pattern or the cross-polarization pattern;

[0014] Step 5) Calculate the spatial correlation matrix based on the adjustment points. Decompose:

[0015] ;

[0016] in, and For the projection matrix, , , It is the identity matrix. To adjust the parameters;

[0017] Step 6) Perform the k-th iteration: The spatial angle adjusted in the k-th iteration is... The previous weight vector The two components are respectively , ;

[0018] Step 7) Obtain the desired voltage level based on the cross-polarization pattern and the main polarization pattern. expression:

[0019] ;

[0020] Step 8) Use the weight vector obtained from the previous iteration. Medium component and and known expected level values Calculate adjustment parameters Two alternative results and :

[0021] ;

[0022] in, To obtain the real part, Indicates taking the matrix Row 1, Column 2 Indicates taking the matrix Row 2, Column 2;

[0023] ;

[0024] ;

[0025] Step 9) and As adjustment parameters respectively Input function Calculate, choose to make The smaller value is used as the adjustment parameter in the k-th iteration. optimal solution Thus, the weight vector is determined in the k-th iteration. , ;

[0026] ;

[0027] in, It is a 2-norm;

[0028] Step 10) Determine if the iteration stopping condition has been met. If so, obtain the weight vector from the k-th iteration. As the optimal emission weight vector Used for conformal array transmit beamforming; otherwise, update k=k+1 and return to step 3); the iteration stops when the weight vector is obtained from the k-th iteration. The given launch pattern satisfies the constraints or k reaches its maximum value.

[0029] This invention discloses an algorithm for fast and efficient beamforming of the transmit pattern of a conformal array. The invention ingeniously provides the expressions for the main polarization steering vector and the cross-polarization steering vector, and designs an optimization problem based on the maximum output signal-to-noise ratio criterion to obtain the initial weight vector, thereby constraining the polarization. Combining the initial weight vector with the minimum variance distortionless response algorithm, the transmit weight vector is obtained, and orthogonal decomposition is performed on the transmit weight vector. By adjusting the parameters, effective beamforming of the transmit pattern is achieved.

[0030] The beneficial effects of this invention are that it can achieve the performance requirements of reducing peak sidelobe levels and forming a dip, while ensuring that the main beam of the conformal array transmission pattern is aligned with the desired transmission direction. In addition, it achieves polarization constraint on the conformal array transmission pattern. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the angles and coordinate system of the present invention;

[0032] Figure 2 This is a flowchart of the method of the present invention;

[0033] Figure 3 The initial transmit beam pattern under linear polarization;

[0034] Figure 4 Initial transmitted beam under linear polarization Direction diagram;

[0035] Figure 5 Initial transmitted beam under linear polarization Direction diagram;

[0036] Figure 6 The above are the total transmission beam patterns of the three algorithms under linear polarization in this invention.

[0037] Figure 7 This is a top view of the overall transmission beam pattern of the three algorithms under linear polarization in this invention;

[0038] Figure 8 The three algorithms under linear polarization in this invention Direction diagram;

[0039] Figure 9 The three algorithms under linear polarization in this invention Direction diagram;

[0040] Figure 10 The diagram shows the main polarization direction patterns of the three algorithms under linear polarization in this invention.

[0041] Figure 11 This is a cross-polarization direction pattern of the three algorithms under linear polarization in this invention;

[0042] Figure 12 These are pitch dimension profiles of the three algorithms under linear polarization in this invention.

[0043] Figure 13 These are azimuth profiles of the three algorithms under linear polarization in this invention.

[0044] Figure 14 The total transmission beam pattern of the three algorithms under circular polarization in this invention is shown below.

[0045] Figure 15 This is a top view of the overall transmission beam pattern of the three algorithms under circular polarization in this invention;

[0046] Figure 16 The three algorithms under circular polarization in this invention Direction diagram;

[0047] Figure 17 The three algorithms under circular polarization in this invention Direction diagram;

[0048] Figure 18 The diagram shows the main polarization direction patterns of the three algorithms under circular polarization in this invention.

[0049] Figure 19 This is a cross-polarization direction pattern of the three algorithms under circular polarization in this invention;

[0050] Figure 20 These are pitch dimension profiles of the three algorithms under circular polarization in this invention.

[0051] Figure 21 These are the azimuth profiles of the three algorithms under circular polarization in this invention. Detailed Implementation

[0052] The specific embodiments and working principles of the present invention will be further described in detail below with reference to the accompanying drawings.

[0053] To better describe this, we first define the following:

[0054] Rectangular microstrip antenna: The array element adopts a rectangular microstrip patch antenna, which is located in the YOZ plane. The length of the rectangle is parallel to the y-axis, and the radiation pattern is as follows:

[0055] ;

[0056] ;

[0057] in and They are respectively and Radiation pattern of a directional antenna.

[0058] Array element orientation pattern: By combining the array element coordinates and using Euler rotation, the orientation of the nth array element in the local coordinate system can be obtained. Based on the element carrier blocking effect and the radiation pattern of the rectangular microstrip patch antenna, the element radiation pattern in the local coordinate system is as follows:

[0059] ;

[0060] ;

[0061] , In the local coordinate system of the nth element and Polarization pattern.

[0062] The element pattern in the global coordinate system can ultimately be obtained through Euler rotation. , .

[0063] Pitch and Azimuth: Pitch The angle between the incident signal and the positive z-axis is the azimuth angle. Let be the angle between the projection of the incident signal onto the XOY plane and the positive x-axis. Consider a coordinate system where the positive z-axis points vertically downwards, the y-axis points to the left, and the x-axis is perpendicular to the YOZ plane and points outwards. A schematic diagram of the angle and coordinate system is shown below. Figure 1 As shown, the pitch angle range is The azimuth range is .

[0064] Conformal array of hemispherical surface: The vertex of the hemispherical surface is located on the positive z-axis, the center of the sphere coincides with the origin, the radius of the hemispherical surface is R, and the array elements are placed alternately along concentric rings on the hemispherical surface, parallel to and perpendicular to the tangents of the rings.

[0065] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings. Assume that the number of array elements is N, and the desired transmission beam direction of the conformal array is... The polarization parameters are ,in It is the polarization angle. This represents the phase difference.

[0066] like Figure 2 The flowchart shown is for a conformal array transmit beamforming algorithm based on pre-weighted orthogonal projection decomposition, which specifically includes the following steps:

[0067] Step 1: Based on the position of array elements and the direction of the transmitted beam Define array space steering vector :

[0068] ;

[0069] in, , , For the signal wavelength, This represents the position of the nth array element.

[0070] Step 2: The array element pattern matrix can be obtained from the array element pattern.

[0071] ;

[0072] ;

[0073] , for and Directional element pattern matrix, and The steering vector in the direction can be represented as and Further, we can obtain and Spatial response of direction , .

[0074] Step 3, from polarization parameters This allows us to obtain the current principal polarization direction:

[0075] ;

[0076] At this point, the actual expected spatial response is The components on are and The inner product is:

[0077] ;

[0078] Therefore, the principal polarization steering vector can be expressed as:

[0079] ;

[0080] Cross-polarization parameters can be determined from polarization information. Similarly, the cross-polarization steering vector can be obtained:

[0081] ;

[0082] Step 4: Weight the main polarization steering vector and the cross-polarization steering vector pointing towards the desired beam to obtain the spatial response in the main polarization direction and the spatial response in the cross-polarization direction. , The amplitude of the conformal array transmitted beam pattern can be expressed as:

[0083] ;

[0084] From the spatial response of the main polarization direction and the spatial response of the cross-polarization direction, we can obtain the cross-polarization spatial response, which is normalized based on the main polarization spatial response. This response is denoted as the cross-polarization level. .

[0085] Step 5: Based on the maximum output signal-to-noise ratio criterion, constrain the desired beam pointing and polarization mode. The optimization problem is:

[0086] ;

[0087] Solving the above equation yields the initial weight vector. This is pre-weighting, where This is the initial spatial correlation matrix related to the cross-polarization pointing downwards from the main beam.

[0088] Step 6: Considering adjustment points other than the main beam pointing, design the optimal adaptive weights using the Minimum Variance Distortionless Response (MVDR) algorithm. The algorithm is described in detail below.

[0089] ;

[0090] The constraints can be set according to the requirements, i.e., when considering constraints on the principal polarization pattern. When cross-polarization constraints are applied .

[0091] The weight vector can be obtained by solving for the weight vector. ,in , Adjust the point power for the launch pattern.

[0092] Next, the weight vector is decomposed by orthogonal projection.

[0093] Step 7: Using the matrix inversion rule, we can... Decompose:

[0094] ;in, and Let be the projection matrix, and there exist Relationship:

[0095] ;

[0096] To adjust the parameters, .

[0097] Therefore, the optimal weight vector can be orthogonally projected and decomposed as follows:

[0098] ;

[0099] in , .

[0100] By adjusting the parameters By making adjustments, the direction of adjustment can be changed. The adjustment of the signal power received by the desired pole is given below, along with the adjustment parameters. Solve for it.

[0101] Step 8: Assume the beam pointing for the k-th adjustment is... , It can be derived from existing weight vectors To obtain, that is ,in , Given the pole adjusted in the kth order Expected level value at It can be obtained by solving the normalized power response. The normalized power response expression is as follows:

[0102] ;

[0103] Step 9: Adjust parameters There are two feasible solutions, namely:

[0104] ;

[0105] in,

[0106] ;

[0107] ;

[0108] Choose the adjustment parameter that minimizes the change in the radiation pattern between two iterations as the current adjustment parameter, and use it. The change in the pattern between two iterations is measured as follows: ,in:

[0109] ;

[0110] After multiple iterations, the optimal transmit beam weight vector is obtained. This achieves conformal array beamforming, thereby enabling the adjustment direction in each iteration. This represents the direction that deviates most from the desired pattern in the pattern obtained in the (k-1)th iteration.

[0111] To make the objectives, technical solutions, and technical effects of this invention clearer, a simulation experiment is conducted to provide a more detailed description of the invention.

[0112] This experiment simulates the proposed conformal array transmit beamforming algorithm (PW-WORD) based on pre-weighted orthogonal projection decomposition. In the following simulations, the incident signals are all narrowband signals with wavelengths of... The array is a lower hemispherical array with a radius of... The arc length between adjacent rings and the interval between adjacent array elements in the same ring are both... The total number of array elements is 933. Signal transmission direction. Main lobe angle range , The depression consists of two parts, with an angle range of 1. , Angle range 2 is , The methods used for comparison include the alternating projection algorithm (AP) under the same simulation conditions and the beamforming algorithm based on convex optimization (CVX), as well as the initial transmitted beam pattern that only performs spatial steering vector phase supplementation weighting, i.e. .

[0113] Consider different polarization modes, namely linear polarization and circular polarization: When the polarization mode is linear polarization, the principal polarization is considered to be the horizontal polarization component, i.e. In the direction pattern, the cross-polarization becomes the vertical polarization component, i.e. Direction pattern, polarization parameters are , principal polarization parameters , Cross-polarization parameters , When the polarization mode is circular polarization, considering the primary polarization as left-handed circular polarization, the cross polarization becomes right-handed circular polarization, i.e., the polarization parameter is... , Principal polarization parameters , Cross-polarization parameters , .

[0114] Simulation Experiment 1: This simulation focuses on the initial transmit beam pattern after only spatial steering vector phase supplementation and weighting. The overall transmit beam pattern is shown below. Figure 3 As shown, Direction diagram as follows Figure 4 As shown, Direction diagram as follows Figure 5 As shown.

[0115] Simulation Experiment 2: In this simulation, linear polarization is considered. The PW-WORD algorithm, AP algorithm, and beamforming algorithm based on convex optimization (CVX) are simulated. The total transmit beam patterns of the three algorithms are shown below. Figure 6 As shown, the top view of the overall radiation pattern of the transmitted beam is as follows. Figure 7 As shown, Direction diagram as follows Figure 8 As shown, Direction diagram as follows Figure 9 As shown, the main polarization pattern is as follows: Figure 10 As shown, the cross-polarization pattern is as follows Figure 11 As shown, the pitch dimension profile is as follows: Figure 12 As shown, the azimuth profile pattern is as follows: Figure 13 As shown in the table below, the performance of each algorithm is as follows:

[0116] Algorithm performance Initial performance AP CVX PW-WORD <![CDATA[γ * ]]> 0.4517 0.0183 1.2764e-15 4.4862e-04 <![CDATA[η * ]]> 3.1416 -2.6951 -0.3646 -1.9151 Peak sidelobe level (dB) -0.2167 -25.42 -27.31 -27.78 Cross-polarization level (dB) -0.3689 -28.33 -16.47 -29.57 Maximum dimpling level (dB) -26.90 -37.71 -54.25 -51.63 Average dip level (dB) -31.52 -46.02 -60.20 -56.37

[0117] It should be noted that in linear polarization, the principal polarization is considered horizontal polarization, and the cross polarization is considered vertical polarization. Therefore, as... Therefore, it can be assumed that the polarization mode pointing downwards by the desired beam satisfies the polarization parameters.

[0118] Simulation Experiment 3: In this simulation, circular polarization is considered. The PW-WORD algorithm, AP algorithm, and beamforming algorithm based on convex optimization are simulated. The total transmit beam patterns of the three algorithms are shown below. Figure 14 As shown, the top view of the overall radiation pattern of the transmitted beam is as follows. Figure 15 As shown, Direction diagram as follows Figure 16 As shown, Direction diagram as follows Figure 17 As shown, the main polarization pattern is as follows: Figure 18 As shown, the cross-polarization pattern is as follows Figure 19 As shown, the pitch dimension profile is as follows: Figure 20 As shown, the azimuth profile pattern is as follows: Figure 21 As shown in the table below, the performance of each algorithm is as follows:

[0119] Algorithm performance Initial performance AP CVX PW-WORD <![CDATA[γ * ]]> 0.4517 0.7657 0.7854 0.7852 <![CDATA[η * ]]> 3.1416 1.5536 1.5708 1.5707 Peak sidelobe level (dB) -0.2167 -25.50 -27.37 -26.69 Cross-polarization level (dB) 0.1875 -27.91 14.69 -29.51 Maximum dimpling level (dB) -26.90 -39.91 -53.92 -51.64 Average dip level (dB) -31.52 -47.50 -60.00 -56.79

[0120] As can be seen from the simulation experiments above, the method of this invention solves the problem of conformal array transmit beamforming by designing adaptive weight vectors. The method of this invention ensures that the main beam direction is aligned with the desired beam direction and reduces peak sidelobe levels, forming a concave shape within a specified angle range. Simultaneously, this invention also constrains polarization, suppressing cross-polarization and constraining the polarization mode of the main beam direction. Compared with traditional conformal array transmit beamforming methods, this invention achieves radiation pattern performance close to that of beamforming algorithms based on convex optimization. However, beamforming algorithms based on convex optimization do not effectively constrain cross-polarization. Furthermore, this invention does not require the use of the CVX toolbox for solving, enabling faster and more efficient acquisition of the optimal weight vector with less computation time. Compared with the alternating projection algorithm, the performance of this invention is superior in all aspects, and the main beam direction can be effectively aligned with the desired transmit beam direction.

[0121] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification, unless specifically stated otherwise, may be replaced by other equivalent or similar alternative features. All disclosed features, or steps in all methods or processes, except for mutually exclusive features and / or steps, may be combined in any way. Any non-essential additions or substitutions made by those skilled in the art based on the technical features of the present invention shall fall within the protection scope of the present invention.

Claims

1. A conformal array transmit beamforming method based on pre-weighted orthogonal projection decomposition, characterized in that, The total number of elements in a conformal array in Cartesian coordinates is The array elements are rectangular microstrip antennas, placed at horizontal and vertical intervals. The nth array element is located at the azimuth angle. and pitch angle The element radiation pattern in the direction is , , ,in For azimuth angle variables, The elevation angle is a variable; the conformal array transmit beam direction is... The polarization parameters are ,in It is the polarization angle. The phase difference is; the conformal array spatial steering vector is ,exist and The steering vectors in the directions are respectively and ; The specific steps of the transmit beam assignment are: Step 1) Using polarization parameters Indicates the main polarization direction : ； Step 2) Determine the cross-polarization parameters , representing the cross-polarization steering vector : ； Step 3) Constrain the downward polarization of the main beam to obtain the weight vector. initial value ,in This is the initial spatial correlation matrix related to the cross-polarization pointing downwards from the main beam; Step 4) Determine the adjustment points other than the main beam pointing to obtain the weight vector. for , The spatial correlation matrix is ​​based on the adjustment points. , Adjusting the point power for the launch pattern It is the conjugate transpose; To adjust the beam direction, The steering vector represents the adjustment point of the conformal array emission pattern. By adjusting the components, it can be... Set it to either the main polarization pattern or the cross-polarization pattern; Step 5) Adjustment point based spatial correlation matrix Decomposition: ； in, and For the projection matrix, , , It is the identity matrix. To adjust the parameters; Step 6) Perform the k-th iteration: The spatial angle adjusted in the k-th iteration is... The previous weight vector The two components are respectively , ; Step 7) Obtaining preset expected level values from the cross-polarization pattern and the main-polarization pattern Expression: ； Step 8) Use the weight vector obtained from the previous iteration. Medium component and and known expected level values Calculate adjustment parameters Two alternative results and : ； in, To obtain the real part, Indicates taking the matrix Row 1, Column 2 Indicates taking the matrix Row 2, Column 2; ； Step 9) and As adjustment parameters respectively Input function Calculate, choose to make The smaller value is used as the adjustment parameter in the k-th iteration. optimal solution Thus, the weight vector is determined in the k-th iteration. , ; ； wherein is a two-norm; Step 10) Determine if the iteration stopping condition has been met. If so, obtain the weight vector from the k-th iteration. As the optimal emission weight vector Used for conformal array transmit beamforming; otherwise, update k=k+1 and return to step 3); the iteration stops when the weight vector is obtained from the k-th iteration. The given launch pattern satisfies the constraints or k reaches its maximum value.

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