A method, device and medium for joint optimization of gain-axis ratio of small-scale phased array low elevation scanning

Abstract

The present invention discloses a method, device and medium for joint optimization of gain axis ratio of a small-scale phased array at low elevation scanning, and belongs to the technical field of gain optimization of airborne phased array antennas. The method of the present invention comprises: inputting the right-handed circularly polarized electric field of the electric field unit pattern of each array unit in a small-scale array of a uniform planar phased array antenna, and the components of the electric field in the azimuth and elevation planes; constructing a joint optimization model for gain axis ratio of low elevation scanning based on scanning axis ratio and gain, wherein the objective function is a slack variable that minimizes the scanning axis ratio, and the constraints of the joint optimization model include: scanning axis ratio constraint, gain constraint and constant excitation amplitude modulus constraint; solving the optimization model, and outputting array excitation, scanning axis ratio and gain in a predetermined scanning direction. The present invention improves the circular polarization performance by reducing the low elevation scanning axis ratio while ensuring the scanning gain, thereby avoiding the degradation of circular polarization performance during low elevation scanning and causing a decrease in gain.

Description

Technical Field

[0001] The present application relates to the technical field of airborne phased array antenna gain optimization, and in particular to a method, device and medium for joint optimization of gain axial ratio of a small-scale phased array at low elevation angle scanning. Background Art

[0002] In the field of airborne communication antennas, in order to reduce aircraft wind resistance and aircraft weight, most airborne antennas consider smaller-scale phased array antennas; in order to reduce the overall operating power loss of the aircraft, most airborne phased array antennas adopt passive phased array antennas. Passive phased arrays have the problem of unadjustable amplitude, which reduces the optimization freedom of phased array antennas; for the communication function of airborne communication antennas, especially emergency communications, the antenna needs to be able to achieve large-angle scanning, that is, low-elevation scanning, but due to structural and scale limitations, when a small-scale array is covered at a low-elevation beam, the deterioration of the scanning axis ratio will cause the gain to drop sharply, and even degenerate into a single polarization mode.

[0003] Small-scale phased array antennas used in airborne communications have limited space resources on aircraft. When using a passive phased array design architecture, the unit spacing is closely arranged, which will form a tightly coupled feeding form. Tightly coupled feeding will cause the coupling effect between units to significantly affect the axial ratio performance of low-elevation scanning during large-angle scanning of small-scale phased arrays, because the unit spacing is less than half a wavelength. Therefore, by taking the scanning axial ratio as the optimization target, the circular polarization performance of low-elevation scanning of small-scale arrays can be improved. However, focusing only on the scanning axial ratio performance may lead to gain deterioration.

[0004] For the optimization of scanning performance of phased array antennas, the existing methods mainly include two categories: the first category takes gain as the objective function, such as the typical second-order cone programming, that is, fixing the transmission power as a constant and minimizing the total power; and non-convex quadratic programming, fixing the total power as a constant and minimizing the transmission power. However, this type of method only optimizes the gain, does not control the scanning axis ratio, ignores the circular polarization performance, and the constructed optimization problem is prone to second-order non-convex problems. The second type takes the scanning axis ratio as the objective function, such as fractional programming, by controlling the ratio of the electric field component in the azimuth plane direction of the electric field to the electric field component in the elevation plane direction, and then controls the scanning axis ratio. However, this type of method only optimizes the scanning axis ratio, which will cause a sharp drop in gain. Especially for small-scale arrays, the scanning axis ratio will deteriorate when scanning at low elevation angles, and even become a single polarization mode, and the gain will drop sharply. That is, the existing scanning performance optimization of phased array antennas can only meet a single demand, and it is difficult to improve the overall performance of the antenna.

[0005] Therefore, for small-scale phased array antennas, scanning at low elevation angles will cause the scanning axis ratio to deteriorate, or even turn into a single polarization mode, and the gain will drop sharply. The existing optimization method can only meet a single requirement and it is difficult to improve the overall performance of the antenna. Summary of the invention

[0006] In response to the above problems, the present application proposes a method, device and medium for joint optimization of the gain axis ratio of a small-scale phased array at low elevation angle scanning, which can ensure the circular polarization performance while ensuring the array gain, that is, improve the scanning axis ratio, and can significantly improve the array circular polarization performance of a small-scale phased array at low elevation angle scanning.

[0007] In a first aspect, the present application provides a small-scale phased array low elevation scanning gain axial ratio joint optimization method, which comprises the following steps:

[0008] Step 1, inputting the right-hand circularly polarized electric field of the electric field unit pattern of each array unit in the small-scale array, and the electric field components in the azimuth plane direction and the elevation plane direction of the electric field; wherein the small-scale array is a uniform planar phased array antenna;

[0009] Step 2, determining the scanning axis ratio of the small-scale array based on the array excitation and the two electric field components, and determining the gain of the small-scale array based on the array excitation and the right-hand circularly polarized electric field;

[0010] A low elevation scanning gain-axis ratio joint optimization model is constructed based on the scanning axis ratio and the gain. The objective function of the joint optimization model is to minimize the slack variable of the scanning axis ratio, and the constraints of the joint optimization model include: scanning axis ratio constraint, gain constraint and constant excitation amplitude modulus constraint; wherein the scanning axis ratio constraint is a slack variable that the scanning axis ratio is less than or equal to the scanning axis ratio;

[0011] Step 3, optimize and solve the constructed low-elevation scanning gain-axis ratio joint optimization model, output array excitation, and obtain the scanning axis ratio and gain of the small-scale array in a predetermined scanning direction based on the output array excitation.

[0012] Furthermore, in step 2, the low elevation scanning gain axis ratio joint optimization model constructed is:

[0013]

[0014] in, slack variable representing the scan axis ratio; represents array excitation, where L is the number of array elements in the small-scale array, and , , are the number of elements of the small-scale array in the horizontal and vertical directions, represents the complex domain, , Represents the expected direction The azimuthal component of the circularly polarized electric field at and the pitch plane component The electric field component of , Respectively The excitation amplitude and excitation phase of the array element unit at is the natural base, is an imaginary unit, Indicates the phase, represents circularly polarized electric field Directional component and The ratio of the directional components, , They represent the initial azimuthal direction components of the circularly polarized electric field. and the pitch plane component The electric field unit pattern is, where , Belongs to the spherical coordinate system, the expected direction are the two direction components in the custom coordinate system, and , The mapping relationship is: , ,and The range of is: , represents the propagation constant of electromagnetic waves in free space, Indicates wavelength; Indicates the desired direction The right-hand circularly polarized electric field at Indicates the initial value of the transmit power. represents an all-1 vector of dimension L×1, Used to characterize constant excitation amplitude modulus constraint. The superscript “H” indicates conjugate transpose.

[0015] Furthermore, since the gain constraint is a quadratic concave function and a closed-form solution cannot be found, when optimizing and solving the constructed low-elevation-angle scanning gain-axis ratio joint optimization model in step 3, the gain constraint of the constructed low-elevation-angle scanning gain-axis ratio joint optimization model is transformed to find the gain lower bound so that the constraint lower bound satisfies the constraint, and the gain constraint is converted into a convex function for optimization and solution.

[0016] Furthermore, the gain constraint is converted into a convex function, and then the low elevation scanning gain-axis ratio joint optimization model is solved by an iterative optimization method, including:

[0017] Define the right-hand circular polarization power array factor auxiliary quantity ;

[0018] Define the axis ratio constraint factor auxiliary quantity ;

[0019] Introducing the first auxiliary variable , the second auxiliary variable The Lagrangian function is constructed as:

[0020]

[0021] Based on Lagrangian function The low elevation scanning gain-axis ratio joint optimization model is transformed into:

[0022]

[0023] in, represents the transformed objective function, represents the penalty factor, represents the two-norm, represents the array excitation of the previous iteration, It represents the operation of taking the real part of a complex value;

[0024] Among them, the first auxiliary variable and the second auxiliary variable The initial value of is the preset value, and its update method during the iterative solution process is:

[0025] Based on the current second auxiliary variable and the array excitation solved by the current iteration Update the first auxiliary variable for: ,symbol" " indicates the phase angle;

[0026] Then based on the array excitation solved by the current iteration and the first auxiliary variable after the current update Update the second auxiliary variable for: ,in, Represents the second auxiliary variable after the previous iteration update.

[0027] Furthermore, in step 3, the array excitation The initialization method is: perform eigenvalue decomposition on the directional coefficient matrix composed of the directional coefficients of the small-scale array, and use the eigenvector corresponding to the maximum eigenvalue as the array excitation The initial value of .

[0028] Furthermore, in step 3, when the low elevation scanning gain-axis ratio joint optimization model is solved by iterative optimization, the iterative convergence condition is set to the solved array excitation The value of converges.

[0029] Furthermore, in step 3, the iterative convergence condition is set to the solved array excitation The value of converges, including:

[0030] Define the convergence function ,in, , They represent the array excitations solved by the current iterative optimization and the previous iterative optimization respectively. When the convergence function When the function value of is less than or equal to the specified threshold, the array is considered to be excited Preferably, the threshold value can be set to .

[0031] A second aspect of the present application provides a computer device, comprising: a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to perform a small-scale phased array low-elevation scanning gain-axis ratio joint optimization method as described in the present application.

[0032] A third aspect of the present application provides a computer-readable storage medium having a computer program stored thereon, the program being executed by a processor to perform a small-scale phased array low-elevation scanning gain-axis ratio joint optimization method as described in the present application.

[0033] The technical solution provided by this application brings at least the following beneficial effects:

[0034] Through the small-scale phased array low-elevation scanning gain and axial ratio joint optimization method, device and medium proposed in the present application, for a given scanning angle, the array gain and axial ratio are jointly optimized, and the array excitation is obtained by optimization calculation, which can improve the low-elevation scanning characteristics of the small-scale uniform planar array. While ensuring the scanning gain, the circular polarization performance is improved by reducing the low-elevation scanning axial ratio, thereby avoiding the degradation of the circular polarization performance during low-elevation scanning and causing the gain to decrease. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1 A flowchart of a small-scale phased array low elevation scanning gain-axis ratio joint optimization method provided in an embodiment of the present application;

[0037] Figure 2 This is a comparison diagram of the first low elevation scanning gain axial ratio in the embodiment of the present application;

[0038] Figure 3 This is a comparison diagram of the second low elevation scanning gain axial ratio in the embodiment of the present application;

[0039] Figure 4 It is the convergence curve of the objective function in the embodiment of the present application. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be described in detail and completely in conjunction with the drawings in the implementation of the present application. Obviously, the embodiments described with reference to the drawings are exemplary and are intended to be used to explain the present application, and cannot be understood as limiting the present application.

[0041] Figure 1 The flowchart of a small-scale phased array low elevation scanning gain axial ratio joint optimization method provided according to an embodiment of the present application. Figure 1 As shown, the small-scale phased array low elevation scanning gain axis ratio joint optimization method includes the following steps:

[0042] Step 1, inputting the right-hand circularly polarized electric field of the electric field unit pattern of each array unit in the small-scale array, and the electric field components in the azimuth plane direction and the elevation plane direction of the electric field; wherein the small-scale array is a uniform planar phased array antenna;

[0043] Step 2, determining the scanning axis ratio of the small-scale array based on the array excitation and the two electric field components, and determining the gain of the small-scale array based on the array excitation and the right-hand circularly polarized electric field; constructing a low-elevation-angle scanning gain axis ratio joint optimization model based on the scanning axis ratio and the gain, wherein the objective function of the joint optimization model is a slack variable that minimizes the scanning axis ratio, and the constraints of the joint optimization model include: scanning axis ratio constraint, gain constraint, and constant excitation amplitude modulus constraint; wherein the scanning axis ratio constraint is a slack variable that the scanning axis ratio is less than or equal to the scanning axis ratio;

[0044] Step 3, optimize and solve the constructed low-elevation scanning gain-axis ratio joint optimization model, output array excitation, and obtain the scanning axis ratio and gain of the small-scale array in a predetermined scanning direction based on the output array excitation.

[0045] In step 1, Take a small-scale array of planar phased array antennas as an example. Direction) unit spacing is , the number of array elements is , along the vertical direction ( Direction) unit spacing is , the number of array elements is , then the far-field radiation pattern of the phased array antenna can be expressed as:

[0046] (1)

[0047] In the formula, is the array element unit directional diagram, m and n are the position indexes of the array element unit in the horizontal and vertical directions respectively, , The array element positions are The excitation amplitude and phase of the array element at is the natural base, is an imaginary unit, For phase, spherical coordinates to custom The mapping of the coordinate system is set to: First mapping direction , the second mapping direction , the pitch and azimuth directions in the spherical coordinate system The range of is: , represents the propagation constant of electromagnetic waves in free space, Indicates wavelength.

[0048] The corresponding far-field directivity coefficient can be defined as:

[0049] (2)

[0050] in, express The center point of the main lobe in the coordinate system.

[0051] Both equations (1) and (2) can be simplified into matrix form:

[0052] (3)

[0053] (4)

[0054] in, represents the array excitation vector, which is used to characterize the complex weighting coefficients of the array elements. Respectively, about the first mapping direction , the second mapping direction The matrix of is the array factor, , represents the auxiliary matrix for calculating the transmit power, The denominator in the expression is the total power, and the numerator is the transmission power. , is a Hermitian symmetric matrix representing the auxiliary matrix for calculating the total power, where the matrix For calculation The auxiliary matrix, representing the total power component factor, can be obtained by eigendecomposition , and Respectively represent matrices and The inverse matrix of , H represents the conjugate transpose, Represents the field of real numbers.

[0055] In step 2, the low elevation scanning gain-axis ratio joint optimization model constructed in this embodiment is a gain-axis ratio joint optimization problem under constant modulus constraints, which can be described as:

[0056] (5)

[0057] In the formula, represents the array excitation, represents the active unit pattern of right-hand circular polarization, that is, Indicates the desired direction The right-hand circularly polarized electric field at is the slack variable, is the initial value of the transmit power, represents the desired scanning direction, , Represents the expected direction The azimuthal component of the circularly polarized electric field at and the pitch plane component The electric field component of , Respectively The excitation amplitude and excitation phase of the array element unit at is the natural base, is an imaginary unit, Indicates the phase, represents circularly polarized electric field Directional component and The ratio of the directional components, represents an all-1 vector of dimension L×1; ,in , They represent the initial azimuthal direction components of the circularly polarized electric field. and the pitch plane component The electric field unit pattern of . This problem is a non-convex problem and the closed-form solution cannot be directly obtained. Therefore, transformations are performed according to different constraints.

[0058] The scan axis ratio constraint is a first-order convex function with an upper bound, so it can be further simplified to

[0059] (6)

[0060] In the formula, the auxiliary amount .

[0061] The gain constraint is a quadratic concave function, and it is impossible to find a closed-form solution. Therefore, the gain constraint is lowerbounded simplified to find the lower bound of the function so that the lower bound satisfies the constraint condition. The lower bound of the constraint is

[0062] (7)

[0063] In the formula Represents the array excitation of the previous iteration, the auxiliary amount .

[0064] The constant modulus constraint is also a difficult non-convex constraint, and the array excitation is updated in alternating directions. Solve and introduce auxiliary variables , The Lagrangian function is constructed as

[0065] (8)

[0066] Auxiliary variables The update method is:

[0067] (9)

[0068] Among them, the symbol " ” indicates the phase angle.

[0069] Auxiliary variables The update method is:

[0070] (10)

[0071] Therefore, the optimization problem (6) can be transformed into:

[0072] (11)

[0073] in, represents the transformed objective function, represents the penalty factor, represents the two-norm, Represents the operation of taking the real part of a complex value.

[0074] During each iteration, the auxiliary variables are fixed and , then the problem can be transformed into a second-order cone problem, which can be solved by existing solvers such as Gurobi, Mosek, etc.

[0075] For a uniform planar phased array, the ideal maximum gain can be obtained by matching the phase according to the opposite number of the relative path difference. Therefore, the initial value of the gain constraint of this problem should be set to the transmission power obtained by matching the phase according to the opposite number of the relative path difference. As shown in formula (4), this form is the standard Rayleigh entropy form, which is greater than its minimum eigenvalue and less than its maximum eigenvalue. Therefore, the eigenvector corresponding to the maximum eigenvalue is taken The maximum gain can be obtained as an initial value.

[0076] (12)

[0077] in, Represents the initial value of the array excitation.

[0078] The specific solution process of solving the optimization problem described by formula (10) includes the following steps:

[0079] Step S1: Initialization ; The superscript “(1)” is used to indicate the initial number of iterations;

[0080] Step S2: Enter the loop and fix the variables , use Gurobi or mosek and other optimization solvers to solve the elevation scanning gain-axis ratio joint optimization model shown in formula (11); based on the solution results, the array excitation for the next iteration is obtained, which is recorded as ; Among them, the superscript " " represents the number of iterations, and its initial value is 1;

[0081] Step S3: Fixing variables , update the first auxiliary variable according to formula (9) , get the first auxiliary variable of the next iteration, denoted as ;

[0082] Step S4: Fixing variables , update the second auxiliary variable according to formula (10) , get the second auxiliary variable for the next iteration, denoted as ;

[0083] Step S5: Calculate the convergence function And store the convergence function of each iteration to determine whether the convergence condition is met. , then let the number of iterations After incrementing by 1, continue to execute step S2; if , then go to step S6;

[0084] Step S6: Output the currently obtained array excitation, that is, the most recently obtained , and then based on the array excitation output, the scanning axis ratio and array gain of the predetermined scanning direction are determined.

[0085] In this embodiment, tight coupling Taking the microstrip antenna as an example, the active unit radiation pattern is obtained through full-wave simulation software. The joint optimization method proposed in this embodiment is adopted. When compared with the ideal phase matching situation, it can be found that through actual experimental simulation, it is proved that the joint optimization method proposed in this embodiment can effectively reduce the scanning axis ratio and improve the gain.

[0086] Figure 2 and Figure 3 The method proposed in this embodiment is used at different scanning angles The comparison chart of low-elevation scanning gain axial ratio under the following conditions is shown in Table 1. The "Gain ideal" and "Gain Proposed" in the figure refer to the optimized gain and ideal phase matching, respectively. The "AxialRatio Ideal" and "Axial Ratio Proposed" refer to the optimized scanning axial ratio and the ideal phase matching axial ratio, respectively. Compared with the ideal phase matching, the small-scale phased array low-elevation scanning gain axial ratio joint optimization method proposed in this embodiment can further improve the scanning axial ratio performance while ensuring the gain, and ensure the circular polarization performance and gain performance of the small-scale phased array during low-elevation scanning. The specific change data is shown in Table 1. The scanning axial ratio improvement range is 1.24dB~1.80dB, and the gain change is stable at 0.03dBi~0.33dBi.

[0087] Table 1 Array gain axis ratio data

[0088]

[0089] Figure 4 is the objective function The convergence curve of Figure 4 As shown, the joint optimization method proposed in this embodiment converges after about 7 iterations, with a faster convergence speed.

[0090] In an exemplary embodiment, the embodiment of the present application also provides a computer device, which includes a processor and a memory, and at least one computer program is stored in the memory. The at least one computer program is loaded and executed by one or more processors to implement a small-scale phased array low-elevation scanning gain axis ratio joint optimization method provided in the embodiment of the present application. Furthermore, the computer device also includes a communication interface for communication between the memory and the processor, and the memory for storing the computer program that can be run on the processor may also include a high-speed random access memory and may also include a non-volatile memory, such as at least one disk memory. If the memory, processor and communication interface are implemented independently, the communication interface, memory and processor can be interconnected through a bus and complete mutual communication. Among them, the bus can be an industrial standard architecture bus, an external device interconnect bus or an extended industrial standard architecture bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0091] Optionally, in a specific implementation, if the memory, processor and communication interface are integrated on a chip, the memory, processor and communication interface can communicate with each other through an internal interface. The processor may be a central processing unit, or a specific integrated circuit, or one or more integrated circuits configured to implement the embodiments of the present application.

[0092] In an exemplary embodiment, the embodiment of the present invention further provides a computer-readable storage medium, in which at least one computer program is stored, and the at least one computer program is loaded and executed by a processor of a computer device to implement a small-scale phased array low-elevation scanning gain-axis ratio joint optimization method provided by the embodiment of the present invention. Optionally, the computer-readable storage medium of this embodiment can be a read-only memory, a random access memory, a read-only optical disk, a magnetic tape, an optical data storage device, etc.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0094] The above are only some embodiments of the present invention. For those skilled in the art, several modifications and improvements can be made without departing from the creative concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A small-scale phased array low elevation scanning gain axial ratio joint optimization method, characterized in that: The following steps are involved: Step 1, inputting the right-hand circularly polarized electric field of the electric field unit pattern of each array unit in the small-scale array, and the electric field components in the azimuth plane direction and the elevation plane direction of the electric field; wherein the small-scale array is a uniform planar phased array antenna; Step 2, determining the scanning axis ratio of the small-scale array based on the array excitation and the two electric field components, and determining the gain of the small-scale array based on the array excitation and the right-hand circularly polarized electric field; A low elevation scanning gain-axis ratio joint optimization model is constructed based on the scanning axis ratio and the gain. The objective function of the joint optimization model is to minimize the slack variable of the scanning axis ratio, and the constraints of the joint optimization model include: scanning axis ratio constraint, gain constraint and constant excitation amplitude modulus constraint; wherein the scanning axis ratio constraint is a slack variable that the scanning axis ratio is less than or equal to the scanning axis ratio; Step 3, optimizing and solving the constructed low elevation scanning gain-axis ratio joint optimization model, outputting array excitation, and obtaining the scanning axis ratio and gain of the small-scale array in a predetermined scanning direction based on the output array excitation; Among them, the low elevation scanning gain axis ratio joint optimization model constructed in step 2 is: Among them, ε represents the relaxation variable of the scan axis ratio, represents array excitation, where L is the number of array elements of the small-scale array, and L = M × N, where M and N are the number of array elements in the horizontal and vertical directions of the small-scale array, respectively. represents the complex domain, a θ (u m ,v m ) represent the desired direction (u m ,v m ) is the azimuthal component of the circularly polarized electric field at and the electric field component in the pitch plane direction θ, represents circularly polarized electric field The ratio of the directional component to the θ directional component, γ0, Respectively represent (u m ,v m ), e is the natural base, j is the imaginary unit, δ0 represents the phase, They represent the initial azimuthal direction components of the circularly polarized electric field. and the electric field unit pattern of the pitch plane component θ0, where θ belongs to the spherical coordinate system, and the desired direction (u m ,v m ) are the two direction components in the custom coordinate system, and The mapping relationship of θ is: m = sin(θ)cos(φ), v m = sin(θ)sin(φ), and the range of θ and φ is: represents the propagation constant of electromagnetic waves in free space, λ represents the wavelength; a RHCP (u m ,v m ) represents the desired direction (u m ,v m ), G0 represents the initial value of the transmitting power, 1 L×1 represents a vector of all 1s with dimension L×1, |w|=1 L×1 Used to characterize constant excitation amplitude modulus constraint. The superscript "H" indicates conjugate transpose.

2. The small-scale phased array low elevation scanning gain axial ratio joint optimization method according to claim 1, characterized in that: In step 3, when optimizing and solving the constructed low-elevation scanning gain-axis ratio joint optimization model, the gain constraint of the constructed low-elevation scanning gain-axis ratio joint optimization model is transformed, and the gain lower bound is found so that the constraint lower bound satisfies the constraint, and the gain constraint is converted into a convex function for optimization and solution.

3. The small-scale phased array low elevation scanning gain axial ratio joint optimization method as claimed in claim 2, characterized in that: In step 3, the gain constraint is converted into a convex function, and then the low elevation scanning gain-axis ratio joint optimization model is solved by an iterative optimization method, including: Define the right-hand circular polarization power array factor auxiliary quantity A RHCP =a RHCP (u m ,v m ) RHCP (u m ,v m ) H ; Define the axis ratio constraint factor auxiliary quantity Introducing the first auxiliary variable Second auxiliary variable The Lagrangian function is constructed as: Based on Lagrangian function The low elevation scanning gain-axis ratio joint optimization model is transformed into: Among them, f(w,ε,ψ,υ) represents the transformed objective function, ρ represents the penalty factor, and ||·||2 represents the second norm. represents the array excitation of the previous iteration, Re{·} represents the real part operation of the complex value; Among them, the initial values ​​of the first auxiliary variable ψ and the second auxiliary variable υ are preset values, and their update method in the iterative solution process is: Based on the current second auxiliary variable υ and the array excitation w solved by the current iteration, the first auxiliary variable ψ is updated as: ψ=exp(j∠(w+υ)), where the symbol "∠" represents the phase angle; Then, based on the array excitation w solved by the current iteration and the first auxiliary variable ψ after the current update, the second auxiliary variable υ is updated as: in, Represents the second auxiliary variable after the previous iteration update.

4. The small-scale phased array low elevation scanning gain axial ratio joint optimization method as claimed in claim 3, characterized in that: In step 3, the array excitation w is initialized by performing eigenvalue decomposition on the directional coefficient matrix composed of the directional coefficients of the small-scale array, and taking the eigenvector corresponding to the maximum eigenvalue as the initial value of the array excitation w.

5. The small-scale phased array low elevation scanning gain axial ratio joint optimization method as claimed in claim 3, characterized in that: In step 3, when the low elevation scanning gain-axis ratio joint optimization model is solved by an iterative optimization method, the iterative convergence condition is set to the convergence of the value of the solved array excitation w.

6. A small-scale phased array low elevation scanning gain axial ratio joint optimization method as claimed in claim 5, characterized in that: In step 3, the iterative convergence condition is set to converge the value of the solved array excitation w, including: Define the convergence function Among them, w (iter+1) 、w (iter) They represent the array excitations solved by the current iterative optimization and the previous iterative optimization respectively. When the convergence function f iter When the function value of (w) is less than or equal to the specified threshold, the value of the array excitation w is considered to converge.

7. A computer device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a small-scale phased array low-elevation scanning gain-axis ratio joint optimization method as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: The computer program is executed by a processor to implement a small-scale phased array low-elevation-angle scanning gain-axis ratio joint optimization method as claimed in any one of claims 1 to 6.

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