Array antenna multi-beam directional diagram synthesis method based on reciprocity theorem

Abstract

The invention discloses a reciprocity theorem-based array antenna multi-beam pattern synthesis method, which comprises the following steps of: establishing an array antenna model in electromagnetic simulation software, and extracting a radiation pattern of each antenna unit; defining the number and direction of to-be-formed beams and the gain ratio between the beams; establishing an array antenna energy transmission efficiency transfer function, calculating scattering parameters of each antenna unit of the array antenna through a reciprocal theorem and coordinate transformation, and constructing a scattering parameter matrix of a multi-antenna system; automatically adjusting parameters by using a particle swarm algorithm, and dynamically regulating and controlling the gain proportion between the beams; the optimal excitation value of each antenna unit is obtained, and a target beam is generated after actual loading. According to the invention, the multi-beam synthesis result of the array antenna is more convenient, more stable and more flexible.

Description

Technical Field

[0001] The present invention relates to a design method for the multi-beam pattern of an array antenna, specifically to a method for synthesizing the multi-beam pattern of an array antenna based on the reciprocity theorem, which is applicable to the automatic synthesis of the multi-beam pattern of an array antenna and belongs to the technical field of electromagnetic field and array pattern synthesis. Background Art

[0002] The multi-beam synthesis technology of array antennas is an advanced wireless communication and sensing technology that generates multiple independent beams simultaneously by controlling the phase and amplitude of multiple antenna elements. Its core is to achieve flexible beam control through spatial signal processing. This technology can be applied to application scenarios such as 5G / 6G communication and radar systems to enhance beam coverage and flexibility, and improve the anti-interference ability and reliability of the system. With the continuous deepening of application scenarios, the requirements for reliability, flexibility, and real-time performance of the multi-beam synthesis technology of array antennas are getting higher and higher. Related technologies have gradually evolved from fixed multi-beam modes to adaptive dynamic multi-beam technologies. The multi-beam technology of array antennas has a wide range of application prospects under the background of the generational upgrade of wireless communication systems and the technical application requirements of the intelligence of radar and sensing systems. Therefore, it is necessary to study a new method for synthesizing the multi-beam pattern of array antennas to provide support for the above technical requirements.

[0003] Currently, the multi-beam synthesis technology of array antennas uses traditional synthesis methods, such as using a Butler matrix to calculate the input signals of antennas. Although it has low cost and fast response speed, the beams formed by it have poor flexibility; the Rotman lens maps multiple input ports to different output beam directions, but its structure has a large volume and high loss. Modern synthesis methods apply algorithms such as neural networks and machine learning to the multi-beam synthesis of array antennas, but these methods require high costs to construct training sets, and at the same time, their output results lack a certain degree of stability and are difficult to reproduce the same radiation pattern. In addition, the output results of such high-order algorithms are usually predicted based on past training experience, and their results are difficult to ensure that they are the optimal solutions for beam excitation. Summary of the Invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a method for synthesizing the multi-beam pattern of an array antenna based on the reciprocity theorem. By using the Lorentz reciprocity theorem of electromagnetic fields, a virtual equivalent array antenna energy transmission model is constructed, and a transfer function of the energy transmission efficiency of the array antenna is established. The number and azimuth of the beam synthesis of the array antenna can be represented by the azimuth of the virtual receiving antenna, and the gain distribution between each beam can be regulated by an appropriate particle swarm algorithm, making the result of the multi-beam synthesis of the array antenna more convenient, more stable, and more flexible.

[0005] The object of the present invention is achieved by the following technical solutions:

[0006] A method for synthesizing multi-beam patterns of an array antenna based on the reciprocity theorem, characterized by comprising the following steps:

[0007] Step 1: Establish an array antenna model in an electromagnetic simulation software and extract the radiation pattern of each antenna element;

[0008] Step 2: Define the number and directions of the beams to be formed, as well as the gain ratio between the beams;

[0009] Step 3: Establish a transfer function for the energy transmission efficiency of the array antenna, calculate the scattering parameters of each antenna element of the array antenna through the reciprocity theorem and coordinate transformation, and construct a scattering parameter matrix of the multi-antenna system;

[0010] Step 4: Automatically adjust the parameters using the particle swarm algorithm to dynamically control the gain ratio between the beams;

[0011] Step 5: Obtain the optimal excitation value of each antenna element, and generate the target beam after actual loading.

[0012] Furthermore, the Step 1 includes:

[0013] S1: Obtain the array antenna model structure for the multi-beam pattern to be designed;

[0014] S2: Define the coordinate system of the far-field radiation of the antenna in the electromagnetic simulation software;

[0015] S3: Obtain the radiation pattern of the array antenna element in the electromagnetic simulation software;

[0016] S4: Obtain the radiation pattern of the receiving antenna.

[0017] Furthermore, in the Step S3, in order to eliminate the influence of the coupling between array elements and introduce new error interference for pattern synthesis, in the complete array antenna model, extract the radiation pattern data of N array elements respectively, where N is the number of array antenna elements;

[0018] Among them, the extraction process of the radiation direction data of a single array element is as follows:

[0019] S3.1: In the electromagnetic simulation software, load an excitation with an amplitude of 1V and a phase of 0 degrees to the port of the array element i to be simulated;

[0020] S3.2: Remove the excitation of other array element ports;

[0021] S3.3: Move the origin of the coordinate system of the far-field radiation of the antenna to the phase center of the array element i to be simulated;

[0022] S3.4: Export the radiation pattern data of the antenna element;

[0023] S3.5: Derive the return loss parameter S at the antenna element port ii , i represents the array element number of the current array element in the array antenna.

[0024] Furthermore, the step three includes:

[0025] S6: Establish the transfer function of energy transmission efficiency of array antenna;

[0026] S7: Based on the reciprocity theorem, the scattering parameters between the virtual receiving antenna and the transmitting array element antenna are calculated and the scattering parameter matrix [S rt ];

[0027] S8: Extract the scattering parameters of each transmitting element of the simulation model array antenna by electromagnetic simulation software, and synthesize the scattering parameter matrix]S tt ].

[0028] Furthermore, step S6 includes:

[0029] S6.1: The N transmitting ports and M virtual receiving ports of the array antenna energy transmission system together form an N+M port network; [S tt ] represents the scattering parameter matrix between all transmitting array elements, with a dimension of N×N; [S rt ] represents the scattering parameter matrix between all virtual receiving antennas and all transmitting array element antennas, with a dimension of M×N; [W] represents the gain distribution weight between all virtual receiving antennas, which is a diagonal matrix with the same dimension as the number of virtual receiving antennas, with a dimension of M×M; the excitation of the array antenna is expressed as [a t ], dimension is N×1;

[0030] S6.2: Construct the receiving transfer coefficient matrix [A] = [S rt ] H [W] H [W][S rt ], and the transmission transfer coefficient matrix [B] = 1-[S tt ] H [S tt ];

[0031] S6.3: The transfer function of the energy transmission efficiency of the array antenna is expressed as:

[0032]

[0033] S6.4: The excitation of the array antenna element is expressed as:

[0034]

[0035] st[B] -1 [A][a t* = λ max [a t *

[0036] In the formula, λ represents the eigenvalue, and λ max represents the maximum eigenvalue.

[0037] Further, the step S7 includes:

[0038] S7.1: Set the phase center coordinate system of the array antenna as the basic coordinate system;

[0039] S7.2: Establish a spherical coordinate system of the receiving antenna from the receiving antenna; on the spherical coordinate system of the receiving antenna, at a radius of r, establish a spherical surface S, and this spherical surface S represents a cross-section of a point-source spherical field sufficient to accommodate all the structures of the receiving antenna; take a point P on this spherical surface S; establish a spherical coordinate system from the transmitting antenna coordinate system, and calculate the coordinate point of the point P on the spherical surface S in the spherical coordinate system of the transmitting antenna;

[0040] S7.3: Extract the electric field vector and magnetic field vector in this direction from the radiation pattern of the transmitting antenna according to the P position coordinates;

[0041] S7.4: Extract the electric field vector and magnetic field vector in this direction from the radiation pattern of the receiving antenna according to the P position coordinates;

[0042] S7.5: The scattering parameter between the receiving antenna and the transmitting antenna is calculated by the following formula:

[0043]

[0044] where, E1 represents the electric field of the transmitting antenna, E2 represents the electric field of the receiving antenna, H1 represents the magnetic field of the transmitting antenna, H2 represents the magnetic field of the receiving antenna; a1 represents the normalized input impedance of the transmitting antenna, and a2 represents the normalized input impedance of the receiving antenna;

[0045] S7.6: The scattering parameter matrix [Srt] has MxN elements. By performing the above steps S7.1 to S7.5 to calculate one element in the matrix [Srt], completing the above calculation process MxN times completes the construction of the matrix [Srt].

[0046] Further, the step S7.3 includes:

[0047] S7.31: Extract the electric field vector in this direction from the radiation pattern of the transmitting antenna according to the P position coordinates:

[0048] The electric field vector includes the real part and the imaginary part of the E θ component, the real part and the imaginary part of the component; the electric field vector is expressed by the following formula:​​

[0049]

[0050] Among them, k is the spatial wave number, and r1 represents the distance from the origin of the transmitting antenna coordinate system to the position P; θ1, represents the position of the position P relative to the transmitting antenna coordinate system; represents the θ component of the radiation pattern of the transmitting antenna, represents the radiation pattern of the transmitting antenna component;

[0051] S7.32: Re-decompose the electric field vector into the vector basis components of the rectangular coordinate system of the transmitting antenna representation;

[0052] S7.33: According to the mapping relationship between the receiving antenna coordinate system and the transmitting antenna coordinate system calculated in S7.1, convert the electric field vector to the vector basis components of the rectangular coordinate system of the receiving antenna representation, and further convert it to the vector basis components of the spherical coordinate system of the receiving antenna representation;

[0053] S7.34: According to the coordinates of the position P, extract the magnetic field vector in this direction from the radiation pattern of the transmitting antenna, and the magnetic field vector is obtained by converting the electric field vector as follows:

[0054]

[0055] In the formula, η is the spatial wave impedance; k is the spatial wave number; r1 represents the distance from the origin of the transmitting antenna coordinate system to the position P; θ1, represents the position of the position P relative to the transmitting antenna coordinate system; represents the θ component of the radiation pattern of the transmitting antenna; represents the radiation pattern of the transmitting antenna component;

[0056] S7.35: Re-decompose the magnetic field vector into the vector basis components of the rectangular coordinate system of the transmitting antenna representation, and according to the mapping relationship between the receiving antenna coordinate system and the transmitting antenna coordinate system calculated in S7.1, convert the magnetic field vector to the vector basis components of the rectangular coordinate system of the receiving antenna representation, and further convert it to the vector basis components of the spherical coordinate system of the receiving antenna representation.

[0057] Furthermore, the fourth step includes:

[0058] S9.1: Initial parameter setting:

[0059] Take the values [w1, w2, …, w m on the diagonal of the gain distribution weight [W] as the optimization parameters of the particle swarm algorithm; randomly initialize n particles, set the number of iterations to k rounds, the upper and lower boundaries of the value range of the optimization parameters, and the list of beam peak azimuths

[0060] S9.2: Set the iterative update rule as follows:

[0061] v i = ω × v i + c1 × rand() × (pbest i - x i ) + c2 × rand() × (gbest i - x i )

[0062] x i = x i + v i

[0063] In the formula, ω represents the inertia factor, c1 and c2 represent the learning factors, x i represents the current position of the particle, and v i represents the update speed of the particle;

[0064] Among them, ω, c1, and c2 all decrease linearly with the increase of the number of iterations;

[0065]

[0066] In the formula, T max represents the maximum number of iterations;

[0067] S9.3: Calculate the fitness:

[0068] S9.31: Set the evaluation rule;

[0069] S9.32: Set the target value calculation rule;

[0070] S9.33: Calculate the fitness, and the calculation rule is as follows:

[0071] 1) Take the current particle position as [W] and substitute it into step S6.4 to solve for t ;

[0072] 2) Substitute the solution into step S9.32 to calculate the target value;

[0073] 3) Calculate the fitness:

[0074]

[0075] Where γ represents the maximum transmission efficiency and the effectiveness weight of the evaluation strategy;

[0076] S9.4: Perform iterative update according to the iterative update rule:

[0077] S9.41: Calculate the particle population diversity in real time. When it is less than the threshold, some particles will be randomly reset to avoid falling into the local optimal trap. The particle population diversity formula is:

[0078]

[0079] S9.42: When the algorithm reaches the number of iterations set in S9.1 or the calculation fitness no longer decreases in the continuous loop iteration, the algorithm terminates and outputs the particle position at this time, i.e., the gain distribution weight [W];

[0080] S9.5: Calculate the optimal excitation array: Substitute the gain distribution weight [W] into step S6.2 to calculate the receiving transfer coefficient matrix [A] and the transmitting transfer coefficient matrix [B]; after steps S6.3 and S6.4, the array excitation is finally calculated.

[0081] Furthermore, in S9.31, the evaluation function sets two rules for achieving different goals. The strategies are as follows:

[0082] Strategy 1: When the beams maintain balanced gain, the optimization objective is set to

[0083] Strategy 2: When a certain gain distribution ratio α1:α2:…:α is maintained between beams m When , the optimization goal is set to

[0084] in, Indicates The gain of the array antenna at .

[0085] Furthermore, in S9.32, two rules are set for the calculation of the target value, one for the array factor synthesis of the simple conditional array antenna and the other for the pattern superposition synthesis considering the influence of array antenna coupling:

[0086] Strategy 1: Based on the array antenna array factor synthesis, the target value is calculated using the following formula:

[0087]

[0088] in is an N×1 dimensional matrix,

[0089] Strategy 2: Based on the superposition of the unit direction patterns of the array antenna, the target value is calculated using the following formula:

[0090]

[0091] where is a 1×N dimensional matrix,

[0092] The present invention has the following beneficial effects:

[0093] In order to reduce the complexity of the multi-beam pattern synthesis of the array antenna and improve the flexibility of the beam pointing, the present invention equates the multi-beam formation of the array antenna to the energy transmission process of the array antenna, uses the efficiency of the system radiation energy and the input energy as the optimization target, and the beam focusing area represents the area where the system energy transmission efficiency is the best. The present invention places virtual receiving antennas in the beam focusing area of the array antenna, and based on the Lorentz reciprocity theorem of the electromagnetic field and the radiation pattern of the array antenna unit, solves the scattering parameters between the antennas; constructs the energy transmission efficiency transfer function between the array antenna and the virtual receiving antenna, and solves the array antenna excitation under the condition of the best radiation energy efficiency; at the same time, moderately introduces the particle swarm optimization algorithm to dynamically adjust the gain ratio of each beam to ensure the balance or on-demand distribution between the beams.

[0094] This method can solve the array antenna excitation from the transfer function, and the number and pointing azimuth of the beams depend on the number and azimuth of the virtual receiving antennas, with higher reliability and flexibility. It gets rid of the limitation of constructing the simulation model of the array antenna energy transmission system, reduces the dependence on the simulation software, and has important significance and value for realizing the multi-beam pattern synthesis of the array antenna and the design of the array antenna excitation.

[0095] The method of the present invention can have the same performance as the comprehensive beam based on the full simulation model of the array antenna energy transmission system, and gets rid of the disadvantages of large memory requirement and long calculation time of the full simulation model of the array antenna energy transmission system. The input of the method of the present invention is the direction pattern of the array antenna unit and the number and azimuth of the target beams, and the output is the array antenna excitation, which is applicable to solving the power distribution of the RF channels for various types of array antennas and providing numerical support for the design of the feeding network of the multi-beam array antenna. Description of the Drawings

[0096] Figure 1 is the flow chart of a method for synthesizing the multi-beam pattern of an array antenna based on the reciprocity theorem of the present invention;

[0097] Figure 2 is the array antenna model used in the embodiment of the present invention;

[0098] Figure 3 is the flow chart of the calculation method of the scattering parameters between two antennas in the embodiment of the present invention;

[0099] Figure 4 Schematic diagram of the scattering parameter calculation model in the embodiments of the present invention;

[0100] Figure 5 Flow chart of the moderate particle swarm optimization algorithm in the embodiments of the present invention;

[0101] Figure 6 Multi-beam pattern with gain equalization characteristics generated in the embodiments of the present invention;

[0102] Fig. 7(a) is the YOZ plane of the beam radiation pattern generated in the embodiments of the present invention (the coordinate system refers to the coordinate system marked in Fig. 2);

[0103] Fig. 7(b) is the XOZ plane of the beam radiation pattern generated in the embodiments of the present invention (the coordinate system refers to the coordinate system marked in Fig. 2). Detailed implementation manners

[0104] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0105] The present invention is a method for synthesizing multi-beam patterns of an array antenna based on the reciprocity theorem, which includes the following steps:

[0106] Step 1, modeling and simulation: Establish an array antenna model in an electromagnetic simulation software, and extract the radiation pattern of each antenna element.

[0107] S1: Obtain the structure of the array antenna model for the multi-beam pattern to be designed, including necessary parameters such as the size, spacing, and material of the antenna radiation elements, the material, thickness, and number of array elements of the antenna substrate, and establish a simulation model of the array antenna in the electromagnetic simulation software.

[0108] S2: Define the coordinate system of the far-field radiation field of the antenna in the electromagnetic simulation software. In this embodiment, the FEKO software is used. In the simulation configuration of the FEKO software, insert the far-field sphere (Far fields), select the spherical coordinate system, the starting angle of θ is 0, the ending angle is 180, and the increment is 1; The starting angle of the angle is 0, the ending angle is 360, the increment is 1, and set the ASCII file for exporting the field, that is, the *.ffe file (hereinafter referred to as the ffe file).

[0109] S3: Obtain the radiation pattern of the array antenna element in the electromagnetic simulation software. In order to eliminate the influence caused by the coupling between array elements and introduce new error interference into the pattern synthesis, in the complete array antenna model, extract the radiation pattern data of N array elements respectively, where N is the number of array antenna elements. Among them, the extraction process of the radiation direction data of a single array element is as follows:

[0110] S3.1: In the electromagnetic simulation software, apply an excitation with an amplitude of 1V and a phase of 0 degrees to the port of the array element i to be simulated.

[0111] S3.2: Remove the excitations from the ports of other array elements.

[0112] S3.3: Move the origin of the coordinate system of the antenna far-field radiation pattern to the phase center of the array element i to be simulated.

[0113] S3.4: Export the radiation pattern data of the antenna element.

[0114] S3.5: Export the return loss parameter S of the antenna element port, where i represents the element number of the current array element in the array antenna. ii

[0115] S4: Obtain the radiation pattern of the receiving antenna. Generally, the receiving antenna can use the same model as the array antenna element, or any type of antenna that is polarization-matched with the array antenna element. The specific implementation steps for obtaining the radiation pattern of the receiving antenna are the same as those in Step 3.

[0116] Step 2: Define the target beam: Determine the number and direction of the beams to be formed (how many beams need to be generated and which directions they point to).

[0117] S5: Define the number and azimuth of the beams to be formed, and the gain ratio between the beams. The position of the beam to be synthesized is associated with the phase center position of the complete array antenna, that is, the defined azimuth of the beam to be synthesized is a translation and rotation relative to the coordinates at the phase center of the complete array antenna.

[0118] Step 3: Energy transfer calculation: Establish the transfer function of the energy transfer efficiency of the array antenna, calculate the scattering parameters of each antenna element of the array antenna through the reciprocity theorem and coordinate transformation, and construct the scattering parameter matrix of the multi-antenna system.

[0119] S6: Establish the transfer function of the energy transfer efficiency of the array antenna.

[0120] S6.1: The N transmitting ports and M virtual receiving ports of the array antenna energy transfer system together form an N+M-port network. [S] represents the scattering parameter matrix between all transmitting elements, with a dimension of N×N. [S] represents the scattering parameter matrix between all virtual receiving antennas and all transmitting element antennas, with a dimension of M×N. [W] represents the gain distribution weight between all virtual receiving antennas, which is a diagonal matrix with the same dimension as the number of virtual receiving antennas, with a dimension of M×M. The excitation of the array antenna is represented as [a], with a dimension of N×1. tt rt t

[0121] S6.2: Construct the receiving transfer coefficient matrix [A] = [S rt H [W] H [W][S rt , and the transmitting transfer coefficient matrix [B] = 1 - [S tt H [S tt .

[0122] S6.3: The transfer function of the array antenna energy transfer efficiency (PTE) is expressed as:

[0123]

[0124] S6.4: The excitation of the array antenna elements can be expressed as:

[0125]

[0126] s.t. [B] -1 [A][a t * = λ max [a t *

[0127] The first line of the formula represents finding the maximum eigenvector of the right - hand side expression; the second line of the formula represents that the maximum eigenvector obtained in the first line should satisfy the corresponding maximum eigenvalue of the left - hand side expression;

[0128] In the formula, λ represents the eigenvalue, and λ max represents the maximum eigenvalue.

[0129] S7: Calculate the scattering parameters between two antennas based on the reciprocity theorem, and construct the scattering parameter matrix [S rt , as Figure 3 shown.

[0130] S7.1: Set the phase - center coordinate system of the array antenna as the basic coordinate system. According to the positions of the element arrangements, obtain the mapping relationship between the transmitting - antenna coordinate system and the basic coordinate system. According to the azimuth of the beam to be synthesized, obtain the mapping relationship between the receiving - antenna coordinate system and the basic coordinate system. Calculate the mapping relationship between the receiving - antenna coordinate system and the transmitting - antenna coordinate system. Generally, it involves multiple calculations of coordinate translation along the axis and rotation around the axis.

[0131] ​​​​S7.2: Establish a spherical coordinate system of the receiving antenna with the receiving antenna. On the spherical coordinate system of the receiving antenna, at a radius of r, establish a sphere S. The selection of the radius r needs to be determined according to the antenna structure size. This sphere S represents a cross-section of a point-source spherical field sufficient to accommodate all the structures of the receiving antenna. Take point P on this sphere. Establish a spherical coordinate system with the transmitting antenna coordinate system, and calculate the coordinate point of point P on sphere S in the spherical coordinate system of the transmitting antenna.

[0132] S7.3: According to the P position coordinates, extract the electric field vector and magnetic field vector in this direction from the radiation pattern of the transmitting antenna.

[0133] S7.31: According to the P position coordinates, extract the electric field vector in this direction from the radiation pattern of the transmitting antenna:

[0134] Generally, the electric field vector will include the real part and imaginary part of the E θ component, the real part and imaginary part of the component. In the far-field region, the radial component in the electric field has decayed to 0. Therefore, the electric field vector can be expressed by the following formula:

[0135]

[0136] where k is the spatial wave number, and r1 represents the distance from the origin of the transmitting antenna coordinate system to the P position. θ1, represents the position of the P position relative to the transmitting antenna coordinate system. represents the θ component of the transmitting antenna radiation pattern, represents the transmitting antenna radiation pattern component.

[0137] S7.32: Redecompose the electric field vector (abbreviated as E1) into the vector basis components of the transmitting antenna rectangular coordinate system representation.

[0138] S7.33: According to the mapping relationship between the receiving antenna coordinate system and the transmitting antenna coordinate system calculated in S7.1, convert the electric field vector E1 to the vector basis component representation of the receiving antenna rectangular coordinate system and further convert it to the vector basis component representation of the receiving antenna spherical coordinate system representation.

[0139] S7.34: According to the P position coordinates, extract the magnetic field vector in this direction from the radiation pattern of the transmitting antenna. The magnetic field vector can be obtained by converting the electric field vector E1:

[0140]

[0141] Where η is the spatial wave impedance; k is the spatial wave number; r1 represents the distance from the origin of the transmitting antenna coordinate system to the P position; θ1, represents the position of the P position relative to the transmitting antenna coordinate system; represents the θ component of the radiation pattern of the transmitting antenna; represents the radiation pattern of the transmitting antenna component.

[0142] S7.35: Re - decompose the magnetic field vector (abbreviated as H1) into the vector basis components of the right - hand coordinate system of the transmitting antenna. According to the mapping relationship between the receiving antenna coordinate system and the transmitting antenna coordinate system calculated in S7.1, convert the magnetic field vector H1 to the vector basis components of the right - hand coordinate system of the receiving antenna and further convert it to the vector basis components of the spherical coordinate system of the receiving antenna representation. representation.

[0143] S7.4: Extract the electric field vector and magnetic field vector in this direction from the radiation pattern of the receiving antenna according to the P - position coordinates.

[0144] S7.41: Extract the electric field vector in this direction from the radiation pattern of the receiving antenna according to the P - position coordinates.

[0145] Generally, this electric field vector will include the real part and the imaginary part of the E θ component, the real part and the imaginary part of the component. In the far - field region, the radial component in the electric field has decayed to 0. Therefore, the electric field vector E2 can be expressed by the following formula:

[0146]

[0147] Where k is the spatial wave number, and r2 represents the distance from the origin of the receiving antenna coordinate system to the P position. θ2, represents the position of the P position relative to the receiving antenna coordinate system. represents the θ component of the radiation pattern of the receiving antenna, represents the radiation pattern of the receiving antenna component.

[0148] S7.42: Extract the magnetic field vector in this direction from the radiation pattern of the receiving antenna according to the P - position coordinates. The magnetic field vector can be obtained by converting the electric field vector E2:

[0149]

[0150] Where η is the spatial wave impedance, k is the spatial wave number, and r2 represents the distance from the origin of the receiving antenna coordinate system to the P position. θ2, Indicates the position of the P position relative to the receiving antenna coordinate system. Indicates the θ component of the radiation pattern of the receiving antenna, Indicates the radiation pattern of the receiving antenna Component. Abbreviated as (H2);

[0151] S7.5: The scattering parameter between the receiving antenna and the transmitting antenna can be calculated by the following formula:

[0152]

[0153] Among them, E1 represents the electric field of the transmitting antenna, E2 represents the electric field of the receiving antenna, H1 represents the magnetic field of the transmitting antenna, and H2 represents the magnetic field of the receiving antenna. a1 represents the normalized input impedance of the transmitting antenna, and a2 represents the normalized input impedance of the receiving antenna.

[0154] R s Represents the input port impedance.

[0155] S7.6: The [Srt] matrix has MxN elements. Only one element in the [Srt] matrix is calculated through the previous steps S7.1 to S7.5. The above 5 small steps need to be calculated MxN times to complete the construction of the [Srt] matrix.

[0156] Using multi-core parallel computing technology, assign a computing process to each element in the [S rt matrix to improve the calculation efficiency of the scattering parameter, and finally synthesize the [S rt matrix.

[0157] S8: Extract the scattering parameters of each transmitting unit of the simulation model array antenna by the electromagnetic simulation software, and synthesize the scattering parameter matrix [S tt .

[0158] Step 4. Optimize the excitation parameters: Use the particle swarm algorithm to automatically adjust the parameters and dynamically control the gain ratio between the beams.

[0159] S9: Use the particle swarm dynamic optimization algorithm to optimize the gain distribution weight [W], control the gain ratio between the beams, and finally output the excitation of the array antenna.

[0160] S9.1: Initialize the parameter settings. Take the values [w1, w2,..., w m on the diagonal of the gain distribution weight [W] as the optimization parameters of the particle swarm algorithm. Randomly initialize n particles, set the number of iterations to k rounds, the upper and lower boundaries of the optimization parameter value range, and the list of beam peak azimuths

[0161] S9.2: Set the iterative update rule as follows:

[0162] v i = ω × v i + c1 × rand() × (pbest i - x i ) + c2 × rand() × (gbest i - x i )

[0163] x i = x i + v i

[0164] In the formula, ω represents the inertia factor, c1 and c2 represent the learning factors, and x i represents the current position of the particle, and v i represents the updated velocity of the particle;

[0165] Among them, ω, c1, and c2 all decrease linearly with the increase of the number of iterations;

[0166]

[0167] In the formula, T max represents the maximum number of iterations;

[0168] S9.3: Calculate the fitness:

[0169] S9.31: The setting of the evaluation function provides two rules for achieving different goals, and the strategies are as follows.

[0170] 1) Strategy 1: When the equal gain is maintained between the beams, the optimization goal is set to Among them, represents the gain of the array antenna at .

[0171] 2) Strategy 2: When a certain gain distribution ratio α1:α2:…:α m is maintained between the beams, the optimization goal is set to

[0172] S9.32: The calculation strategy of the target value provides two rules, which are respectively used for the synthesis of the array factor of the simple condition array antenna and the superposition synthesis of the pattern considering the influence of the array antenna coupling.

[0173] 1) Strategy 1: Based on the synthesis of the array factor of the array antenna, the target value is calculated using the following formula.

[0174]

[0175] Among them is an N×1 dimensional matrix,

[0176] 2) Strategy 2: Based on the superposition of the unit direction patterns of the array antennas, the target value is calculated using the following formula.

[0177]

[0178] Where is a 1×N dimensional matrix,

[0179] S9.33: The fitness function is used to ensure that the solution [a t satisfies the best energy transfer efficiency of the array antenna and meets the requirements set by the evaluation function. The setting rules for calculating the fitness are as follows.

[0180] 1) Take the current particle position as [W], substitute it into step 6.4, and solve for [a t .

[0181] 2) Substitute this solution into step 9.4 to calculate the target value.

[0182] 3) Calculate the fitness:

[0183]

[0184] Where γ represents the weight of the maximum transmission efficiency PTE and the effectiveness of the evaluation strategy.

[0185] S9.4: Iterative update

[0186] S9.41: Calculate the diversity of the particle population in real time. When it is less than the threshold, randomly reset the positions of some particles to avoid falling into the local optimal trap. The formula for the diversity of the particle population is:

[0187]

[0188] S9.42: When the algorithm executes to the number of iterations set in S9.1 or the calculated fitness no longer decreases in continuous loop iterations, the algorithm terminates and outputs the particle position at this time, that is, the gain distribution weight [W].

[0189] S9.5: Calculate the optimal excitation array: Substitute the gain distribution weight [W] into step S6.2 to calculate the receiving transfer coefficient matrix [A] and the transmitting transfer coefficient matrix [B]; after steps S6.3 and S6.4, finally calculate the array excitation.

[0190] Step Five: Output the result: Obtain the optimal excitation value of each antenna element, and the target beam can be generated after actual loading.

[0191] S10: The array excitation [a t] can synthesize multiple beams with balanced gain or gain distribution ratio. t ] is sent to the RF channel of each unit of the array antenna, so as to realize the multi-beam synthesis of the array antenna.

[0192] In order to ensure the real-time performance of multi-beam synthesis of array antenna, usually, steps 1 to 7 are the pre-steps of algorithm application, and the extraction of [S rt ] matrix, the algorithm can achieve a second-level response to multi-beam synthesis in different directions.

[0193] Example

[0194] like Figure 1 As shown, the embodiment of the present invention is a method for synthesizing multi-beam patterns of array antennas based on the reciprocity theorem, comprising the following steps:

[0195] S1: Obtain an array antenna model, including necessary parameters such as the antenna radiating element size, spacing, and material, the antenna substrate material and thickness, and the number of array elements. Based on these parameters, create a simulation model of the antenna in the electromagnetic simulation software FEKO, and automatically divide the network size. In this embodiment, a 6×6 uniformly spaced planar array antenna with an operating frequency of 2.45 GHz is used. The FEKO model of this antenna is shown in Figure 2. The antenna array element ports use line ports with a radius of 0.25 mm, and the excitation source is a voltage source.

[0196] S2: In the FEKO software simulation configuration, insert the far field sphere (Far fields), and select the spherical coordinate system as the coordinate system. The definition of the spherical coordinate system is as follows: Figure 3 As shown. The angle θ starts at 0, ends at 180, and increments by 1. Set the angle starting at 0, ending at 360, and incrementing to 1. Set the exported field ASCII file, *.ffe file (hereinafter referred to as ffe file). Move the far-field sphere reference system to the geometric center of the array antenna's radiating surface, and define the secondary reference system as the base coordinate system.

[0197] S3: Obtain the radiation pattern of the array antenna unit. To eliminate the influence of inter-element coupling that introduces new error interference into the pattern synthesis, the radiation pattern data of 36 elements are extracted from the complete array antenna model. The specific steps are as follows:

[0198] 3.1 Load an excitation with an amplitude of 1 V and a phase of 0 degrees to the port of the array element i to be simulated.

[0199] 3.2 Remove the excitation of other array element ports.

[0200] 3.3 Move the origin of the coordinate system of the antenna far-field radiation field to the phase center of the array element i to be simulated.

[0201] 3.4 Derive the radiation pattern data of the antenna element.

[0202] 3.5 Derive the S-parameter of the antenna element port 11 .

[0203] S4: Obtain the radiation pattern of the receiving antenna. Use the same structure as the transmitting antenna element of the array antenna as the receiving antenna. Load an excitation with an amplitude of 1V and a phase of 0 degrees to the input port of the receiving antenna, move the origin of the coordinate system of the far-field radiation field to the phase center of the receiving antenna, and export the radiation pattern data after simulation.

[0204] S5: Define four equalized beams pointing to the following azimuths. The azimuths of the beam pointing are respectively located at

[0205]

[0206] S6: Establish the transfer function of the energy transfer efficiency of the array antenna.

[0207] 6.1 The 36 transmitting ports and 4 virtual receiving ports of the array antenna energy transfer system together form a 40-port network. [S tt represents the scattering parameter matrix dimension of all transmitting array elements is 36×36. [S rt represents the scattering parameter matrix between all virtual receiving antennas and all transmitting array element antennas, and the dimension is 4×36. [W] represents the gain distribution weight between all virtual receiving antennas, which is a diagonal matrix with the same dimension as the number of virtual receiving antennas, and the dimension is 4×4. The excitation of the array antenna is expressed as [a t , and the dimension is 36×1.

[0208] 6.2 Construct the matrix [A] = [S rt H [W] H [W][S rt , the matrix [B] = 1 - [S tt H [S tt .

[0209] 6.3 The transfer function of the energy transfer efficiency (PTE) of the array antenna is expressed as:

[0210]

[0211] 6.4 The excitation of the array antenna element can be expressed as:

[0212] ​​

[0213] such that [B] -1 [A][a t * =λ max [a t *

[0214] S7: Construct the [S rt matrix based on the reciprocity theorem. The [S rt matrix has 4×36 elements, and 4×36 scattering parameter solving calculations are required. The flow chart of the calculation method for the scattering parameters between two antennas is as Figure 3 shown.

[0215] 7.1 Set the phase center coordinate system of the array antenna as the basic coordinate system. According to the arrangement positions of the array elements, obtain the offset between the transmitting antenna coordinate system and the basic coordinate system. Four virtual receiving antennas are respectively placed in the basic coordinate system azimuth, and the radial distance requires that the virtual receiving antennas be placed in the far-field region of the transmitting antenna. In this embodiment, the radial distance r = 5m is set. Calculate the mapping relationship between the receiving antenna coordinate system and the transmitting antenna coordinate system.

[0216] 7.2 Establish the spherical coordinate system of the receiving antenna from the receiving antenna. On the spherical coordinate system of the receiving antenna, at a radius of r = 0.65m, establish a spherical surface S. This spherical surface S represents a cross-section of a point-source spherical field sufficient to accommodate all the structures of the receiving antenna. Take a point P on this spherical surface. Establish a spherical coordinate system from the transmitting antenna coordinate system, and calculate the coordinate point of point P on the spherical surface S in the spherical coordinate system of the transmitting antenna. The schematic diagram of the double-antenna scattering parameter calculation model is as Figure 4 shown.

[0217] 7.3 According to the P position coordinates, extract the electric field vector in this direction from the transmitting antenna radiation pattern ffe file. This electric field vector includes the real part and the imaginary part of the E θ component, the real part and the imaginary part of the component. In the far-field region, the radial component in the electric field has decayed to 0. Therefore, the electric field vector E1 can be expressed by the following formula, where k is the spatial wave number.

[0218]

[0219] 7.4 Re-decompose the electric field vector E1 into the vector basis components of the transmitting antenna rectangular coordinate system.

[0220] 7.5 According to the mapping relationship between the receiving antenna coordinate system and the transmitting antenna coordinate system calculated in 7.1, convert the electric field vector E1 into the vector basis components of the receiving antenna rectangular coordinate system and further convert it to the spherical coordinate system of the receiving antenna​​ Vector basis component representation.

[0221] 7.6 According to the P position coordinates, extract the magnetic field vector H1 in this direction from the radiation pattern of the transmitting antenna. The magnetic field vector H1 can be obtained by converting the electric field vector E1, where η is the space wave impedance.

[0222]

[0223] 7.7 Similar to steps 7.4 - 7.5, convert the magnetic field vector H1 to the spherical coordinate system of the receiving antenna. Vector basis component representation.

[0224] 7.8 Similar to steps 7.3 and 7.6, according to the P position coordinates, extract the electric field vector and magnetic field vector in this direction from the radiation pattern of the receiving antenna.

[0225] 7.9 The scattering parameter between the receiving antenna and the transmitting antenna can be calculated by the following formula:

[0226]

[0227] The resolution of the far - field radiation pattern of the transmitting and receiving antennas is 1°, and the scattering parameter result formula is calculated by two - dimensional discrete integration.

[0228] Where a represents the normalized input impedance. In this example, the input impedance R of the array antenna element port s is 50Ω.

[0229] 7.10 Use multi - core parallel computing technology to assign a computing process to each element in the [S rt matrix, improve the calculation efficiency of the scattering parameter, and finally synthesize the [S rt matrix.

[0230] S8: Extract the scattering parameters of each transmitting unit of the array antenna in the simulation model by FEKO and synthesize [S tt .

[0231] S9: Use the particle swarm dynamic optimization algorithm to optimize the gain distribution weight [W], regulate the gain ratio between each beam, and finally output the excitation of the array antenna. The flow chart of the moderate particle swarm optimization algorithm is as Figure 5 shown.

[0232] 9.1 Initialize the parameter settings. Take the values [w1, w2, w3, w4] on the diagonal of the gain distribution weight [W] as the optimization parameters of the particle swarm algorithm. Randomly initialize 40 particles, set the number of iterations to 50 rounds, the upper and lower boundaries of the optimization parameter value range are [0 - 2], and the list of beam peak azimuths

[0233] 9.2 Set the iterative update rule as follows. ω represents the inertia factor, and c1 and c2 represent the learning factors.

[0234] v i = ω × v i + c1 × rand() × (pbest i - x i ) + c2 × rand() × (gbest i - x i )

[0235] x i = x i + v i

[0236] Among them, ω, c1, and c2 all decrease linearly with the increase of the number of iterations.

[0237]

[0238] In this example, ω takes the interval [0.4 - 0.9], and c1 and c2 take the intervals [0.5 - 2.5] respectively.

[0239] 9.3 Set the evaluation function strategy so that when the beams maintain an equal gain, the optimization objective is set as:

[0240]

[0241] 9.4 Calculate the target value using the pattern superposition synthesis method considering the influence of array antenna coupling.

[0242] Calculate the target value using the following formula.

[0243]

[0244] Among them is a 1×36 dimensional matrix,

[0245] 9.5 The fitness function is used to ensure that the solution [a t meets the best array antenna energy transfer efficiency and the requirements set by the evaluation function. The setting rules for calculating the fitness are as follows.

[0246] 1) Take the current particle position as [W], substitute it into step 6.4, and solve for [a t .

[0247] 2) Substitute this solution into step 9.4 to calculate the target value.

[0248] 3) Calculate the fitness.

[0249] 9.6 Calculate the diversity of the particle swarm in real time. When it is less than the threshold (10e-5), randomly reset the positions of 10% of the particles to avoid falling into the local optimal trap. The formula for the diversity of the particle swarm is as follows:

[0250]

[0251] S10: The array excitation [a t optimized in step nine can synthesize multi-beams with balanced gain. Import the array excitation [a t into the FEKO model to simulate and verify the multi-beam synthesis effect, and the results are as Figure 6 shown. It can be seen from the results that the method has successfully completed the multi-beam synthesis with balanced gain for the planar array antenna.

[0252] As an extension, in this example, the virtual receiving antennas are placed at intervals of 1° along the XOZ plane and the YOZ plane, and the beam scanning effect along the XOZ plane and the YOZ plane can be achieved. The beam scanning results are shown in Figure 7.

[0253] This method is used to construct the multi-beam radiation pattern of the array antenna. The input of the method of the present invention is the direction pattern of the array antenna elements, the number and azimuth of the target beams, and the output is the array antenna excitation, which is applicable to solving the power distribution of the RF channels for various types of phased array antennas and providing numerical support for the design of the feeding network of the multi-beam array antenna.

Claims

1. A multi-beam pattern synthesis method for array antennas based on the reciprocity theorem, characterized in that, It includes the following steps: Step 1: Establish an array antenna model in an electromagnetic simulation software and extract the radiation pattern of each antenna element; Step 2: Define the number and direction of the beams to be formed, as well as the gain ratio between the beams; Step 3: Establish a transfer function for the energy transfer efficiency of the array antenna, calculate the scattering parameters of each antenna element of the array antenna through the reciprocity theorem and coordinate transformation, and construct a scattering parameter matrix of the multi-antenna system; Step 4: Automatically adjust the parameters using the particle swarm algorithm to dynamically control the gain ratio between the beams; Step 5: Obtain the optimal excitation value of each antenna element, and generate the target beam after actual loading.

2. The multi-beam pattern synthesis method of an array antenna based on the reciprocity theorem according to claim 1, wherein The said Step 1 includes: S1: Obtain the array antenna model structure of the multi-beam pattern to be designed; S2: Define the coordinate system of the antenna far-field radiation field in the electromagnetic simulation software; S3: Obtain the radiation pattern of the array antenna element in the electromagnetic simulation software; S4: Obtain the radiation pattern of the receiving antenna.

3. A method for synthesizing multi-beam radiation patterns of an array antenna based on the reciprocity theorem according to claim 2, characterized in that, In the said Step S3, in order to eliminate the influence caused by the coupling between array elements and introduce new error interference for pattern synthesis, in the complete array antenna model, extract the radiation pattern data of N array elements respectively, where N is the number of array antenna elements; Among them, the extraction process of the radiation direction data of a single array element is as follows: S3.1: In the electromagnetic simulation software, load an excitation with an amplitude of 1V and a phase of 0 degrees to the port of the array element i to be simulated; S3.2: Remove the excitation of other array element ports; S3.3: Move the origin of the coordinate system of the antenna far-field radiation field to the phase center of the array element i to be simulated; S3.4: Export the radiation pattern data of the antenna element. S3.5: Export the echo loss parameter S of the antenna unit port ii , where i represents the element number of the current element in the array antenna.

4. A method for synthesizing the multi-beam pattern of an array antenna based on the reciprocity theorem as claimed in claim 1, wherein, The said Step 3 includes: S6: Establish a transfer function for the energy transfer efficiency of the array antenna; S7: Calculate the scattering parameters between the virtual receiving antenna and the transmitting array element antenna based on the reciprocity theorem, and construct the scattering parameter matrix [S rt ; S8: Extract the scattering parameters of each transmitting element in the simulated model array antenna by electromagnetic simulation software, and synthesize the scattering parameter matrix [S tt .

5. A method for synthesizing multi-beam radiation patterns of an array antenna based on the reciprocity theorem according to claim 4, characterized in that, The said Step S6 includes: S6.1: The N transmitting ports and M virtual receiving ports of the array antenna energy transmission system together form an N+M-port network; [S tt represents the scattering parameter matrix between all transmitting array elements, with a dimension of N×N; [S rt represents the scattering parameter matrix between all virtual receiving antennas and all transmitting array element antennas, with a dimension of M×N; [W] represents the gain distribution weight between all virtual receiving antennas, which is a diagonal matrix with the same dimension as the number of virtual receiving antennas, with a dimension of M×M; The excitation of the array antenna is represented as [a t , with a dimension of N×1; S6.2: Construct the receiving transfer coefficient matrix [A] = [S rt H [W] H [W][S rt , and the transmitting transfer coefficient matrix [B] = 1 - [S tt H [S tt ;​​ S6.3: The transfer function of the energy transfer efficiency of the array antenna is expressed as: S6.4: The excitation of the array antenna element is expressed as: s.t.[B] -1 [A][a t * =λ max [a t * ​​ where λ represents the eigenvalue, and λ max represents the maximum eigenvalue.

6. A multi-beam pattern synthesis method for an array antenna based on the reciprocity theorem according to claim 5, characterized in that, The said Step S7 includes: S7.1: Set the coordinate system of the array antenna phase center as the basic coordinate system; S7.2: Establish a spherical coordinate system of the receiving antenna from the receiving antenna; on the spherical coordinate system of the receiving antenna, at a radius of r, establish a spherical surface S, and this spherical surface S represents a cross-section of a point-source spherical field sufficient to accommodate all the structures of the receiving antenna; take a point P on this spherical surface S; establish a spherical coordinate system from the coordinate system of the transmitting antenna, and calculate the coordinate point of the point P on the spherical surface S in the spherical coordinate system of the transmitting antenna; S7.3: According to the P position coordinates, extract the electric field vector and magnetic field vector in this direction from the radiation pattern of the transmitting antenna; S7.4: According to the P position coordinates, extract the electric field vector and magnetic field vector in this direction from the radiation pattern of the receiving antenna; S7.5: The scattering parameter between the receiving antenna and the transmitting antenna is calculated by the following formula: Among them, E1 represents the electric field of the transmitting antenna, E2 represents the electric field of the receiving antenna, H1 represents the magnetic field of the transmitting antenna, H2 represents the magnetic field of the receiving antenna; a1 represents the normalized input impedance of the transmitting antenna, and a2 represents the normalized input impedance of the receiving antenna; S7.6: The scattering parameter matrix [Srt] has MxN elements. One element in the matrix [Srt] is calculated through the previous steps S7.1 to S7.

5. Completing the above calculation process MxN times completes the construction of the matrix [Srt].

7. A multi-beam pattern synthesis method for an array antenna based on the reciprocity theorem according to claim 6, characterized in that, The step S7.3 includes: S7.31: According to the P position coordinates, extract the electric field vector in this direction from the radiation pattern of the transmitting antenna: The electric field vector includes the real and imaginary parts of the E θ components, the real and imaginary parts of the components; the electric field vector is expressed by the following formula: Among them, k is the spatial wave number, and r1 represents the distance from the origin of the transmitting antenna coordinate system to the position P; θ1, represents the position of the P position relative to the transmitting antenna coordinate system; represents the θ component of the radiation pattern of the transmitting antenna, represents the radiation pattern of the transmitting antenna component; S7.32: Re-decompose the electric field vector into the vector basis components in the rectangular coordinate system of the transmitting antenna for representation; S7.33: According to the mapping relationship between the receiving antenna coordinate system and the transmitting antenna coordinate system calculated in S7.1, convert the electric field vector into the rectangular coordinate system of the receiving antenna vector basis component representation, and further convert it into the spherical coordinate system of the receiving antenna vector basis component representation; S7.34: According to the P position coordinates, extract the magnetic field vector in this direction from the radiation pattern of the transmitting antenna, and the magnetic field vector is obtained by conversion: Where η is the space wave impedance; k is the space wave number; r1 represents the distance from the origin of the transmitting antenna coordinate system to the P position; θ1, represents the position of the P position relative to the transmitting antenna coordinate system; represents the θ component of the transmitting antenna radiation pattern; represents the transmitting antenna radiation pattern component; S7.35: Re-decompose the magnetic field vector into the vector basis components in the rectangular coordinate system of the transmitting antenna. According to the mapping relationship between the receiving antenna coordinate system and the transmitting antenna coordinate system calculated in S7.1, convert the magnetic field vector into the vector basis components in the rectangular coordinate system of the receiving antenna and further convert it into the vector basis components in the spherical coordinate system of the receiving antenna . Vector basis components representation.

8. A multi-beam pattern synthesis method for an array antenna based on the reciprocity theorem according to claim 5, characterized in that The step four includes: S9.1: Initialize parameter settings: Take the values [w1, w2, …, w m on the diagonal of the gain distribution weight [W] as the optimization parameters of the particle swarm algorithm; randomly initialize n particles, set the number of iterations to k rounds, the upper and lower boundaries of the value range of the optimization parameters, and the list of beam peak azimuths S9.2: Set the iterative update rule as follows: v i = ω × v i + c1 × rand() × (pbest i - x i ) + c2 × rand() × (gbest i - x i ) x i = x i + v i where ω represents the inertia factor, c1 and c2 represent the learning factors, and x i represents the current position of the particle, and v i represents the updated velocity of the particle; Among them, ω, c1, and c2 all decrease linearly with the increase of the number of iterations; where T max represents the maximum number of iterations; S9.3: Calculate the fitness: S9.31: Set the evaluation rule; S9.32: Set the target value calculation rule; S9.33: Calculate the fitness, and the calculation rule is as follows: 1) Substitute the current particle position as [W] into the said step S6.4 to solve for [a t ; 2) Substitute this solution into the step S9.32 to calculate the target value; 3) Calculate the fitness: Among them, γ represents the effective weight of the maximum transmission efficiency and the evaluation strategy; S9.4: Perform iterative update according to the iterative update rule: S9.41: Calculate the particle population diversity in real time. When it is less than the threshold, randomly reset the positions of some particles to avoid them falling into the local optimal trap; the particle population diversity formula is: S9.42: When the algorithm executes to the number of iterations set in S9.1 or the calculated fitness no longer decreases in continuous loop iterations, the algorithm terminates and outputs the particle positions at this time, that is, the gain distribution weight [W]; S9.5: Calculate the optimal excitation array: Substitute the gain distribution weight [W] into the step S6.2 to calculate the received transfer coefficient matrix [A] and the transmitted transfer coefficient matrix [B]; through the steps S6.3 and S6.4, finally calculate the array excitation.

9. A method for synthesizing multi-beam radiation patterns of an array antenna based on the reciprocity theorem as claimed in claim 8, wherein, In the S9.31, two rules are set for the evaluation function to achieve different goals, and the strategy is as follows: Strategy 1: When the equal gain is maintained between beams, the optimization objective is set to Strategy 2: When a certain gain allocation ratio α1:α2:…:α is maintained between the beams m the optimization objective is set to Among them, represents the gain of the array antenna at the place.

10. A method for synthesizing multi-beam radiation patterns of an array antenna based on the reciprocity theorem according to claim 8, characterized in that In the S9.32, two rules are set for the calculation of the target value, which are respectively used for the synthesis of the array factor of the simple condition array antenna and the superposition synthesis of the radiation pattern considering the influence of the array antenna coupling: Strategy 1: Based on the synthesis of the array factor of the array antenna, use the following formula to calculate the target value: Among them is an N×1 dimensional matrix, Strategy 2: Based on the superposition of the unit radiation patterns of the array antenna, use the following formula to calculate the target value: Among them, is a 1×N dimensional matrix,

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