Multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation

Abstract

The invention discloses a multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation. The method comprises the steps that 1, initial array configuration parameters are determined according to a fitting statistical formula of a vortex wave beam field angle and a circular array radius, wherein the initial array configuration parameters comprise the radius of each circle in a circular ring array and the number of array elements; step 2, establishing a to-be-optimized objective function based on the HFSS full-wave simulation data; 3, an IWO-PSO optimization algorithm is adopted to optimize the target function based on the HFSS full-wave simulation data; and 4, setting a convergence condition of the IWO-PSO optimization algorithm, repeating the steps 1 to 3 until the convergence condition is met, considering that an optimal array configuration is obtained at the moment, and outputting an optimal electromagnetic vortex wave beam. According to the method, the target function based on the HFSS / CST full-wave simulation data is established, the multi-mode low-sidelobe co-directional vortex beam is realized through the optimization algorithm and multiple iterations of the HFSS / CST, the problem of generating the multi-mode low-sidelobe co-directional vortex beam of the electromagnetic vortex wave is solved, and the practical value is very high.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic vortex wave generation, and in particular relates to a multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation. Background Art

[0002] Antenna array synthesis is a complex nonlinear optimization problem. Currently available methods include traditional analytical optimization methods, numerical algorithms, and intelligent algorithms. However, traditional analytical optimization methods are difficult to implement for some complex beam shapes and array configurations. Although numerical algorithms have a wide range of applications, some numerical algorithms often have strict requirements on the selection of initial values. Compared with the previous two algorithms, the optimization algorithm has strong randomness and robustness, and has no special requirements for the search space. It has been widely used in antenna array synthesis.

[0003] Common antenna array optimization methods include Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Invasive Weed Optimization (IWO), IWO-PSO, etc. The IWO-PSO algorithm introduces the position and speed update formula of the PSO algorithm in the process of invasive weed growth and reproduction, that is, before the weeds generate new seeds, the position and speed of the weeds are updated by the PSO algorithm, and then the new seeds are obtained for reproduction and spatial diffusion, while ensuring the search depth and search breadth. At present, the IWO-PSO optimization algorithm has been applied to the antenna array synthesis method based on plane waves and the antenna array error correction method, but there is no public report on the application of the IWO-PSO optimization algorithm to the array synthesis problem based on electromagnetic vortex waves.

[0004] At present, the main methods of generating electromagnetic vortex waves include spiral phase plates, array antennas, and metamaterials. Among them, array antennas have been favored by scholars in many fields, including wireless communications and OAM electromagnetic imaging, due to their flexible and precise feeding methods. The existing vortex array optimization method based on ideal data models cannot take into account the requirements of multi-modal low-sidelobe co-directional vortex beams, which limits the efficient operation of vortex arrays in complex environments with electromagnetic interference. Summary of the invention

[0005] The technical problem solved by the present invention is that the vortex array optimization method based on the ideal data model reported in the existing public data cannot take into account the requirements of multi-modal low sidelobe co-directional vortex wave beams, which limits the efficient operation of the vortex array in a complex environment of electromagnetic interference. The present invention proposes a multi-modal electromagnetic vortex wave array optimization method based on full-wave simulation to achieve the generation of multi-modal low sidelobe co-directional electromagnetic vortex waves.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation specifically comprises the following steps:

[0008] Step 1, determining initial array configuration parameters according to a fitting statistical formula of a vortex beam angle and a circular array radius, wherein the initial array configuration parameters include the radius of each circle in the circular array and the number of array elements;

[0009] Step 2, establishing the objective function to be optimized based on HFSS full-wave simulation data, including the following steps:

[0010] Step 21, according to the initial array configuration parameters of the circular array in step 1, automatically optimize and build the corresponding multi-layer circular array configuration in HFSS, simulate and obtain the far-field radiation pattern of the OAM beam, and read the main lobe pointing angle θ of the OAM beam. 0 , half power beam width HPBW and maximum side lobe level SLL max ;

[0011] Step 22, establishing an objective function to be optimized based on HFSS full-wave simulation data;

[0012] Step 3, using the IWO-PSO optimization algorithm to optimize the objective function based on the HFSS full-wave simulation data;

[0013] Step 4, set the convergence condition of the IWO-PSO optimization algorithm, repeat steps 1 to 3 until the convergence condition is met, at which time it is considered that the optimal array configuration is obtained and the optimal electromagnetic vortex wave beam is output.

[0014] Furthermore, in step 1, for a single-layer circular array, the OAM main lobe direction is mainly determined by the circular array radius. Through curve fitting, the statistical mapping relationship between the OAM main lobe direction and the circular array radius is approximately:

[0015]

[0016] Among them, l is the modal value, l∈[1,l max ],l max is the maximum mode number, θ 0 is the OAM main lobe direction, k = 2π / λ, λ is the wavelength, and r(l) is the radius of the circular array when the mode is l.

[0017] Furthermore, in step 2, the objective function to be optimized is as follows:

[0018]

[0019] Where w1 and w2 are weight coefficients, which are usually determined by the characteristics of the desired pattern; θ des represents the desired main lobe pointing direction, Δδ des represents the expected pointing error, SLL des Indicates the expected sidelobe level.

[0020] Furthermore, step 3 includes the following sub-steps:

[0021] Step 31, set IWO-PSO parameters, randomly initialize the population Y = [Y 1 ,...,Y P ], where Y i =[(r i,1 ,N i,1 ,A i,1 ),...,(r i,M ,N i,M ,A i,M )], P is the maximum population size, i represents the serial number of the individual in the population; r i,1 represents the radius of the first circle of the i-th individual, N i,1 represents the number of array elements in the first circle of the i-th individual, A i,1 represents the feeding amplitude of the first cycle of the i-th individual, and M represents the number of cycles;

[0022] Step 32, using the objective function to be optimized based on the HFSS full-wave simulation data established in step 2, calculate the fitness value in the current iteration number, arrange the fitness values ​​from large to small, and obtain the global optimal solution p gd (iter) and maximum fitness value f max And the minimum fitness value f min ;

[0023] Step 33, updating the moving speed and position of the weeds according to the particle swarm algorithm to form a new weed population; the specific process is as follows:

[0024] v id (iter+1)=wv id (iter)+c 1 r 1 (p id (iter)-x id (iter))

[0025] +c 2 r 2 (p gd (iter)-x id (iter))

[0026] x id (iter+1)=x id(iter)+v id (iter+1)

[0027] Among them, v id (iter+1) and x id (iter+1) represent the search speed and position of the dth array element in the ith particle at the iter+1th generation; p id (iter) represents the optimal solution found by the particle itself at the current moment; w is the inertia weight factor; c 1 and c 2 is the learning factor, usually 1; r 1 and r 2 is a random number uniformly distributed between 0 and 1;

[0028] Step 34, growth and reproduction, the number of seeds produced by each weed in the weed population is:

[0029]

[0030] Among them, f is the fitness value of the current weed; f max and f min are the maximum and minimum fitness values ​​of weeds in the current population respectively; s max and min are the maximum and minimum number of seeds a weed can produce, respectively;

[0031] Step 35, spatial diffusion, the seeds produced by the weeds are scattered around the weeds according to a normal distribution with a mean of 0 and a standard deviation of σ; as the number of evolutionary generations increases, the standard deviation changes according to the following formula:

[0032]

[0033] In the formula, iter is the current evolutionary generation; iter max is the maximum evolutionary generation; σ cur is the current standard deviation; σ init and σ final are the initial and final values ​​of the standard deviation respectively; n is the nonlinear harmonic factor;

[0034] Step 36, competitive survival criterion, arrange the fitness values ​​of all seeds from large to small and grow them into new weeds, select the first P weeds as the new population, and eliminate the weeds that exceed the maximum population number P.

[0035] Furthermore, in step 4, when the sidelobe level and mainlobe pointing error of each mode simultaneously meet the following conditions, the IWO-PSO optimization algorithm converges and the cycle ends;

[0036]

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention utilizes the advantages of IWO-PSO in nonlinear optimization, establishes an objective function based on HFSS / CST full-wave simulation data, and realizes multi-modal low-sidelobe co-directional vortex beams through the IWO-PSO optimization algorithm and multiple iterations of HFSS / CST, breaking through the difficulty of generating multi-modal low-sidelobe co-directional vortex beams of electromagnetic vortex waves, and has high practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of the method of the present invention.

[0040] Figure 2 Full-wave simulation radiation pattern and far-field phase distribution (mode 1-mode 7). DETAILED DESCRIPTION

[0041] The implementation of the present invention is described in further detail below.

[0042] The application scenarios of the present invention are:

[0043] The initial array configuration parameters are determined based on the fitting statistical formula of the vortex beam angle and the circular array radius; based on the current multi-mode vortex array configuration parameters, the MATLAB-HFSS-API is called to automatically optimize and build the corresponding multi-layer circular ring array configuration in HFSS; based on the OAM beam far-field pattern obtained by HFSS simulation, the OAM beam far-field pattern is simulated and the main lobe pointing angle θ of the OAM beam is read 0 , half power beam width HPBW and maximum side lobe level SLL max ; Establish an objective function based on HFSS full-wave simulation data, use the IWO-PSO optimization algorithm to optimize the objective function, and judge whether the sidelobe level and mainlobe pointing error of each mode meet the requirements. If they meet the requirements, the IWO-PSO optimization algorithm converges and outputs a multi-mode low sidelobe co-directional vortex beam.

[0044] The present invention provides a multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation. HFSS and CST are the same type of antenna full-wave simulation software. The following content takes HFSS as an example, and the implementation steps are as follows:

[0045] Step 1: determine the initial array configuration parameters according to the fitting statistical formula of the vortex beam angle (the vortex beam angle is equal to the OAM main lobe direction) and the circular array radius. The initial array configuration parameters include the radius of each circle in the circular array and the number of array elements.

[0046] Specifically, the initial arrangement of the circular array is determined according to the OAM main lobe direction and the number of OAM modes, that is, the radius of each circle in the circular array and the number of array elements are determined. For a single-layer circular array, the OAM main lobe direction is mainly determined by the circular array radius. Through curve fitting, the statistical mapping relationship between the OAM main lobe direction and the circular array radius is approximately:

[0047]

[0048] Among them, l is the modal value, l∈[1,l max ],l max is the maximum mode number, θ 0 is the OAM main lobe direction, k = 2π / λ, λ is the wavelength, and r(l) is the radius of the circular array when the mode is l.

[0049] Step 2: Establish the objective function to be optimized based on HFSS full-wave simulation data.

[0050] Step 21, according to the initial array configuration parameters of the circular array in step 1, automatically optimize and build the corresponding multi-layer circular array configuration in HFSS, simulate and obtain the far-field radiation pattern of the OAM beam, and read the main lobe pointing angle θ of the OAM beam. 0 , half power beam width HPBW and maximum side lobe level SLL max .

[0051] Step 22, establishing the objective function to be optimized based on the HFSS full-wave simulation data:

[0052]

[0053] Where w1 and w2 are weight coefficients, which are usually determined by the characteristics of the desired pattern; θ des represents the desired main lobe pointing direction, Δδ des represents the expected pointing error, SLL des Indicates the expected sidelobe level.

[0054] There are two parameters that determine the array configuration, namely the array radius and the number of array elements of each circle of the circular array. In order to obtain a lower sidelobe level, the feed amplitude needs to be optimized. The specific parameters to be optimized can be expressed as:

[0055]

[0056] In the formula, r is the radius vector, N is the number of array elements vector, A is the magnitude vector of the defect point, and r is 1 Indicates the radius of the first circle, N 1 Indicates the number of array elements in the first circle, A 1 It indicates the feeding amplitude of the first circle, and M indicates the number of circles.

[0057] Step 3: Use the IWO-PSO optimization algorithm to optimize the objective function based on the HFSS full-wave simulation data.

[0058] The IWO-PSO algorithm introduces the position and speed update formula of the PSO algorithm during the growth and reproduction of invasive weeds. That is, before the weeds generate new seeds, the position and speed of the weeds are updated by the PSO algorithm, and then new seeds are obtained for reproduction and spatial diffusion, while ensuring the search depth and search breadth. Step 3 includes the following sub-steps:

[0059] Step 31, set the IWO-PSO parameters as shown in Table 1, and randomly initialize the population Y = [Y 1 ,…,Y P ], where Y i =[(r i,1 ,N i,1 ,A i,1 ),…,(r i,M ,N i,M ,A i,M )], P is the maximum population size, i represents the serial number of the individual in the population; r i,1 represents the radius of the first circle of the i-th individual, N i,1 represents the number of array elements in the first circle of the i-th individual, A i,1 represents the feeding amplitude of the first cycle of the i-th individual, and M represents the number of cycles;

[0060] Table 1 IWO-PSO algorithm parameters

[0061]

[0062] Step 32, using the objective function to be optimized based on the HFSS full-wave simulation data established in step 2, calculate the fitness value in the current iteration number, arrange the fitness values ​​from large to small, and obtain the global optimal solution p gd (iter) and maximum fitness value f max And the minimum fitness value f min .

[0063] Step 33, update the moving speed and position of the weeds according to the particle swarm algorithm to form a new weed population. The specific process is as follows:

[0064]

[0065] x id (iter+1)=x id (iter)+v id (iter+1)(6)

[0066] Among them, v id (iter+1) and xid (iter+1) represent the search speed and position of the dth array element in the ith particle at the iter+1th generation; p id (iter) represents the optimal solution found by the particle itself at the current moment; w is the inertia weight factor; c 1 and c 2 is the learning factor, usually 1; r 1 and r 2 is a random number uniformly distributed between 0 and 1;

[0067] By continuously updating the position and velocity of each particle and continuously iterating the search, the optimal solution to the problem is finally obtained.

[0068] Step 34, growth and reproduction. The number of seeds produced by each weed in the weed population is:

[0069]

[0070] Among them, f is the fitness value of the current weed; f max and f min are the maximum and minimum fitness values ​​of weeds in the current population respectively; s max and min are the maximum and minimum number of seeds a weed can produce.

[0071] Step 35, spatial diffusion. The seeds produced by the weeds are scattered around the weeds according to a normal distribution with a mean of 0 and a standard deviation of σ. As the number of evolutionary generations increases, the standard deviation changes according to the following formula:

[0072]

[0073] In the formula, iter is the current evolutionary generation; iter max is the maximum evolutionary generation; σ cur is the current standard deviation; σ init and σ final are the initial and final values ​​of the standard deviation respectively; n is the nonlinear harmonic factor.

[0074] Step 36, competitive survival criterion. Arrange the fitness values ​​of all seeds from large to small and grow them into new weeds, select the first P weeds as the new population, and eliminate the weeds that exceed the maximum population number P.

[0075] Step 4, set the convergence condition of the IWO-PSO optimization algorithm, repeat steps 1 to 3 until the convergence condition is met, at which time it is considered that the optimal array configuration is obtained and the optimal electromagnetic vortex wave beam is output.

[0076] Specifically, when the sidelobe level and mainlobe pointing error of each mode simultaneously meet the following conditions, the IWO-PSO optimization algorithm converges and the cycle ends.

[0077]

[0078] The effect of the present invention is further illustrated below by means of simulation data.

[0079] The operating frequency is 10 GHz, and the concentric ring array has 7 circles. The IWO-PSO optimization algorithm is used to optimize the ring radius, the number of array elements, and the feeding amplitude to generate low-sidelobe co-directional electromagnetic vortex waves in modes 1-7. The expected OAM main lobe direction is 8°. The parameters of the IWO-PSO optimization algorithm are shown in Table 1.

[0080] The full-wave simulation directivity and phase distribution of each mode are shown in Figure 2 .from Figure 2 It can be seen that the 7-circle concentric ring array successfully produces 7-mode OAM phase distribution and low sidelobe radiation pattern. Figure 2 The phase distribution and radiation pattern of the RF power amplifier were further quantitatively analyzed. From the data analysis, it can be seen that the main lobe angle of each mode OAM is basically consistent with the expected direction (8°), the pointing deviation of each mode is less than 1.3%, the side lobe level of each mode is better than -13dB, and the purity of each mode is above 99%.

[0081] Table 2 OAM full-wave simulation radiation pattern parameters for each mode

[0082]

[0083]

[0084] Parts not described in detail in the present invention belong to common knowledge of those skilled in the art.

Claims

1. A multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation, characterized in that: The specific steps include: Step 1, determining initial array configuration parameters according to a fitting statistical formula of a vortex beam angle and a circular array radius, wherein the initial array configuration parameters include the radius of each circle in the circular array and the number of array elements; Step 2, establishing the objective function to be optimized based on HFSS full-wave simulation data, including the following steps: Step 21, according to the initial array configuration parameters of the circular array in step 1, automatically optimize and build the corresponding multi-layer circular array configuration in HFSS, simulate and obtain the far-field radiation pattern of the OAM beam, and read the main lobe pointing angle θ0, half-power beam width HPBW and maximum sidelobe level SLL of the OAM beam max ; Step 22, establishing an objective function to be optimized based on HFSS full-wave simulation data; Step 3, using the IWO-PSO optimization algorithm to optimize the objective function based on the HFSS full-wave simulation data; Step 4, set the convergence condition of the IWO-PSO optimization algorithm, repeat steps 1 to 3 until the convergence condition is met, at which time it is considered that the optimal array configuration is obtained and the optimal electromagnetic vortex wave beam is output.

2. The multi-modal electromagnetic vortex wave array optimization method based on full-wave simulation as claimed in claim 1, characterized in that: In step 1, for a single-layer circular array, the OAM main lobe direction is mainly determined by the circular array radius. Through curve fitting, the statistical mapping relationship between the OAM main lobe direction and the circular array radius is approximately: Among them, l is the modal value, l∈[1,l max ],l max is the maximum mode number, θ0 is the OAM main lobe direction, k = 2π / λ, λ is the wavelength, and r(l) is the radius of the circular array when the mode is l.

3. The multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation as claimed in claim 2, characterized in that: In step 2, the objective function to be optimized is as follows: Where w1 and w2 are weight coefficients, which are usually determined by the characteristics of the desired pattern; θ des represents the desired main lobe pointing direction, Δδ des represents the expected pointing error, SLL des Indicates the expected sidelobe level.

4. The multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation as claimed in claim 3, characterized in that: Step 3 includes the following sub-steps: Step 31, set IWO-PSO parameters, randomly initialize the population Y = [Y1, ..., Y P ], where Y i =[(r i,1 ,N i,1 ,A i,1 ),...,(r i,M ,N i,M ,A i,M )], P is the maximum population size, i represents the serial number of the individual in the population; r i,1 represents the radius of the first circle of the i-th individual, N i,1 represents the number of array elements in the first circle of the i-th individual, A i,1 represents the feeding amplitude of the first cycle of the i-th individual, and M represents the number of cycles; Step 32, using the objective function to be optimized based on the HFSS full-wave simulation data established in step 2, calculate the fitness value in the current iteration number, arrange the fitness values ​​from large to small, and obtain the global optimal solution p gd (iter) and maximum fitness value f max And the minimum fitness value f min ; Step 33, updating the moving speed and position of the weeds according to the particle swarm algorithm to form a new weed population; the specific process is as follows: v id (iter+1)=wv id (iter)+c1r1(p id (iter)-x id (iter))+c2r2(p gd (iter)-x id (iter)) x id (iter+1)=x id (iter)+v id (iter+1) Among them, v id (iter+1) and x id (iter+1) represent the search speed and position of the dth array element in the ith particle at the iter+1th generation; p id (iter) represents the optimal solution found by the particle itself at the current moment; w is the inertia weight factor; c1 and c2 are learning factors, which are 1; r1 and r2 are random numbers uniformly distributed between 0 and 1; Step 34, growth and reproduction, the number of seeds produced by each weed in the weed population is: Among them, f is the fitness value of the current weed; f max and f min are the maximum and minimum fitness values ​​of weeds in the current population respectively; s max and min are the maximum and minimum number of seeds a weed can produce, respectively; Step 35, spatial diffusion, the seeds produced by the weeds are scattered around the weeds according to a normal distribution with a mean of 0 and a standard deviation of σ; as the number of evolutionary generations increases, the standard deviation changes according to the following formula: In the formula, iter is the current evolutionary generation; iter max is the maximum evolutionary generation; σ cur is the current standard deviation; σ init and σ final are the initial and final values ​​of the standard deviation respectively; n is the nonlinear harmonic factor; Step 36, competitive survival criterion, arrange the fitness values ​​of all seeds from large to small and grow them into new weeds, select the first P weeds as the new population, and eliminate the weeds that exceed the maximum population number P.

5. The multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation as claimed in claim 3, characterized in that: In step 4, when the sidelobe level and mainlobe pointing error of each mode simultaneously meet the following conditions, the IWO-PSO optimization algorithm converges and the cycle ends;

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