A multi-modal electromagnetic vortex wave array optimization method based on full-wave simulation

Abstract

The application discloses a multi-mode electromagnetic vortex wave array optimization method based on full-wave simulation, which comprises the following steps: step 1, determining initial array configuration parameters according to a fitting statistical formula of a vortex wave beam opening angle and a circular array radius, wherein the initial array configuration parameters comprise the radius and the number of array elements of each circle in the circular ring array; step 2, establishing a target function to be optimized based on HFSS full-wave simulation data; step 3, optimizing the target function based on the HFSS full-wave simulation data by using an IWO-PSO optimization algorithm; and step 4, setting a convergence condition of the IWO-PSO optimization algorithm, repeating steps 1 to 3 until the convergence condition is met, at this time, the optimal array configuration is considered to be obtained, and the optimal electromagnetic vortex wave beam is output. The application establishes a target function based on HFSS / CST full-wave simulation data, and realizes multi-mode low-sidelobe same-direction vortex wave beams through optimization algorithm and HFSS / CST multiple iterations, thus breaking through the generation difficulty of the multi-mode low-sidelobe same-direction vortex wave beams of electromagnetic vortex waves, and having high practical value.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic vortex wave generation, and particularly relates to a multi-modal electromagnetic vortex wave array optimization method based on full-wave simulation. BACKGROUND

[0002] Antenna array synthesis is a complex nonlinear optimization problem. Currently available methods include traditional analytical optimization methods, numerical algorithms and intelligent algorithms. However, the traditional analytical optimization method is difficult to implement for some complex beam shapes and array arrangement forms. Although the numerical algorithm has a wide range of applications, some numerical algorithms often have strict requirements for the selection of initial values. Compared with the first 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] Commonly used antenna array optimization methods include genetic algorithm (Genetic Algorithm, GA), particle swarm optimization algorithm (Particle Swarm Optimization, PSO), invasive weed optimization algorithm (Invasive Weed Optimization, IWO), IWO-PSO algorithm, 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, the position and speed of the weed are updated by the PSO algorithm before the weed generates new seeds to reproduce and spatially diffuse, 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 wave and the antenna array error correction method, but there is no public report of the IWO-PSO optimization algorithm applied to the array synthesis problem based on electromagnetic vortex wave.

[0004] At present, the main ways to generate electromagnetic vortex waves include spiral phase plates, array antennas and metamaterials, etc. Among them, array antennas have been favored by scholars in the fields of wireless communication, OAM electromagnetic imaging and other fields due to their flexible and accurate feeding methods. The existing vortex array optimization method based on ideal data model cannot meet the requirements of multi-modal low sidelobe and same direction vortex beam, which limits the efficient work of vortex array in complex electromagnetic interference environment. SUMMARY

[0005] The technical problem solved by the present application is that the existing vortex array optimization method based on ideal data model cannot meet the requirements of multi-modal low sidelobe and same direction vortex beam, which limits the efficient work of vortex array in complex electromagnetic interference environment. The present application proposes a multi-modal electromagnetic vortex wave array optimization method based on full-wave simulation, which realizes the generation of multi-modal low sidelobe and same direction electromagnetic vortex wave.

[0006] To achieve the above object, the present application adopts the following technical solutions:

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

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

[0009] Step 2, establish the target function to be optimized based on the 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 the corresponding multi-layer circular array configuration in HFSS, simulate to obtain the OAM beam far-field pattern, read the main lobe pointing angle θ0, half-power beam width HPBW and maximum side lobe level SLL of the OAM beam max ;

[0011] Step 22, establish the target function to be optimized based on the HFSS full-wave simulation data;

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

[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 this time the optimal array configuration is considered to be obtained, and the optimal electromagnetic vortex wave beam is output.

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

[0015]

[0016] Wherein, l is the mode 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 circular array radius when the mode is l.

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

[0018]

[0019] In the formula, w1 and w2 are weight coefficients, which are usually determined by the characteristics of the desired pattern; θ desrepresents the desired main lobe pointing, Δδ des represents the desired pointing error, SLL des represents the desired side lobe level.

[0020] Further, step 3 comprises the following sub-steps:

[0021] Step 31, set IWO-PSO parameters, randomly initialize population Y = [Y1,..., Y P ], wherein 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 number, i represents the serial number of individuals in the population; r i,1 represents the radius value of the first circle of the i-th individual, N i,1 represents the number of elements of the first circle of the i-th individual, A i,1 represents the feed amplitude value of the first circle of the i-th individual, and M represents the number of circles;

[0022] Step 32, using the target 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 to obtain the global optimal solution p gd (iter) and the maximum fitness value f max and the minimum fitness value f min ;

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

[0024] v id (iter+1) = wv id (iter) + c1r1(p id (iter) - x id (iter))

[0025] + c2r2(p gd (iter) - x id (iter))

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

[0027] Wherein, v id (iter+1) and x id(iter+1) represents the search speed and position of the i-th particle in the d-th array element at the (iter+1)-th generation; p id (iter) represents the optimal solution found by the particle itself at the current time; w is an inertia weight factor; c1 and c2 are learning factors, usually 1; r1 and r2 are random numbers 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] Wherein, f is the fitness value of the current weed; f max and f min are the maximum and minimum fitness values of the weeds in the current population, respectively; s max and s min are the maximum and minimum number of seeds that 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 evolution generations increases, the standard deviation changes according to the following formula:

[0032]

[0033] Wherein, iter is the current evolution generation; iter max is the maximum evolution generation; σ cur is the current standard deviation; σ init and σ final are the initial value and final value of the standard deviation, respectively; n is a nonlinear harmonic factor;

[0034] Step 36, competitive survival criteria, arrange all the seeds in descending order of fitness value and grow new weeds, select the first P weeds as the new population, and eliminate weeds exceeding the maximum population number P.

[0035] Further, in step 4, when the sidelobe level of each mode and the main lobe pointing error satisfy the following conditions at the same time, the IWO-PSO optimization algorithm converges, and the loop ends.

[0036]

[0037] Compared with the prior art, the present application has the beneficial effects of:

[0038] The application utilizes the advantage of IWO-PSO in nonlinear optimization, establishes a target function based on HFSS / CST full-wave simulation data, realizes multi-modal low-sidelobe same-direction vortex beams through IWO-PSO optimization algorithm and HFSS / CST multiple iterations, breaks through the generation difficulty of multi-modal low-sidelobe same-direction vortex beams of electromagnetic vortex waves, and has high practical value. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 A flowchart of the method of the application.

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

[0041] The application is further described in detail below.

[0042] The use scenario of the application is:

[0043] The initial array configuration parameters are determined according to the fitting statistical formula of the vortex beam opening angle and the circular array radius; the corresponding multi-layer circular ring array configuration is automatically optimized and built in HFSS by calling MATLAB-HFSS-API according to the current multi-modal vortex array configuration parameters; the OAM beam far-field pattern is simulated according to the OAM beam far-field pattern obtained by HFSS simulation, and the main lobe pointing angle θ0, the half-power beam width HPBW and the maximum sidelobe level SLL of the OAM beam are read max ; the target function based on the HFSS full-wave simulation data is established, the IWO-PSO optimization algorithm is used to optimize the target function, whether the sidelobe level and the main lobe pointing error of each mode meet the requirements is judged, if the requirements are met, the IWO-PSO optimization algorithm converges, and the multi-modal low-sidelobe same-direction vortex beam is output.

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

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

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

[0047]

[0048] wherein, l is a mode 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.

[0049] Step 2, establish the target function to be optimized based on the HFSS full-wave simulation data.

[0050] Step 21, according to the initial array configuration parameters of the circular ring array in step 1, automatically optimize the corresponding multi-layer circular ring array configuration in HFSS, simulate to obtain the OAM beam far-field pattern, and read the main lobe pointing angle θ0, half-power beam width HPBW and maximum side lobe level SLL max of the OAM beam.

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

[0052]

[0053] wherein, 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, Δδ des represents the desired pointing error, and SLL des represents the desired side lobe level.

[0054] The parameters that determine the array configuration include two, which are the array radius and the number of array elements of each circle. In order to obtain a lower side lobe level, the feeding amplitude also needs to be optimized. The specific parameters to be optimized can be represented as:

[0055]

[0056] wherein, r is the radius vector, N is the array element number vector, A is the amplitude of the null point vector, r1 represents the radius value of the first circle, N1 represents the number of array elements of the first circle, A1 represents the feeding amplitude of the first circle, and M represents the number of circles.

[0057] Step 3, use the IWO-PSO optimization algorithm to optimize the target function based on the HFSS full-wave simulation data.

[0058] The IWO-PSO algorithm introduces the position and speed updating formula of the PSO algorithm in the process of invasion of the weed growth and reproduction, that is, the position and speed of the weed are updated by the PSO algorithm before the weed generates new seeds to reproduce and spread in space, and the search depth and search breadth are ensured. 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 = [Y1,..., YP], wherein Y = [(r1, N1, A1),..., (ri, Ni, Ai)], P is the maximum population number, i represents the serial number of individuals in the population; ri represents the radius value of the first circle of the i-th individual, Ni represents the number of elements of the first circle of the i-th individual, Ai represents the feeding amplitude of the first circle of the i-th individual, and M represents the number of circles. P i i,1 i,1 i,1 i,M i,M i,M i,1 i,1 i,1

[0060] Table 1 IWO-PSO algorithm parameter table

[0061]

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

[0063] Step 33, update the moving speed and position of the weed 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] Wherein, v id (iter+1) and x id (iter+1) represent the search speed and position of the d-th element of the i-th particle at the iter+1 generation, respectively; p id ​​​​​​​​​​​​​​iter represents the optimal solution found by the particle itself at the current time; w is an inertia weight factor; c1 and c2 are learning factors, usually 1; r1 and r2 are random numbers uniformly distributed between 0 and 1;

[0067] The position and velocity of each particle are updated constantly, and the optimal solution of the problem is obtained through iterative search.

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

[0069]

[0070] Where f is the fitness value of the current weed; f max and f min are the maximum and minimum fitness values of the weeds in the current population, respectively; s max and s min are the maximum and minimum number of seeds that can be produced by a weed, respectively.

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

[0072]

[0073] Where iter is the current number of evolution generations; iter max is the maximum number of evolution generations; σ cur is the current standard deviation; σ init and σ final are the initial value and final value of the standard deviation, respectively; n is a nonlinear harmonic factor.

[0074] Step 36, competitive survival criteria. Arrange all the seeds in descending order of fitness value and grow new weeds. Select the top P weeds as the new population and eliminate weeds that exceed the maximum population size 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 this time the optimal array configuration is obtained, and the optimal electromagnetic vortex wave beam is output.

[0076] Specifically, when the sidelobe level and main lobe pointing error of each mode meet the following conditions at the same time, the IWO-PSO optimization algorithm converges and the loop ends.

[0077]

[0078] The effect of the present application is further illustrated by simulation data.

[0079] The working frequency is 10GHz, 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, so as to generate 1-7 mode low side lobe same direction electromagnetic vortex wave, the expected OAM main lobe direction is 8°, and the parameters of the IWO-PSO optimization algorithm are as shown in Table 1.

[0080] The full-wave simulation pattern and phase distribution of each mode are shown in Figure 2 It can be seen from Figure 2 that the 7-circle concentric ring array successfully generates 7-mode OAM phase distribution and low side lobe pattern. Table 2 further quantitatively analyzes the phase distribution and pattern of Figure 2 From the analysis of various data, 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 average side lobe of each mode is better than-13dB, and the purity of each mode is more than 99%.

[0081] Table 2: Full-wave simulation radiation pattern parameters of each mode OAM

[0082]

[0083]

[0084] The part not described in detail in the application belongs to the common knowledge of those skilled in the art.

Claims

1. A method for optimization of multi-modal electromagnetic vortex wave array based on full-wave simulation, characterized in that, Specifically comprising the following steps: Step 1, determining initial array configuration parameters according to the fitting statistical formula of the vortex beam opening angle and the radius of the circular array, the initial array configuration parameters including the radius and the number of array elements of each circle in the circular array; Step 2, establishing an optimization target function based on the HFSS full-wave simulation data, comprising the following steps: Step 21, according to the initial array configuration parameters of the circular ring array in step 1, automatically optimize the corresponding multi-layer circular ring array configuration in HFSS, simulate to obtain the far-field pattern of the OAM beam, read the main lobe pointing angle of the OAM beam , half-power beam width HPBW , and maximum side lobe level ; Step 22, establishing an optimization target function based on the HFSS full-wave simulation data; Step 3, optimizing the target function based on the HFSS full-wave simulation data by using the IWO-PSO optimization algorithm; specifically comprising the following sub-steps: Step 31, setting IWO-PSO parameters, randomly initializing population wherein , P is the maximum population number, i denotes the serial number of individuals in the population; denotes the radius value of the first circle of the i th individual, denotes the element number of the first circle of the i th individual, denotes the feeding amplitude value of the first circle of the i th individual, and M denotes the circle number; Step 32, using the HFSS full-wave simulation data-based optimization target function established in step 2, the fitness value in the current iteration number is calculated, the fitness values are arranged from large to small, and the global optimal solution is obtained and the maximum fitness value and the minimum fitness value ; Step 33, updating the moving speed and position of the grass according to the particle swarm algorithm to form a new grass population; the specific process is shown as follows: wherein, and respectively represent the search speed and position of the i-th particle in the j-th array element at the k-th generation; respectively represent the search speed and position of the i-th particle in the j-th array element at the k-th generation; respectively represent the search speed and position of the i-th particle in the j-th array element at the k-th generation; represents the optimal solution found by the particle itself at the current time; represents the optimal solution found by the particle itself at the current time; is an inertia weight factor; and is a learning factor, being 1; and is a random number uniformly distributed between 0 and 1. Step 34, growth and reproduction, the number of seeds produced by each grass in the grass population is: wherein, is the fitness value of the current weed; and are the maximum and minimum fitness values of the corresponding weed in the current population, respectively; and are the maximum and minimum number of seeds that can be produced by a weed, respectively; Step 35, Spatial Diffusion, the weed produces seeds that are distributed around the weed according to a normal distribution with mean 0 and standard deviation that changes with the number of generations according to the following formula: wherein is the current generation number; is the maximum generation number; is the current standard deviation; and are the initial and final values of the standard deviation, respectively; is a non-linear harmonics factor; Step 36, competitive survival criteria, arrange all seed fitness values from large to small and grow into new grass, select the first P grass as the new population, eliminate the grass exceeding the maximum population number P; Step 4, setting the convergence condition of the IWO-PSO optimization algorithm, repeating steps 1 to 3 until the convergence condition is met, at this time the optimal array configuration is considered to be obtained, and the optimal electromagnetic vortex wave beam is output; Wherein, when the sidelobe level and the main lobe pointing error of each mode meet the following conditions at the same time, the IWO-PSO optimization algorithm converges, and the loop ends; 。 2. The full-wave simulation based multi-modal electromagnetic vortex beam array optimization method of claim 1, wherein, In step 1, for a single-layer circular array, the OAM main lobe direction is mainly determined by the radius of the circular array, and through curve fitting, the statistical mapping relationship between the OAM main lobe direction and the radius of the circular array is approximately: wherein, is the modal value, , is the maximum modal number, is the OAM lobe direction, , is the wavelength, is the radius of the circular array for a mode with a modal number 3. The full-wave simulation based multi-modal electromagnetic vortex beam array optimization method of claim 2, wherein, In step 2, the optimization target function is as follows: wherein and are weight coefficients, usually determined by the characteristics of the desired pattern; denotes the desired main lobe pointing, denotes the desired pointing error, denotes the desired side lobe level.

Images