Sparse array antenna optimization method based on improved zebra algorithm

Abstract

The invention discloses a sparse array antenna optimization method based on an improved zebra algorithm, is used for reducing the peak side lobe level of a sparse array antenna, and belongs to the technical field of radio frequency phased array antennas. The implementation process of the method comprises the following steps: firstly, adding a probability estimation model on the basis of an original zebra optimization algorithm, and converting a real number variable into a binary code; secondly, an adaptive T distribution disturbance strategy and a dynamic selection strategy are introduced, the global search capability of the algorithm is enhanced, the algorithm is prevented from falling into local optimum, and the convergence speed is effectively improved; and finally, an optimal solution is obtained through iterative optimization for a certain number of times. In order to verify the performance of the method, three groups of simulation experiments are carried out, and the result shows that compared with other optimization algorithms, the method can obtain a lower array antenna peak sidelobe level within shorter optimization time, so that the performance of the antenna is improved.

Description

Technical Field

[0001] The invention belongs to the field of array antenna synthesis and relates to a sparse array antenna optimization method based on an improved zebra algorithm. Background Art

[0002] Antennas are important devices for converting energy and directional radiation and receiving electromagnetic waves, and are key components of radio equipment. Phased array antennas consist of multiple antenna units that can be independently controlled to form and point to specific radiation directions. Compared with single antenna units with poor directivity and low gain, array antennas have higher flexibility and adjustability, fast beam scanning speed, and excellent beam forming, spatial filtering, and anti-interference capabilities. Therefore, studying the optimization methods and techniques of phased array antennas is of great significance for improving antenna performance, coping with complex communication environments, and meeting diverse needs.

[0003] However, each antenna unit in a phased array antenna requires a T / R component that controls the excitation amplitude and excitation phase. In some application scenarios, such as array radar, in order to pursue higher performance indicators, they often develop in a larger scale, with the number of units easily reaching tens of thousands or even hundreds of thousands. Nearly half of the manufacturing cost will be spent on a large number of T / R components. Therefore, how to reduce the number of T / R components and thus reduce manufacturing costs and complexity has become one of the research focuses in the field of phased array antennas.

[0004] Sparse optimization is one of the important methods to reduce the manufacturing cost of array antennas. Sparse array is to remove some array elements in the uniform array while improving the antenna performance, thereby reducing the manufacturing cost and the peak sidelobe level (PSLL). This optimization method is widely used in wireless communication systems and radar fields. The main methods of sparse optimization are matrix pencil method, Bayesian compressed sensing method and swarm intelligence optimization algorithm. However, since the first two methods are unstable during the calculation process and the control variables in the optimization process are not easy to adjust, the swarm intelligence optimization algorithm can obtain the optimal or near-optimal solution within a reasonable time, so it has been more widely used in sparse optimization.

[0005] At present, there have been many studies on the use of swarm intelligence algorithms and their improved methods in the sparse optimization of array antennas, such as binary genetic algorithm (BGA), new binary differential evolution algorithm (NBDE), Boolean particle swarm optimization algorithm (Boolean PSO), etc. However, these algorithms have the problems of slow optimization process, poor optimization results, etc. Therefore, it is particularly important to study a method with fast optimization speed and good optimization results. The Zebra Optimization Algorithm (ZOA) is a new swarm intelligence algorithm proposed by Trojovská et al. in 2022. Compared with other algorithms, this algorithm has good optimization effect and fast convergence speed.

[0006] In summary, this method combines the probability estimation model with the zebra optimization algorithm, and introduces an adaptive t-distribution perturbation strategy and a dynamic selection strategy to improve the algorithm's global search capability in the early iteration, avoid it from falling into the local optimum, and enable rapid convergence in the later iteration. Through simulation experiments on two groups of array antennas of different sizes, the convergence speed and the peak sidelobe level of the array are comprehensively compared, verifying the excellence of this method in terms of optimization speed and optimization results. Summary of the invention

[0007] In view of the limitations of the prior art, the object of the present invention is to propose an optimization method for sparse array antennas based on an improved zebra algorithm (IZOA).

[0008] The specific technical solutions of the present invention are as follows:

[0009] A sparse array antenna optimization method based on an improved zebra algorithm comprises the following steps:

[0010] Step 1: Establish a rectangular planar array antenna model and initialize array parameters; the array parameters include array aperture, minimum element spacing, number of elements and constraints, take the array peak sidelobe level as the optimization target, and determine the fitness function;

[0011] Step 2: Set the relevant parameters of the zebra algorithm, including the population size, the maximum number of iterations, and the optimization variable. Calculate the fitness function value of each individual through the fitness function, and sort the population according to the fitness function value. The individual with the lowest fitness value is the best individual.

[0012] Step 3: Iterate and update the population through the update formulas of the population foraging phase and defense phase; during the population update process, introduce the adaptive t-distribution mutation strategy and dynamic selection strategy to perturb the population; the new population individuals obtained after each iterative update are real number optimization variables from 0 to 1, and introduce the probability estimation model to convert the real number optimization variables into binary codes of 0 or 1; use the binary coding results to calculate the fitness function value of each individual;

[0013] Step 4: After each iteration is completed, determine whether the number of iterations reaches the maximum number of iterations; if not, repeat step 3; if so, end the iteration and save the best optimization result. The best optimization result is the array distribution result corresponding to the lowest fitness function.

[0014] Furthermore, in step 1, the fitness function is defined as and The sum of the maximum sidelobe levels in the two planes:

[0015]

[0016] Fi is the maximum sidelobe level of the array antenna, and Fitness represents the fitness function, where F max is the maximum value of the array main lobe, and F(u,v) is the directional pattern function of the planar array, expressed as:

[0017]

[0018] Where k = 2π / λ is the wave number, λ is the wavelength, θ, is the elevation angle and azimuth angle; let the coordinates of each array element be (x m ,y n ), 1≤m≤M, 1≤n≤N, assuming the array element is an ideal point source, I mn is the excitation of the (m,n)th array element. When the array element needs to be removed, I mn =0, when the array element needs to be retained, then I mn =1.

[0019] Furthermore, in step 3, the population is updated during the foraging phase using the following formula:

[0020]

[0021] PZ j represents the individual with the lowest fitness function, namely the pioneer zebra, where represents the position of the i-th individual in the j-th dimension, is the new position of the individual, r is a random number in [0,1], I∈{1,2}, F i t 、F i t+1 They represent the fitness function values ​​of the current and new generations of individuals respectively. In the defense stage, zebras will choose different defense strategies when facing different predators, which are modeled by S1 and S2 in the following formulas:

[0022]

[0023] Where c is a constant of 0.01, P s Represents the random probability of switching between strategies S1 and S2, and AZ represents the state of the zebra being attacked.

[0024] Furthermore, the adaptive t-distribution variation introduced in step 3 combines the advantages of the global search capability of the Cauchy distribution and the local development capability of the Gaussian distribution. Its degree of freedom changes adaptively with the number of iterations. When the degree of freedom is large, it is close to the Gaussian distribution, and when the degree of freedom is 1, it is the Cauchy distribution, as shown in the following formula:

[0025]

[0026] trnd(tn) represents the t distribution with degrees of freedom tn;

[0027] The t distribution mutation operator is as follows:

[0028]

[0029] in For individuals after t-distribution variation, the value of tn increases nonlinearly, and is calculated as follows:

[0030] tn=exp(4·(t / max_t) 2 )

[0031] If the adaptive t-distribution mutation is used indiscriminately for all individuals in each iteration, the calculation time of the algorithm will be greatly increased. The dynamic selection probability p can adjust the use of the adaptive t-distribution mutation operator and reduce the impact of the adaptive t-distribution mutation on the algorithm's optimization ability, as shown in the following formula:

[0032] p=w1-w2×(Tt) / T

[0033] Among them, w1 determines the upper limit of the dynamic selection probability, and w2 determines the variation range of the dynamic selection probability.

[0034] Furthermore, the probability estimation model used in step 3 can convert real variables between 0 and 1 into binary codes of 0 or 1, as shown in the following formula:

[0035]

[0036] Among them, the probability estimation model P(X ij )=P(X i,1 ,X i,2 ,...,X i,dim ), F is the mutation control parameter, b is the bandwidth factor and is a positive integer used to adjust the range and shape of the probability distribution model; MO is the new individual calculated based on the individual in the previous iteration and the algorithm update function, and then the real number is converted to a binary number according to the following formula:

[0037]

[0038] Among them, R=rand(0,1) is a random number between 0 and 1.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] 1. Compared with other swarm intelligence optimization algorithms, the present invention adopts an improved zebra algorithm to optimize sparse rectangular planar array antennas, which reduces the peak sidelobe level, improves the performance of the antenna, and significantly improves the optimization speed.

[0041] 2. The present invention introduces an adaptive t-distribution mutation strategy and a dynamic selection strategy, which enables the algorithm to have excellent global development capabilities, and will not converge prematurely and fall into a local optimal solution, thereby improving the local exploration capability in the later stage of iteration and improving the convergence speed of the algorithm.

[0042] 3. In order to convert real number variables into binary variables, the present invention introduces a probability estimation model, so that the algorithm is suitable for the optimization of sparse array antennas.

[0043] In general, the present invention applies the improved zebra optimization algorithm to the sparse design of planar rectangular array antennas. Compared with other methods, it can significantly speed up the optimization speed while reducing the peak sidelobe level, and reduce the number of array elements, effectively saving time, calculation and manufacturing costs. It has certain reference significance and value in the design and application of actual array antenna systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is the overall flow chart of the method of the present invention;

[0045] Figure 2 It is a comparison of the convergence speed of the two methods in the simulation example 1 of the method of the present invention;

[0046] Figure 3 are two plane directional diagrams of simulation example 1 of the method of the present invention;

[0047] Figure 4 is a three-dimensional top view of simulation example 1 of the method of the present invention;

[0048] Figure 5 These are two plane direction diagrams and a three-dimensional top view of a simulation example 2 of the method of the present invention;

[0049] Figure 6 is a three-dimensional top view of simulation example 2 of the method of the present invention;

[0050] Figure 7 is a schematic diagram of the overall array layout of simulation example 2 of the method of the present invention;

[0051] Figure 8 These are two plane directional diagrams of simulation example 3 of the method of the present invention;

[0052] Fig. 9 is a three-dimensional top view of simulation example 3 of the method of the present invention;

[0053] Fig.10 is a schematic diagram of the overall array layout of simulation example 3 of the method of the present invention; DETAILED DESCRIPTION

[0054] The following will illustrate the implementation of the present invention through a specific simulation example. The simulation example is not intended to be a limitation of the present invention, but is only used to explain the present invention, thereby more clearly showing the advantages and effects of the present invention. It can also be applied through other specific implementations.

[0055] Figure 1 For the implementation flow chart of the present invention, refer to Figure 1 , the implementation steps of the present invention are as follows:

[0056] Step 1: Establish the xoy coordinate system with the center of the array as the origin. The array aperture is 2L×2H, the number of array elements is 2M×2N, and the array is symmetrical about the x-axis and y-axis. The spacing between the array elements is d on the x-axis and d on the y-axis respectively. x ,d y , so that the array is symmetrically distributed about the coordinate center, so only one quarter of the array elements need to be optimized. Then the array factor of the array antenna can be expressed as:

[0057]

[0058] Where k = 2π / λ is the wave number, λ is the wavelength, θ, is the elevation angle and azimuth angle; let the coordinates of each array element be (x m ,y n ), 1≤m≤M, 1≤n≤N, assuming the array element is an ideal point source, I mn is the excitation of the (m,n)th array element. When the array element needs to be removed, I mn =0, when the array element needs to be retained, then I mn =1.

[0059] The optimization target of this algorithm is the peak sidelobe level (PSLL) of the array antenna, which is expressed as:

[0060]

[0061] Where S is the side lobe area of ​​the array antenna except the main lobe. Considering the PSLL of the two planes, the fitness function is set to the sum of the PSLL of the two planes:

[0062]

[0063] Step 2: Initialize parameters and population. Generate NP individuals randomly, set the maximum number of iterations T, the current number of iterations t, calculate the fitness function of the initial population and sort them, select the best individual and update its position. The best individual is the pioneer zebra PZ, which leads the entire population to forage. The population is updated during the foraging phase using the following formula:

[0064]

[0065] in, represents the position of the i-th individual in the j-th dimension, is the new position of the individual, r is a random number in [0,1], I∈{1,2}, and the zebra will choose different defense strategies when facing different predators, which are modeled by S1 and S2 in the following formulas:

[0066]

[0067] Finally, the population is updated using the following formula:

[0068]

[0069] Among them, F i t 、F i t+1 Represent the fitness function values ​​of the current and new generations of individuals respectively.

[0070] Step 3: Introduce an adaptive t-distribution mutation strategy. The t-distribution mutation combines the advantages of the strong global search capability of the Cauchy distribution and the strong local development capability of the Gaussian distribution, making the algorithm have excellent global development capabilities, and will not converge too early and fall into the local optimal solution, improving the local exploration capability in the later stage of iteration and improving the convergence speed of the algorithm. The degrees of freedom of the t-distribution mutation change adaptively with the number of iterations. When the degrees of freedom are large, it is close to the Gaussian distribution, and when the degrees of freedom are 1, it is the Cauchy distribution, as shown in the following formula:

[0071]

[0072] trnd(tn) represents the t distribution with degrees of freedom tn. The expression of the t distribution mutation operator is:

[0073]

[0074] in For individuals after t-distribution variation, the value of tn increases nonlinearly, and is calculated as follows:

[0075] tn=exp(4·(t / max_t) 2 )

[0076] However, although the above-mentioned adaptive t-distribution mutation operator can greatly improve the optimization performance of the algorithm, if it is used indiscriminately for all individuals in each iteration, it will increase the calculation time of the algorithm. To address this phenomenon, the use of the dynamic selection probability p can adjust the use of the adaptive t-distribution mutation operator and reduce the impact of the t-distribution mutation on the algorithm's optimization ability. The specific formula is as follows:

[0077] p=w1-w2×(Tt) / T

[0078] Among them, w1 determines the upper limit of the dynamic selection probability, and w2 determines the variation range of the dynamic selection probability. In this method, when w1=0.5 and w2=0.1 are used, the adjustment effect is optimal.

[0079] Step 4: Introduce the probability estimation model. The zebra optimization algorithm updates the real numbers between 0 and 1. Therefore, if you want to apply it to the sparse optimization of array antennas, you need to convert the real numbers between 0 and 1 into 0 or 1. 0 represents removing the array element, and 1 represents retaining the array element. This operation is completed by a probability estimation model, as shown in the following formula:

[0080]

[0081] Among them, the probability estimation model P(X ij )=P(X i,1 ,X i,2 ,...,X i,dim ), F is the mutation control parameter, b is the bandwidth factor and is a positive integer, which is used to adjust the range and shape of the probability distribution model. In this method, F is 1 and b is 20. MO is a new individual calculated based on the individual in the previous iteration and the algorithm update function.

[0082] Next, we need to convert the real number into a binary number, as follows:

[0083]

[0084] Among them, R=rand(0,1) is a random number between 0 and 1.

[0085] Step 5: Determine whether the iteration is completed. If not, continue the iteration. If completed, retain the best array element distribution result.

[0086] The present invention will be described below through three simulation examples.

[0087] In simulation example 1, a sparse optimization is performed on a rectangular array antenna with 200 array elements of 2M×2N=20×10, 54% of the array elements are retained, the element spacing is dx=dy=0.5λ, the population size is NP=200, and the maximum number of iterations is T=500. Perform the above steps 2, 3, and 4 to finally obtain the optimized array element position results and the corresponding peak sidelobe level values.

[0088] Figure 2 Convergence speed comparison between this method and NBDE. Figure 3 and Figure 4 They are two plane direction diagrams and a three-dimensional top view of simulation example 1. Table 1 compares the results of the four methods.

[0089] Table 1 Comparison of the results of four algorithms

[0090]

[0091]

[0092] In simulation example 2, a sparse optimization is performed on a rectangular array antenna with 576 elements of 2M×2N=24×24, 252 elements are retained, the element spacing is dx=dy=0.5λ, the population size is NP=200, and the maximum number of iterations is T=1000. Perform steps 2, 3, and 4 above, and finally obtain the optimized element position results and the corresponding peak sidelobe level values, and observe the PSLL at different scanning angles. Figure 5 and Figure 6 These are the two plane direction diagrams and the three-dimensional top view of simulation example 2. Figure 7 is a schematic diagram of the overall array layout of simulation example 2. Table 2 compares the results of this method and the IMOBWO-IFT method at different scanning angles.

[0093] Table 2 Comparison of IMOBWO-IFT and IBZOA results

[0094]

[0095] In simulation example 3, a sparse optimization is performed on a rectangular array antenna with 1024 elements of 2M×2N=32×32, 512 elements are retained, the element spacing is dx=dy=0.5λ, the population size is NP=200, and the maximum number of iterations is T=2000. Perform steps 2, 3, and 4 above, and finally obtain the optimized element position results and the corresponding peak sidelobe level values. The results obtained by IZOA are Better than NBDE Change the scanning angle to observe and get the result: and It can be seen that the IZOA optimized array antenna can achieve lower PSLL at different scanning angles. Figure 8 and Fig. 9 These are the two plane direction diagrams and the three-dimensional top view of simulation example 3. Fig.10 This is a schematic diagram of a quarter array layout of simulation example 3.

[0096] In summary, the present invention proposes an improved zebra algorithm, which is combined with a probability estimation model, and introduces an adaptive t-distribution mutation strategy and a dynamic selection strategy to avoid the algorithm from falling into a local optimal solution, enhance the algorithm's global search capability, and accelerate the convergence speed. By sparsely optimizing the array element positions of the rectangular planar array antenna, the peak sidelobe level can be further reduced while reducing the number of array elements and saving manufacturing costs, and the optimization speed is fast, which can better meet the current application requirements for rectangular planar array antennas.

Claims

1. A sparse array antenna optimization method based on an improved zebra algorithm, characterized in that The following steps are involved: Step 1: Establish a rectangular planar array antenna model and initialize the array parameters; The array parameters include array aperture, minimum spacing between array elements, number of array elements and constraints. The array peak sidelobe level is taken as the optimization target to determine the fitness function. Step 2: Set the relevant parameters of the zebra algorithm, including the population size, the maximum number of iterations, and the optimization variable. Calculate the fitness function value of each individual through the fitness function, and sort the population according to the fitness function value. The individual with the lowest fitness value is the best individual. Step 3: Iterate and update the population through the update formulas of the population foraging phase and defense phase; during the population update process, introduce the adaptive t-distribution mutation strategy and dynamic selection strategy to perturb the population; the new population individuals obtained after each iterative update are real number optimization variables from 0 to 1, and introduce the probability estimation model to convert the real number optimization variables into binary codes of 0 or 1; use the binary coding results to calculate the fitness function value of each individual; Step 4: After each iteration is completed, determine whether the number of iterations reaches the maximum number of iterations; if not, repeat step 3; if so, end the iteration and save the best optimization result. The best optimization result is the array distribution result corresponding to the lowest fitness function.

2. The sparse array antenna optimization method based on the improved zebra algorithm according to claim 1, characterized in that: In step 1, the fitness function is defined as and The sum of the maximum sidelobe levels in the two planes: Fi is the maximum sidelobe level of the array antenna, and Fitness represents the fitness function, where F max is the maximum value of the array main lobe, and F(u,v) is the directional pattern function of the planar array, expressed as: Where k = 2π / λ is the wave number, λ is the wavelength, θ, is the elevation angle and azimuth angle; let the coordinates of each array element be (x m ,y n ), 1≤m≤M, 1≤n≤N, assuming the array element is an ideal point source, I mn is the excitation of the (m,n)th array element. When the array element needs to be removed, I mn =0, when the array element needs to be retained, then I mn =1.

3. The sparse array antenna optimization method based on the improved zebra algorithm according to claim 1, characterized in that: In step 3, the population is updated during the foraging phase using the following formula: PZ j represents the individual with the lowest fitness function, namely the pioneer zebra, where represents the position of the i-th individual in the j-th dimension, is the new position of the individual, r is a random number in [0,1], I∈{1,2}, F i t 、F i t+1 They represent the fitness function values ​​of the current and new generations of individuals respectively. In the defense stage, zebras will choose different defense strategies when facing different predators, which are modeled by S1 and S2 in the following formulas: Where c is a constant of 0.01, P s Represents the random probability of switching between strategies S1 and S2, and AZ represents the state of the zebra being attacked.

4. The sparse array antenna optimization method based on the improved zebra algorithm according to claim 1, characterized in that: The adaptive t-distribution variation introduced in step 3 combines the advantages of the global search capability of the Cauchy distribution and the local development capability of the Gaussian distribution. Its degree of freedom changes adaptively with the number of iterations. When the degree of freedom is large, it is close to the Gaussian distribution, and when the degree of freedom is 1, it is the Cauchy distribution, as shown in the following formula: trnd(tn) represents the t distribution with degrees of freedom tn; The t distribution mutation operator is as follows: in For individuals after t-distribution variation, the value of tn increases nonlinearly, and is calculated as follows: tn=exp(4·(t / max_t) 2 ) If the adaptive t-distribution mutation is used indiscriminately for all individuals in each iteration, the calculation time of the algorithm will be greatly increased. The dynamic selection probability p can adjust the use of the adaptive t-distribution mutation operator and reduce the impact of the adaptive t-distribution mutation on the algorithm's optimization ability, as shown in the following formula: p=w1-w2×(Tt) / T Among them, w1 determines the upper limit of the dynamic selection probability, and w2 determines the variation range of the dynamic selection probability.

5. The sparse array antenna optimization method based on the improved zebra algorithm according to claim 1, characterized in that: The probability estimation model used in step 3 can convert real variables between 0 and 1 into binary codes of 0 or 1, as shown in the following formula: Among them, the probability estimation model P(X ij )=P(X i,1 ,X i,2 ,...,X i,dim ), F is the mutation control parameter, b is the bandwidth factor and is a positive integer used to adjust the range and shape of the probability distribution model; MO is a new individual calculated based on the individual in the previous iteration and the algorithm update function, and then the real number is converted to a binary number according to the following formula: Among them, R=rand(0,1) is a random number between 0 and 1.

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