An antenna sparse array design method based on binary snake optimization algorithm

Abstract

The application provides a binary snake optimization algorithm-based antenna sparse array design method, and belongs to the field of antenna array pattern synthesis. The application is based on a snake optimization algorithm, a probability estimation model is added in the algorithm, a new binary coding snake optimization algorithm is provided, and the new binary coding snake optimization algorithm is applied to a sparse planar array layout optimization problem. The new probability estimation model can better map the slight change caused by the update function in the algorithm to the binary coding, maintain the diversity of the population, enhance the global search ability, and also reserve the exploration and development ability of the original algorithm. The method has the global search ability and fast convergence, and improves the sidelobe suppression ability of the sparse antenna.

Description

Technical Field

[0001] This invention belongs to the field of radio frequency antenna technology and is mainly applied in the field of antenna array pattern synthesis. Background Technology

[0002] With the widespread application of array antennas in wireless communication systems, the optimization of array antennas has attracted much attention. To ensure that the antenna array radiation pattern does not exhibit grating lobes, the spacing between adjacent elements in a uniform antenna array cannot exceed half a wavelength. Therefore, when high gain and high resolution are required for the antenna array, the array aperture length must be very large. Uniformly spaced arrays require a considerable number of antenna elements, making them very expensive. Using sparsely spaced array antennas with non-uniform spacing can significantly reduce costs. Optimizing the array layout involves studying the relationship between antenna array performance and array geometry, and then optimizing the array structure to obtain superior performance indicators.

[0003] Antenna array synthesis is the inverse problem of array analysis. Given radiation characteristics, it synthesizes the total number of antenna elements, their spatial distribution, the excitation amplitude distribution of each element, and the excitation phase distribution of each element to ensure that certain radiation characteristics of the array meet given requirements or that the radiation pattern approximates a predetermined pattern as closely as possible. Currently, there are two main optimization methods in array optimization: one is a sparse array where elements are randomly placed in a uniform grid, and the other is a sparse array with a certain aperture and element spacing. Although sparse arrays cannot compare with sparse arrays in terms of optimization degrees of freedom, they are easier to encode, have a simpler structure, and their element arrangement follows a predictable pattern, making them widely used in array optimization.

[0004] Many problems in engineering can be transformed into function evaluation problems, and array antenna optimization is no exception. Traditional mathematical optimization methods, such as linear programming and gradient descent, have limitations in solving complex optimization problems. Each computation can only provide a feasible solution based on given weights, but cannot provide solutions tailored to the preferences of different decision-makers. Therefore, intelligent algorithms offer new approaches to providing universal solutions. Examples include Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Differential Evolutionary Algorithms (DE), and Artificial Bee Colony Algorithms (ABC). These swarm intelligence algorithms are conceptually simple, easy to implement, and possess strong search capabilities. For the application of intelligent algorithms in array optimization, the main concerns are the algorithms' tendency to get trapped in local optima and their slow convergence speed. Summary of the Invention

[0005] The purpose of this invention is to provide an antenna sparse array design method based on the binary snake optimization algorithm, which has the advantages of fast convergence speed and good global search performance.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for designing sparse antenna arrays based on the binary snake optimization algorithm includes the following steps:

[0008] Step 1: Establish a sparse antenna array model, which is a uniformly arranged planar array;

[0009] Step 2: Generate the initial snake group and divide it into male and female snake groups of equal size; the initial snake group is a randomly generated two-dimensional matrix, and the row vectors of the matrix represent individuals in the snake group, corresponding to the arrangement of array elements in the antenna sparse array model. The matrix element is 1 at the position of array element and 0 at the position of no array element.

[0010] Step 3: Calculate the fitness value using the fitness function to obtain the best male individual, the best female individual, and the globally best individual in the snake group;

[0011] Step 4: Calculate the temperature and food quantity to determine the stage of snake population development, then proceed to step 5 or step 6;

[0012] Step 5: Exploration phase, the snake selects random locations to search for food and updates its own location;

[0013] Step 6: During the development phase, the snake moves towards food and updates its own position, or randomly enters combat mode or mating mode;

[0014] Step 7: Recalculate fitness values, update the best male individuals, the best magnetic individuals, and the globally best individuals, and initialize the globally worst individuals;

[0015] Step 8: Check the termination condition. If the termination condition is met, end the process; otherwise, return to step 4 and iterate.

[0016] Furthermore, the array elements of the sparse antenna array model are distributed in an M*N grid array, with a horizontal grid spacing of d. m The vertical grid spacing is d n The snake swarm uses matrix x NP,dim Let NP represent the snake swarm size, dim be M*N, and each individual snake can be rearranged into an M*N matrix f. The element f in the m-th row and n-th column of the matrix is... mn f takes the value 0 or 1. mn =1 indicates that there is an array element at the corresponding grid point position, f mn =0 indicates that there is no array element at the corresponding grid point position;

[0017] The antenna array radiation pattern AF is:

[0018]

[0019] Among them, the M array elements along the y-direction are spaced at intervals d. m Arranged, N array elements along the z-direction at intervals d n Arrangement, θ and For azimuth and elevation angles, This represents the maximum beam direction.

[0020] Furthermore, in step 2, the initial population x is divided equally. NP,dim Male population and female population

[0021] In step 3, the fitness function is defined as:

[0022]

[0023] Where S1 and S2 represent the sidelobe intervals in the azimuth and pitch directions, respectively, and Fit is the sum of the maximum sidelobe levels in the azimuth and pitch directions of the planar array; calculate the corresponding fitness value for each individual in the snake swarm, with the minimum fitness value corresponding to the optimal individual.

[0024] Further, in step 4, the temperature and the amount of food are calculated using the following formula:

[0025]

[0026]

[0027] Where t is the current iteration number, T is the maximum iteration number, and c1 is a constant with a value of 0.5;

[0028] If Q < 0.25, then proceed to the exploration phase;

[0029] If Q ≥ 0.25 and Temp > 0.6, then proceed to the first case of the development phase: move towards the food.

[0030] If Temp ≤ 0.6, then the second scenario in the development phase will occur: randomly entering either combat mode or mating mode.

[0031] Furthermore, in step 5, the formula for updating the male snake's position is as follows:

[0032]

[0033] Where MO is a one-dimensional matrix representing the updated snake position, and c2 is a constant with a value of 0.8. It is the position of the i-th male snake. The position of the male snake is randomly selected. rand(1,dim) generates a row vector with values ​​in the interval between 0 and 1.m This refers to the foraging ability of male snakes, as shown in the following formula:

[0034]

[0035] in, yes fitness value, yes fitness value;

[0036] The formula for female snakes to update their positions is as follows:

[0037]

[0038]

[0039] This formula is the same as the update position formula for male snakes, except that both the superscript f and the subscript f represent female snakes;

[0040] The real matrix obtained after position update is mapped to a binary matrix. The mapping rule is determined by the probability estimation model, as follows:

[0041] p(x i (t+1))=1 / [1+exp(-2b*(MO-0.5) / 2F)]

[0042]

[0043] Where p is the calculated probability estimate factor, x i (t+1) represents the newly generated individual, F is the scaling factor, b is the bandwidth factor, which is a positive integer used to adjust the range and shape of the probability distribution model, and rand(1,dim) is used to generate a row vector with element values ​​in the range of 0 to 1.

[0044] Furthermore, in step 6, when Q > 0.25, if Temp > 0.6, the snake will move towards the food, at which point a new position MO is obtained. A probability estimation model is then calculated to obtain the new position x. i (t+1); At this point, the formula for calculating position MO is as follows:

[0045] MO = x food ±c3×Temp×rand×(x food -x i (t))

[0046] Where c3 is a constant with a value of 0.48, x food It is the globally optimal individual position, x i It indicates the location of either the male or female snake.

[0047] If Temp ≤ 0.6, then randomly enter either battle mode or mating mode;

[0048] In combat mode, the formula for calculating the male snake's position (MO) update is as follows:

[0049]

[0050] in, This indicates the male snake's location; FM represents the male snake's combat stats. It represents the position of the optimal male and female individuals, and rand is a random number between 0 and 1;

[0051] The formula for calculating the female snake's new position is as follows:

[0052]

[0053] The formula is the same as the formula for calculating the male snake's updated position, except that FF represents the female snake's combat value, and the superscript f indicates the female snake.

[0054] The calculation methods for FM and FF are as follows:

[0055]

[0056]

[0057] In mating mode, the update formula for male snakes is as follows:

[0058]

[0059]

[0060] The female snake's renewal formula is as follows:

[0061]

[0062]

[0063] Furthermore, the termination condition in step 8 is reaching the maximum number of iterations. At this point, the final globally optimal result is output, which is the sparse arrangement result of the antenna array.

[0064] The beneficial effects of this invention are as follows:

[0065] 1. This invention designs the sparse antenna construction problem as a constrained optimization problem, and then applies the binary snake optimization algorithm to the sparse antenna array construction problem. This improves the shortcomings of intelligent algorithms in solving discrete optimization problems in terms of low convergence speed and convergence accuracy, while overcoming the shortcomings of traditional intelligent algorithms such as genetic algorithms in getting trapped in local optima.

[0066] 2. This invention effectively suppresses the maximum relative sidelobe level when dealing with sparsity problems. Simulation results show that the proposed design method has good convergence accuracy and speed when handling array problems. Attached Figure Description

[0067] Figure 1 This is a flowchart of an antenna sparse synthesis method based on the binary snake optimization algorithm;

[0068] Figure 2 This is the convergence curve of the simulation example algorithm;

[0069] Figure 3 This is a simulation example of sparse antenna element distribution.

[0070] Figure 4 This is a simulation example of the elevation pattern of a sparse antenna.

[0071] Figure 5 This is a simulation example of the azimuth radiation pattern of a sparse antenna. Detailed Implementation

[0072] like Figure 1 As shown, a sparse synthesis method for antenna arrays based on the binary snake optimization algorithm includes the following steps:

[0073] Step 1: Establish a sparse antenna array model, and place the array elements sequentially according to the number of array elements in the sparse antenna array and the spacing between array elements in the full array;

[0074] Step 2: Generate an initial population and divide it into male and female groups of equal size. The initial population is the arrangement of array elements in a randomly generated antenna array, where 1 indicates the presence of array elements and 0 indicates the absence of array elements, corresponding to the position of the snake in the population.

[0075] Step 3: Construct a fitness function, evaluate the population, and obtain the best male, best female, and optimal individual through the fitness function;

[0076] Step 4: Calculate the temperature and food quantity to determine the stage of snake population development;

[0077] Step 5: Exploration phase, the snake selects random locations to search for food and updates its own location;

[0078] Step 6: Development phase, snakes move towards food and update their position, entering combat mode or mating mode;

[0079] Step 7: Recalculate fitness values, update global and local optima, and initialize the worst individual;

[0080] Step 8: Check the termination condition. If the termination condition is met, the process ends; otherwise, return to step 4.

[0081] The elements of the sparse array antenna model are distributed in an M*N lattice array with a horizontal lattice spacing of d. m The vertical grid spacing is d n The snake swarm uses matrix x NP,dim Let NP represent the snake swarm size, dim be M*N, and each individual snake can be rearranged into an M*N matrix f. The element f in the m-th row and n-th column of the matrix is... mn f takes the value 0 or 1. mn =1 indicates that there is an array element at the corresponding grid point position, f mn =0 indicates that there is no array element at the corresponding grid point position;

[0082] The antenna array radiation pattern AF is:

[0083]

[0084] Among them, the M array elements along the y-direction are spaced at intervals d. m Arranged, N array elements along the z-direction at intervals d n Arrangement, θ and For azimuth and elevation angles, This represents the maximum beam direction.

[0085] In step 3, the fitness function is defined as:

[0086]

[0087] Where S1 and S2 represent the sidelobe intervals in the azimuth and pitch directions, respectively, and Fit is the sum of the maximum sidelobe levels in the azimuth and pitch directions of the planar array; calculate the corresponding fitness value for each individual in the snake swarm, with the minimum fitness value corresponding to the optimal individual.

[0088] In step 4, the temperature and the amount of food are calculated using different methods, as shown in the following formulas:

[0089]

[0090]

[0091] Where t is the current iteration number and T is the maximum iteration number. c1 is a constant with a value of 0.5. If Q < 0.25, the exploration phase begins; if Q ≥ 0.25 and Temp > 0.6, the first step of the development phase begins: moving towards food; if Temp ≤ 0.6, the second step of the development phase begins: randomly entering either combat mode or mating mode.

[0092] In step 5, food is randomly located and its location is updated, using the following formula:

[0093] MO = xrand,m (t)±c2×A m ×rand(1,dim)

[0094] Where c2 is a constant with a value of 0.8, x i,m It is the position of the i-th male snake, x rand,m The position of the male snake is randomly selected, and rand(1,dim) generates a row vector with values ​​between 0 and 1. m This refers to the foraging ability of male snakes, as shown in the following formula:

[0095]

[0096] in, yes The fitness function value, yes The fitness value. The formulas for updating the location and calculating the foraging ability of female snakes are similar to those for male snakes.

[0097] The real matrix obtained after position update is mapped to a binary matrix. The mapping rule is determined by the probability estimation model, as follows:

[0098]

[0099]

[0100] Where F is the scaling factor; b is the bandwidth factor, a positive integer used to adjust the range and shape of the probability distribution model. A suitable value of b can improve search efficiency while maintaining population diversity.

[0101] In step 6, when Q > 0.25, if Temp > 0.6, the snake will move towards the food, and at this point, MO can be obtained:

[0102] MO = x food ±c3×Temp×rand×(x food -x i (t))

[0103] Where c3 is a constant with a value of 0.48, x food It's the location of the food, x i It refers to the position of an individual (male or female).

[0104] Then, by calculating the probability estimation operator, the new position x is obtained. i (t+1).

[0105] If Temp ≤ 0.6, it will randomly enter either battle mode or mating mode.

[0106] In battle mode, the position update formula is:

[0107] MO = x i,m (t)±c3×FM×rand×(Q×x best,f -x i,m (t))

[0108] Where, x i,m It is the location of the male individual, x best,f This is the position where males and females are most distinct; FM is the combat value of the male individual. In this mode, the update method for females and males is similar, as shown in the following formula:

[0109] MO = x i,f (t)±c3×FF×rand×(Q×x best,m -x i,f (t))

[0110] The calculation methods for FM and FF are as follows:

[0111] FM = exp(-f best,f / f i )

[0112] FF = exp(-f best,m / f i )

[0113] In the mating pattern, the male individual renewal formula is:

[0114] MO = x i,m (t)±c3×M m ×rand×(Q×x i,f (t)-x i,m (t))

[0115] M m =exp(-f i,f / f i,m )

[0116] The formula for female individual renewal is:

[0117] MO = x i,f (t)±c3×M f ×rand×(Q×x i,m (t)-x i,f (t))

[0118] M f =exp(-f i,m / f i,f )

[0119] In step 7, the updated individuals are re-introduced into the fitness function to calculate the sidelobes, update the individual optimum and the global optimum, and thus update the velocity formula.

[0120] In step 8, after reaching the maximum number of iterations, the final global optimal result is output, which is the sparse arrangement of the antenna array.

[0121] Simulation experiment: Sidelobe level optimization was performed on an array with 1024 elements and a 32×32 azimuth and elevation angle, with a sparsity of 50%. Figure 2 , 3 4 and 5 are the optimization results. Figure 2 This is the convergence curve of the fitness function, which shows that the fitness function converges rapidly. Figure 3 This is the optimized array arrangement; Figure 4 and Figure 5 This describes the optimized suppression of sidelobe levels in the pitch and azimuth directions of the array.

[0122] In summary, this invention proposes a novel binary-coded snake optimization algorithm by incorporating a probabilistic estimation model, based on the snake optimization algorithm, and applies it to the sparse planar array layout optimization problem. The new probabilistic estimation model not only better maps the subtle changes brought about by the update function in the algorithm to the binary code, maintaining population diversity and enhancing global search capabilities, but also retains the original algorithm's exploratory and developmental capabilities. This method combines global search capabilities with fast convergence, improving the sidelobe suppression capability of sparse antennas. It can be used to address the problem that intelligent optimization algorithms easily get trapped in local optima and have slow convergence speeds during the sidelobe suppression process of sparse antennas, thus reducing the sidelobe suppression capability of sparse antennas.

Claims

1. A method for designing sparse antenna arrays based on a binary snake optimization algorithm, characterized in that, Includes the following steps: Step 1: Establish a sparse antenna array model, which is a uniformly arranged planar array; Step 2: Generate the initial snake group and divide it into male and female snake groups of equal size; the initial snake group is a randomly generated two-dimensional matrix, and the row vectors of the matrix represent individuals in the snake group, corresponding to the arrangement of array elements in the antenna sparse array model. The matrix element is 1 at the position of array element and 0 at the position of no array element. Step 3: Calculate the fitness value using the fitness function to obtain the best male individual, the best female individual, and the globally best individual in the snake group; Step 4: Calculate the temperature and food quantity to determine the stage of snake population development, then proceed to step 5 or step 6; Step 5: Exploration phase, the snake selects random locations to search for food and updates its own location; Step 6: During the development phase, the snake moves towards food and updates its own position, or randomly enters combat mode or mating mode; Step 7: Recalculate fitness values, update the best male individuals, the best magnetic individuals, and the globally best individuals, and initialize the globally worst individuals; Step 8: Check the termination condition. If the termination condition is met, end the process; otherwise, return to step 4 and iterate.

2. The antenna sparse array design method based on binary snake optimization algorithm according to claim 1, characterized in that, The array elements of the sparse array model are distributed in an M*N grid array, with a horizontal grid spacing of d. m The vertical grid spacing is d n The snake swarm uses matrix x NP,dim Let NP represent the snake swarm size, dim be M*N, and each individual snake can be rearranged into an M*N matrix f. The element f in the m-th row and n-th column of the matrix is... mn f takes the value 0 or 1. mn =1 indicates that there is an array element at the corresponding grid point position, f mn =0 indicates that there is no array element at the corresponding grid point position; The antenna array radiation pattern AF is: Among them, the M array elements along the y-direction are spaced at intervals d. m Arranged, N array elements along the z-direction at intervals d n Arrangement, θ and For azimuth and elevation angles, This represents the maximum beam direction.

3. The antenna sparse array design method based on binary snake optimization algorithm according to claim 2, characterized in that, In step 2, the initial population x is divided equally. NP,dim Male population and female population In step 3, the fitness function is defined as: Where S1 and S2 represent the sidelobe intervals in the azimuth and pitch directions, respectively, and Fit is the sum of the maximum sidelobe levels in the azimuth and pitch directions of the planar array; calculate the corresponding fitness value for each individual in the snake swarm, with the minimum fitness value corresponding to the optimal individual.

4. The antenna sparse array design method based on binary snake optimization algorithm according to claim 3, characterized in that, In step 4, the temperature and the amount of food are calculated using the following formula: Where t is the current iteration number, T is the maximum iteration number, and c1 is a constant with a value of 0.5; If Q < 0.25, then proceed to the exploration phase; If Q ≥ 0.25 and Temp > 0.6, then proceed to the first case of the development phase: move towards the food. If Temp ≤ 0.6, then the second scenario in the development phase will occur: randomly entering either combat mode or mating mode.

5. The antenna sparse array design method based on binary snake optimization algorithm according to claim 4, characterized in that, In step 5, the formula for updating the male snake's position is as follows: Where MO is a one-dimensional matrix representing the updated snake position, and c2 is a constant with a value of 0.

8. It is the position of the i-th male snake. The position of the male snake is randomly selected. rand(1,dim) generates a row vector with values ​​in the interval between 0 and 1. m This refers to the foraging ability of male snakes, as shown in the following formula: in, yes fitness value, yes fitness value; The formula for female snakes to update their positions is as follows: This formula is the same as the update position formula for male snakes, except that both the superscript f and the subscript f represent female snakes; The real matrix obtained after position update is mapped to a binary matrix. The mapping rule is determined by the probability estimation model, as follows: p(x i (t+1))=1 / [1+exp(-2b*(MO-0.5) / 2F)] Where p is the calculated probability estimate factor, x i (t+1) represents the newly generated individual, F is the scaling factor, b is the bandwidth factor, which is a positive integer used to adjust the range and shape of the probability distribution model, and rand(1,dim) is used to generate a row vector with element values ​​in the range of 0 to 1.

6. The antenna sparse array design method based on binary snake optimization algorithm according to claim 5, characterized in that, In step 6, when Q > 0.25, if Temp > 0.6, the snake will move towards the food, at which point a new position MO is obtained. A probability estimation model is then calculated to obtain the new position x. i (t+1); At this point, the formula for calculating position MO is as follows: MO<x food ±c3×Temp×rand×(x food -x i (t)) Where c3 is a constant with a value of 0.48, x food It is the globally optimal individual position, x i It indicates the location of either the male or female snake. If Temp ≤ 0.6, then randomly enter either battle mode or mating mode; In combat mode, the formula for calculating the male snake's position (MO) update is as follows: in, This indicates the male snake's location; FM represents the male snake's combat stats. It represents the position of the optimal male and female individuals, and rand is a random number between 0 and 1; The formula for calculating the female snake's new position is as follows: The formula is the same as the formula for calculating the male snake's updated position, except that FF represents the female snake's combat value, and the superscript f indicates the female snake. The calculation methods for FM and FF are as follows: In mating mode, the update formula for male snakes is as follows: The female snake's renewal formula is as follows:

7. The antenna sparse array design method based on binary snake optimization algorithm according to claim 1, characterized in that, The termination condition in step 8 is reaching the maximum number of iterations. At this point, the final global optimal result is output, which is the sparse arrangement result of the antenna array.

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