Large-scale antenna array sparse method based on foraging mechanism of egret group

Abstract

The invention relates to the technical field of array antennas, in particular to a sparse design of a large-scale linear array antenna, and aims to construct a target function for sparse array optimization of a large-scale antenna. The large-scale antenna sparse array is mainly characterized in that the placement form of antenna array elements is optimized according to targets such as the sidelobe level of an antenna array, if the array elements are placed in a specified grid, the grid flag bit is marked as' 1 ', if no array elements are placed, the grid flag bit is marked as' 0 ', and' 1 'and' 0 'represent the flag bits of the grids, so that two conditions exist in the grids, and the grid flag bit is marked as' 0 '. According to the method, array elements exist and no array elements exist, that is, whether the array elements exist in the grid position, namely, the placing position of an antenna is optimized, the grid flag bit vector is I = [I1, I2, I3,..., IN], and compared with a traditional particle swarm optimization algorithm using sigmoid function mapping, the egret group foraging optimization mechanism adopts a hyperbolic tangent function for mapping to achieve individual position updating, and the optimization efficiency is greatly improved. Probability selection variation can be better carried out, and the optimization strategy is further improved.

Description

Technical Field

[0001] The present invention relates to the technical field of array antennas, in particular to the sparse design of large linear array antennas, and specifically to a sparse array antenna optimization method based on a heron flock foraging mechanism. Background Art

[0002] In actual engineering, array antennas have been widely used in many electronic countermeasure fields such as radar and wireless communications. Array antennas are composed of thousands of antenna units, which will increase the cost of engineering investment and complicate the equipment. In application, the system will be affected when processing, the speed will be reduced, and the performance of the antenna will be reduced. Sparse arrays can effectively solve the above problems. Its advantages are large antenna aperture and few antenna array units. While saving resources, the processing and stability of the system are also improved to a certain extent. However, the disadvantage of this type of antenna is that it has a high sidelobe level. The placement of the antenna is an important factor affecting the sidelobe level. Therefore, in practice, the position of the sparse array antenna unit is mainly optimized to obtain a lower sidelobe level.

[0003] The main principle of sparse array synthesis is to reduce the maximum sidelobe level of the antenna by using 0,1 to plan the working state of the array unit, so as to improve the performance of the antenna. In order to achieve the ideal radiation characteristics and sidelobe level, the working state of the array unit is taken as an unknown quantity, the distribution density of the antenna unit within the array aperture is optimized, and the excitation coefficient of the antenna array unit is selected to realize the layout and optimization of the antenna unit. Traditional genetic algorithms and particle swarm algorithms can solve most optimization problems, but genetic algorithms have more steps and relatively complex calculations. In practical applications, they can reduce the sidelobe level but have poor convergence accuracy and slow speed. Compared with genetic algorithms, particle swarm algorithms have better performance in solving the problem of sparse array antenna optimization, and their convergence accuracy and speed are better than genetic algorithms.

[0004] Many scholars have also proposed other related algorithms to solve the problem of sparse construction of array antennas. Liang Shuang et al. published "Improved Cuckoo Algorithm for Array Antenna Pattern Optimization" in the Journal of Xidian University (2019, Vol. 46, No. 1). They introduced a diffusion mutation strategy in the cuckoo algorithm to improve the diversity of the population and enhance the global search capability. Both strategies can improve the performance of the algorithm, but the method of using cumulative optimization of the objective function value has uncertainty in actual engineering applications, which can easily lead to unstable algorithm optimization performance. Chen Zhikun et al. published "Constrained Optimization of Planar Sparse Arrays Based on Hybrid Triangular Mutation Differential Evolution Algorithm" in the Journal of Electronics and Information Technology (2020, Vol. 42, No. 4). The paper mixes the improved differential evolution algorithm with the triangular mutation differential evolution algorithm, maintaining the population diversity in the early stage of the algorithm while further improving the convergence speed of the algorithm in the later stage. The sidelobe nulling concave constraint matrix is ​​introduced to realize the peak sidelobe level optimization of sparse planar arrays with sidelobe nulling concave constraints. However, the algorithm tends to global search in the early stage and local convergence in the later stage, and is prone to fall into local optimal solutions. Sun Jianbang et al. published "Sparse Array Optimization Based on Genetic Model to Improve Bee Colony Algorithm" in "High Power Laser and Particle Beams" (2021, Vol. 33, No. 12). The algorithm integrates the global optimal solution information into the neighborhood search process to guide the bee colony to find the best nectar source. In order to escape the local optimum, a genetic model was established to perform genetic operations on the nectar source after the best retention, enriching the diversity of nectar sources and overcoming local convergence. However, this algorithm combines the model in the genetic algorithm, and the parameters and algorithm steps increase. Although the population diversity is increased to overcome convergence, the calculation time of the algorithm is sacrificed, and there are many limitations in actual engineering.

[0005] The above literature introduces corresponding strategies into the algorithm steps or combines them with other algorithms to increase the diversity of the population to ensure that the global search performance does not fall into local convergence, but it also increases the steps, parameters and calculation time of the algorithm, and easily causes unstable performance. Summary of the invention

[0006] In view of the above-mentioned background technology, in order to further reduce the maximum sidelobe level value, the present invention is based on the foraging search mechanism of a bird group - a heron flock, and designs a new mapping function to optimize the sparse array. On the basis of not increasing the calculation complexity and calculation time, the convergence performance and speed are improved, and the maximum sidelobe level in the sparse array radiation pattern can be further reduced, thereby improving the performance of the antenna.

[0007] To achieve lower sidelobe levels and improve convergence performance and speed, the following steps are mainly included:

[0008] Step 1: Construct the objective function for optimizing large-scale antenna sparse arrays.

[0009] Large-scale antenna sparse arrays mainly optimize the placement of antenna elements based on the sidelobe level of the antenna array and other targets. If the array elements are placed in the specified grid, the grid mark bit is recorded as "1", and if the array elements are not placed, the grid mark bit is recorded as "0", where "1" and "0" represent the grid mark bit, so there are two situations in the grid, with array elements and without array elements, that is, whether there are array elements at the grid position, that is, the placement position of the antenna is optimized. The grid mark bit vector is I = [I1, I2, I3, ..., I N ].

[0010] Assume that a large-scale linear array to be optimized is composed of D non-directional array elements randomly arranged in N grids, N is an even number, the angle between the incoming wave direction in the linear array and the normal of the array is defined as θ, the number of antenna array elements is D, the excitation amplitude vector is a, and the phase vector is The spacing vector between array elements is represented by d, then the three parameter vectors can be represented as a = [a1, a2, a3, …, a N ]、 and d=[d1,d2,d3,…,d N ], the directional pattern of each array element is a D-element sparse array in all directions, and the directional pattern function is defined as where j is the complex unit, k is the wave number, λ is the operating wavelength, is the excitation phase of the nth grid antenna, a n is the excitation amplitude of the nth grid antenna, d n Indicates the distance between n grid antennas and the first grid antenna.

[0011] One of the optimization goals of large-scale antenna array sparseness is to obtain the maximum relative peak sidelobe level of the directional pattern. The maximum relative peak sidelobe level can be reduced to improve the anti-interference performance of the antenna. The directional pattern can vividly describe the properties of the sparse array and can also be expressed in logarithmic form as Among them, M max = max{|F(θ)|}, taking the maximum relative sidelobe level and the constrained null as the optimization target, the grid marker vector I is calculated according to the directional pattern as follows: Where L PSL is the maximum relative sidelobe level, max{|F(θ)|} is the main lobe peak of the pattern, and S represents the sidelobe area in the pattern. There are K interferences, and the kth interference direction is ψ k When the zero sink depth is A Nul (I) is the actual relative null depth and obtained by the grid marker vector I, E Nul(k) is the expected null depth against the kth disturbance.

[0012] Step 2: Initialize the position and speed of each individual in the heron group foraging behavior.

[0013] Assume that there are M herons in N-dimensional space, the position of the i-th heron in the t-th generation is defined as The n-dimensional position of the ith heron in the tth generation in the population is The speed of the i-th heron in the t-th generation is defined as If the foraging mechanism of the heron group is too fast during the search process, it will miss the optimal position. It is necessary to perform boundary detection on the flight speed of the individual herons in the population to ensure that the speed of the n-th dimension of the i-th heron in the t-th generation is within the speed range. v nmax It is the maximum speed of the heron flying in the nth dimension during the optimization process. In the initial generation, let t = 0, and the speed and position of each heron are randomly initialized in the definition domain.

[0014] Step three, construct a fitness function, calculate the fitness values ​​of all habitat locations searched by each heron during the foraging process, and compare them to determine the local optimal position and the global optimal position.

[0015] Combined with the optimal solution and objective function to be obtained in the optimization process, the filling rate is considered in the large-scale antenna sparse array when setting the fitness function. The current position of the ith heron in the tth generation can be expressed as According to the fitness function, the fitness value of the ith heron in the tth generation can be calculated as The weights are ω1 and ω2, the penalty factor is α1, is the sign vector The maximum relative sidelobe level value of the antenna placement position, E PSL is the expected maximum relative sidelobe level, c Rat is the calculated fill rate, e Rat is the expected population rate. All herons search in the N-dimensional space until the tth generation. The local optimal position searched by the i-th heron is expressed as Compare the fitness values ​​of all local optimal positions found by the herons, find the position corresponding to the optimal fitness, and record it as the global optimal position searched until the tth generation

[0016] Step 4: Update the speed and position of each individual heron during the foraging search process of the heron population.

[0017] The update equation for the nth dimension of the velocity of the ith heron in the t+1th generation is in is the nth dimension of the speed of the ith heron in the tth generation, is the n-th dimension position of the ith heron in the tth generation, is the nth dimension of the local optimal position searched by the i-th heron until the t-th generation, is the nth dimension of the global optimal position searched by all herons up to the tth generation. e1 and e2 are the individual learning factor and the individual social factor, respectively. The value determines and right The size of the impact, and are uniform random numbers between [0,1]. The hyperbolic tangent function is used to map the n-dimensional velocity of the ith heron in the t+1th generation Mapped to [0,1] as the decision probability, the update equation for the position of the ith heron in the nth dimension in the t+1th generation is in is a random number that satisfies a uniform distribution.

[0018] Step 5: Calculate the fitness value of each heron's new position and update the local optimal position and the global optimal position.

[0019] The speed of updating the i-th heron in the t+1th generation is And calculate the n-th velocity of the ith heron in the t+1th generation Perform boundary detection, 1≤i≤M, 1≤n≤N, v nmax is the maximum speed of the heron in the nth dimension during the optimization process. If the speed in one dimension exceeds the limit, it will be restricted to the boundary. After updating the position, the position of the i-th heron in the t+1 generation is Update the position of the i-th heron in the t+1 generation Substitute it into the fitness function, calculate the corresponding fitness function value to determine the local optimal position of the i-th heron in the t+1th generation. If the position fitness value of the i-th heron in the t+1th generation is better than the local optimal position fitness value of the i-th heron in the tth generation, the local optimal position of the i-th heron in the t+1th generation is expressed as otherwise, Compare the fitness values ​​of all local optimal positions after update, and select the best updated local optimal position as the global optimal position updated by the t+1th generation heron group.

[0020] Step 6, determine whether the maximum number of iterations has been reached. If not, set t=t+1 and return to step 4. If reached, terminate the iteration loop and output the global optimal position obtained by the foraging search mechanism of the heron group at this time, corresponding to the optimal sparse antenna array form.

[0021] Beneficial effects:

[0022] Compared with the traditional particle swarm algorithm using the sigmoid function, the heron group foraging optimization mechanism of the present invention uses the hyperbolic tangent function to map the individual position update, which can perform better probability selection mutation, further improve the optimization strategy, and have better convergence performance in sparse array antenna optimization, better convergence speed and accuracy. Compared with the optimization using traditional function mapping, the problems of premature maturity and easy to fall into the local optimal solution are optimized. Compared with the genetic algorithm, the search mechanism of the present invention has a simpler operation process, reduces the complexity of calculation in the optimization process, saves calculation time, simplifies the parameters and calculation process in the optimization process, can find the optimal solution faster in the search optimization process, and improves the search performance of the optimization mechanism, which further reflects the intelligence of the present invention based on the heron group foraging optimization mechanism.

[0023] Compared with traditional algorithms such as genetic algorithms and particle swarm algorithms, for the maximum allowed number of iterations, a larger number of iterations enables traditional algorithms to better search the solution space, so the possibility of finding the global optimal solution is also greater. Correspondingly, a smaller maximum allowed number of iterations will reduce the possibility of the algorithm finding the global optimal solution. For basic continuous PSO, due to the lack of effective jump-out local optimal operation, once the particle is trapped in the local extreme value, it is difficult to jump out, and the position update is in a stagnant state. At this time, the number of iterations cannot improve the optimization effect, and only wastes computing resources. However, too small a number of iterations will cause the algorithm to stop updating before an effective search is achieved in the target area, which will seriously affect the algorithm performance. The mapping function used in the search mechanism of the present invention can better select the probability of individual position variation, jump out of the local optimal solution as soon as possible, prevent premature maturity in the optimization process, and miss the optimal solution in the sparse array optimization process. Since the position update mapping function in the heron group foraging search mechanism does not have a high requirement for the number of iterations, the possibility of finding the optimal solution will not be reduced due to the reduction in the number of iterations, and in the optimization of the minimum value of the objective function, a lower function value can be achieved, the optimization performance is improved, and a lower sidelobe level value is achieved in the sparse array antenna. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 :Flowchart of large-scale antenna sparse array optimization method based on the foraging mechanism of heron flocks;

[0025] Figure 2 : The fitness function curves of genetic algorithm, particle swarm algorithm and heron flock foraging mechanism when the number of grids is 800 and the filling rate is 77%;

[0026] Figure 3 : The fitness function curves of genetic algorithm, particle swarm algorithm and heron flock foraging mechanism when the number of grids is 800 and the filling rate is 70%;

[0027] Figure 4 : Sparse array antenna pattern based on foraging search mechanism of heron flocks and particle swarm algorithm.

[0028] The simulation parameters are set as follows: binary coding is used for encoding, an antenna is placed at the starting position and the final position of the antenna array, the excitation amplitude of all grid antennas is 1, the initial population size of various intelligent method parameters is set to 50, the maximum number of iterations is 500, the fitness function value is the average of 50 times, the weights ω1=1, ω2=0, α=0.0001, the individual learning factor e1 and the individual social factor e2 are both 2, β1=0.45, β2=0.5, E PSL =-25dB,E Nul (k) = -50dB, the maximum flight speed v of the n-th heron group nmax =5, minimum speed -v nmax =-5, the crossover probability of the genetic algorithm GA is set to 0.8, the mutation probability is set to 0.01, and the parameter settings of the particle swarm algorithm PSO refer to “Sparse array constrained optimization based on discrete particle swarm algorithm with dynamic search strategy” published by Zeng Hao et al. in the Journal of Electronics.

[0029] Figure 2 It is a fitness function curve diagram when the number of sparse array antenna grids is 800 and the filling rate is 77%. It can be seen that the heron swarm foraging optimization mechanism of the present invention is better than the genetic algorithm and the particle swarm algorithm in terms of fitness function value performance. The heron swarm foraging mechanism has higher population diversity in the search process, better global search performance, and higher convergence accuracy. The comprehensive convergence speed and accuracy of the heron swarm foraging mechanism of the present invention have better performance in the optimization of large-scale antenna sparse arrays.

[0030] Figure 3 This is the fitness function curve when the number of sparse array antenna grids is 800 and the filling rate is 70%. The heron swarm foraging mechanism has begun to converge after about 90 iterations, and its fitness function value performance is better than that of the genetic algorithm and the particle swarm algorithm. The heron swarm foraging mechanism has better global search performance during the search process and is more suitable for the optimization of large-scale sparse array antennas. Figure 4 It can be seen that the maximum sidelobe level achieved by the foraging mechanism of herons when optimizing large-scale sparse arrays is -22.41dB. When the maximum sidelobe level of the large-scale sparse array pattern implemented based on the particle swarm algorithm is -18.94dB, it can be seen that the foraging mechanism of herons can further reduce the maximum sidelobe level of the pattern when optimizing large-scale antenna sparse arrays. DETAILED DESCRIPTION

[0031] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0032] In the description of the present invention, it should be understood that the terms "upper", "middle", "outer", "inner" and the like indicating directions or positional relationships are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the components or elements referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as limiting the present invention.

[0033] Step 1: Construct the objective function for optimizing large-scale antenna sparse arrays.

[0034] Large-scale antenna sparse arrays mainly optimize the placement of antenna elements based on the sidelobe level of the antenna array and other targets. If the array elements are placed in the specified grid, the grid mark bit is recorded as "1", and if the array elements are not placed, the grid mark bit is recorded as "0", where "1" and "0" represent the grid mark bit, so there are two situations in the grid, with array elements and without array elements, that is, whether there are array elements at the grid position, that is, the placement position of the antenna is optimized. The grid mark bit vector is I = [I1, I2, I3, ..., I N ].

[0035] Assume that a large-scale linear array to be optimized is composed of D non-directional array elements randomly arranged in N grids, N is an even number, the angle between the incoming wave direction in the linear array and the normal of the array is defined as θ, the number of antenna array elements is D, the excitation amplitude vector is a, and the phase vector is The spacing vector between array elements is represented by d, then the three parameter vectors can be represented as a = [a1, a2, a3, …, a N ]、 and d=[d1,d2,d3,…,d N ], the directional pattern of each array element is a D-element sparse array in all directions, and the directional pattern function is defined as where j is the complex unit, k is the wave number, λ is the operating wavelength, is the excitation phase of the nth grid antenna, a n is the excitation amplitude of the nth grid antenna, d n Indicates the distance between n grid antennas and the first grid antenna.

[0036] One of the optimization goals of large-scale antenna array sparseness is to obtain the maximum relative peak sidelobe level of the directional pattern. The maximum relative peak sidelobe level can be reduced to improve the anti-interference performance of the antenna. The directional pattern can vividly describe the properties of the sparse array and can also be expressed in logarithmic form as Among them, M max = max{|F(θ)|}, taking the maximum relative sidelobe level and the constrained null as the optimization target, the grid marker vector I is calculated according to the directional pattern as follows: Where L PSL is the maximum relative sidelobe level, max{|F(θ)|} is the main lobe peak of the pattern, and S represents the sidelobe area in the pattern. There are K interferences, and the kth interference direction is ψ k When the zero sink depth is A Nul (I) is the actual relative null depth and obtained by the grid marker vector I, E Nul (k) is the expected null depth against the kth disturbance.

[0037] Step 2: Initialize the position and speed of each individual in the heron group foraging behavior.

[0038] Assume that there are M herons in N-dimensional space, the position of the i-th heron in the t-th generation is defined as The n-dimensional position of the ith heron in the tth generation in the population is The speed of the i-th heron in the t-th generation is defined as If the foraging mechanism of the heron group is too fast during the search process, it will miss the optimal position. It is necessary to perform boundary detection on the flight speed of the individual herons in the population to ensure that the speed of the n-th dimension of the i-th heron in the t-th generation is within the speed range. v nmax It is the maximum speed of the heron flying in the nth dimension during the optimization process. In the initial generation, let t = 0, and the speed and position of each heron are randomly initialized in the definition domain.

[0039] Step three, construct a fitness function, calculate the fitness values ​​of all habitat locations searched by each heron during the foraging process, and compare them to determine the local optimal position and the global optimal position.

[0040] Combined with the optimal solution and objective function to be obtained in the optimization process, the filling rate is considered in the large-scale antenna sparse array when setting the fitness function. The current position of the ith heron in the tth generation can be expressed as According to the fitness function, the fitness value of the ith heron in the tth generation can be calculated as The weights are ω1 and ω2, the penalty factor is α1, is the sign vector The maximum relative sidelobe level value of the antenna placement position, E PSL is the expected maximum relative sidelobe level, c Rat is the calculated fill rate, e Rat is the expected population rate. All herons search in the N-dimensional space until the tth generation. The local optimal position searched by the i-th heron is expressed as Compare the fitness values ​​of all local optimal positions found by the herons, find the position corresponding to the optimal fitness, and record it as the global optimal position searched until the tth generation

[0041] Step 4: Update the speed and position of each individual heron during the foraging search process of the heron population.

[0042] The update equation for the nth dimension of the velocity of the ith heron in the t+1th generation is in is the nth dimension of the speed of the ith heron in the tth generation, is the n-th dimension position of the ith heron in the tth generation, is the nth dimension of the local optimal position searched by the i-th heron until the t-th generation, is the nth dimension of the global optimal position searched by all herons up to the tth generation. e1 and e2 are the individual learning factor and the individual social factor, respectively. The value determines and right The size of the impact, and are uniform random numbers between [0,1]. The hyperbolic tangent function is used to map the n-dimensional velocity of the ith heron in the t+1th generation Mapped to [0,1] as the decision probability, the update equation for the position of the ith heron in the nth dimension in the t+1th generation is in is a random number that satisfies a uniform distribution.

[0043] Step 5: Calculate the fitness value of each heron's new position and update the local optimal position and the global optimal position.

[0044] The speed of updating the i-th heron in the t+1th generation is And calculate the n-th velocity of the ith heron in the t+1th generation Perform boundary detection, 1≤i≤M, 1≤n≤N, v nmax is the maximum speed of the heron in the nth dimension during the optimization process. If the speed in one dimension exceeds the limit, it will be restricted to the boundary. After updating the position, the position of the i-th heron in the t+1 generation is Update the position of the i-th heron in the t+1 generation Substitute it into the fitness function, calculate the corresponding fitness function value to determine the local optimal position of the i-th heron in the t+1th generation. If the position fitness value of the i-th heron in the t+1th generation is better than the local optimal position fitness value of the i-th heron in the tth generation, the local optimal position of the i-th heron in the t+1th generation is expressed as otherwise, Compare the fitness values ​​of all local optimal positions after update, and select the best updated local optimal position as the global optimal position updated by the t+1th generation heron group.

[0045] Step 6, determine whether the maximum number of iterations has been reached. If not, set t=t+1 and return to step 4. If reached, terminate the iteration loop and output the global optimal position obtained by the foraging search mechanism of the heron group at this time, corresponding to the optimal sparse antenna array form.

[0046] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0047] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A large-scale antenna array sparse method based on the foraging mechanism of heron flocks, characterized in that: include: Construct the objective function for optimizing large-scale antenna sparse arrays; Large-scale antenna sparse arrays mainly optimize the placement of antenna elements based on the sidelobe level of the antenna array and other targets. If the array elements are placed in the specified grid, the grid mark bit is recorded as "1", and if the array elements are not placed, the grid mark bit is recorded as "0", where "1" and "0" represent the grid mark bit, so there are two situations in the grid, with array elements and without array elements, that is, whether there are array elements at the grid position, that is, the placement position of the antenna is optimized. The grid mark bit vector is I = [I1, I2, I3, ..., I N ]; Assume that a large-scale linear array to be optimized is composed of D non-directional array elements randomly arranged in N grids, N is an even number, the angle between the incoming wave direction in the linear array and the normal of the array is defined as θ, the number of antenna array elements is D, the excitation amplitude vector is a, and the phase vector is The spacing vector between array elements is represented by d, then the three parameter vectors can be represented as a = [a1, a2, a3, …, a N ]、 and d=[d1,d2,d3,…,d N ], the directional pattern of each array element is a D-element sparse array in all directions, and the directional pattern function is defined as where j is the complex unit, k is the wave number, λ is the operating wavelength, is the excitation phase of the nth grid antenna, a n is the excitation amplitude of the nth grid antenna, d n Indicates the spacing between n grid antennas and the first grid antenna; One of the optimization goals of large-scale antenna array sparseness is to obtain the maximum relative peak sidelobe level of the directional pattern. The maximum relative peak sidelobe level can be reduced to improve the anti-interference performance of the antenna. The directional pattern can vividly describe the properties of the sparse array and can also be expressed in logarithmic form as Among them, M max = max{|F(θ)|}, taking the maximum relative sidelobe level and the constrained null as the optimization target, the grid marker vector I is calculated according to the directional pattern as follows: Where L PSL is the maximum relative sidelobe level, max{|F(θ)|} is the main lobe peak of the pattern, S represents the sidelobe area in the pattern; there are K interferences, and the kth interference direction is ψ k When the zero sink depth is k=1,2,…,K,A Nul (I) is the actual relative null depth and obtained by the grid marker vector I, E Nul (k) is the expected null depth against the kth disturbance.

2. The large-scale antenna array sparse method based on the foraging mechanism of heron flocks according to claim 1 is characterized in that: Initialize the position and speed of each individual in the heron group foraging behavior; Assume that there are M herons in N-dimensional space, the position of the i-th heron in the t-th generation is defined as The n-dimensional position of the ith heron in the tth generation in the population is The speed of the i-th heron in the t-th generation is defined as If the foraging mechanism of the heron group is too fast during the search process, it will miss the optimal position. It is necessary to perform boundary detection on the flight speed of the individual herons in the population to ensure that the speed of the n-th dimension of the i-th heron in the t-th generation is within the speed range. v nmax It is the maximum speed of the heron flying in the nth dimension during the optimization process. In the initial generation, let t = 0, and the speed and position of each heron are randomly initialized in the definition domain.

3. The large-scale antenna array sparse method based on the foraging mechanism of heron flocks according to claim 2 is characterized in that: Construct a fitness function, calculate the fitness values ​​of all habitat locations searched by each heron during foraging, and compare them to determine the local optimal location and the global optimal location; Combined with the optimal solution and objective function to be obtained in the optimization process, the filling rate is considered in the large-scale antenna sparse array when setting the fitness function. The current position of the ith heron in the tth generation can be expressed as According to the fitness function, the fitness value of the ith heron in the tth generation can be calculated as The weights are ω1 and ω2, the penalty factor is α1, is the sign vector The maximum relative sidelobe level value of the antenna placement position, E PSL is the expected maximum relative sidelobe level, c Rat is the calculated fill rate, e Rat is the expected population rate; all herons search in the N-dimensional space until the tth generation. The local optimal position searched by the i-th heron is expressed as Compare the fitness values ​​of all local optimal positions found by the herons, find the position corresponding to the optimal fitness, and record it as the global optimal position searched until the tth generation 4. The large-scale antenna array sparse method based on the foraging mechanism of heron flocks according to claim 3 is characterized in that: Update the speed and position of each individual heron during the foraging search of the heron population; The update equation for the nth dimension of the velocity of the ith heron in the t+1th generation is in is the nth dimension of the speed of the ith heron in the tth generation, is the n-th dimension position of the ith heron in the tth generation, is the nth dimension of the local optimal position searched by the i-th heron until the t-th generation, is the nth dimension of the global optimal position searched by all herons up to the tth generation. e1 and e2 are the individual learning factor and the individual social factor, respectively. The value determines and right The size of the impact, and They are all uniform random numbers between [0,1]; The hyperbolic tangent function is used to map the n-dimensional velocity of the ith heron in the t+1 generation Mapped to [0,1] as the decision probability, the update equation for the position of the ith heron in the nth dimension in the t+1th generation is in is a random number that satisfies a uniform distribution.

5. The large-scale antenna array sparse method based on the foraging mechanism of heron flocks according to claim 4 is characterized in that: Calculate the fitness value of each heron's new position, and update the local optimal position and the global optimal position; The speed of updating the i-th heron in the t+1th generation is And calculate the n-th velocity of the ith heron in the t+1th generation Perform boundary detection, 1≤i≤M, 1≤n≤N, v nmax It is the maximum speed of the heron individual in the nth dimension during the optimization process. If the speed of a certain dimension exceeds the limit, it will be restricted to the boundary; After the position update, the position of the i-th heron in the t+1 generation is Update the position of the i-th heron in the t+1 generation Substitute it into the fitness function, calculate the corresponding fitness function value to determine the local optimal position of the i-th heron in the t+1th generation. If the position fitness value of the i-th heron in the t+1th generation is better than the local optimal position fitness value of the i-th heron in the tth generation, the local optimal position of the i-th heron in the t+1th generation is expressed as otherwise, Compare the fitness values ​​of all local optimal positions after update, and select the best updated local optimal position as the global optimal position updated by the t+1th generation heron group.

6. The large-scale antenna array sparse method based on the foraging mechanism of heron flocks according to claim 5 is characterized in that: Determine whether the maximum number of iterations has been reached. If not, set t=t+1 and return to step 4. If reached, terminate the iteration loop and output the global optimal position obtained by the foraging search mechanism of the heron group at this time, corresponding to the optimal sparse antenna array form.

Images