CN113447904B - Sparse array optimization method based on permutation discrete differential evolution algorithm - Google Patents
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Abstract
The invention discloses a sparse array optimization method based on a permutation discrete differential evolution algorithm, and aims to solve the problem that the maximum side lobe level of an optimization result is higher due to binary coding and random variation operation which can generate an infeasible solution when a genetic algorithm is used for optimizing a sparse array in the prior art. The method comprises the following steps: constructing an optimization control objective function; coding the sparse array elements based on the arrangement positions; screening the initial population to obtain an optimal individual; carrying out mutation operation on the sparse array elements based on the arrangement positions; performing cross operation on the sparse array elements based on the arrangement positions; selecting the filial generation individuals after the cross operation; and (5) ending iteration to obtain the optimized sparse array. When the sparse array is optimized, the sparse array with lower maximum side lobe level can be obtained, and the efficiency of sparse array optimization is improved while higher resolution is obtained.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and further relates to a sparse array optimization method based on a permutation discrete differential evolution algorithm in the technical field of array design. The method can be used for sparse array optimization, the minimization of the maximum side lobe level is realized as a constraint condition, and a plurality of array elements are optimally selected to compress data volume and reduce signal processing pressure.
Background
Sparse array synthesis mainly reduces the maximum side lobe level of the antenna and improves the performance of the antenna by reasonably planning the working state of the array unit. In order to narrow the antenna beam width and increase the resolution of modern phased array radar, the number of array elements is often thousands, and the cost, volume and complexity of radar systems are increasing due to the large number of antenna elements and the corresponding receiving channels.
Masezhei proposed an array sparsity optimization method based on an improved genetic algorithm in a published paper "sparse antenna array optimization technical research" (Master paper of electronic science and technology university, 2019). The method comprises the following implementation steps: initializing a population by adopting a binary coding mode; (2) carrying out cross operation on the chromosome; (3) Carrying out mutation operation on a chromosome, randomly selecting a plurality of gene points on the chromosome for an individual needing mutation, and turning over the values, namely changing '1' into '0' and changing '0' into '1'; (4) And calculating the population fitness and obtaining an optimal result according to the population fitness. Although the method reduces the maximum side lobe level of the antenna through a genetic algorithm, the performance of the antenna is improved. However, the method still has the disadvantages that: because the method directly operates a random individual during mutation operation, the method is very sensitive to a plurality of preset parameters (such as mutation rate, crossing rate and the like), the optimization algorithm can often converge early, and the maximum side lobe level of the obtained sparse array is higher.
The patent document of Hangzhou electronic science and technology university (patent application number: 201910021619.3 application publication number: CN 109885872A) applied by the Hangzhou electronic technology university provides an array sparse optimization method based on a differential evolution algorithm. The method comprises the following implementation steps: (1) Initializing population, adopting binary coding mode, i.e. introducing antenna identification bit a = [ a = 1 ,a 2 ,...,a m ,...,a M-1 ,a M ]M =1,2, M, where a m =1 denotes that the m-th array element is in working state, a m =0 indicates that the m-th array element is idle; (2) carrying out mutation and cross operation; (3) And calculating the population fitness and obtaining an optimal result according to the population fitness. The method reduces the maximum side lobe level of the array antenna by improving the mutation operator, but the method still has the following defects: because the binary coding method is adopted when the population is initialized, the number of array elements in a working state and an idle state can be changed when the crossing and mutation operations are carried out, an infeasible solution is generated, a plurality of operation results are wasted, and the maximum side lobe level of the obtained sparse array is higher under the limit of limited iterative algebra.
Disclosure of Invention
The invention aims to provide a sparse array optimization method based on an array discrete differential evolution algorithm aiming at overcoming the defects of the prior art, and aims to solve the problem that the maximum side lobe level obtained within the limited iteration times is higher due to binary codes which can generate more infeasible solutions and completely random variation operation when a genetic evolution algorithm is used for optimizing a sparse array in the prior art.
The specific idea for realizing the purpose of the invention is to carry out coding operation based on the arrangement position on the sparse array elements, correspond each array element to a unique integer, and keep the number of the array elements in a working state and an idle state unchanged during the mutation and cross operation, thereby ensuring that all the obtained sparse arrays are usable and overcoming the problem that the binary coding can generate more infeasible solutions. When the mutation operation is carried out, the sequence number difference of the array elements between two individuals in the parent population is utilized, and the other individual in the population is added to generate a mutated offspring individual, so that the sensitivity degree of the mutated offspring individual to the preset parameter variation rate is greatly reduced, and the problem of high sensitivity degree of the preset parameter caused by completely random mutation operation is solved.
The specific steps for realizing the purpose of the invention are as follows:
(1) Constructing an optimization control objective function:
an optimization control target is constructed according to the relationship between the array element distribution of the sparse array antenna and the maximum side lobe level of an array directional diagram, and comprises the following steps:
wherein MSLL represents the maximum side lobe level of the sparse array antenna, max represents the maximum operation, theta represents the included angle between the array scanning beam and the array normal, S represents the side lobe range interval of the array directional diagram, and when the main lobe width of the array directional diagram is (-theta) 1 ，θ 1 ) When the angle is larger than or equal to-90 degrees and smaller than or equal to-theta 1 And theta 1 S is equal to or less than 90 degrees, I represents absolute value operation, N represents the total number of array elements in the sparse array antenna, N is equal to or more than 3,n represents the position serial number of the array elements in the array antenna, N =1,2And operation e (.) Expressing exponential operation with a natural constant e as the base, j expressing an imaginary unit symbol, pi expressing a circumferential ratio, lambda expressing the operating wavelength of the array antenna, d n Representing the spacing of the elements in the array antenna, sin representing the sine operation, theta 0 Representing the angle between the direction of the array target beam and the array normal, f n The working state of the nth array element in the array antenna is shown when f n If =0, the array element is idle, f n When the number is not less than 1, the array element works;
(2) Coding the sparse array elements based on the arrangement positions:
randomly generating an initial population comprising a plurality of groups of sparse array antenna distribution, and coding each array element in each group of sparse array antenna individuals;
(3) Screening the initial population to obtain optimal individuals:
3a) Determining the working state of each array element in the individuals by judging the array element coding size of each individual in the initial population: if V i,n Q is less than or equal to Q, f i,n =0; if V i,n > Q, then f i,n =1, wherein V i,n Representing the code of the nth array element in the ith individual in the initial population, Q representing the number of idle array elements in the ith individual in the initial population, Q = N multiplied by gamma, and gamma representing the sparse rate of the sparse array;
3b) Calculating the maximum side lobe level of each individual in the initial population by using an optimization control objective function, selecting the minimum value of all the maximum side lobe levels, and reserving the individual corresponding to the minimum value as the optimal individual of the initial population;
(4) Carrying out mutation operation on the sparse array elements based on the arrangement positions:
performing variation operation based on the arrangement position on each individual in the contemporary population to obtain an updated contemporary population;
(5) Performing cross operation on the sparse array elements based on the arrangement positions:
performing cross operation based on arrangement positions on each individual in the updated current generation population to obtain a child generation population;
(6) And (3) carrying out selection operation on the filial generation individuals after the cross operation:
6a) Obtaining the optimal individuals of the filial generation population by adopting the same method as the steps 3 a) and 3 b) for each individual in the filial generation population;
6b) Taking the individuals with the smaller maximum side lobe level of the current generation population optimal individuals and the offspring population optimal individuals as the current generation population optimal individuals;
6c) Judging whether the maximum sidelobe level of the optimal individual of the current generation population meets an expected target or not, if so, executing the step (7); if not, executing the step (4);
(7) And (5) iteration is terminated to obtain an optimized sparse array:
and 3 a) judging the working state of each array element in the optimal individual of the contemporary population by adopting the same method as the step 3 a) to obtain the optimized sparse array.
Compared with the prior art, the invention has the following advantages:
firstly, because the array elements of the sparse array are subjected to coding operation based on the arrangement positions, each array element corresponds to a unique integer, the number of the array elements in a working state and an idle state is unchanged during mutation and cross operation, and all the obtained sparse arrays are ensured to be usable, so that the problems that an infeasible solution is generated during the mutation and cross operation and the maximum sidelobe level of an optimization result is higher due to the fact that a binary coding mode is used for the array elements of the sparse array in the prior art are effectively solved, and when the sparse array is optimized according to the scheme of the invention, the sparse array with the lower maximum sidelobe level can be obtained under the condition that the iteration times are the same, so that higher resolution is obtained;
secondly, when the invention is used for carrying out variation operation on individuals in the population, the sequence number difference of the array elements between two individuals in the parent population is utilized, and the other individual in the population is added to generate a variant offspring individual, so that the problem that the variation operation is very sensitive to the preset parameter in the prior art is solved, the sensitivity of the individual to the variation rate of the preset parameter is obviously reduced when the variation operation is carried out according to the scheme of the invention, the convergence speed of an optimization algorithm is slowed down, a sparse array with a lower maximum minor lobe level is obtained, and the optimization efficiency of the sparse array is improved while higher resolution is obtained.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of a sparse array model of the present invention;
FIG. 3 is an array element distribution diagram of a sparse array obtained by optimization in a simulation experiment of the present invention under the condition of determining the total number of array elements, the sparse rate and the array element spacing;
FIG. 4 is an array pattern of a sparse array obtained by optimization in a simulation experiment of the present invention under the condition of determining the total number of array elements, the sparse rate, and the array element spacing;
FIG. 5 is a variation diagram of individual fitness when the optimal individual is obtained by optimization under the condition of determining the total number of array elements, the sparse rate and the array element spacing in the simulation experiment of the present invention.
Detailed Description
The invention is further described below with reference to the figures and examples.
The specific steps implemented by the present invention are further described with reference to fig. 1.
An optimization control target is constructed according to the relationship between the array element distribution of the sparse array antenna and the maximum side lobe level of an array directional diagram, and comprises the following steps:
wherein MSLL represents the maximum side lobe level of the sparse array antenna, max represents the maximum operation, theta represents the included angle between the array scanning beam and the array normal, S represents the side lobe range of the array directional diagram, and when the main lobe width of the array directional diagram is (-theta) 1 ，θ 1 ) When the angle is larger than or equal to-90 degrees and smaller than or equal to-theta 1 And theta 1 S is equal to or less than 90 degrees, | | represents absolute value operation, N represents the total number of array elements in the sparse array antenna, N is equal to or more than 3,n represents the position serial number of the array elements in the array antenna, N =1,2, (.) expressing an exponential operation based on a natural constant eWhere j denotes an imaginary unit symbol, pi denotes a circumferential ratio, λ denotes an operating wavelength of the array antenna, and d n Representing the spacing of the elements in the array antenna, sin representing the sine taking operation, theta 0 Representing the angle between the direction of the array target beam and the array normal, f n The working state of the nth array element in the array antenna is shown when f n If =0, it means that the array element is idle, f n And when =1, the array element is working.
The sparse array of the present invention is further described with reference to fig. 2.
In fig. 2, the abscissa represents the relative position of the sparse array element, the ordinate represents the normal direction of the sparse array radiation pattern, the black dots represent that the array element is in a working state, the white dots represent that the array element is in an idle state, and the numbers 1,2,3 are.
And the phase difference between adjacent array elements is represented, theta represents the included angle between the array scanning beam and the array normal, and d represents the distance between the adjacent array elements in the array antenna.
And 2, coding the sparse array elements based on the arrangement positions.
Randomly generating an initial population comprising a plurality of groups of sparse array antenna distribution, coding each array element in each group of sparse array antenna individuals, and respectively representing all integers in 1-N after random sequencing
Of the N array elements, wherein,
denotes the ith group of sparse array antennas in the initial population, i =1,2.
And 3, screening the initial population to obtain the optimal individual.
and 2, calculating the maximum side lobe level of each individual in the initial population by using an optimization control objective function, selecting the minimum value of all the maximum side lobe levels, and keeping the individual corresponding to the minimum value as the optimal individual of the initial population.
And 4, performing mutation operation on the sparse array elements based on the arrangement positions.
Performing variation operation based on the arrangement position on each individual in the current generation population to obtain an updated current generation population: for three random individuals x in the contemporary population j 、x p 、x k Performing array element position conversion operation to calculate x j And x p The position sequence number difference L of the middle and same coding array elements; x is to be k And respectively summing the position serial numbers of the middle array element codes and L to obtain an updated current generation individual.
And 5, performing cross operation on the sparse array elements based on the arrangement positions.
Performing cross operation based on arrangement positions on each individual in the updated current generation population to obtain a child generation population: for two random individuals x in the contemporary population m 、x l Performing array element position cross operation to generate two unequal random numbers C 1 、C 2 ，C 1 ∪C 2 Less than or equal to N, x m Middle position with serial number C 1 ～C 2 Is replicated into a child individual, at x l Deleting the corresponding array element code, and copying the rest array element codes to the same filial generation individual.
And 6, obtaining the optimized sparse array.
And 7, terminating iteration to obtain the optimized sparse array.
And (3) judging the working state of each array element in the optimal individual of the contemporary population by adopting the same method as the step 1 in the step 3 to obtain the optimized sparse array.
The effect of the present invention is further explained by combining the simulation experiment as follows:
1. experimental conditions of the simulation experiment:
the hardware platform of the simulation experiment of the invention is as follows: the processor is an Intel i7 5930k CPU, the main frequency is 3.5GHz, and the memory is 16GB.
The software platform of the simulation experiment of the invention is as follows: windows 10 operating system and MATLAB R2020b.
2. Simulation content and simulation result analysis:
the sparse array is optimized by using a permutation-based discrete differential evolution algorithm in the simulation, the total number of array grids is 82, the sparsity rate is 73%, the spacing between adjacent grids is 0.9 lambda, the population scale is 100, the cross probability is 0.5, and the variation probability is 0.1.
The sparse array element distribution map obtained by the simulation experiment is further described with reference to fig. 3.
Fig. 3 is a diagram of simulation output results, and the black dots in fig. 3 represent array elements in an operating state, and the white dots represent array elements in an idle state. The abscissa in fig. 3 represents the relative position of the sparse array elements in λ.
The sparse array pattern resulting from the simulation experiment is further described with reference to fig. 4.
And (4) drawing the sparse array normalized gain calculated by the sparse linear array directional diagram function into figure 4. The abscissa in fig. 4 represents the angle between the array scanning beam and the array normal, the ordinate represents the normalized gain of the array pattern, the maximum side lobe level of the array antenna shown in fig. 4 is lower than-10 dB, specifically about-10.47 dB, and the half-power main lobe width is 0.74 °. The sparse linear array pattern function is shown below,
where F (θ) represents a sparse linear array direction coefficient.
Referring to fig. 5, the iterative process of population in the simulation experiment is further described.
The maximum side lobe level of the current generation population optimal individual reserved in the optimization process is drawn into a graph 5, the abscissa in the graph 5 represents the evolution algebra of the population in the optimization process, the ordinate represents the maximum side lobe level of the current generation population optimal individual, the unit is dB, and the discrete differential evolution algorithm shown in the graph 5 optimizes the maximum side lobe level of the current generation population optimal individual from-9.7 dB to about-11.5 dB.
The above simulation experiments show that: the invention effectively optimizes the maximum sidelobe level of the sparse array by using the permutation-based discrete differential evolution algorithm, solves the problems of infeasible solution generated in the optimization process caused by binary coding and high sensitivity to preset parameters caused by random variation operation in the prior art, improves the sparse array optimization efficiency, and is a very practical sparse array optimization method.
Claims (2)
1. A sparse array optimization method based on a permutation discrete difference evolution algorithm is characterized in that a permutation discrete difference evolution algorithm is adopted, and coding, variation and cross operation are sequentially carried out on sparse array elements based on permutation positions; the method comprises the following steps:
(1) Constructing an optimization control objective function:
an optimization control target is constructed according to the relationship between the array element distribution of the sparse array antenna and the maximum side lobe level of an array directional diagram, and comprises the following steps:
wherein MSLL represents the maximum side lobe level of the sparse array antenna, max represents the maximum operation, theta represents the included angle between the array scanning beam and the array normal, S represents the side lobe range of the array directional diagram, and when the main lobe width of the array directional diagram is (-theta) 1 ，θ 1 ) When the angle is between-90 DEG and S DEG and theta 1 And theta 1 S is equal to or less than 90 degrees, | | represents absolute value operation, N represents the total number of array elements in the sparse array antenna, N is equal to or more than 3,n represents the position serial number of the array elements in the array antenna, N =1,2, (.) expressing exponential operation with a natural constant e as the base, j expressing an imaginary unit symbol, pi expressing a circumferential ratio, lambda expressing the operating wavelength of the array antenna, d n Representing the spacing of the elements in the array antenna, sin representing the sine taking operation, theta 0 Representing the angle between the direction of the array target beam and the array normal, f n The working state of the nth array element in the array antenna is shown when f n If =0, it means that the array element is idle, f n When the number is not less than 1, the array element works;
(2) Coding the sparse array elements based on the arrangement positions:
randomly generating an initial population comprising a plurality of groups of sparse array antenna distribution, and coding each array element in each group of sparse array antenna individuals;
the coding refers to that all integers in 1-N after random sequencing respectively represent
Of the N array elements, wherein,
representing the ith group of sparse array antennas in the initial population, i =1,2., np representing the size of the population;
(3) Screening the initial population to obtain optimal individuals:
3a) Determining the work of each array element in an individual by judging the array element coding size of each individual in the initial populationThe state is as follows: if V i,n Q is less than or equal to Q, then f i,n =0; if V i,n > Q, then f i,n =1, wherein V i,n Representing the code of the nth array element in the ith individual in the initial population, Q representing the number of idle array elements in the ith individual in the initial population, Q = N multiplied by gamma, and gamma representing the sparse rate of the sparse array;
3b) Calculating the maximum side lobe level of each individual in the initial population by using an optimal control objective function, selecting the minimum value of all the maximum side lobe levels, and reserving the individual corresponding to the minimum value as the optimal individual of the initial population;
(4) Carrying out mutation operation on the sparse array elements based on the arrangement positions:
performing variation operation based on the arrangement position on each individual in the contemporary population to obtain an updated contemporary population;
the mutation operation refers to the mutation operation of three random individuals x in the contemporary population j 、x p 、x k Performing array element position conversion operation to calculate x j And x p The position sequence number difference L of the middle and same coding array elements; x is to be k Respectively summing the position serial number of the middle array element code and L to obtain an updated current generation individual;
(5) Performing cross operation on the sparse array elements based on the arrangement positions:
performing cross operation based on arrangement positions on each individual in the updated current generation population to obtain a child generation population;
(6) And (3) carrying out selection operation on the filial generation individuals after the cross operation:
6a) Adopting the same method as the steps 3 a) and 3 b) for each individual in the filial generation population to obtain the optimal individual in the filial generation population;
6b) Taking the individuals with smaller maximum side lobe levels of the best individuals of the current generation population and the best individuals of the offspring population as the best individuals of the current generation population;
6c) Judging whether the maximum sidelobe level of the optimal individual of the current generation population meets an expected target or not, if so, executing the step (7); if not, executing the step (4);
(7) And (5) iteration is terminated to obtain an optimized sparse array:
and 3 a) judging the working state of each array element in the optimal individual of the contemporary population by adopting the same method as the step 3 a) to obtain the optimized sparse array.
2. The sparse array optimization method based on the permutation discrete differential evolution algorithm of claim 1, wherein the interleaving operation in step (5) refers to the operation of two random individuals x in the contemporary population m 、x l Performing array element position cross operation to generate two unequal random numbers C 1 、C 2 ，C 1 ∪C 2 Less than or equal to N, x m Middle position with serial number C 1 ～C 2 Is replicated in a descendant individual, at x l And deleting the corresponding array element codes, and copying the rest array element codes to the same filial generation individual.
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