CN109725294B - Radar array sparse optimization method based on improved genetic algorithm - Google Patents
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Abstract
The invention discloses a radar array sparse optimization method based on an improved genetic algorithm, which is based on a radar array which is a spirally distributed hemispherical array, so that array elements in the array are encoded, a mathematical model of the genetic algorithm is established, a population is initialized, cross variation operation is performed on chromosomes in the population, the optimal chromosome is selected, and an array element sparse mode corresponding to the optimal chromosome is used as an optimal arrangement mode of the array elements in the radar array. According to the radar array sparse optimization method based on the improved genetic algorithm, due to the fact that an array element sparse mode is adopted and the 3dB wave beam width is used as a constraint condition, the method has the advantages of being simple in array arrangement, simple in engineering implementation, capable of effectively reducing the complexity of a subsequent signal processing part and the like, and the spatial performance of the radar array is guaranteed.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a radar array sparse optimization method based on an improved genetic algorithm, which is suitable for a spiral-distribution hemispherical radar array with a large number of array elements, and optimizes and selects a plurality of array elements to compress data volume and reduce signal processing pressure by using the minimization of 3dB wave beam width as a constraint condition.
Background
Throughout the development process of radar, compared with the existing array radar with tens of thousands of array elements, the early single-array-element radar has the advantages of good directivity, strong interference clutter suppression capability, long detection distance, high detection precision and the like, and particularly has the advantages of wide beam viewing angle and the like in a hemispherical array. However, the early single-element radar has the defects of large volume, heavy weight, high power, high engineering implementation complexity, difficult signal processing and the like. In view of the above disadvantages, researchers have studied a sparse optimization method for hemispherical arrays to reduce the engineering complexity of radar arrays and optimize the radar correlation performance.
The sparse optimization method of the radar array is mainly divided into two types: the method is characterized in that firstly, an analytic method is adopted, the optimization is mainly carried out by utilizing a special mathematical relation between specific array distribution and excitation, the method is small in operand and easy to realize, but the general applicability is poor; and the intelligent optimization algorithm mainly aims at simulating some behaviors in the nature to realize the purpose of sparseness, has strong universality, and can optimize some performances of the radar array while sparseness is realized.
When the array is sparse, the number of array elements is reduced, the system complexity is reduced, and improper array arrangement mode may cause problems of beam broadening, side lobe level reduction, grating lobe occurrence and the like, so that the beam width, the side lobe level, the grating lobe and the like are used as constraint conditions while the number of array elements is optimized.
Disclosure of Invention
In order to solve the problems, the invention discloses a radar array sparse optimization method based on an improved genetic algorithm, which converts the physical problem of radar array sparse optimization into a mathematical model of the genetic algorithm for optimization, applies the genetic algorithm and takes 3dB beam width as a constraint condition to preferably select an optimal chromosome, and an array arrangement mode corresponding to the optimal chromosome is taken as the optimal arrangement mode of a radar array, so that the aims of strong radar array beam directivity and high spatial resolution are fulfilled.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a radar array sparse optimization method based on an improved genetic algorithm, the method comprising the following steps:
Step 2, initializing a population A: firstly, the number of array elements of the radar array needing to be sparse is setIs N, then N = S × γ spar Wherein γ is spar Is the radar array sparsity ratio; correspondingly, the codes of N array elements in the S array elements are 0, and the codes of the S array elements form a binary long string with the length of S and N0;
secondly, determining the length of the chromosome as S, wherein S encoding bits of the chromosome are provided, and the mth encoding bit corresponds to the encoding of the mth array element, so that the chromosome is a binary long string with the length of S and N encoding bits of 0;
finally, determining that the size of the population A is N, wherein N is an even number, the population A comprises N chromosomes, and each chromosome is a binary long string with the length of S and N coding bits of 0; and determining the cross probability, the mutation probability, the iteration times and the selection probability of the genetic algorithm of the population A.
Step 3, crossing: pairing n chromosomes in the population A according to any two chromosomes to obtain n/2 sets of chromosomes;
determining the crossing position of each chromosome group, selecting a crossing part, determining whether the chromosomes cross according to the crossing probability, obtaining two chromosomes of a new population B after the crossing operation of the two chromosomes of each group, and obtaining n chromosomes of the new population B after the crossing operation of all the chromosomes of the population A is finished;
and (4) computing n chromosomes in the population B by adopting a fixed-point random method, and obtaining n chromosomes of the new population C after computing.
And 4, mutation: determining a mutation position of each chromosome in the population C, selecting a mutation coding bit, determining whether to mutate according to the mutation probability, and obtaining a chromosome corresponding to the new population D after mutation operation of each chromosome;
and (4) computing the n chromosomes in the population D by adopting a fixed-point random method, and obtaining the n chromosomes of the new population E after the computation is completed.
And 5, calculating the fitness: and establishing a fitness function by taking the 3dB beam width of the radar array as a constraint condition, and further calculating the fitness value of each chromosome in the population E.
And 6, selecting and calculating: firstly, calculating the selection probability of each chromosome in the population E according to the fitness value of each chromosome in the population E calculated in the step 5;
secondly, calculating the cumulative probability of each chromosome according to the selection probability of each chromosome;
and finally, according to the accumulated probability of the chromosomes, preferably selecting n chromosomes in the population E for genetic next generation, and preferably obtaining n chromosomes of a new population F for n times.
And 7, optimizing a result: performing the operations from step 3 to step 6 on the population F, and iterating for G times;
and (5) optimizing n fitness values corresponding to n chromosomes in the new population obtained from the G iteration to the step (5), selecting the chromosome with the minimum fitness value as the optimal chromosome, and taking the binary long string of the optimal chromosome as the optimal sparse mode of the array elements in the radar array.
Compared with the prior art, the invention has the following advantages: (1) The sparse array is adopted, so that the method has the advantages of simple array arrangement, simple engineering realization and the like, and the complexity of a subsequent signal processing part is effectively reduced; (2) Because the spatial performance of the radar array is sensitive to the array arrangement mode of the array, in order to prevent the loss of the array spatial performance caused in the process of sparse array elements, the spatial performance of the radar array is effectively ensured by taking the 3dB wave beam width as a constraint condition.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a radar array sparse optimization method based on an improved genetic algorithm according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a fixed point random method according to an embodiment of the present invention;
FIG. 3 is a three-dimensional distribution diagram of the radar array according to the embodiment of the present invention before array element sparseness;
FIG. 4 is a diagram illustrating an X-Y distribution diagram of an array element in a radar array according to an embodiment of the present invention before being thinned;
FIG. 5 is a graph of the number of iterations of the improved genetic algorithm versus fitness value of an embodiment of the present invention;
FIG. 6 is a three-dimensional pattern of a radar array of an embodiment of the present invention prior to optimization;
FIG. 7 is a two-dimensional pattern of a radar array of an embodiment of the present invention prior to optimization;
FIG. 8 is an optimized three-dimensional pattern of a radar array according to an embodiment of the present invention;
FIG. 9 is an optimized two-dimensional pattern of a radar array in accordance with an embodiment of the present invention;
FIG. 10 is a comparison of the pre-and post-optimization azimuth slices of a radar array in accordance with an embodiment of the present invention;
FIG. 11 is a comparison graph of a radar array optimized pitch slice according to an embodiment of the present invention;
FIG. 12 is a three-dimensional distribution diagram of the radar array according to the embodiment of the present invention after array element sparsity optimization;
FIG. 13 is a diagram illustrating an X-Y distribution of array elements in a radar array after sparse optimization.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a schematic flowchart of a radar array sparsity optimization method based on an improved genetic algorithm according to an embodiment of the present invention.
As shown in fig. 1, the method for optimizing the sparsity of a radar array based on an improved genetic algorithm provided by the embodiment of the present invention includes the following steps:
In the step 1, the total number of the array elements in the radar array is S, corresponding spatial rectangular coordinates are distributed in space of each array element, and each array element is numbered to obtain a number 1, a number 2, \8230;, a number S. Each array element is then encoded, the encoding being 1 or 0, and the encoding being 1 or 0 being random.
Step 2, initializing the population A: firstly, the number of array elements needing to be thinned of the radar array is set to be N, and then N = S multiplied by gamma spar Wherein γ is spar The radar array sparsity ratio; correspondingly, the codes of N array elements in the S array elements are 0, and the codes of the S array elements form a binary long string with the length of S and N0;
secondly, determining the length of the chromosome as S, wherein S encoding bits of the chromosome are provided, and the mth encoding bit corresponds to the encoding of the mth array element, so that the chromosome is a binary long string with the length of S and N encoding bits of 0;
finally, determining that the size of the population A is N, wherein N is an even number, the population A comprises N chromosomes, and each chromosome is a binary long string with the length of S and N coding bits of 0; and determining the cross probability, the mutation probability, the iteration times and the selection probability of the genetic algorithm of the population A.
In this step 2, the sparsity ratio γ spar For setting, the binary long string of a chromosome in the population A corresponds to a sparse mode of array elements in the radar array. For example, if the first coding bit of the chromosome is 1, and the code of the array element numbered 1 is 1, the array element numbered 1 in the radar array is reserved; the 105 th coding bit of the chromosome is 0, correspondingly, the code of the number 105 array element is 0, and the number 105 array element in the radar array is sparse. In the subsequent genetic algorithm, the population is setEach chromosome in a is S in length and has N long binary strings with code bits of 0.
Step 3, crossing: pairing n chromosomes in the population A according to any two chromosomes to obtain n/2 groups of chromosomes;
determining the crossing position of each chromosome group, selecting a crossing part, determining whether the chromosomes cross according to the crossing probability, obtaining two chromosomes of the new population B after the crossing operation of the two chromosomes of each chromosome group is finished, and obtaining n chromosomes of the new population B after the crossing operation of all the chromosomes of each chromosome group is finished;
and (4) computing the n chromosomes in the population B by adopting a fixed-point random method, and obtaining the n chromosomes of the new population C after the computation is completed.
Wherein, the step 3 specifically comprises the following substeps:
(3a) Pairing: and selecting any two chromosomes in the population A as a set of chromosomes, and performing chromosome pairing.
In the process (3 a), the two chromosomes are arbitrarily selected. For example: for six chromosomes with numbers of 1,2, 3, 4, 5 and 6 respectively, numbers 1 and 2 can be selected as a first group of chromosomes to be paired, numbers 3 and 4 can be selected as a second group of chromosomes to be paired, and numbers 4 and 5 can be selected as a third group of chromosomes to be paired; it is also possible that the numbers 1 and 5 are grouped together as a first group of chromosomes, the numbers 2 and 4 are grouped together as a second group of chromosomes, and the numbers 3 and 6 are grouped together as a third group of chromosomes. In summary, the two chromosomes in a pair are freely combinable, but it must be ensured that each chromosome in population A is not selected repeatedly.
(3b) And (3) cross operation: for any set of chromosomes, a random number cross _ rand between 0 and 1 is randomly generated. If the random number cross _ rand is less than or equal to the cross probability, generating an integer cross _ point between 0 and S, and defining the coding bit from the first cross _ point to the second coding bit of the chromosome as the cross part of the two chromosomes of the group, and exchanging the codes of the two chromosomes of the group at the cross part to obtain a new two chromosomes which are used as the two chromosomes of the new population B; if the random number cross _ rand is greater than the crossover probability, the codes of the two chromosomes, which are two chromosomes of the new population B, are not interchanged.
In this (3 b) process, S is the length of the chromosome, and is the number of bits encoded in the chromosome, or corresponds to the total number of array elements in the radar array. The value of the cross probability is generally selected to be between 0.9 and 0.99. When the randomly generated random number cross _ rand is less than or equal to the cross probability, generating an integer cross _ point between 0 and S, and then taking the coding bit of the first cross _ point of the chromosome as the cross position of the two chromosomes of the set for cross operation, and defining the coding bits from the coding bit of the first cross _ point to the coding bit of the second cross as a cross part, and correspondingly exchanging the codes of the two chromosomes of the set on each coding bit of the cross part to form a new two chromosomes which are used as two chromosomes of a new population B; when the randomly generated random number cross _ rand is greater than the crossover probability, then all codes of the two chromosomes of the set are not interchanged, and the two chromosomes of the set serve as two chromosomes of the new population B.
(3c) And (3) operation results: and carrying out cross operation on the chromosomes of all the groups in the population A to obtain a new population B.
(3d) The n chromosomes in the population B are operated by adopting a fixed-point random method, the operation flow is shown in figure 2, and the specific process is as follows:
(3d1) Pairing: and (3) carrying out pairing on n chromosomes in the population B, wherein the pairing method is the same as that in the step (3 a), so as to obtain n/2 groups of chromosomes, and one of the two chromosomes in each group is set as a first chromosome, and the other chromosome is set as a second chromosome.
In the process of (3 d 1), firstly, n chromosomes in the population B are paired to obtain n/2 groups of chromosomes, and the pairing method adopted is completely the same as that in the process of (3 a). Secondly, a first chromosome and a second chromosome are respectively set for two chromosomes of any group in the n/2 groups of chromosomes, wherein which of the two chromosomes in each group is taken as the first chromosome is selected arbitrarily, one chromosome is taken as the first chromosome, and the other chromosome is taken as the second chromosome.
(3d2) Fixed-point operation step 1: for any set of chromosomes, a random integer num between the integers cross point-S is generated:
if the code of the first chromosome at the num coding bit is 1, or the code of the first chromosome at the num coding bit is 0 and the code of the second chromosome at the num coding bit is 0, the random integer num is abandoned, and another random integer num between the integers cross _ point-S is regenerated, and the process is circulated until when the code of the first chromosome at the num coding bit is 0 and the code of the second chromosome at the num coding bit is 1, the codes of the two chromosomes of the set at the num coding bit are respectively inverted, so that the corresponding first chromosome and the second chromosome in the new set are obtained.
In the (3 d 2) process, for any set of chromosomes, a random integer num between the integers cross _ point to S is randomly generated, if the code of the first chromosome at the num coding bit is 1, or the code of the first chromosome at the num coding bit is 0 and the code of the second chromosome at the num coding bit is 0, the random integer num is discarded, another integer num is randomly generated again, the judgment is performed, and the process is repeated until the generated random integer num meets the condition that the code of the first chromosome at the num coding bit is 0 and the code of the second chromosome at the num coding bit is 1, the codes of the two chromosomes of the set at the num coding bit are respectively inverted to obtain a first chromosome and a second chromosome of a new set, and the next operation is to be performed.
(3d3) And 2, fixed point operation: checking the number of 0 in the codes of the first chromosome and the second chromosome in the new group obtained in the fixed-point operation step 1, and if the number of 0 in the code of the first chromosome is larger than the specified number of 0, continuing 4 b) the fixed-point operation step 1; if the number of 0 in the code of the first chromosome is less than or equal to the specified number of 0, the fixed point operation is ended, and the corresponding first chromosome and the second chromosome in the new group are used as the two chromosomes of the new population C.
In the step (3 d 3), the first chromosome and the second chromosome in the new group obtained after the fixed point operation in the step (3 d 2) step 1 are checked, the number of 0 in the codes of the two new chromosomes is checked, the specified number of 0 is the number N of the array elements to be thinned set by the radar array, and then the number of 0 in the codes of the two new chromosomes is checked to ensure that the codes of the two new chromosomes have N0's and also to ensure the thinning rate of the array elements in the corresponding radar array. When the number of 0 in the code of the first chromosome is larger than the specified number of 0 in the operation, continuing the operation process of (3 d 2); if the number of 0's in the code of the first chromosome is equal to or less than the predetermined number of 0's, the fixed-point operation is terminated, and the first chromosome and the second chromosome in the new group to be examined are set as two chromosomes of the new population C.
(3d4) And (3) fixed point operation result: and (4) carrying out fixed-point random method operation on all sets of chromosomes in the population B, and obtaining n chromosomes of the new population C after the operation is finished.
And 4, mutation: determining a mutation position of each chromosome in the population C, selecting a mutation coding position, determining whether mutation occurs according to the mutation probability, and obtaining a chromosome corresponding to the new population D after mutation operation of each chromosome;
and (4) computing the n chromosomes in the population D by adopting a fixed-point random method, and obtaining the n chromosomes of the new population E after the computation is completed.
Wherein, the step 4 specifically comprises the following substeps:
(4a) Performing mutation operation: randomly generating a random number variable _ rand between 0 and 1 for any chromosome, if the random number variable _ rand is less than or equal to the variation probability, generating an integer variable _ point between 0 and S, and defining the coding bit of the second variable _ point of the chromosome as the variation coding bit, and negating the coding of the chromosome at the coding bit of the second variable _ point to obtain a new chromosome which is used as a chromosome of the new population D; if the random number vari _ rand is greater than the mutation probability, the code of the chromosome remains unchanged and the chromosome serves as a chromosome of the new population D.
In the process (4 a), the value of the mutation probability is generally selected to be between 0 and 0.1. When the randomly generated random number variable _ rand is less than or equal to the mutation probability, generating an integer variable _ point between 0 and S, taking the coding bit of the first variable _ point of the chromosome as a mutation position, and defining the coding bit of the first variable _ point of the chromosome as the mutation coding bit, and taking the coding of the chromosome at the coding bit of the first variable _ point as a inversion to obtain a new chromosome which is used as a chromosome of the new population D; when the random number vari _ rand is greater than the mutation probability, all codes of the chromosome remain unchanged and serve as a chromosome of the new population D.
(4b) And (3) operation results: and (4) carrying out mutation operation on all chromosomes in the population C to obtain a new population D.
(4c) And (4) computing the n chromosomes in the population D by adopting a fixed-point random method, wherein the computing method and the steps are the same as those in the step (3D), and obtaining a new population E after the computing is finished.
Step 5, calculating a fitness value: and establishing a fitness function by taking the 3dB beam width of the radar array as a constraint condition, and further calculating the fitness value of each chromosome in the population E.
In the step 5, the fitness value of any chromosome is calculated, firstly, a fitness function of the chromosome is established, the binary long string of the chromosome corresponds to a sparse mode of array elements in the radar array, and the 3dB wave beam width of the radar array is selected as a constraint condition according to the requirement, so that the fitness function of the ith chromosome in the population E is established
Wherein i =1,2, \8230;, S, calculating the fitness value p of the ith chromosome from the fitness function i The method specifically comprises the following substeps:
(5a) According to the formula
A directional pattern function of the radar array is calculated.
Wherein the content of the first and second substances,
is the angle of the azimuth angle, theta is the angle of the pitch angleThe degree of the magnetic field is measured,
angle of target azimuth, θ 0 Is the angle of a target pitch angle, S is the total number of array elements in the radar array, H represents conjugate transpose,
represents the product of Han De Monde, h i Is a binary long string of the ith chromosome, L m Is the spatial position of the m-th array element in the radar array, and L m ＝[x m y m z m ] T M is more than or equal to 1 and less than or equal to s, r is the propagation direction of a beam of narrow-band electromagnetic waves in space, and
for spatial position pointing of m-th array element
Are weighted values of (a) and
is the m-th array element directional diagram function, and
substituting the known conditions into the formula (5-1) to obtain the target direction
Independent variable of direction
And the directional pattern function of theta
(5b) Will theta 0 Substituting target pointing
Independent variable of direction
And the directional pattern function of theta
Obtaining a target orientation
About the direction
Azimuthal direction directional diagram function of independent variable
And a formula
Refer to a target point
The azimuth of the direction is 3dB beamwidth. Wherein beta is azi Is directed to a target
About of direction
Azimuthal direction directional diagram function of independent variable
The right side of the highest point on the corresponding azimuth directional diagram is lowered by an angle alpha corresponding to 3dB azi Is pointed to by a target
About the direction
Azimuthal direction directional diagram function of independent variable
The left side of the highest point on the corresponding azimuth directional diagram is lowered by an angle corresponding to 3dB, and the known data is substituted into the target direction
About the direction
Azimuthal direction directional diagram function of independent variable
The target direction represented by the formula (5-2) can be obtained
Azimuth of direction is a value of 3dB beamwidth.
(5c) Will be provided with
Pointing to substituted target
Independent variable of direction
And theta as a function of the antenna pattern
Obtaining a target orientation
Pitch direction diagram function of direction with respect to theta independent variable
And a formula
Refer to a target point
The elevation of the direction is towards the 3dB beamwidth. Wherein beta is ele Is pointed to by a target
Pitch direction diagram function of direction with respect to theta independent variable
The right side of the highest point on the corresponding pitching directional diagram is lowered by an angle alpha corresponding to 3dB ele Is pointed to by a target
Function of direction with respect to theta argument
Corresponding elevation directional diagram is decreased by an angle corresponding to 3dB at the left side of the highest point, and known data are substituted into the target direction
Pitch direction directional diagram function of direction with respect to theta independent variable
The target direction represented by the formula (5-3) can be obtained as
The elevation of the direction is to a value of 3dB beamwidth.
(5d) According to the formula
Calculating the fitness value p of the ith chromosome i Further calculating the adaptation of each chromosome in the population EAnd (4) measuring values.
And 6, selecting and calculating: firstly, calculating the selection probability of each chromosome in the population E according to the fitness value of each chromosome in the population E calculated in the step 5;
secondly, calculating the cumulative probability of each chromosome according to the selection probability of each chromosome;
and finally, according to the accumulated probability of the chromosomes, preferably selecting n chromosomes in the population E for genetic next generation, and preferably obtaining n chromosomes of a new population F for n times.
In step 6, the calculation of the selection probability of chromosomes in the population E by using the roulette selection method specifically includes the following substeps:
(6a) Fitness value p for ith chromosome in population E i The following transformations are made:
p c,i ＝M-p i (6-1)
in the formula, p c,i Expressing fitness value p of ith chromosome i Making a new fitness value after transformation; m is a value of (max (p) i ) And ∞) is determined. And (4) calculating according to the formula (6-1) to obtain new fitness values of n chromosomes in the population E.
(6b) Calculating the selection probability q of the ith chromosome in the population E according to the following formula i ：
Wherein n is the size of the population E, and the selection probability values of n chromosomes in the population E are calculated according to a formula (6-2).
(6c) Calculating the cumulative probability of the ith chromosome in the population E according to the following formula:
and (4) calculating the cumulative probability values of the n chromosomes in the population E according to the formula (6-3).
(6d) Preferred for the inheritance of a chromosome of the next generation:
randomly generating a random number, choice _ rand, between 0 and 1 when C i ≤choice_rand≤C i+1 Then, the ith chromosome in the population E is selected as the chromosome for the next generation of inheritance.
In this (6 d) process, n times of operations are performed, and n chromosomes for genetic next generation are preferably selected and used as n chromosomes of the new population F.
And 7, optimizing a result: performing the operations from the step 3 to the step 6 on the population F, and iterating for G times in the way;
and G, iterating to the step 5 for the G time to obtain fitness values of n chromosomes in the new population, selecting the chromosome with the minimum fitness value as an optimal chromosome, and taking the binary long string of the optimal chromosome as an optimal sparse mode of array elements in the radar array.
In step 7, as can be seen by referring to the relationship between the iteration number and the fitness value shown in fig. 5, as the iteration number increases, the fitness value of the chromosome slightly fluctuates within a certain range, and the fitness function of the chromosome approaches convergence, so that the optimal result finally obtained by iterative computation is reliable.
According to the radar array sparse optimization method based on the improved genetic algorithm, array elements in the array are sparse, so that not only is array arrangement simple and engineering realization simple, but also the complexity of a subsequent signal processing part is reduced; the method optimizes the sparse mode of the array elements in the radar array by using the improved genetic algorithm, takes the 3dB wave beam width as a constraint condition, effectively ensures the spatial performance of the array, and optimizes the optimal sparse mode of the array elements in the array, so that the radar detection angular resolution is greatly improved.
The effect of the method provided by the embodiment of the invention is verified through a simulation experiment as follows:
1. simulation experiment environment and data:
the experimental environment is as follows: inter (R) Core (TM) i5-6500CPU @3.20HGz, 64-bit Windows operating system and MATLAB 2016b simulation software.
Experimental data: the total number S of array elements of the radar array is 200, and the iteration number G is 500The sparsity ratio is 0.15, the population size n is 200, the cross probability is 0.95, the variation probability is 0.03, and the angle of the azimuth angle
The value range is-90 degrees, the angle theta of the pitch angle is 0-90 degrees, and the target direction is
Is (0 deg., 20 deg.) and M is 15.
2. Simulation experiment results:
according to a spherical coordinate formula of the radar array at the spatial position:
obtaining a three-dimensional distribution diagram before array elements in the radar array are sparse as shown in FIG. 3, wherein theta m The angle representing the pitch angle of the m-th array element,
and the azimuth angle of the mth array element is represented, and S is the total number of the array elements in the radar array.
Assuming that the spherical radius is R, converting the spherical coordinates into rectangular coordinates can obtain the formula:
wherein x is m The coordinate of the m-th array element in the radar array on the x axis of a rectangular coordinate system is represented, y m The coordinate of the m-th array element on the y-axis of the rectangular coordinate system is expressed, z m And representing the seating of the m-th array element on the z-axis of the rectangular coordinate system. According to the formula (2-2), an X-Y dimensional distribution diagram before array element sparseness in the radar array shown in FIG. 4 can be obtained.
The sparsity ratio is selected to be 0.15, and a three-dimensional distribution diagram after array element sparsity optimization in the radar array shown in fig. 12 and an X-Y dimensional distribution diagram after array element sparsity optimization in the radar array shown in fig. 13 are respectively obtained according to formulas (2-1) and (2-2). Fig. 12 and fig. 13 are respectively corresponding to fig. 3 and fig. 4, and 30 array elements in the radar array are reduced after sparse optimization, relatively speaking, the arraying is simplified, the engineering is simplified, and the complexity of the subsequent signal processing part is reduced.
According to the directional diagram function formulas (6-1), (2-1) and (2-2) of the radar array, a three-dimensional directional diagram before optimization of the radar array and a two-dimensional directional diagram before optimization of the radar array shown in fig. 6 and 7 are obtained through simulation calculation, and a three-dimensional directional diagram after optimization of the radar array and a two-dimensional directional diagram after optimization of the radar array shown in fig. 8 and 9 are obtained through simulation calculation, the 3dB beam widths of the azimuth direction and the elevation direction are respectively compared with those of the 3dB beam widths of the azimuth direction and the elevation direction of the radar array shown in fig. 8 and 9, and the 3dB beam widths of the azimuth direction and the elevation direction of the radar array shown in fig. 10 and 11 are particularly compared with those of the 3dB beam widths of the azimuth direction and the elevation direction of the radar array shown in fig. 7 and 9, so that the 3dB beam widths of the azimuth direction before sparse optimization of the radar array are 16.36 degrees, and the 3dB beam widths of the azimuth direction after sparse optimization of the radar array are 13 degrees, so that the 3dB of the sparse optimization of the radar array is reduced by 3.36 degrees; according to the graph 11, the pitch 3dB beam width before and after the radar array sparse optimization is 4.19 °, the pitch 3dB beam width after the radar array optimization is 3.77 °, and the pitch 3dB beam width before and after the radar array sparse optimization is reduced by 0.42 °. Therefore, through the sparse optimization of the array elements in the radar array, the number of the array elements in the array is reduced, and meanwhile, the 3dB beam width of a directional diagram of the radar array is also reduced, so that the directivity of radar beams is enhanced, and the spatial resolution is improved.
According to simulation experiments, the method disclosed by the invention not only sparsely removes part of array elements and reduces the system complexity, but also effectively reduces the beam width and improves the radar beam performance on the basis of the existing array node, thereby verifying the effectiveness and reliability of the method.
Those of ordinary skill in the art will understand that: all or part of the steps for realizing the method embodiments can be completed by hardware related to program instructions, the program can be stored in a computer readable storage medium, and the program executes the steps comprising the method embodiments when executed; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (8)
1. A radar array sparse optimization method based on an improved genetic algorithm is characterized by comprising the following steps:
step 1, encoding: the radar array is a semispherical array with S array elements in total number and spirally distributed, firstly, each array element is numbered, and the spatial rectangular coordinate of the mth array element in spatial distribution is set as (x) m ,y m ,z m ) The mth array element is numbered m, wherein m =1,2, \8230, S; secondly, coding each array element, wherein the coding of 1 indicates that the array element corresponding to the number is reserved, and the coding of 0 indicates that the array element corresponding to the number is sparse;
step 2, initializing a population A: firstly, the number of array elements required to be sparse of the radar array is set to be N, and then N = S multiplied by gamma spar Wherein γ is spar Is the radar array sparsity ratio; correspondingly, the codes of N array elements in the S array elements are 0, and the codes of the S array elements form a binary long string with the length of S and N0;
secondly, determining the length of the chromosome as S, wherein S encoding bits of the chromosome are provided, and the mth encoding bit corresponds to the encoding of the mth array element, so that the chromosome is a binary long string with the length of S and N encoding bits of 0;
finally, determining that the size of the population A is N, wherein N is an even number, the population A comprises N chromosomes, and each chromosome is a binary long string with the length of S and N coding bits of 0; determining the cross probability, the variation probability, the iteration times and the selection probability of the genetic algorithm of the population A;
step 3, crossing: pairing n chromosomes in the population A according to any two chromosomes to obtain n/2 sets of chromosomes;
determining the crossing position of each group of chromosomes, selecting a crossing part, determining whether the chromosomes cross according to the crossing probability, obtaining two chromosomes of the new population B after the crossing operation of the two chromosomes of each group, and obtaining n chromosomes of the new population B after the crossing operation of all the chromosomes of the group is completed;
calculating n chromosomes in the population B by adopting a fixed-point random method, and obtaining n chromosomes of a new population C after the calculation is finished;
and 4, mutation: determining a mutation position of each chromosome in the population C, selecting a mutation coding bit, determining whether to mutate according to the mutation probability, and obtaining a chromosome corresponding to the new population D after mutation operation of each chromosome;
calculating n chromosomes in the population D by adopting a fixed-point random method, and obtaining n chromosomes of a new population E after the calculation is finished;
step 5, fitness calculation: establishing a fitness function by taking the 3dB wave beam width of the radar array as a constraint condition, and further calculating the fitness value of each chromosome in the population E;
and 6, selecting and calculating: firstly, calculating the selection probability of each chromosome in the population E according to the fitness value of each chromosome in the population E calculated in the step 5;
secondly, calculating the cumulative probability of each chromosome according to the selection probability of each chromosome;
finally, according to the accumulated probability of the chromosomes, n chromosomes in the population E are selected for inheriting the next generation of chromosomes, and n chromosomes of the new population F are obtained for n times;
and 7, optimizing a result: performing the operations from step 3 to step 6 on the population F, and iterating for G times;
and (5) optimizing n fitness values corresponding to n chromosomes in the new population obtained from the G iteration to the step (5), selecting the chromosome with the minimum fitness value as the optimal chromosome, and taking the binary long string of the optimal chromosome as the optimal sparse mode of the array elements in the radar array.
2. The method for optimizing the sparsity of the radar array based on the improved genetic algorithm, as claimed in claim 1, wherein the cross algorithm in the step 3 is a single-point cross algorithm, and the sub-steps of the algorithm are as follows:
2a) Pairing: pairing n chromosomes in the population A according to any two chromosomes to obtain n/2 groups of chromosomes;
2b) And (3) cross operation: randomly generating a random number cross _ rand between 0 and 1 for any set of chromosomes: if the random number cross _ rand is less than or equal to the cross probability, generating an integer cross _ point between 0 and S, and defining the coding bit from the first cross _ point to the second coding bit of the chromosome as the cross part of the two chromosomes of the group, and exchanging the codes of the two chromosomes of the group at the cross part to obtain a new two chromosomes which are used as the two chromosomes of the new population B;
if the random number cross _ rand is larger than the cross probability, the codes of the two chromosomes are not interchanged, and the two chromosomes are used as two chromosomes of the new population B;
2c) And (3) operation results: and carrying out cross operation on the chromosomes of all the groups in the population A to obtain a new population B.
3. The method for optimizing the sparsity of a radar array based on an improved genetic algorithm as claimed in claim 1, wherein the cross probability is selected from a range of 0.9 to 0.99.
4. The method for optimizing the sparsity of the radar array based on the improved genetic algorithm, according to claim 1, is characterized in that the specific sub-steps of the fixed point stochastic method algorithm in the steps 3 and 4 are as follows:
4a) Pairing: pairing n chromosomes in the population B or the population D according to any two chromosomes to obtain n/2 groups of chromosomes, and setting one of the two chromosomes in each group as a first chromosome and the other chromosome as a second chromosome;
4b) Fixed point operation step 1: generating a random integer num between the integers cross _ point-S for any group of chromosomes in the population B or the population D:
if the coding of the first chromosome at the num coding position is 1, or the coding of the first chromosome at the num coding position is 0 and the coding of the second chromosome at the num coding position is 0, abandoning the random integer num, and regenerating a random integer num between the other integers cross _ point-S, and circulating in such a way until the coding of the first chromosome at the num coding position is 0 and the coding of the second chromosome at the num coding position is 1, respectively negating the coding of the two chromosomes of the group at the num coding position, thereby obtaining the corresponding first chromosome and the second chromosome in the new group;
4c) And 2, fixed point operation: checking the number of 0's in the codes of the first chromosome and the second chromosome in the new set obtained in the fixed-point operation step 1:
if the number of 0 in the code of the first chromosome is larger than the specified number of 0, continuing 4 b) the fixed-point operation step 1;
if the number of 0 in the code of the first chromosome is less than or equal to the specified number of 0, the fixed point operation is ended, and the corresponding first chromosome and the corresponding second chromosome in the new group are used as two chromosomes of a new population C or a new population E;
4d) And (3) fixed point operation result: and (4) carrying out fixed-point random method operation on all sets of chromosomes in the population B or the population D, and obtaining n chromosomes of the new population C or the new population E after the operation is finished.
5. The method for optimizing the sparsity of the radar array based on the improved genetic algorithm as claimed in claim 1, wherein the mutation algorithm in step 4 adopts a single-point mutation algorithm, and the specific sub-steps of the algorithm are as follows:
5a) And (3) mutation operation: randomly generating a random number vari _ rand between 0 and 1 for any chromosome in the population C:
if the random number variable _ rand is less than or equal to the variation probability, generating an integer variable _ point between 0 and S, and defining the coding bit of the second variable _ point of the chromosome as the variation coding bit, and negating the coding of the chromosome at the coding bit of the second variable _ point to obtain a new chromosome which is used as a chromosome of the new population D;
if the random number vari _ rand is greater than the mutation probability, the code of the chromosome remains unchanged, and the chromosome is used as a chromosome of the new population D;
5b) And (3) operation results: and (4) carrying out mutation operation on all chromosomes in the population C to obtain n chromosomes of the new population D.
6. The method of claim 1, wherein the mutation probability is selected from a range of 0 to 0.1.
7. The method for optimizing the sparsity of the radar array based on the improved genetic algorithm, according to claim 1, wherein the fitness calculation in the step 5 is specifically performed in the following sub-steps:
7a) According to the formula
A directional pattern function of the radar array is calculated,
wherein, the first and the second end of the pipe are connected with each other,
is the angle of the azimuth angle, theta is the angle of the pitch angle,
angle of target azimuth, θ 0 Is the angle of a target pitch angle, S is the total number of array elements in the radar array, H represents conjugate transpose,
represents the product of Han De Monde, h i Is a binary long string of the ith chromosome, L m Is the spatial position of the m-th array element in the radar array, and L m ＝[x m y m z m ] T M is more than or equal to 1 and less than or equal to s, r is the propagation direction of a beam of narrow-band electromagnetic waves in space, and
for spatial position pointing of m-th array element
Weighted value of, and
is the m-th array element directional diagram function, and
substituting the above known conditions into the formula
The target direction can be obtained
Independent variable of direction
And the directional pattern function of theta
7b) Will theta 0 Substituting target pointing
Independent variable of direction
And the directional pattern function of theta
Obtaining a target orientation
About of direction
Azimuthal direction directional diagram function of independent variable
And a formula
Refer to a target point
Azimuth of direction 3dB beamwidth:
wherein, beta azi Is directed to a target
About the direction
Azimuth directional pattern function of independent variable
The right side of the highest point on the corresponding azimuth directional diagram is reduced by an angle alpha corresponding to 3dB azi Is pointed to by a target
About of direction
Azimuthal direction directional diagram function of independent variable
The left side of the highest point on the corresponding azimuth directional diagram is lowered by an angle corresponding to 3dB, and the known data is substituted into the target direction
About the direction
Azimuth directional pattern function of independent variable
Then the formula can be obtained
Target pointing of the representation
Azimuth of direction a value of 3dB beamwidth;
7c) Will be provided with
Substituting target pointing
Independent variable of direction
And theta as a function of the antenna pattern
Obtaining a target orientation
Pitch direction directional diagram function of direction with respect to theta independent variable
And a formula
Pointing to a target
Elevation of direction to 3dB beamwidth:
wherein, beta ele Is pointed to by a target
Pitch direction directional diagram function of direction with respect to theta independent variable
The right side of the highest point on the corresponding pitching directional diagram is lowered by an angle alpha corresponding to 3dB ele Is pointed to by a target
Function of direction with respect to theta argument
Corresponding elevation directional diagram is decreased by an angle corresponding to 3dB at the left side of the highest point, and known data are substituted into the target direction
Pitch direction diagram function of direction with respect to theta independent variable
Then the formula can be obtained
The object represented is pointed at
The elevation of the direction is a numerical value of 3dB beamwidth;
7d) According to the formula
Calculating the fitness value p of the ith chromosome in the population E i And further calculating the fitness value of each chromosome in the population E.
8. The method for optimizing the sparsity of a radar array based on an improved genetic algorithm as claimed in claim 1, wherein the selective calculation in step 6 adopts a roulette selection mode to calculate the selective probability, and the specific calculation sub-steps are as follows:
8a) Fitness value p for ith chromosome in population E i The following transformations are made:
p c,i ＝M-p i
in the formula, p c,i Representing the fitness value p of the ith chromosome in population E c,i Making a new fitness value after transformation; m is a value in the range of (max (p) i ) Infinity), calculating a new fitness value of n chromosomes in the population E according to a formula;
8b) Calculating the selection probability q of the ith chromosome in the population E according to the following formula i ：
Wherein n is the size of the population E, and the selection probability values of n chromosomes in the population E are calculated according to the formula;
8c) Calculating the cumulative probability of the ith chromosome in the population E according to the following formula:
calculating the cumulative probability values of n chromosomes in the population E according to the formula;
8d) Preferred for the inheritance of the next generation of chromosomes:
randomly generating a random number choice _ rand between 0 and 1 when C i ≤choice_rand≤C i+1 Then, the ith chromosome in the population E is selected as the chromosome for the next generation of inheritance.
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