CN112465142A - Optical phased array antenna sidelobe suppression method under genetic algorithm framework - Google Patents

Optical phased array antenna sidelobe suppression method under genetic algorithm framework Download PDF

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CN112465142A
CN112465142A CN202011322702.3A CN202011322702A CN112465142A CN 112465142 A CN112465142 A CN 112465142A CN 202011322702 A CN202011322702 A CN 202011322702A CN 112465142 A CN112465142 A CN 112465142A
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CN112465142B (en
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李明飞
袁梓豪
刘院省
邓意成
王学锋
赵琳琳
孙晓洁
董鹏
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Beijing Aerospace Control Instrument Institute
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/12—Computing arrangements based on biological models using genetic models
    • G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
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Abstract

The invention belongs to the technical field of optimization algorithms of optical phased array antennas, and particularly relates to a sidelobe suppression method of an optical phased array antenna under a genetic algorithm framework. The invention discloses a sidelobe suppression method of an optical phased array antenna under a genetic algorithm frame, which comprises the steps of establishing a coordinate optimized data set by designing a concentric ring arrangement antenna array set, randomly extracting an initial coordinate position from the set according to the number of required antennas, optimizing the sidelobe suppression of the optical phased array antenna coordinate by adopting the genetic algorithm frame, realizing high-efficiency calculation of a fitness function through fast Fourier transform, designing a chromosome gene point-by-point crossing method to improve the optimization efficiency, realizing a globally optimal light field arrangement scheme by utilizing variation and the like, and solving the problem of the maximization of the energy of a main beam of the optical phased array antenna. The method has application value in the fields of optical phased array radar, laser communication, laser beam synthesis and the like.

Description

Optical phased array antenna sidelobe suppression method under genetic algorithm framework
Technical Field
The invention belongs to the technical field of optimization algorithms of optical phased array antennas, and particularly relates to a sidelobe suppression method of an optical phased array antenna under a genetic algorithm framework.
Background
The optical antenna array configuration optimization technology is a new technology which is proposed along with the maturity of the optical phased array antenna technology in recent years, such as the performance indexes of coherent light sources such as an optical fiber laser and a semiconductor laser are improved, and the cost is greatly reduced, so that the practicability of the optical antenna array becomes possible. In the technologies of optical phased array radar, laser communication, laser beam synthesis, quantum imaging and the like, the arrangement optimization of optical antennas determines the concentration of main beam (main lobe) energy in a light field, and the method is a core technology and a key technology in the technical field. The optical band wavelength is short, the optical antenna is limited by the process, the distance is larger than the wavelength, so the optical antenna is different from the constraint condition and the calculation mode of the optimization of the microwave antenna, but the optimization method of the optical antenna is similar to the sparse array principle of the microwave antenna, and the optimization can be carried out by adopting a genetic algorithm, a particle swarm algorithm, an ant colony algorithm, an iterative Fourier algorithm and the like. In the existing optimization method for optical antenna array arrangement, problems still remain to be solved.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method overcomes the defects of the prior art, provides a side lobe suppression method of the optical phased array antenna under a genetic algorithm framework, can obtain an optical antenna arrangement scheme with high concentration of light field main lobe light beam energy and lowest peak value of side lobe light beams, improves the light beam quality used in the technologies of optical phased array radar, laser communication, laser beam synthesis, quantum imaging and the like, and achieves the purpose of improving the system performance index.
The solution of the invention is: aiming at the problems that the traditional optimization method adopts a polygonal antenna array, such as a rectangular array, a hexagonal array and the like, and the horizontal and vertical orthogonal directions cannot be simultaneously optimized, and the problem that the calculation efficiency of an optical physical field is low point by point, a solution is provided, and a new intersection strategy is provided to improve the optimization speed of the algorithm.
The initialized gene (coordinate) set U is a concentric ring array, has higher dimension rotational symmetry compared with a rectangle and a hexagon, and solves the problem that the horizontal and vertical orthogonal directions of the rectangle and hexagon arrays cannot be optimized simultaneously. Initializing a population, randomly extracting genes (coordinates) to form chromosomes (coordinate sets) of individuals, and realizing relatively low side lobe initial values; the method is suitable for application function calculation, and the optical field intensity is obtained by performing Fast Fourier Transform (FFT) modulus extraction on the electric field intensity of the light source plane, so that the problem of low calculation efficiency caused by point-by-point calculation according to an optical physical field is solved; the method is suitable for evaluation of a response function, the application degree functions of the system are sorted, and the optimal result is selected from small to large through sorting to be inherited, namely crossed; the crossing operation adopts the crossing exchange of chromosome (coordinate set) genes (coordinates) for any two pairs of individuals, the number of the genes (coordinates) of the reciprocal chromosome (coordinate set) is gradually exchanged point by point, namely 1 gene (coordinate) is exchanged for the first time, 2 genes (coordinates) are exchanged for the second time, and the like until N-1 times of the interchange is carried out, the interchange of all the genes (coordinates) is completed, if the values of the genes (coordinates) are repeated, the values of the genes (coordinates) are randomly extracted from the complementary sets of the set U and the set { Pos (N-1) and Pos (N) } intersection to replace the repeated genes (coordinates), the crossing of all the genes (coordinates) is realized, and the number of the groups after the crossing is changed into N0Compared with the traditional genetic algorithm for fixing gene (coordinate) proportion crossing, the method has the advantages that the iteration number required for reducing the side lobe is less, and the optimization speed is higher. The variation adopts a fixed variation individual number MmuteThe variant individuals are derived from randomly extracting N genes (coordinates) from the set U, and selecting M in the later ordermuteAnd (4) realizing gene variation (coordinate replacement) by each individual, finally judging whether the gene is the final output result according to whether the genetic algebra is met or not, obtaining the final chromosome (coordinate set) gene (coordinate), and realizing optimization of optical antenna array arrangement.
A sidelobe suppression method of an optical phased array antenna under a genetic algorithm framework comprises the following steps:
step S1, initializing a gene (coordinate) set, setting the number M of circular rings, and setting the number k of optical antennas placed in each circular ring1，k2，k3，...km，...，kM(ii) a Setting the radius of the mth circular ring of the optical antenna arrangement set to be RmLet the mth ring place kmAn optical antenna, each optical antenna coordinate interval d on each ringmThe radius of the circular ring and the number of coordinate points per ring, namely the number k of the optical antennasmThe following relationships exist:
dm＝2RmSin(π/km) (1)
minimum coordinate spacing dmin＝min{dm,ΔRmWherein Δ Rm＝Rm-Rm-1The coordinate set U is set according to specific task requirements;
step S2, initializing population: randomly extracting N genes (coordinates) from the set U to form chromosomes (coordinate set) of the individual, and repeating NpopNext as the initial population { Pos (1), Pos (2), Pos (3), …, Pos (N)pop)}，NpopFor the number of individuals in the population, Pos (n) corresponds to a two-dimensional set of spatial coordinates
Figure BDA0002793436970000031
Figure BDA0002793436970000032
N is the number of genes (coordinates), corresponding to the number of the optical antennas, and U represents a coordinate set of the optical antennas;
step S3, calculating a fitness function of the individuals in the initial population: according to { Pos (1), Pos (2), Pos (3), …, Pos (N)pop) The distribution of optical antennas corresponding to individual genes (coordinates) in the element is listed as the electric field intensity expressions of the light source plane respectively
Figure BDA0002793436970000033
Said
Figure BDA0002793436970000034
Is a light source plane space coordinate, and a modulus is obtained through Fast Fourier Transform (FFT)
Figure BDA0002793436970000035
Obtaining an optical field intensity expression
Figure BDA0002793436970000036
Said
Figure BDA0002793436970000037
Is the space coordinate of the light field irradiation plane to find the intensity plane
Figure BDA0002793436970000038
Peak value, denoted as main lobe peak value I(i) mls(ii) a Plane of strength
Figure BDA0002793436970000039
After the peak area is removed, the maximum value of the residual area is found and is recorded as a side lobe peak value I(i) sl(ii) a The ratio of the side lobe peak value and the main lobe peak value is obtained and is the fitness function value of the individual and is recorded as
Figure BDA00027934369700000310
The above i represents the number of individuals in the current group and the sequence number of the current calculation, i is 1,2,3, …, Npop；
Step S4, fitness function evaluation: the fitness function value of the individual
Figure BDA00027934369700000311
The original chromosomes (coordinate sets) are replaced by sequences from small to large according to fitness function values after the sequences are sorted from small to large, wherein the sequences are { nPos (1), nPos (2), nPos (3), … and nPos (N)pop) }, notation nPos () is used to distinguish individual chromosomes (coordinate sets) Pos () before sorting;
step S5, individual selection: truncating N in step S40Individual chromosomes (coordinate set) { nPos (1), nPos (2), nPos (3), …, nPos (N)0) N of said0≤Npop；
Step S6, cross: the chromosomes (coordinate sets) { nPos (1), nPos (2), nPos (3), …, nPos (N) obtained in step S50) Pairwise pairing of individuals in the { nPos (N-1) }, nPos (N) }, wherein N is 2,3, 4, … and N0Performing cross exchange of chromosome (coordinate set) genes (coordinates) on any two pairs of individuals,
Figure BDA00027934369700000312
Figure BDA00027934369700000313
the number of genes (coordinates) of the reciprocal chromosome (coordinate set) is gradually interchanged point by point, namely the 1 st gene (coordinate) is interchanged for the first time,
Figure BDA0002793436970000041
Figure BDA0002793436970000042
interchanging 2 genes (coordinates) at 2 nd time,
Figure BDA0002793436970000043
Figure BDA0002793436970000044
the above exchanges are carried out in sequence until the N-1 exchange is completed,
Figure BDA0002793436970000045
Figure BDA0002793436970000046
m is 2,3, 4, … and N in sequence0And the above-mentioned steps are repeated,
Figure BDA0002793436970000047
Figure BDA0002793436970000048
interchanging 2 genes (coordinates) at 2 nd time,
Figure BDA0002793436970000049
Figure BDA00027934369700000410
sequentially, …, until N-1 interchanges,
Figure BDA00027934369700000411
Figure BDA00027934369700000412
complete the interchange of all genes (coordinates).
If the value of the gene (coordinate) is repeated, randomly extracting the value of the gene (coordinate) from the complementary set intersected by the set U and the set { Pos (N-1), Pos (N)) } to replace the repeated gene (coordinate), realizing the intersection of all the genes (coordinate), and changing the number of the population into N after all the { Pos (N-1), Pos (N)) } are intersected0X (N-1), re-population as follows:
group 1: { xPos(1)(1)，xPos(1)(2)，xPos(1)(3)}，…，xPos(1)(N0)}；
Group 2: { xPos(2)(1)，xPos(2)(2)，xPos(2)(3)}，…，xPos(1)(N0)}；
Group 3: { xPos(3)(1)，xPos(3)(2)，xPos(3)(3)，…，xPos(3)(N0)}；
，…，
Group N-1: { xPos(N-1)(1)，xPos(N-1)(2)，xPos(N-1)(3)}，…，{xPos(N-1)(N0)}；
Step S7, mutation: setting N0Then, the number of individuals M of the variation is setmuteThe variant individuals are derived from randomly extracting N genes (coordinates) from the set U to form individuals Pos (i), and repeating MmuteNext, a population of individuals with 1 set of variations { mPos (1), mPos (2), mPos (3), …, mPos (M)mute) }, said Mmute≤N0，MmuteRepeating the N-1 mutation processes as a natural number to obtain N-1 groups of mutation populations:
group 1: { mPos(1)(1),mPos(1)(2),mPos(1)(3),…,mPos(1)(Mmute)}，
Group 2: { mPos(2)(1),mPos(2)(2),mPos(2)(3),…,mPos(2)(Mmute)}，
Group 3: { mPos(3)(1),mPos(3)(2),mPos(3)(3),…,mPos(3)(Mmute)}，
，…，
Group N-1: { mPos(N-1)(1),mPos(N-1)(2),mPos(N-1)(3),…,mPos(N-1)(Mmute)}；
Recombining the N-1 group of variant individuals with the N-1 group of individual chromosomes (coordinate sets) obtained in step S6 into an N-1 group population:
group 1: { xPos(1)(1)，xPos(1)(2)，xPos(1)(3)}，…，xPos(1)(N0)，mPos(1)(1),mPos(1)(2),mPos(1)(3),…,mPos(1)(Mmute)}；
Group 2: { xPos(2)(1)，xPos(2)(2)，xPos(2)(3)}，…，xPos(1)(N0)，mPos(2)(1),mPos(2)(2),mPos(2)(3),…,mPos(2)(Mmute)}；
Group 3: { xPos(3)(1)，xPos(3)(2)，xPos(3)(3)，…，xPos(3)(N0)，mPos(3)(1),mPos(3)(2),mPos(3)(3),…,mPos(3)(Mmute)}；
，…，
Group N-1: { xPos(N-1)(1)，xPos(N-1)(2)，xPos(N-1)(3)}，…，{xPos(N-1)(N0)，mPos(N-1)(1),mPos(N-1)(2),mPos(N-1)(3),…,mPos(N-1)(Mmute)}；
The number of individuals in each group after recombination is NpopObtaining N from crossing in each group after recombination0Individual, obtaining M from variationmuteAnd (4) respectively.
Step S8, determining whether the number of genetic generations N is up to a set numbergThe requirement of (1) is added to the genetic algebra every time steps S3-S7 are executed, and if the current genetic algebra is less than the set NgThen, the method continues to execute steps S3-S8 until the genetic algebra equals to the predetermined Ng；
Step S9, outputting the optimized result, if the current genetic algebra in step S8 is larger than the set NgAnd outputting an optimization result: the individual corresponding to the minimum fitness function value is the optimal individual, and the optimal individual is output
Figure BDA0002793436970000061
Figure BDA0002793436970000062
The optical antenna is a laser array with the same wave band, the same phase and the same polarization, and the laser array can be a fiber laser array, a semiconductor laser array or a solid, gas or liquid laser array.
Compared with the prior art, the invention has the advantages that:
(1) in the invention, a concentric ring coordinate lattice is selected as an optical antenna locus set, and because of the annular omnibearing symmetry, the problem that side lobes cannot be simultaneously inhibited in horizontal and vertical orthogonal directions due to the adoption of a polygonal antenna array such as a rectangular array, a hexagonal array and the like is solved;
(2) in the invention, the physical light field generated by the optical antenna array is calculated by adopting fast Fourier transform, and the parallel operation on the GPU can further accelerate the operation, so that the method has higher calculation efficiency compared with a point-by-point physical field calculation method;
(3) in the invention, the optimized arrangement of the optical antennas is carried out by adopting an improved genetic algorithm, and a point-by-point gene exchange strategy is adopted in a chromosome gene crossing link instead of the traditional fixed proportion genetic strategy, so that the optimization speed of the genetic algorithm is increased, and the optimization efficiency is improved.
(4) The invention discloses a sidelobe suppression method of an optical phased array antenna under a genetic algorithm frame, which comprises the steps of establishing a coordinate optimized data set by designing a concentric ring arrangement antenna array set, randomly extracting an initial coordinate position from the set according to the number of required antennas, optimizing the sidelobe suppression of the optical phased array antenna coordinate by adopting the genetic algorithm frame, realizing high-efficiency calculation of a fitness function through fast Fourier transform, designing a chromosome gene point-by-point crossing method to improve the optimization efficiency, realizing a globally optimal light field arrangement scheme by utilizing variation and the like, and solving the problem of the maximization of the energy of a main beam of the optical phased array antenna. The method has application value in the fields of optical phased array radar, laser communication, laser beam synthesis and the like.
Drawings
The method for optimizing the optical antenna array layout is described in detail below with reference to a specific example, it should be emphasized that the following embodiments simplify the setting parameters for illustrating the implementation process, and the actual implementation process parameter setting is larger in the non-preferred embodiments.
Fig. 1 is a flowchart illustrating steps of a method for optimizing an optical antenna array configuration according to an embodiment of the present invention.
FIG. 2 is a set of genes (coordinates) U that create a concentric ring optical antenna in an embodiment of the present invention.
FIG. 3 shows genes (coordinates) contained in chromosomes (coordinate sets) of individuals randomly selected after population initialization in an embodiment of the present invention.
Fig. 4 is a result of outputting the minimum side lobe value in the iterative process in the embodiment of the present invention.
FIG. 5 shows genes (coordinates) contained in an optimized individual according to an embodiment of the present invention.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
With reference to the flowchart of the steps of the method for optimizing the arrangement of the optical antenna array in fig. 1, a method for suppressing sidelobes of an optical phased array antenna under the framework of a genetic algorithm includes the steps of:
in step S1, a set of genes (coordinates) is initialized, the number M of loops is set to 5, and the number k of optical antennas placed in each loop is set to1＝6，k2＝12，k3＝18，k4＝25，k531; setting radius of 1 st circular ring of optical antenna arrangement set as R1250 μm, radius of the 2 nd ring is R 2500 μm, radius of the 3 rd ring is R3750 μm, radius of the 4 th ring is R 41000 μm, radius of the 5 th ring being R51250 μm, the optical antenna coordinate spacing d on each circlemThe radius of the circular ring and the number of coordinate points per ring, namely the number k of the optical antennasmThe following relationships exist:
dm＝2RmSin(π/km) (1)
d1＝251.0μm,d2＝258.8μm,d3＝260.4μm,d4＝250.9μm；
arbitrary two ring spacing Δ Rm-1＝Rm-Rm-1；ΔR1＝R2-R1＝250μm，ΔR2＝R3-R2＝250μm，
ΔR3＝R4-R3＝250μm，ΔR4＝R5-R4＝250μm。
Minimum coordinate spacing dmin＝min{dm,ΔRmMin {251.0,258.8,260.4,250.9,252.9,250,250,250,250,250} mum 250μm, the coordinate set U is defined by setting the specific number M of the circular rings to 5, and the number k of the optical antennas placed in each circular ring1＝6，k2＝12，k3＝18，k4＝25，k531; and the radius of each ring R1＝250μm，R2＝500μm，R3＝750μm，R4＝1000μm，R5The coordinate set U determined in this embodiment is shown in fig. 2, where 1250 μm is commonly determined.
Step S2, initializing population: randomly extracting N-10 genes (coordinates) from the coordinate set U of the optical antenna to form individual chromosomes (coordinate sets), which is shown in fig. 3;
repeat NpopAs initial population, 8 times resulted in { Pos (1), Pos (2), Pos (3), …, Pos (8) }, NpopPos (n) corresponds to a two-dimensional set of spatial coordinates for the number of groups
Figure BDA0002793436970000081
Figure BDA0002793436970000082
N is 10, which is the number of genes (coordinates), and the specific values of the genes (coordinates) in this embodiment are:
Pos(1)＝[(662,1061),(309,951),(-705,-256),(-432,251),(249,-432),(126,218),(-250,-432),(876,482),(-765,989),(-130,738)]；
Pos(2)＝[(500,0),(662,-1060),(-765,-988),(63,999),(-1192,-373),(-1243,-126),(-250,-432),(-637,771),(249,-432),(-432,-249)]；
Pos(3)＝[(-574,-481),(-930,369),(-249,432),(705,-256),(125,-217),(-948,815),(1148,492),(309,951),(1001,0),(-1192,374)]；
Pos(4)＝[(251,0),(1026,-714),(-810,-588),(969,-249),(1250,0),(1001,0),(-750,0),(251,432),(-574,482),(1148,-492)]；
Pos(5)＝[(0,-499),(249,-432),(662,1061),(-930,-369),(-765,-988),(251,0),(-1243,126),(-948,815),(-313,1209),(1250,0)]；
Pos(6)＝[(1148,492),(705,257),(375,-649),(861,-906),(1224,252),(0,500),(-948,-814),(750,0),(861,906),(432,-250)]；
Pos(7)＝[(705,-256),(-993,-126),(251,432),(-948,-814),(-1243,126),(309,951),(861,-906),(-313,1209),(750,0),(249,-432)]；
Pos(8)＝[(-1192,-373),(750,0),(-1243,-126),(-993,-126),(-637,-771),(434,1172),(1250,0),(-499,0),(251,432),(309,951)]；
step S3, calculating a fitness function of the individuals in the initial population: extraction of colonies { Pos (1), Pos (2), Pos (3), …, Pos (N)pop) Number of individuals NpopExample NpopAs 8, populations { Pos (1), Pos (2), Pos (3), …, Pos (8) }, according to chromosome (coordinate set) Pos (n):
Pos(1)＝[(662,1061),(309,951),(-705,-256),(-432,251),(249,-432),(126,218),(-250,-432),(876,482),(-765,989),(-130,738)]；
Pos(2)＝[(500,0),(662,-1060),(-765,-988),(63,999),(-1192,-373),(-1243,-126),(-250,-432),(-637,771),(249,-432),(-432,-249)]；
Pos(3)＝[(-574,-481),(-930,369),(-249,432),(705,-256),(125,-217),(-948,815),(1148,492),(309,951),(1001,0),(-1192,374)]；
Pos(4)＝[(251,0),(1026,-714),(-810,-588),(969,-249),(1250,0),(1001,0),(-750,0),(251,432),(-574,482),(1148,-492)]；
Pos(5)＝[(0,-499),(249,-432),(662,1061),(-930,-369),(-765,-988),(251,0),(-1243,126),(-948,815),(-313,1209),(1250,0)]；
Pos(6)＝[(1148,492),(705,257),(375,-649),(861,-906),(1224,252),(0,500),(-948,-814),(750,0),(861,906),(432,-250)]；
Pos(7)＝[(705,-256),(-993,-126),(251,432),(-948,-814),(-1243,126),(309,951),(861,-906),(-313,1209),(750,0),(249,-432)]；
Pos(8)＝[(-1192,-373),(750,0),(-1243,-126),(-993,-126),(-637,-771),(434,1172),(1250,0),(-499,0),(251,432),(309,951)]electric field intensity expression listing light source plane
Figure BDA0002793436970000091
Said
Figure BDA0002793436970000092
Is the gene (coordinate) corresponding to each chromosome (coordinate set) { Pos (1), Pos (2), Pos (3), … and Pos (8) } in the population, and sequentially passes through Fast Fourier Transform (FFT) to obtain a modulus square
Figure BDA0002793436970000093
Obtaining an optical field intensity expression
Figure BDA0002793436970000094
Said
Figure BDA0002793436970000095
Is the space coordinate of the light field irradiation plane to find the intensity plane
Figure BDA0002793436970000096
Peak value, denoted as main lobe peak value I(i) mls(ii) a Plane of strength
Figure BDA0002793436970000097
After the peak area is removed, the maximum value of the residual area is found and is recorded as a side lobe peak value I(i) sl(ii) a The ratio of the side lobe peak value and the main lobe peak value is obtained and is the fitness function value of the individual and is recorded as
Figure BDA0002793436970000098
The above-mentioned i represents the currently calculated chromosome (coordinate set) number, i is 1,2,3, …, NpopIn this embodiment, Npop＝8；
Step S4, fitness function evaluation: the fitness function value of the individual
Figure BDA0002793436970000099
In order from small to large, the specific values of the individual fitness function corresponding to this embodiment are {0.8095, 0.7645, 0.8180, 0.9013, 0.7839, 0.7794, 0.9206 and 0.8096 which are sequentially ranked from small to large as {0.7645, 0.7794, 0.7839, 0.8095, 0.8096, 0.8180, 0.9013 and 0.9206}, the sequence number of the corresponding fitness function is {2,6,5,1,8,3,4 and 7}, and the sequence numbers of the fitness functions of the individuals are rearranged
Figure BDA00027934369700000910
Figure BDA0002793436970000101
Figure BDA0002793436970000102
Renaming chromosomes (coordinate sets) { nPos (1), nPos (2), nPos (3), …, nPos (8) } according to fitness function sequence numbers {2,6,5,1,8,3,4,7}, wherein the notation nPos () is used for distinguishing the difference of Pos () before and after sorting, and the specific corresponding relationship after renaming the sorted chromosomes (coordinate sets) is as follows:
nPos(1)＝Pos(2)＝
[(500,0),(662,-1060),(-765,-988),(63,999),(-1192,-373),(-1243,-126),(-250,-432),(-637,771),(249,-432),(-432,-249)]；
nPos(2)＝Pos(6)＝
[(1148,492),(705,257),(375,-649),(861,-906),(1224,252),(0,500),(-948,-814),(750,0),(861,906),(432,-250)]；
nPos(3)＝Pos(5)＝
[(0,-499),(249,-432),(662,1061),(-930,-369),(-765,-988),(251,0),(-1243,126),(-948,815),(-313,1209),(1250,0)]；
nPos(4)＝Pos(1)＝
[(662,1061),(309,951),(-705,-256),(-432,251),(249,-432),(126,218),(-250,-432),(876,482),(-765,989),(-130,738)]；
nPos(5)＝Pos(8)＝
[(-1192,-373),(750,0),(-1243,-126),(-993,-126),(-637,-771),(434,1172),(1250,0),(-499,0),(251,432),(309,951)]；
nPos(6)＝Pos(3)＝
[(-574,-481),(-930,369),(-249,432),(705,-256),(125,-217),(-948,815),(1148,492),(309,951),(1001,0),(-1192,374)]；
nPos(7)＝Pos(4)＝
[(251,0),(1026,-714),(-810,-588),(969,-249),(1250,0),(1001,0),(-750,0),(251,432),(-574,482),(1148,-492)]；
nPos(8)＝Pos(7)＝
[(705,-256),(-993,-126),(251,432),(-948,-814),(-1243,126),(309,951),(861,-906),(-313,1209),(750,0),(249,-432)]；
step S5, individual selection: truncating the top N in step S40A chromosome (coordinate set), said N0≤NpopIn this embodiment, N is set0(6) to yield { nPos (1), nPos (2), nPos (3), nPos (4), nPos (5), nPos (6) };
step S6, cross: the chromosomes (coordinate sets) { nPos (1), nPos (2), nPos (3), …, nPos (N) obtained in step S50) Pairwise pairing of individuals in the { nPos (N-1), nPos (N) }, wherein N takes the value 2,3, 4, …, N0In this embodiment, the individual pairs are: { nPos (1), nPos (2) }, { nPos (3), nPos (4) } { nPos (5), nPos (6) }, where any two pairs of individuals are subjected to cross-exchange of chromosome (coordinate set) genes (coordinates), and the number of chromosome (coordinate set) genes (coordinates) is exchanged point by point, that is, 1 gene (coordinate) is exchanged for the first time, 2 genes (coordinates) are exchanged for the second time, … is exchanged until N-1 times is exchanged, so as to complete the exchange of all genes (coordinates), specifically in this embodiment, the { nPos (1), nPos (2) } genes (coordinates) are exchanged for example, before the genes (coordinates) are exchanged:
nPos(1)＝[(500,0),(662,-1060),(-765,-988),(63,999),(-1192,-373),(-1243,-126),(-250,-432),(-637,771),(249,-432),(-432,-249)]；
nPos(2)＝[(1148,492),(705,257),(375,-649),(861,-906),(1224,252),(0,500),(-948,-814),(750,0),(861,906),(432,-250)]；
after 1 st interchange of 1 st gene (coordinates):
xPos(1)(1)＝[(1148,492),(662,-1060),(-765,-988),(63,999),(-1192,-373),(-1243,-126),(-250,-432),(-637,771),(249,-432),(-432,-249)]；
xPos(1)(2)＝[(500,0),(705,257),(375,-649),(861,-906),(1224,252),(0,500),(-948,-814),(750,0),(861,906),(432,-250)]；
after the 2 nd interchange of the first 2 genes (coordinates):
xPos(2)(1)＝[(1148,492),(705,257),(-765,-988),(63,999),(-1192,-373),(-1243,-126),(-250,-432),(-637,771),(249,-432),(-432,-249)]；
xPos(2)(2)＝[(500,0),(662,-1060),(375,-649),(861,-906),(1224,252),(0,500),(-948,-814),(750,0),(861,906),(432,-250)]；
after the 3 rd interchange of the first 3 genes (coordinates):
xPos(3)(1)＝[(1148,492),(705,257),(375,-649),(63,999),(-1192,-373),(-1243,-126),(-250,-432),(-637,771),(249,-432),(-432,-249)]；
xPos(3)(2)＝[(500,0),(662,-1060),(-765,-988),(861,-906),(1224,252),(0,500),(-948,-814),(750,0),(861,906),(432,-250)]；
…
and so on, until the N-1 st interchange is completed, in this embodiment, N is 10, and 9 total interchanges need to be completed to obtain the intersected individual:
{xPos(1)(1)，xPos(1)(2)}，
{xPos(2)(1)，xPos(2)(2)}，
{xPos(3)(1)，xPos(3)(2)}，
{xPos(4)(1)，xPos(4)(2)}，
{xPos(5)(1)，xPos(5)(2)}，
{xPos(6)(1)，xPos(6)(2)}，
{xPos(7)(1)，xPos(7)(2)}，
{xPos(8)(1)，xPos(8)(2)}，
{xPos(9)(1)，xPos(9)(2)}，
xPos(i)(n) for distinguishing differences in the reciprocal pre-chromosomes (coordinate sets);
after the { nPos (1), nPos (2) } gene (coordinate) is crossed, according to the { nPos (1), nPos (2) } gene (coordinate) interchange method, the crossing of { nPos (3), nPos (4) } and { nPos (5), nPos (6) } is completed, and the final result is as follows:
{xPos(1)(3)，xPos(1)(4)}，
{xPos(2)(3)，xPos(2)(4)}，
{xPos(3)(3)，xPos(3)(4)}，
{xPos(4)(3)，xPos(4)(4)}，
{xPos(5)(3)，xPos(5)(4)}，
{xPos(6)(3)，xPos(6)(4)}，
{xPos(7)(3)，xPos(7)(4)}，
{xPos(8)(3)，xPos(8)(4)}，
{xPos(9)(3)，xPos(9)(4)}；
{xPos(1)(5)，xPos(1)(6)}，
{xPos(2)(5)，xPos(2)(6)}，
{xPos(3)(5)，xPos(3)(6)}，
{xPos(4)(5)，xPos(4)(6)}，
{xPos(5)(5)，xPos(5)(6)}，
{xPos(6)(5)，xPos(6)(6)}，
{xPos(7)(5)，xPos(7)(6)}，
{xPos(8)(5)，xPos(8)(6)}，
{xPos(9)(5)，xPos(9)(6)}；
after recombination:
group 1: { xPos(1)(1)，xPos(1)(2)，xPos(1)(3)}，{xPos(1)(4)，xPos(1)(5)}，{xPos(1)(6)}；
Group 2：{xPos(2)(1)，xPos(2)(2)，xPos(2)(3)}，{xPos(2)(4)，xPos(2)(5)}，{xPos(2)(6)}；
Group 3: { xPos(3)(1)，xPos(3)(2)，xPos(3)(3)}，{xPos(3)(4)，xPos(3)(5)}，{xPos(3)(6)}；
…
Group 9: { xPos(9)(1)，xPos(9)(2)，xPos(9)(3)}，{xPos(9)(4)，xPos(9)(5)}，{xPos(9)(6)}；
If the value of the gene (coordinate) is repeated, randomly extracting the value of the gene (coordinate) from the complementary set intersected by the set U and the set { Pos (N-1), Pos (N) } to replace the repeated gene (coordinate), realizing the intersection of the genes (coordinate), and changing the number of the groups after the intersection into N0X (N-1), in this example 6 x (10-1) ═ 54, with 6 individuals in each group;
step S7, mutation: setting N0Then, the number of individuals M of the variation is setmuteThe variant individuals are derived from randomly extracting N genes (coordinates) from the set U to form individuals mPOS (i), and repeating MmuteNext, a population of variant individuals { mPos (1), mPos (2), mPos (3), …, mPos (M)mute) Replacing any M in steps S5-S6 with mutated individualsmuteIndividuals, typically select M ranked further downmuteIndividual, effecting genetic variation (coordinate) replacement, said MmuteIs arbitrarily less than N0Natural number of (1), N in this example0＝6,N＝10,Mmute2, the individual population of variants { mPos (1), mPos (2) }, and the specific variant genes (coordinates) in this example are:
mPos(1)＝
[(209,851),(1047,392),(-163,-1348),(-1344,26),(474,-582),(150,332),(-910,488),(900,-100),(-651,1022),(-1293,-474)]；
mPos(2)＝
[(150,-100),(-1048,-915),(332,149),(-288,882),(89,-1335),(-526,806),(-865,888),(761,-1006),(-675,381),(-532,150)]；
the variation is repeated 9 times, in this example N-10, Mmute2, the 9 groups of variant individuals are obtained
{mPos(1)(1),mPos(1)(2)}，
{mPos(2)(1),mPos(2)(2)}，
{mPos(3)(1),mPos(3)(2)}，
{mPos(4)(1),mPos(4)(2)}，
{mPos(5)(1),mPos(5)(2)}，
{mPos(6)(1),mPos(6)(2)}，
{mPos(7)(1),mPos(7)(2)}，
{mPos(8)(1),mPos(8)(2)}，
{mPos(9)(1),mPos(9)(2)}；
Recombining the 9 groups of variant individuals with the 9 groups of individual chromosomes (coordinate sets) obtained in step S6 into 9 populations:
group 1: { xPos(1)(1)，xPos(1)(2)，xPos(1)(3)}，{xPos(1)(4)，xPos(1)(5)}，{xPos(1)(6)，mPos(1)(1),mPos(1)(2)}；
Group 2: { xPos(2)(1)，xPos(2)(2)，xPos(2)(3)}，{xPos(2)(4)，xPos(2)(5)}，{xPos(2)(6)，mPos(2)(1),mPos(2)(2)}；
Group 3: { xPos(3)(1)，xPos(3)(2)，xPos(3)(3)}，{xPos(3)(4)，xPos(3)(5)}，{xPos(3)(6)，mPos(3)(1),mPos(3)(2)}；
…
Group 9: { xPos(9)(1)，xPos(9)(2)，xPos(9)(3)}，{xPos(9)(4)，xPos(9)(5)}，{xPos(9)(6)，mPos(9)(1),mPos(9)(2)}；
The number of individuals of each group after recombination is 8, 6 are obtained by crossing, 2 are obtained by variation, and the number of the individuals of the group and the number N of the initialized groupspopThe number of 8 remains the same.
Step S8, determining whether the number of genetic generations N is up to a set numbergThe requirement of (1) is added to the genetic algebra every time steps S3-S7 are executed, and if the current genetic algebra is less than the set NgThen, the method continues to execute steps S3-S8 until the genetic algebra equals to the predetermined NgIn this embodiment, the genetic number N is setgThe minimum side lobe value corresponding to each iteration result is shown in fig. 4 as 100;
step S9, outputting the optimized result, if the current genetic algebra in step S8 is larger than the set NgAnd outputting an optimization result: minimum fitness function value
Figure BDA0002793436970000152
The corresponding individual is the optimal individual, and the optimal individual is
Figure BDA0002793436970000151
In this embodiment, N is setgThe corresponding optimization results are [ Pos ═ (561,960), (900, -100), (150,332), (332,149), (474,381), (-738, -871), (-1048, -915), (435, -945), (-1192, -706), (-475,549) at 100]The optimized layout result is shown in fig. 5.
The optical antenna is a laser array with the same wave band, the same phase and the same polarization, and the laser array can be a fiber laser array, a semiconductor laser array or a solid, gas or liquid laser array.

Claims (10)

1. A sidelobe suppression method of an optical phased array antenna under a genetic algorithm framework is characterized by comprising the following steps:
step S1, initializing a coordinate set to obtain a coordinate set U;
step S2, initializing a group;
step S3, calculating the fitness function of the individuals in the initial population;
step S4, evaluating the fitness function obtained in step S3;
step S5, selecting an individual;
step S6, performing intersection;
step S7, performing mutation;
step S8, determining whether the number of genetic generations N is up to a set numbergThe requirements of (1);
and step S9, outputting an optimization result and finishing sidelobe suppression of the optical phased array antenna.
2. The sidelobe suppression method of the optical phased array antenna under the genetic algorithm framework of claim 1, characterized in that: in step S1, the method for initializing the coordinate set includes: setting the number M of the circular rings, wherein the number of the optical antennas arranged on each circular ring is k1，k2，k3，...km，...，kM(ii) a Setting the radius of the mth circular ring of the optical antenna arrangement set to be RmLet the mth ring place kmAn optical antenna, each optical antenna coordinate interval d on each ringmThe radius of the circular ring and the number of coordinate points per ring, namely the number k of the optical antennasmThe following relationships exist:
dm＝2RmSin(π/km) (1)
minimum coordinate spacing dmin＝min{dm,ΔRmWherein Δ Rm＝Rm-Rm-1And the coordinate set U is set according to specific task requirements.
3. The sidelobe suppression method of the optical phased array antenna under the genetic algorithm framework of claim 2, characterized in that: in step S2, the method for initializing the population includes: randomly extracting N coordinates from the set U to form an individual coordinate set, and repeating NpopNext as the initial population { Pos (1), Pos (2), Pos (3), …, Pos (N)pop)}，NpopFor the number of individuals in the population, Pos (n) corresponds to a two-dimensional set of spatial coordinates
Figure FDA0002793436960000011
N is a seatThe standard quantity corresponds to the number of the optical antennas, and U represents a coordinate set of the optical antennas.
4. The sidelobe suppression method of the optical phased array antenna under the genetic algorithm framework of claim 3, characterized in that: in step S3, the method for calculating the fitness function of the individuals in the initial population includes: automatic identification of populations { Pos (1), Pos (2), Pos (3), …, Pos (N)pop) Number of individuals Npop(ii) a According to the distribution of the optical antenna corresponding to the individual coordinates in pos (n), listing the electric field intensity expression of the light source plane
Figure FDA0002793436960000021
Said
Figure FDA0002793436960000022
Is a light source plane space coordinate, and a modulus is obtained through Fast Fourier Transform (FFT)
Figure FDA0002793436960000023
Obtaining an optical field intensity expression
Figure FDA0002793436960000024
Said
Figure FDA0002793436960000025
Is the space coordinate of the light field irradiation plane to find the intensity plane
Figure FDA0002793436960000026
Peak value, denoted as main lobe peak value I(i) mls(ii) a Plane of strength
Figure FDA0002793436960000027
After the peak area is removed, the maximum value of the residual area is found and is recorded as a side lobe peak value I(i) sl(ii) a The ratio of the side lobe peak value and the main lobe peak value is obtained and is the fitness function value of the individual and is recorded as
Figure FDA0002793436960000028
The above i represents the number of individuals in the current group and the sequence number of the current calculation, i is 1,2,3, …, Npop。
5. The sidelobe suppression method of the optical phased array antenna under the genetic algorithm framework of claim 4, characterized in that: in step S4, the fitness function evaluation method includes: the fitness function value of the individual
Figure FDA0002793436960000029
In order from small to large.
6. The sidelobe suppression method of the optical phased array antenna under the genetic algorithm framework of claim 5, characterized in that: in step S5, the method of individual selection is: truncating N in step S40An
Figure FDA00027934369600000210
The value of the one or more of,
Figure FDA00027934369600000211
corresponding coordinate sets { Pos (1), Pos (2), Pos (3), …, Pos (N)0) N of said0≤Npop。
7. The sidelobe suppression method of the optical phased array antenna under the genetic algorithm framework of claim 6, characterized in that: in step S6, the method of interleaving is: the set of coordinates { Pos (1), Pos (2), Pos (3), …, Pos (N) obtained in step S5 is added0) Pairwise pairing of individuals in the { Pos (N-1), Pos (N) }, N taking the value 2,3, 4, …, N0And carrying out cross exchange of coordinates of the coordinate sets on any two pairs of individuals, wherein the number of coordinates of the coordinate sets is gradually exchanged point by point, namely 1 coordinate is exchanged for the first time, 2 coordinates are exchanged for the second time, …, until N-1 times of exchange is carried out, the exchange of all coordinates is completed, and if the values of the coordinates are repeated, the coordinates are randomly exchanged from the complementary set of the intersection of the set U and the set { Pos (N-1) and Pos (N) } at randomExtracting coordinate values to replace repeated coordinates, realizing the intersection of all coordinates, and changing the number of the groups after the intersection into N0×(N-1)。
8. The sidelobe suppression method of the optical phased array antenna under the genetic algorithm framework of claim 7, characterized in that: in step S7, the mutation method includes: setting the number of variant individuals MmuteThe variant individuals are derived by randomly extracting N coordinates from the set U to form individuals mPOS (i), and repeating MmuteNext, a population of variant individuals { mPos (1), mPos (2), mPos (3), …, mPos (M)mute) Replacing any M in steps S5-S6 with mutated individualsmuteIndividuals, typically select M ranked further downmuteIndividual, realizes coordinate replacement, the Mmute＝Npop-N0Is a natural number of (1).
9. The sidelobe suppression method of the optical phased array antenna under the genetic algorithm framework of claim 8, characterized in that: in step S8, it is determined whether the number of genetic generations N set has been reachedgThe requirement of (1) is added to the genetic algebra every time steps S3-S7 are executed, and if the current genetic algebra is less than the set NgThen, the method continues to execute steps S3-S8 until the genetic algebra equals to the predetermined Ng。
10. The sidelobe suppression method of the optical phased array antenna under the genetic algorithm framework of claim 9, characterized in that: step S9, outputting the optimized result, if the current genetic algebra in step S8 is larger than the set NgAnd outputting an optimization result: optimal individuals
Figure FDA0002793436960000031
Figure FDA0002793436960000032
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Publication number Priority date Publication date Assignee Title
CN106342323B (en) * 2011-12-27 2014-06-18 中国航空工业集团公司雷华电子技术研究所 The submatrix weighted value of phased-array radar difference beam Sidelobe Suppression is determined method
CN111313158A (en) * 2018-12-12 2020-06-19 南京理工大学 Method for thinning circular array
CN111881624A (en) * 2020-07-30 2020-11-03 重庆邮电大学 Sparse optimization method for electromagnetic vortex wave multi-input multi-output rectangular array

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106342323B (en) * 2011-12-27 2014-06-18 中国航空工业集团公司雷华电子技术研究所 The submatrix weighted value of phased-array radar difference beam Sidelobe Suppression is determined method
CN111313158A (en) * 2018-12-12 2020-06-19 南京理工大学 Method for thinning circular array
CN111881624A (en) * 2020-07-30 2020-11-03 重庆邮电大学 Sparse optimization method for electromagnetic vortex wave multi-input multi-output rectangular array

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