CN108508424B - Low side lobe complex weight vector optimization method based on antenna array error - Google Patents

Low side lobe complex weight vector optimization method based on antenna array error Download PDF

Info

Publication number
CN108508424B
CN108508424B CN201810251335.9A CN201810251335A CN108508424B CN 108508424 B CN108508424 B CN 108508424B CN 201810251335 A CN201810251335 A CN 201810251335A CN 108508424 B CN108508424 B CN 108508424B
Authority
CN
China
Prior art keywords
value
individual
array
complex weight
weight vector
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201810251335.9A
Other languages
Chinese (zh)
Other versions
CN108508424A (en
Inventor
冯大政
徐怡飒
董泉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xidian University
Original Assignee
Xidian University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xidian University filed Critical Xidian University
Priority to CN201810251335.9A priority Critical patent/CN108508424B/en
Publication of CN108508424A publication Critical patent/CN108508424A/en
Application granted granted Critical
Publication of CN108508424B publication Critical patent/CN108508424B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Variable-Direction Aerials And Aerial Arrays (AREA)

Abstract

The invention belongs to the field of radar signal processing, and discloses a low sidelobe complex weight vector optimization method based on antenna array errors, which comprises the following steps: establishing an array antenna model as a uniform linear array, and acquiring a directional diagram function expression of the uniform linear array; obtaining a directional diagram function expression considering the amplitude-phase error according to the directional diagram function expression of the uniform linear array, wherein the directional diagram function expression considering the amplitude-phase error is a function expression about a complex weight vector; establishing a target cost function related to the complex weight vector according to the directional diagram function expression considering the amplitude-phase error; and solving the target cost function by adopting a differential evolution algorithm to obtain an optimized complex weight vector, and solving the problem that the antenna side lobe level is sensitive to errors under the condition of considering array amplitude-phase errors.

Description

Low side lobe complex weight vector optimization method based on antenna array error
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a low side lobe complex weight vector optimization method based on antenna array errors.
Background
The low side lobe is one of the important technical indexes of the radar antenna. This feature not only overcomes clutter interference, but also reduces the probability of being discovered by an adversary. If the excitation of the array antenna is not weighted, the theoretical value of the first side lobe level is about-13.5 dB, and the requirement of the phased array radar on the side lobe level cannot be met. In the process of actually designing the antenna, random errors are inevitably introduced, so that the aperture distribution of the array is changed, and the performance of the antenna array is directly influenced. The introduction of the random error can be finally expressed as the amplitude error and the phase error of each unit of the array, so that the optimization problem of the array antenna side lobe level under the influence of the random amplitude-phase error needs to be researched.
At present, the problem of low sidelobe can be generally divided into an analytic method and a numerical method. The classical analysis methods include a Chebyshev synthesis method, a Taylor synthesis method and the like, the design of the methods is simple, however, the excitation amplitude of array elements at two ends of an array is greatly different from that of adjacent array elements, great difficulty is brought to feeding of an antenna, and the side lobe level is greatly fluctuated due to small errors of the excitation amplitude of the array elements.
In the evolution algorithm in the numerical method, compared with the particle swarm and the genetic algorithm, the differential evolution algorithm has better overall performance. In the aspect of coding standard, the genetic algorithm adopts binary coding, and has certain error compared with real number coding of particle swarm and differential evolution algorithm; in the aspect of parameter setting, only two parameters of the differential evolution algorithm need to be adjusted, the adjustment of the parameters has little influence on the result, the particle swarm and the genetic algorithm have more parameters, and different parameters have larger influence on the convergence speed and the premature convergence to the local extreme point; for the high-dimensional problem, the convergence speed of the genetic algorithm is very low and even the genetic algorithm cannot converge, but the particle swarm algorithm and the differential evolution algorithm can well solve the problem, particularly the differential evolution algorithm has the advantages of fast convergence and accurate result; in terms of convergence performance, for optimization problems, compared with genetic algorithms, differential evolution algorithms and particle swarm optimization algorithms have high convergence speed, but particle swarm is easy to fall into local extreme points and is unstable.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a low side lobe complex weight vector optimization method based on antenna array errors, which solves the problem that side lobe levels of a directional diagram in the conventional method are very sensitive to array element errors.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme.
A low side lobe complex weight vector optimization method based on antenna array errors comprises the following steps:
step 1, establishing an array antenna model as a uniform linear array, and acquiring a directional diagram function expression of the uniform linear array;
step 2, obtaining a directional diagram function expression considering the amplitude-phase error according to the directional diagram function expression of the uniform linear array, wherein the directional diagram function expression considering the amplitude-phase error is a function expression about a complex weight vector;
step 3, establishing a target cost function related to the complex weight vector according to the directional diagram function expression considering the amplitude-phase error;
and 4, solving the target cost function by adopting a differential evolution algorithm to obtain an optimized complex weight vector.
Compared with the prior art, the invention has the following characteristics:
(1) compared with the prior art, the method takes the channel error of the array into consideration when the antenna array model is established. In the actual design process of the antenna, array errors are inevitably introduced. Array errors can be caused by a variety of factors, such as: the amplitude and phase errors of complex weight vectors, the influence of channel frequency response inconsistency (channel mismatch) on system performance, signal direction estimation errors, quantization errors of weight vectors, errors caused by faults of individual array elements and the like, and both electrical errors and mechanical manufacturing errors can be finally summarized into system errors and random errors. The influence of partial system errors can be easily evaluated and corrected, and random errors are unpredictable (such as random errors caused by climate, temperature, processing errors and the like) and are difficult to correct. The random error can change the aperture distribution of the array and directly influence the performance of the antenna array, and the introduction of the random error can be finally expressed as the amplitude error and the phase error of each unit of the array, so the technical scheme of the invention compensates the amplitude-phase error of the array by optimally weighting the low side lobe complex weight vector.
2. Compared with the prior art, the method has the advantages that the complex weight vector with simultaneously optimized amplitude and phase is adopted, and the real weight vector obtained by analytical methods such as Chebyshev weighting and Taylor weighting can only compensate amplitude errors, so that the obtained optimal weight has certain compensation on the amplitude and phase errors, the analytical methods are sensitive to the errors of the antenna array, and an antenna directional diagram can be distorted by a point error.
3. Compared with the prior art, the method adopts the evolution differential algorithm, and compared with the particle swarm algorithm and the genetic algorithm in the evolution algorithm, the differential evolution algorithm only utilizes two parameters, namely the cross factor CR and the scale factor M, so that the method has stronger global search capability, convergence and stability.
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 flowchart of a method for obtaining an antenna array error-based low side lobe complex weight vector optimization according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a uniform linear array model provided in an embodiment of the present invention;
fig. 3 is a schematic diagram of an implementation flow of a differential evolution algorithm according to an embodiment of the present invention;
fig. 4a is an error-free 48-element linear array antenna directional pattern provided by the embodiment of the present invention;
FIG. 4b is a convergence curve corresponding to the DE algorithm without error according to the embodiment of the present invention;
fig. 5a is a linear array antenna directional pattern of 48 elements with 2% error according to an embodiment of the present invention;
FIG. 5b is a convergence curve corresponding to the DE algorithm with 2% error according to the embodiment of the present invention
FIG. 6a is a linear array pattern of PSO and DE at 0% error provided by an embodiment of the present invention;
FIG. 6b is a convergence curve corresponding to the DE and PSO algorithms at 0% error according to the embodiment of the present invention;
FIG. 7a is a line pattern diagram of PSO and DE at 2% error provided by an embodiment of the present invention;
fig. 7b is a convergence curve corresponding to the DE and PSO algorithms at 2% error according to an embodiment of the present invention.
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.
The embodiment of the invention provides a low side lobe complex weight vector optimization method based on antenna array errors, which comprises the following steps as shown in figure 1:
step 1, establishing an array antenna model as a uniform linear array, and obtaining a directional diagram function expression of the uniform linear array.
The step 1 specifically comprises:
as shown in fig. 2, the array antenna model is set as a uniform linear array composed of N array elements, and the array element spacing d is a half wavelength, so as to obtain a directional diagram function expression F (θ) of the uniform linear array:
Figure BDA0001607854330000051
where k is the wave number (radian/length),
Figure BDA0001607854330000052
Ψnfor the phase difference of the nth array element relative to the first array element, Ψn＝nkd[sin(θ)-sin(θ0)]Theta is the direction of the incoming wave, theta0The beam pointing direction is a uniform linear array, w is a complex weight vector, and w is ═ w1，w2，…，wn…，wN]T，wnFor the complex scalar quantity corresponding to the nth array element, A (theta) is an array steering vector matrix and only depends on the geometrical structure (known) and the incoming wave direction (theta) of the array under the narrow-band condition, wherein the A (theta) is [ a ]1(θ)，a2(θ)，…，an(θ)，…，aN(θ)]T，an(theta) is a steering vector corresponding to the nth array element,
Figure BDA0001607854330000055
n is the total number of array elements contained in the uniform linear array, and d is the array element spacing of the uniform linear array.
And 2, obtaining a directional diagram function expression considering the amplitude-phase error according to the directional diagram function expression of the uniform linear array, wherein the directional diagram function expression considering the amplitude-phase error is a function expression about a complex weight vector.
The step 2 specifically comprises:
obtaining a directional diagram function expression F (theta) considering the amplitude-phase error according to the directional diagram function expression F (theta) of the uniform linear arrayerr(θ)：
Figure BDA0001607854330000053
Wherein k is a wave number (radian/length),
Figure BDA0001607854330000054
Ψnfor the phase difference of the nth array element relative to the first array element, Ψn＝nkd[sin(θ)-sin(θ0)]Theta is the direction of the incoming wave, theta0The beam pointing direction is a uniform linear array, w is a complex weight vector, and w is ═ w1，w2，…，wn…，wN]T，wnA complex scalar quantity corresponding to the nth array element, Aerr(theta) is an array steering vector matrix taking into account amplitude-phase errors, Aerr(θ)＝[a1err(θ)，a2err(θ)，…anerr(θ)，…，aNerr(θ)]T，anerr(theta) is a guide vector corresponding to the nth array element and considering the amplitude-phase error,
Figure BDA0001607854330000061
Δanand Δ ΦnThe amplitude error and the phase error of the nth array element are respectively, the mean value of the amplitude error and the phase error is 0, and the variance is respectively
Figure BDA0001607854330000062
And
Figure BDA0001607854330000063
n is the total number of array elements contained in the uniform linear array, and d is the array element spacing of the uniform linear array.
And 3, establishing a target cost function related to the complex weight vector according to the directional diagram function expression considering the amplitude-phase error.
The step 3 specifically includes:
according to the directional diagram function expression F considering the amplitude-phase errorerr(θ), establishing an objective cost function for the complex weight vector as follows:
Figure BDA0001607854330000064
where, fitness (w) represents a target cost function value calculated from the complex weight vector w, and the expression min fitness (w) ═ α (SLL)s(w)-SLLd)+β(θ0.5(w)-θd) Is intended to make alpha (SLL)s(w)-SLLd)+β(θ0.5(w)-θd) The minimum complex weight vector w, s.t. represents the constraint condition, alpha is the first error coefficient,
Figure BDA0001607854330000065
beta is a second error coefficient and is a first error coefficient,
Figure BDA0001607854330000066
SLLs(w) represents the maximum level of side lobes in the actual pattern, SLLs(w)＝max|wH·Aerr(θs)|，θsIndicating a side lobe region, SLLdRepresenting the target side lobe value, θ0.5(w) represents the actual half-power beamwidth, θdRepresents the target half power width, θ0For a uniform linear array of beam pointing directions, the superscript H denotes the conjugate transpose.
And 4, solving the target cost function by adopting a differential evolution algorithm to obtain an optimized complex weight vector.
Assuming that the number of array elements is N, in the absence of array errors, array antenna symmetry can be exploited, and the dimension of the weight to be optimized is Dim-N/2; after considering the array error, the array antenna will lose symmetry, and the dimension of the weight to be optimized is Dim-N.
Referring to fig. 3, the step 4 specifically includes the following sub-steps:
(4a) setting the dimension number of the complex weight vector w as N, wherein each dimension represents a complex weight scalar corresponding to an array element, and the amplitude value range of each complex weight scalar is [ x [ ]amin，xamax]Each complex weight scalar has a phase with a value in the range of [ xpmin，xpmax]；
Specifically, the amplitude value range of each complex weight scalar is [0.01, 1], and the range can be adjusted, so as to solve the problem of feeding difficulty caused by great difference between the maximum value and the minimum value of array element excitation.
Initializing a population: setting i to represent the ith individual in the population, i to 1, 2, … NP, each individual to represent one value of a complex weight vector w, j to represent the jth dimension of each individual, j to 1, 2, … N, and the one dimension of each individual to represent a complex weight scalar quantity corresponding to one array element in the complex weight vector; t represents the t generation population, i is 1, j is 1, and t is 0;
(4b) j dimension value of i individual in 0 generation population
Figure BDA0001607854330000079
：
Figure BDA0001607854330000071
Figure BDA0001607854330000072
Figure BDA0001607854330000073
Wherein the content of the first and second substances,
Figure BDA0001607854330000074
represents the j dimension amplitude value of the ith individual in the 0 th generation population,
Figure BDA0001607854330000075
represents the j-dimension phase value, x, of the ith individual in the 0 th generation populationamaxAnd xaminRespectively representing an upper and a lower bound of the amplitude, xpmaxAnd xpminRespectively representing the upper and lower bounds of the phase, rand representing [0, 1]Random decimal between;
(4c) adding 1 to the value of j, and repeating the substep (4b) until obtaining the N-dimensional value of the ith individual in the 0 th generation population
Figure BDA0001607854330000076
Form the ith individual in the 0 th generation population
Figure BDA0001607854330000077
And the fitness function value corresponding to the ith individual
Figure BDA0001607854330000078
(4d) Resetting j to 1, adding 1 to the value of i, and repeating the substeps (4b) and (4c) until the NP individuals in the 0 th generation population and the fitness function value corresponding to each individual are obtained;
setting the value of i as 1, setting the value of j as 1, and setting the value of t as 1;
(4e) carrying out variation operation on the ith individual in the tth generation population to obtain the ith variation individual in the tth generation population
Figure BDA0001607854330000081
Wherein the content of the first and second substances,
Figure BDA0001607854330000082
respectively representing any three different individuals in NP individuals of the t generation population, wherein M is a scale factor;
(4f) the t generation is clusteredThe ith individual in the population and the ith variant individual in the population of the t generation are subjected to cross operation to obtain the ith cross individual in the population of the t generation
Figure BDA0001607854330000083
J dimension value of ith cross individual in t generation population
Figure BDA0001607854330000084
Comprises the following steps:
Figure BDA0001607854330000085
wherein the content of the first and second substances,
Figure BDA0001607854330000086
represents the ith variant in the t generation population
Figure BDA0001607854330000087
The value of the j-th dimension of (c),
Figure BDA0001607854330000088
represents the ith individual in the t-th generation population
Figure BDA0001607854330000089
The j-th dimension of (1), rand represents [0, 1]]Random decimal between, CR represents the crossover factor, randn (N) represents [1, N]Random integers within the range;
sequentially taking the value of j to 1, 2 and … N to obtain the ith cross individual of the t generation population
Figure BDA00016078543300000810
(4g) The ith crossed individual of the t generation population
Figure BDA00016078543300000811
Comparing the fitness value with the fitness value of the ith individual of the t-1 generation population, and selecting the individual with a smaller fitness value as the ith individual of the t generation populationBody
Figure BDA00016078543300000812
Figure BDA00016078543300000813
fitness (·) denotes the fitness function;
(4h) adding 1 to the value of i, and repeating the substeps (4e) to (4g) until NP individuals of the population of the t generation are obtained;
(4i) setting a fitness value threshold value and a maximum population generation number, and acquiring an individual with the minimum fitness value from NP individuals of a t-th generation population as an optimal individual;
if the fitness value of the optimal individual is smaller than or equal to the fitness value threshold, taking the complex weight vector corresponding to the optimal individual as a finally optimized complex weight vector; or if the value of t is larger than the maximum population algebra, taking the optimal individual of the population of the last generation as the finally optimized complex weight vector;
otherwise, adding 1 to the value of t, setting the value of i to 1, setting the value of j to 1, and returning to the substep (4 e).
The effect of the invention is further illustrated by the following simulation test:
1. simulation conditions
Array model: adopting N-48 uniform linear array with array element spacing
Figure BDA0001607854330000092
Dividing the azimuth angle into 1801 parts at equal intervals of-90 DEG and constructing an array popular matrix A at the angular interval of 0.1 DEG, so that the ith column of the matrix A
Figure BDA0001607854330000091
Setting a main lobe of an array antenna to be oriented at theta0＝0°。
2. Emulated content analysis
Experiment 1
In the case where the excitation range is 0.01 to 1, a DE optimization algorithm (differential evolution algorithm) is used) Comparing the obtained optimal weight with Chebyshev weighting, wherein the antenna array weighting becomes symmetrical when no error exists, so that the array element number is N-48, and the dimension of the optimized weight is Dim-24; when errors are present, the antenna array weights are not symmetrical, so in the presence of errors, we optimize the weights to have dimension Dim-48. Target maximum side lobe value SLLd-50dB, target half-power beamwidth θd＝3.2°。
The parameters of the DE algorithm are: the population number NP is 72, the crossover factor CR is 0.9, and the mutation factor M is 0.5.
As fig. 4a shows that under the condition of no error, the DE algorithm can obtain low sidelobes like chebyshev, and the sidelobes of the edge array are lower than the chebyshev, and fig. 4b shows the convergence graph of the algorithm, and it can be seen that when the target requirement is reached, the convergence of the algorithm stops for generation, and the convergence is faster.
As shown in fig. 5a, the directional diagram of the array antenna is obtained under the condition that the array element contains 2% of amplitude-phase error, and we can see that chebyshev weighting is greatly influenced by the amplitude-phase error, under the condition of 2% of error, the width of the main lobe of the directional diagram obtained by chebyshev weighting is 3.2 degrees, the maximum side lobe level is-38.86 dB, and the width of the main lobe of the directional diagram obtained by DE algorithm optimization is 3 degrees, the maximum side lobe level is-50 dB, so that the side lobe level required by the target is achieved, the main lobe is reduced by 0.2 degrees, and the maximum side lobe level is reduced by 11.2dB compared with the chebyshev maximum side lobe level. Fig. 5b is a DE algorithm convergence diagram, and it can be seen that when the target requirement is met, the algorithm convergence stops iteration, and since the complex weights are optimized when the amplitude and phase errors exist, and the real numbers are optimized when the errors do not exist, the number of iterations is larger than that in fig. 4b, and the convergence is relatively slow.
Experiment 2
Compared with the improved particle swarm optimization algorithm, the optimal weights obtained by the DE optimization algorithm are similar to those obtained by the improved particle swarm optimization algorithm, and since the antenna array is weighted to be symmetrical, the number of array elements is 48, and the dimension of the weights we optimize without error is Dim 24. The dimension of the weight optimized with error is Dim 48. Target side lobe value SLLd-50dB, target half power width θd＝3.2°。
The parameters of the DE algorithm are: the population number NP is 72, the crossover factor CR is 0.9, and the mutation factor F is 0.5.
Parameters of the improved Particle Swarm Optimization (PSO) are: learning factor c1＝2，c2Maximum value w of weight 2max0.8, minimum value wmin0.3, upper velocity bound vmax0.8, and 0.2.
As shown in fig. 6a, under the condition of no error, the DE algorithm can obtain the target low side lobe and main lobe width, but the PSO algorithm cannot converge to the global optimum point, as can be seen from the convergence curves of the two in fig. 6b, the DE algorithm has strong global search capability, can generate a better value almost every iteration, and can continue to converge only at a slow speed in the later stage until reaching the target function value to terminate the iteration. The PSO algorithm is easy to trap in the local extreme point, multiple iterations are needed for jumping out of the local extreme point, and the local extreme point is harder to jump out in the later period.
FIG. 7a shows that the DE algorithm can achieve an optimized main lobe width θ under the condition of 2% array element error0.5At 3 °, maximum side lobe level SLLmaxApproximately-49.1 dB, the target requirement is achieved. And the main lobe width optimized by the PSO algorithm is theta0.5At 3 °, maximum side lobe level SLLmax-38.81 dB. The DE algorithm improves the maximum side lobe level by approximately 12.2dB compared to the PSO algorithm. As can be seen from the convergence curves of both fig. 7b, the DE algorithm has strong global search capability, and the late convergence is still evolving though slow. The PSO algorithm is easy to fall into the local extreme points in the early stage, multiple iterations are needed for jumping out of the local extreme points, and the local extreme points are harder to jump out in the later stage.
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 (3)

1. A low side lobe complex weight vector optimization method based on antenna array errors is characterized by comprising the following steps:
step 1, establishing an array antenna model as a uniform linear array, and acquiring a directional diagram function expression of the uniform linear array;
step 2, obtaining a directional diagram function expression considering the amplitude-phase error according to the directional diagram function expression of the uniform linear array, wherein the directional diagram function expression considering the amplitude-phase error is a function expression about a complex weight vector;
the step 2 specifically comprises:
obtaining a directional diagram function expression F (theta) considering the amplitude-phase error according to the directional diagram function expression F (theta) of the uniform linear arrayerr(θ)：
Figure FDA0003296840020000011
Wherein k is a wave number,
Figure FDA0003296840020000012
Ψnfor the phase difference of the nth array element relative to the first array element, Ψn＝nkd[sin(θ)-sin(θ0)]Theta is the direction of the incoming wave, theta0The beam pointing direction is a uniform linear array, w is a complex weight vector, and w is ═ w1，w2，…，wn…，wN]T，wnA complex scalar quantity corresponding to the nth array element, Aerr(theta) is an array steering vector matrix taking into account amplitude-phase errors, Aerr(θ)＝[a1err(θ)，a2err(θ)，…anerr(θ)，…，aNerr(θ)]T，anerr(theta) is a guide vector corresponding to the nth array element and considering the amplitude-phase error,
Figure FDA0003296840020000013
Δanand Δ ΦnRespectively the amplitude error and the phase error of the nth array element, wherein N is the total number of the array elements contained in the uniform linear array, and d is the array element interval of the uniform linear array;
step 3, establishing a target cost function related to the complex weight vector according to the directional diagram function expression considering the amplitude-phase error;
step 4, solving the target cost function by adopting a differential evolution algorithm to obtain an optimized complex weight vector;
the step 4 specifically comprises the following substeps:
(4a) setting the dimension number of the complex weight vector w as N, wherein each dimension represents a complex weight scalar corresponding to an array element, and the amplitude value range of each complex weight scalar is [ x [ ]amin，xamax]Each complex weight scalar has a phase with a value in the range of [ xpmin，xpmax]；
Initializing a population: setting i to represent the ith individual in the population, i to 1, 2, … NP, each individual to represent one value of a complex weight vector w, j to represent the jth dimension of each individual, j to 1, 2, … N, and the one dimension of each individual to represent a complex weight scalar quantity corresponding to one array element in the complex weight vector; t represents the t generation population, i is 1, j is 1, and t is 0;
(4b) j dimension value of i individual in 0 generation population
Figure FDA0003296840020000021
Figure FDA0003296840020000022
Figure FDA0003296840020000023
Figure FDA0003296840020000024
Wherein the content of the first and second substances,
Figure FDA0003296840020000025
represents the j dimension amplitude value of the ith individual in the 0 th generation population,
Figure FDA0003296840020000026
represents the j-dimension phase value, x, of the ith individual in the 0 th generation populationamaxAnd xaminRespectively representing an upper and a lower bound of the amplitude, xpmaxAnd xpminRespectively representing the upper and lower bounds of the phase, rand representing [0, 1]Random decimal between;
(4c) adding 1 to the value of j, and repeating the substep (4b) until obtaining the N-dimensional value of the ith individual in the 0 th generation population
Figure FDA0003296840020000027
Form the ith individual in the 0 th generation population
Figure FDA0003296840020000028
And the fitness function value corresponding to the ith individual
Figure FDA0003296840020000029
(4d) Resetting j to 1, adding 1 to the value of i, and repeating the substeps (4b) and (4c) until the NP individuals in the 0 th generation population and the fitness function value corresponding to each individual are obtained;
setting the value of i as 1, setting the value of j as 1, and setting the value of t as 1;
(4e) carrying out variation operation on the ith individual in the tth generation population to obtain the ith variation individual in the tth generation population
Figure FDA0003296840020000031
Wherein the content of the first and second substances,
Figure FDA0003296840020000032
respectively representing any three different individuals in NP individuals of the t generation population, wherein M is a scale factor;
(4f) carrying out cross operation on the ith individual in the tth generation population and the ith variant individual of the tth generation population to obtain the ith cross individual of the tth generation population
Figure FDA0003296840020000033
J dimension value of ith cross individual in t generation population
Figure FDA0003296840020000034
Comprises the following steps:
Figure FDA0003296840020000035
wherein the content of the first and second substances,
Figure FDA0003296840020000036
represents the ith variant individual in the t generation population
Figure FDA0003296840020000037
The value of the j-th dimension of (c),
Figure FDA0003296840020000038
represents the ith individual in the t-th generation population
Figure FDA0003296840020000039
The j-th dimension of (1), rand represents [0, 1]]Random decimal between, CR represents the crossover factor, randn (N) represents [1, N]Random integers within the range;
sequentially taking the value of j to 1, 2 and … N to obtain the ith cross individual of the t generation population
Figure FDA00032968400200000310
(4g) The ith crossed individual of the t generation population
Figure FDA00032968400200000313
Comparing the fitness value with the fitness value of the ith individual of the t-1 generation population, and selecting the individual with a smaller fitness value as the ith individual of the t generation population
Figure FDA00032968400200000311
Figure FDA00032968400200000312
Wherein, fitness (·) represents a fitness function;
(4h) adding 1 to the value of i, and repeating the substeps (4e) to (4g) until NP individuals of the population of the t generation are obtained;
(4i) setting a fitness value threshold value and a maximum population generation number, and acquiring an individual with the minimum fitness value from NP individuals of a t-th generation population as an optimal individual;
if the fitness value of the optimal individual is smaller than or equal to the fitness value threshold, taking the complex weight vector corresponding to the optimal individual as a finally optimized complex weight vector; or if the value of t is larger than the maximum population algebra, taking the optimal individual of the population of the last generation as the finally optimized complex weight vector;
otherwise, adding 1 to the value of t, setting the value of i to 1, setting the value of j to 1, and returning to the substep (4 e).
2. The method for optimizing the low side lobe complex weight vector based on the antenna array error according to claim 1, wherein the step 1 specifically comprises:
setting the array antenna model to be a uniform linear array consisting of N array elements, wherein the array element spacing d is half wavelength, so as to obtain a directional diagram function expression F (theta) of the uniform linear array:
Figure FDA0003296840020000041
wherein k is a wave number,
Figure FDA0003296840020000042
Ψnfor the phase difference of the nth array element relative to the first array element, Ψn＝nkd[sin(θ)-sin(θ0)]Theta is the direction of the incoming wave, theta0The beam pointing direction is a uniform linear array, w is a complex weight vector, and w is ═ w1，w2，…，wn…，wN]T，wnA (theta) is an array steering vector matrix, and A (theta) is [ a ]1(θ)，a2(θ)，…，an(θ)，…，aN(θ)]T，an(theta) is a steering vector corresponding to the nth array element,
Figure FDA0003296840020000043
n is the total number of array elements contained in the uniform linear array, and d is the array element spacing of the uniform linear array.
3. The method for low sidelobe complex weight vector optimization based on antenna array errors according to claim 1, wherein the step 3 specifically comprises:
according to the directional diagram function expression F considering the amplitude-phase errorerr(θ), establishing an objective cost function for the complex weight vector as follows:
Figure FDA0003296840020000044
where, fitness (w) represents a target cost function value calculated from the complex weight vector w, and the expression min fitness (w) ═ α (SLL)s(w)-SLLd)+β(θ0.5(w)-θd) Of (1) containsMeaning as making alpha (SLL)s(w)-SLLd)+β(θ0.5(w)-θd) The minimum complex weight vector w, s.t. represents the constraint condition, alpha is the first error coefficient,
Figure FDA0003296840020000051
beta is a second error coefficient and is a first error coefficient,
Figure FDA0003296840020000052
SLLs(w) represents the maximum level of side lobes in the actual pattern, SLLs(w)＝max|wH·Aerr(θs)|，θsIndicating a side lobe region, SLLdRepresenting the target side lobe value, θ0.5(w) represents the actual half-power beamwidth, θdRepresents the target half power width, θ0For a uniform linear array of beam pointing directions, the superscript H denotes the conjugate transpose.
CN201810251335.9A 2018-03-26 2018-03-26 Low side lobe complex weight vector optimization method based on antenna array error Active CN108508424B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810251335.9A CN108508424B (en) 2018-03-26 2018-03-26 Low side lobe complex weight vector optimization method based on antenna array error

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810251335.9A CN108508424B (en) 2018-03-26 2018-03-26 Low side lobe complex weight vector optimization method based on antenna array error

Publications (2)

Publication Number Publication Date
CN108508424A CN108508424A (en) 2018-09-07
CN108508424B true CN108508424B (en) 2022-01-07

Family

ID=63378434

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810251335.9A Active CN108508424B (en) 2018-03-26 2018-03-26 Low side lobe complex weight vector optimization method based on antenna array error

Country Status (1)

Country Link
CN (1) CN108508424B (en)

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109800474B (en) * 2018-12-27 2023-06-20 南京信息工程大学 Array antenna energy allocation method based on genetic algorithm
CN111985145B (en) * 2019-05-21 2023-09-19 合肥若森智能科技有限公司 Large-space phased array antenna grating valve inhibition method and inhibition system
CN110210111B (en) * 2019-05-29 2023-02-21 重庆邮电大学 Vortex wave generation and optimization method based on time modulation concentric ring array
CN111181583B (en) * 2019-12-30 2021-10-01 华为技术有限公司 Method and device for compensating strength of transmitting and receiving signal, transmitting and receiving equipment
CN111539092A (en) * 2020-03-30 2020-08-14 南京市德赛西威汽车电子有限公司 Millimeter wave radar beam forming optimization method and antenna
CN111487594A (en) * 2020-04-23 2020-08-04 中国民航大学 Circular array beam forming method based on particle swarm optimization
CN112230227B (en) * 2020-09-25 2022-06-28 浙江大学 Array diagnosis method based on near-field measurement data

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104036078A (en) * 2014-06-06 2014-09-10 西安电子科技大学 Comprehensive design method of array antenna radiation and scattering performance based on installation height
CN106486786A (en) * 2016-10-09 2017-03-08 东南大学 A kind of series feed microstrip antenna of the low-sidelobe level of non-homogeneous array element distance
CN106788799A (en) * 2016-11-22 2017-05-31 电子科技大学 A kind of optimization method for processing various array antenna signals errors
CN107534979A (en) * 2015-04-14 2018-01-02 华为技术有限公司 A kind of Wireless Telecom Equipment and method

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8629808B2 (en) * 2006-09-22 2014-01-14 Telecom Italia S.P.A. Method and system for synthesizing array antennas

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104036078A (en) * 2014-06-06 2014-09-10 西安电子科技大学 Comprehensive design method of array antenna radiation and scattering performance based on installation height
CN107534979A (en) * 2015-04-14 2018-01-02 华为技术有限公司 A kind of Wireless Telecom Equipment and method
CN106486786A (en) * 2016-10-09 2017-03-08 东南大学 A kind of series feed microstrip antenna of the low-sidelobe level of non-homogeneous array element distance
CN106788799A (en) * 2016-11-22 2017-05-31 电子科技大学 A kind of optimization method for processing various array antenna signals errors

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Differential Evolution Using a Neighborhood-Based Mutation Operator;Swagatam Das et al.;《IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION》;20090630;第526-553页 *
基于差分进化算子的遗传算法在多波束平面阵天线综合中的应用;章仁婷 等;《遥测遥控》;20140331;第53-59页 *

Also Published As

Publication number Publication date
CN108508424A (en) 2018-09-07

Similar Documents

Publication Publication Date Title
CN108508424B (en) Low side lobe complex weight vector optimization method based on antenna array error
CN108920767B (en) The double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase
CN107302140B (en) Planar antenna array sparse method based on quantum spider swarm evolution mechanism
CN109376329B (en) Array amplitude and phase error correction method based on quantum bird swarm evolution mechanism
CN109597046B (en) Metric wave radar DOA estimation method based on one-dimensional convolutional neural network
CN104615854B (en) A kind of beam-broadening and side lobe suppression method based on sparse constraint
CN108919199A (en) Side lobe suppression method, the array Sparse methods of multi-beam imaging sonar thinned array
CN105306123A (en) Robust beamforming method with resistance to array system errors
CN104020448A (en) Optimized formation method of radar subarray-level sum/difference beams constrained by equal array elements
Ram et al. Optimized hyper beamforming of receiving linear antenna arrays using Firefly algorithm
CN114048431A (en) Beam forming method based on covariance matrix reconstruction and ADMM
CN110069896B (en) Vortex electromagnetic wave generation and optimization method based on sparse 2D linear array
Alijani et al. Development a new technique based on least square method to synthesize the pattern of equally space linear arrays
Zhao et al. Radial basis function neural network optimal modeling for phase-only array pattern nulling
Recioui et al. Synthesis of linear arrays with sidelobe level reduction constraint using genetic algorithms
CN109271735B (en) Array directional diagram synthesis method based on quantum heuristic gravity search algorithm
Ram et al. Optimal design of non-uniform circular antenna arrays using PSO with wavelet mutation
CN116882149A (en) Antenna array synthesis method based on hybrid differential drosophila optimization algorithm
CN116911162A (en) Method and system for synthesizing phase-only satellite-borne phased array antenna based on improved dayfish algorithm
CN109799486B (en) Self-adaptive sum and difference beam forming method
Li et al. Improved artificial bee colony for design of a reconfigurable antenna array with discrete phase shifters
Zhao et al. Optimal Pattern Synthesis of Array Antennas Using Improved Grey Wolf Algorithm
CN114510879A (en) Phase configuration method for arbitrary interval linear array end-fire enhancement
Gomez et al. Design of low-sidelobe linear arrays with high aperture efficiency and interference nulls
CN108828503B (en) Beam space direction finding method based on quantum cause evolution mechanism

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant