CN105205253B - A kind of optimization method of bare cloth circular antenna array - Google Patents

Abstract

The invention discloses an optimization method for a sparsely distributed circular antenna array, which comprises the following steps: (1) adopting an indirect method to generate individuals to construct an initial population; (2) performing genetic pretreatment on the population; (3) performing generalization on the population Crossover and generalized mutation; (4) Perform genetic post-processing on the population, and select dominant individuals according to their fitness; (5) Iterative optimization to obtain the optimal individual and the minimum peak sidelobe level. The feature of the circular array optimized by this method is that the array elements are distributed non-uniformly on the circular aperture and not limited to the auxiliary ring. This method can make greater use of the degrees of freedom of the array elements, which is more efficient than the traditional genetic algorithm and can Make the antenna array get lower side lobe level.

Description

An Optimization Method for Sparse Circular Antenna Array

technical field

The invention relates to an array antenna design method, in particular, it uses an improved genetic algorithm to realize the design of a sparsely distributed circular antenna array with multiple design constraints. With the help of equidistant auxiliary rings designed on the circular aperture, the sparsely distributed antenna array is designed using the characteristics of the circular ring array. Circular array antenna to achieve the lowest possible peak sidelobe level.

Background technique

The circular array antenna is one of the most important array antenna types among the multi-element antenna types, and it is widely used in the fields of communication and radio astronomy. The circular ring array antenna has ideal directional characteristics in its azimuth direction, and its circular structural characteristics make its beam, antenna gain and other performances basically stable. Because the circular array antenna has the above characteristics, it is widely used in many engineering practices, but the circular array antenna has a relatively high peak side lobe level, so the design of the circular array antenna has become an important research topic.

There are two types of circular array antennas according to the distribution of array elements: one is a sparse array where the array elements are sparsely spaced from a regular circular grid with a distance of half a wavelength; the other is that the antenna unit is constrained in the design Random sparse array within a certain aperture range. In recent years, in order to obtain sparse arrays with good peak sidelobe performance, comprehensive methods such as statistical optimization methods, dynamic programming methods, genetic algorithms, simulated annealing methods, and particle swarm optimization methods have emerged. However, there are few studies at home and abroad on sparse arrays with greater degrees of freedom. Therefore, the research on the low sidelobe level of sparse circular array antenna has very practical significance.

Contents of the invention

The object of the present invention is to provide an improved genetic algorithm to optimize the sparsely distributed circular antenna array, and to reduce the peak sidelobe level of the sparsely distributed circular array antenna as much as possible under the constraints of the number of array elements, aperture and minimum spacing.

In order to achieve the above object, the technical solution of the present invention is as follows.

In the case of constrained aperture, number of array elements and minimum spacing, based on the improved genetic algorithm, through the method of indirect representation of individuals, use generalized genetic operations, genetic preprocessing and genetic postprocessing to optimize the position of the array elements, and no longer constrain the array elements It must be located on the auxiliary ring to increase the degree of freedom of each array element and obtain a lower peak sidelobe level.

Model: On a plane circular aperture, the model for calculating the radiation characteristics of the array antenna from the position of the array element is:

in

cosα _n = sinθcos(φ-φ _n ); u = sinθcosφ; 0≤θ≤π

v=sinθsinφ; 0≤φ≤2π;

λ is the working wavelength;

k=2π/λ;

N is the number of optimization variables, that is, the total number of array elements;

0≤θ≤π and are the elevation and azimuth angles, respectively;

I _n is incentive;

ψ _n is the excitation phase of the array element;

r _n is the polar coordinate radius of array element n;

φ _n is the angle of array element n in the polar coordinate system, θ is the azimuth angle, and φ is the elevation angle.

Under the condition that the number of constrained array elements is N, the aperture and the minimum array element spacing d, all array elements have the same excitation, so it is assumed that all array elements I _n =1, ψ _n =0. By optimizing the position of the array element to obtain a lower peak sidelobe level, the optimization function is:

Where D=[d ₁ ,d ₂ ,…,d _N ], the fitness function is expressed as:

The objective function is:

f(d ₁ ,d ₂ ,…,d _N )=min{H(D)} (4)

Among them, d _m and d _n represent the coordinates of the mth and n array elements, d is the minimum array element spacing constraint, R is the aperture, Z is a set of positive integers, F _max is the peak value of the main lobe, and the side lobe area E(θ,φ) θ and The value range of is all areas except the main lobe area.

The detailed steps are as follows:

1: Generation of initial population

In order to make better use of the degrees of freedom of the array elements, the position of the array elements is optimized. A complex vector C is used to indirectly represent the optimization individual. Figure 2 is a uniform circular ring array with aperture r=(a+1)d, where a∈Z is the number of circular rings, and d is the array element spacing. Under the condition of constraining the minimum spacing d of array elements, the distribution of array elements on each ring is uncertain. That is, assuming that the distance between adjacent array elements is not less than d, k _i array elements are distributed on the i-th ring, and k _i can be expressed by the following formula:

where r _i is the radius of the ith ring, is rounded down. For the structure shown in Figure 2, the array element distribution is uncertain under the known ring aperture. Assuming the constrained minimum array element spacing d=λ/2, the maximum number of array elements _{ki on each ring and the corresponding phase angular spacing ρ i can} be calculated, that is, the angular spacing of adjacent array elements on the same ring , as shown in Table 1.

Table I

Because k _i array elements are evenly distributed on the i ring, so ρ _i is:

A complex vector C can be expressed as:

Where a=r/d-1 is the number of rings, k _i (i=1,2,...,a) is the maximum number of elements on the i-th ring, ρ _i (i=1,2,... ,a) is the average angular spacing when there are ki array elements on the _i -th ring. C is related to the array element constraint d and the angular spacing ρ _i , so it is also related to the number of array elements, so C can be regarded as a constraint vector. On the basis of C, the auxiliary vector F _t can be obtained through the following sub-steps:

1.1. Suppose a The real column vector M ₀ of is, its element values are in the range of [0,0.5λ], and they are sorted from small to large. Divide M ₀ into a segment. The k _1th array element is in the first section of M ₀ , and the second section has k ₂ array elements, that is, k ₂ array elements from (k ₁ +1) to (k ₁ +k ₂ +1). So segment a contains the last k _a array elements of M ₀ . Since the array elements are randomly distributed in each segment, a new dimensional random vector:

The vector η has the following characteristics: the array elements on each segment are randomly distributed according to the size, but each element of the (k+1) segment is not smaller than any element on the k segment.

1.2. Assuming a random vector [ξ ₁ ,ξ ₂ ,…,ξ _a ] ^T , the element values are in the range of [0,2π], specifically expressed as:

ζ=[ξ ₁ ,…,ξ ₁ ,ξ ₂ ,…,ξ ₂ ,…ξ _a ,…,ξ _a ] ^T (9)

The first segment has k ₁ ξ ₁ , and so on. From this it can be obtained that ζ also has dimension, there is also a section. The characteristic of ζ is that the elements in different segments are unequal random numbers, but the elements in each segment are equal.

1.3, on the basis of the complex vector C, the auxiliary vector F _t is as shown in formula (10), the element of η is used as the modulus of the complex number, added to the corresponding modulus of the complex vector C, and the ζ element is used as the argument of the complex number, Added to the argument corresponding to the complex vector C, so the auxiliary vector F _t can be expressed as:

It can be proved that F _t satisfies the three design constraints and also makes good use of the degrees of freedom of the array element.

1.4. The individual vector u is a sparsely distributed vector composed of N non-zero array elements, and The search vector S can record which elements in the auxiliary vector F _t are retained, and the search vector is defined as follows:

Definition 1: For vector I, if the qth array element is sparse, the value of the search vector related to the qth array element is '0', otherwise it is '1'.

On the basis of the search vector F _t , the individual vector I can be obtained through the sparse auxiliary vector F _t :

I=S.*F _t (11)

Considering that both F _t and S contain A one-dimensional array of elements, F _t and S scalar multiplication can get the individual vector I.

For example, the search vector S is:

So the individual vector I can be expressed as:

It can be proved that the individual vector I is a feasible solution in the solution space, so it can be used as an optimization variable.

Step 2: Repeat the above operation M times independently to obtain an initial population U consisting of M Is. This unique generation method ensures that each individual in the initial population satisfies the constraints of the number of array elements, array aperture and minimum array element spacing.

Step 3: Genetic Processing

The traditional genetic algorithm cannot describe the individual directly, so it will produce an infeasible solution. In order to prevent the generation of infeasible solutions, some genetic algorithm operations need to be changed. We refer to the modified GA operations as generalized crossover and generalized mutation.

Definition 2: array element matrix: array element matrix G _A , each column is a constraint matrix C, so there is rows and M columns.

Definition 3: Population constraint matrix: The population constraint matrix _{G M} is separated from GA according to the population search matrix S _M .

G _M ＝S _M .*G _A (14)

Definition 4: Genetic preprocessing: Before performing generalized crossover and generalized mutation, genetic preprocessing obtains the genetic information matrix P from the parent population U ₁

where G _M is the population constraint matrix of population U ₁ , |·| represents the modulo operation of complex numbers, Angle operator for complex numbers.

Definition 5: Genetic post-processing operation: After generalized crossover and generalized mutation, genetic post _- processing constructs the population U2 from the genetic information matrix P again

where G _M is the population constraint matrix related to population P. At the same time, the offspring population P is obtained from the parent population P through generalized crossover and generalized mutation.

Step 4: Generalized crossover operation and generalized mutation operation

Like the traditional genetic algorithm crossover, the generalized crossover is used to exchange the elements of the non-zero modulus of the two chromosomes, and then reset the elements of the element modulus. The reset operation makes the modulus vector satisfy the property of η. The detailed reset operation is as follows: the modulus vector, that is, the column vector of |P|, can be divided into a segment, and first find the smallest element of each segment. Suppose the smallest element of the i-th segment is w, and then compare it with the modulus of each element of the (i-1)th segment, if the modulus of an element of the (i-1)th segment is greater than w, replace it with w . Likewise, after performing generalized crossover, in order to satisfy the ζ property, two column vectors elements need to be reset.

Generalized variation changes the genetic information of parent individuals. First randomly select an element from a column of the genetic information matrix P, if this element is 0, use Instead, the largest modulus of the element whose r _i is smaller than the segment i is greater than the smallest modulus of the element, φ _i ∈ [0,2π]. If the selected element is non-zero, replace it with 0. In this process, in order to satisfy the constraint on the number of array elements, the number of non-zero elements must remain unchanged. Second, resetting also makes the vector satisfy the property of η, and makes the angle vector satisfy the property of ζ. Finally, the modulus and angle vectors are able to reconstruct the genetic information matrix P (representing the new genetic information of the offspring).

The traditional genetic algorithm directly performs crossover and mutation operations on the coding of the optimization variable, while the generalized crossover and generalized mutation operate on the genetic information matrix P, instead of directly operating the optimization variable, but derived from the genetic process. On the other hand, including the traditional genetic algorithm, these two generalized genetic operations can ensure that the genetic information of the offspring is valid, that is, _Sson , _ηson and _ζson are valid . The above operations are called generalized crossover and generalized mutation operations. The generalized crossover and generalized mutation operations make the modified genetic algorithm search faster and have better convergence characteristics.

Optimize the initial population through genetic preprocessing, generalized crossover and generalized mutation, and genetic postprocessing, iteratively obtain the optimal individual, and obtain a lower peak sidelobe level. The present invention proposes to use sparse vectors to indirectly represent individuals on the basis of uniform circular arrays, instead of directly describing individuals in traditional genetic algorithms. Using generalized genetic operations, genetic preprocessing and genetic postprocessing can ensure that all individuals are feasible solutions in the iterative process, which greatly improves the efficiency of the modified genetic algorithm.

Description of drawings

Figure 1 The model of sparse planar circular array

Figure 2 Uniform 9-ring array

Radiation pattern of the example in Figure 3

Figure 4 is an example of the far-field pattern when φ=0°, φ=45°, and φ=90°

The array element distribution diagram of the example in Figure 5

Detailed ways

The optimized implementation mode of the present invention is described in detail below

Embodiments of the present invention are given below. It can be seen from the accompanying drawings that the present invention optimizes the position of the array element through the aperture and the sparse ratio, and proves the validity and feasibility of the method. Figure 1 is a model diagram of a sparsely distributed circular loop antenna array. This example is to optimize the element position of the sparsely distributed circular ring antenna array whose design parameters are aperture r≤4.5λ, sparsely distributed rate of 70% and number of array elements of 184 (excluding the array elements on the center of the circle). Figure 3 is the far-field radiation pattern of the optimal planar ring array. On the φ plane, the PSLL is -22.723dB, and the worst PSLL is -22.051dB. Fig. 4 is the far-field pattern at φ=0°, φ=45°, and φ=90°. The optimal array element distribution is shown in Figure 5.

Claims (4)

1. A method for optimizing a sparse circular antenna array, comprising the following steps: Step 1: Generate indirectly described individuals and construct the initial population; Wherein, the initial population generation steps are as follows: Step 1.1: Under the constraint that the distance between adjacent array elements is not less than d, distribute k _i array elements on the i-th ring, where r _i is the radius of the ith ring, is rounded down, because k _i array elements are evenly distributed on the i-th ring, so the angular spacing ρ _i of adjacent array elements on the same ring is From this, the complex vector C is constructed as: Wherein, a=(R/d)-1 is the number of rings, k _i is the maximum array element number on the ith ring; Step 1.2: Get the initial individual from the constructed auxiliary vector F _t and search vector S; structure dimensional random vector The first section has k ₁ elements, the a-th section has k _a elements, all element values are in the range of [0,0.5λ], λ is the working wavelength, and the elements on each section are randomly distributed according to the size, and ( Each element of segment k+1) is not smaller than any element of segment k; Construct a random vector [ξ ₁ ,ξ ₂ ,L,ξ _a ] ^T , the value of each element is in the range of [0,2π], the first element repeats k ₁ times, the ath element repeats k _a times, specifically expressed as ζ=[ξ ₁ ,L,ξ ₁ ,ξ ₂ ,L,ξ ₂ ,L,ξ _a ,L,ξ _a ] ^T , and also Dimensional vector, characterized by: the elements in different segments are not equal, but the elements in each segment are equal; On the basis of the complex vector C, the element of η is used as the modulus of the complex number and added to the corresponding modulus of the complex vector C, and the element of ζ is used as the argument of the complex number and added to the argument corresponding to the complex vector C, so the auxiliary vector _Ft can be expressed as: Step 1.3: On the basis of the search vector S, the individual vector I can be obtained by multiplying the auxiliary vector F _t by a scalar: I=S.*F _t Both F _t and S contain A one-dimensional vector of elements, F _t and S scalar multiplication can get the individual vector I in sparse form; Repeat the above operation M times independently to obtain an initial population consisting of M Is; Step 2: Select dominant individuals and perform genetic pretreatment on the population; Step 3: carry out generalized crossover and generalized mutation operation to population; Step 4: Perform genetic post-processing on the population to complete the extraction of genetic information; Step 5: Iteratively perform steps 2 to 4 to optimize the population, and finally obtain the array with the optimal side lobe level. 2. The method as claimed in claim 1, its uniqueness lies in that, by means of the auxiliary ring, realizes a kind of design method of circular sparse antenna array with unequal distances of the array elements on the circular aperture, and it is not necessary to limit each array element It must be designed on the auxiliary ring to ensure that the array aperture, array element spacing and the total number of array elements meet the given constraints. 3. The method of claim 1, wherein the genetic manipulation is characterized as follows: (1) The object of the genetic operation is not the parent population itself. The genetic operation object of this method is the genetic information matrix P, which is specially extracted from the parent population. Correspondingly, before calculating the fitness value, it is necessary to reconstruct the new population and reconstruct The construction process is the reverse process of the extraction process; (2) The content of the genetic operation is different from the basic genetic algorithm, using generalized crossover and generalized mutation, Generalized crossover is used to exchange the non-zero modulus elements of two individuals, and then reset the order of the elements; the detailed reset operation is as follows: find out a segment, first find the smallest element in each segment, and then Compare with the modulus of each element in the previous adjacent segment, if the modulus of an element in the previous segment is larger, swap; Generalized mutation changes the genetic information of the parent individual. First, an element is randomly selected from the column of the genetic matrix. If the element is 0, use Instead, it is required that r _i is less than the maximum modulus and greater than the minimum modulus of this segment in a segment, φ _i is a random value in the range of 0 to 2π, if the selected element is non-zero, replace it with 0, in this process, non-zero The number of elements remains the same. 4. method as claimed in claim 1 is characterized in that, the function of calculating fitness is: Among them, the electric field strength E is the side lobe area of the radiation pattern function when the position of the array element on the circular plane aperture is arbitrary, and the specific calculation model of the electric field strength E is as follows: Among them, d ₁ , d ₂ ,…, d _N are the position coordinates of the array element cosα _n = sinθcos(φ-φ _n ); N is the number of optimization variables, that is, the total number of array elements; λ is the working wavelength; k=2π/λ; θ, are the elevation and azimuth angles, respectively; I _n is incentive; ψ _n is the phase of the array element; r _n is the radius in polar coordinates of array element n; φ _n is the angular position of array element n in the polar coordinate system; d _m and d _n represent the coordinates of the mth and nth array elements, d is the minimum array element spacing constraint, R is the aperture, and Z is a set of positive integers; u=sinθcosφ; 0≤θ≤π; v=sinθsinφ; 0≤φ≤2π; FF _max is the main lobe peak, θ and The value range of is all side lobe areas except the main lobe area.