CN108808266A - A kind of four-dimensional antenna array combined optimization method for irregular subarray arrangement - Google Patents

Abstract

The invention discloses a four-dimensional antenna array joint optimization algorithm with irregular sub-array arrangement, which introduces the definition of information entropy into the four-dimensional array, divides the original complex optimization problem into two sub-problems, and then divides it into two steps for optimization. In the first step, the genetic algorithm based on information entropy is used to optimize the array topology structure with the largest information entropy value according to the subarray arrangement algorithm. Information such as the static excitation phase of each sub-array, the duration of switch closure, and the start time of switch closure can make the entire optimization problem more efficient. The greatest innovation of the present invention lies in digging out the essential characteristics of the original optimization problem, combining the genetic algorithm based on information entropy and the differential evolution algorithm for optimization, reducing the complexity of the original optimization problem, and saving half of the T/R components. The characteristics of low sidelobe and low sideband under large-angle scanning are guaranteed.

Description

A Joint Optimization Method for 4D Antenna Arrays for Irregular Subarray Arrangement

technical field

The invention belongs to the technical field of antennas, and relates to the synthesis of four-dimensional antenna arrays based on irregular sub-arrays. Specifically, a joint optimization method is used to efficiently synthesize four-dimensional antenna arrays. This joint algorithm mainly uses the principle of information entropy, and divides the synthesis of four-dimensional antenna array into two steps. First, the topology of the irregular array is optimized by genetic algorithm, and then the target pattern is synthesized as needed.

Background technique

Phased array antennas are widely used in the radar and communication fields because they can achieve the purpose of beam scanning by changing the phase. At the same time, the amplitude and phase weighting methods of conventional phased arrays are difficult to meet the requirements of low sidelobes of antenna arrays, which limits the application range of antennas.

The concept of the four-dimensional antenna array was proposed in the 1960s and emerged in the early 21st century. The antenna is designed by introducing time as a new one-dimensional degree of freedom, and the weighting of amplitude and phase is equivalently realized by using time weighting. Both It can control and improve the radiation characteristics of the antenna array, and can design narrow beams, low sidelobes and various shaped beams under the uniform static excitation amplitude, which will greatly simplify the requirements for the feed network, so the four-dimensional The introduction of the antenna idea into the traditional antenna array will be very beneficial to the design of the antenna array feed network. At the same time, the requirements for the processing accuracy of the antenna structure, feed accuracy and tolerance of the feed network will be greatly reduced, and it will have great design flexibility. sex.

In the 1960s and 1970s, foreign countries began to study sparse array antennas. Through optimization algorithms, a smaller number of array elements can be used to achieve narrower beams and pattern scanning through different arrangements. However, for the array calculated by the optimization algorithm, the position of the array elements is generally very irregular, and the processing and arrangement of the array elements are very difficult problems. Although a periodic array with a large unit spacing can solve the above-mentioned arrangement and processing problems, due to the increase of the unit spacing, the sidelobe level of the array increases, and even grating lobes appear, limiting the array to scan only a small angle .

Considering the basic principle of the antenna array, the periodicity of the array arrangement is the main cause of the grating lobes of the pattern, so how to break the periodicity of the array becomes the main idea of suppressing the grating lobes. R.J.Mailloux, Andrea Massa et al proposed The method of using irregular sub-arrays is used to break the periodicity of the array, but because the optimization problem is too complicated, their scheme can only realize one-dimensional scanning, which is poor in engineering applicability. The patent No. CN 107230843 A adopts a similar scheme to realize two-dimensional scanning, but the scanning performance is not strong. The sub-array composed of two units is arranged at a 0.7 wavelength interval under the 20×20 array. Only two-dimensional scanning of ±20° can be realized. This solution has not fully utilized the scanning advantages of irregular sub-arrays, and its applicability in engineering is poor.

Contents of the invention

In view of the above technical background, the present invention proposes a four-dimensional antenna array joint optimization algorithm with irregular sub-array arrangement, the purpose is that compared with the existing optimization technology, the proposed method of the present invention can synthesize large-scale Irregular four-dimensional array.

The joint method proposed by the present invention is mainly aimed at the irregular four-dimensional array of pulse phase shift time sequence. According to the characteristics of the irregular four-dimensional array under this time sequence, the whole joint optimization process can be divided into two steps. The first step is to use the genetic algorithm to optimize the topological structure of the irregular array according to the principle of information entropy; the second step is to use the differential evolution algorithm to optimize the topology of each sub-array on the basis of the first step and according to the known topological structure. Static excitation amplitude, static excitation phase, switch closure duration, switch closure start time to suppress sidelobe level and sideband level.

The present invention has the following contents:

In order to define the disorder degree of irregular sub-array arrangement, we introduce the concept of information entropy. Assuming that X is a random variable, n represents a total of n possible outputs, and P(X) represents the output probability function. Therefore, the information entropy of X is:

H(X)＝E[-log _b (P(X))] (1)

If b is set to 2, formula (1) can be rewritten as

Considering an irregular array of M×N, only the irregular sub-array is composed of two array elements. The situation of multiple elements is similar. The phase center of the sub-array is its center of gravity. The antenna array consists of multiple sub-arrays. The composition of the array arrangement, for the sake of simplicity, it is assumed that the array unit is a square grid, and the spacing between the array elements is d, then the information entropy of the array is

Among them, r _i represents the phase center of gravity of r _i sub-arrays in column i, c _j represents the phase center of gravity of c _j sub-arrays in column j, and T represents the number of sub-arrays in the array. For a sub-array composed of two array elements In other words, it is MN/2 subarrays.

Each sub-array in the irregular four-dimensional array is connected to a high-speed radio frequency switch, and the switching function is U _ij (t). Then the far-field distribution in this sequential form is:

i∈{0.5,1,1.5...M-0.5},j∈{0.5,1,1.5...N-0.5}

in Represents the element pattern of a four-dimensional array; Indicates the array factor pattern of the binary _subarray ; I _{ij indicates} the static excitation amplitude of the array; α _ij indicates the static excitation phase of the array; ; G represents the collection of the center coordinates of all sub-arrays.

The irregular four-dimensional antenna array works at the center frequency f ₀ , the time modulation period of the switch is T _p , and the time modulation frequency f _p =1/T _p . The switching function U _ij (t) with pulse phase shift time modulation is expressed as:

t _ij represents the start moment of the switch closure of the control unit, and τ _ij represents the duration of the switch closure of the control unit. According to signal and system theory, the time-domain expression of the periodic function of the switch can be expanded in the frequency domain by Fourier series:

The expression of the kth harmonic of the far field brought into (4) and (5) is:

Therefore, the whole joint optimization process can be divided into two steps.

The first step is to use the principle of information entropy and genetic algorithm to optimize the arrangement of irregular sub-arrays, in which the optimization variables are only integers, so as to find a solution that satisfies the following optimization problems.

In the second step, the array arrangement obtained in the first step is regarded as known, and the non-integer variables are optimized by using the differential evolution algorithm, that is, the start time of switch closure, the switch closure time, the switch closure duration and the static excitation phase, to Suppresses sideband and sidelobe levels. That is, find a solution W that satisfies the following questions.

Where Θ _sidelobe represents the sidelobe area of the normalized field distribution at the center frequency, t _ij represents the initial moment of switch closure, τ _ij represents the switch closure time, and α _ij represents the static excitation phase.

The innovation of the present invention lies in the development of a joint optimization algorithm to quickly and efficiently synthesize the low-sidelobe and low-sideband pattern of the four-dimensional antenna array in the form of irregular sub-arrays. Compared with the prior art, the present invention has the following advantages:

1. Through a reasonable analysis of the constraint conditions of the center frequency and sideband fields, a step-by-step approach is adopted to decompose an originally very complicated comprehensive problem into two relatively simple comprehensive problems, without losing the generality of the problem Under the premise, the difficulty of synthesis is reduced.

2. The use of irregular sub-arrays can still ensure that the antenna array has the characteristics of low sidelobe, low sidelobe, and high gain under the condition of reducing half of the T/R components, saving costs and reducing the complexity of feeding .

3. The antenna elements are still periodically arranged on the front surface without destroying the consistency of the antenna array, making the antenna array easier to mass produce and process.

4. This solution can maximize the scanning advantages of irregular sub-arrays, and can realize two-dimensional scanning of ±65° in a large array environment.

Description of drawings

Figure 1 is a four-dimensional array structure diagram of an irregular sub-array.

FIG. 2 is an arrangement diagram of the irregular sub-arrays in Example 1 (M×N=16×16).

Fig. 3 is the normalized three-dimensional pattern of side-firing under the phased array system in Example 1.

Fig. 4 is a diagram of static amplitude excitation distribution in side-fire under the phased array system in Example 1.

Fig. 5 is a normalized three-dimensional pattern when the elevation plane is scanned for 30 degrees under the phased array system in Example 1.

Fig. 6 is an excitation distribution diagram of a 30-degree static amplitude scanning on the elevation plane under the phased array system in Example 1.

Figure 7 is the static phase excitation distribution diagram of scanning the elevation plane at 30 degrees in the phased array system in Example 1

Fig. 8 is a normalized three-dimensional pattern when scanning the azimuth plane at 30 degrees under the phased array system in Example 1.

Fig. 9 is a static amplitude excitation distribution diagram when the azimuth plane is scanned at 30 degrees under the phased array system in Example 1.

Figure 10 is the distribution diagram of the static phase excitation when scanning the azimuth plane at 30 degrees under the phased array system in Example 1

Fig. 11 is a three-dimensional direction diagram normalized by the center frequency when shooting sideways under the four-dimensional array system in Example 1.

Fig. 12 is a three-dimensional pattern normalized by the frequency of the first sideband when shooting sideways under the four-dimensional array system in Example 1.

Fig. 13 is a timing diagram of partial switching when shooting sideways under the four-dimensional array system in Example 1.

Fig. 14 is a three-dimensional direction diagram of the 45-degree center frequency of scanning D plane under the four-dimensional array system in Example 1.

Fig. 15 is a three-dimensional direction diagram of the first sideband at 45 degrees of scanning D plane under the four-dimensional array system in Example 1.

Fig. 16 is a static amplitude excitation distribution diagram when scanning the D surface at 45 degrees under the four-dimensional array system in Example 1.

FIG. 17 is a partial switch timing diagram when scanning the D surface at 45 degrees in the four-dimensional array system in Example 1.

FIG. 18 is an arrangement diagram of the irregular sub-arrays in Example 2 (M×N=36×36).

FIG. 19 is a three-dimensional direction diagram of the center frequency at 65 degrees of the scanning elevation plane in Example 2 under the four-dimensional array system.

FIG. 20 is a three-dimensional direction diagram of the first sideband of the scanning elevation plane at 65 degrees under the four-dimensional array system in the second example.

Fig. 21 is a three-dimensional direction diagram of the center frequency of the scanning azimuth plane at 65 degrees under the four-dimensional array system in Example 2.

Fig. 22 is a three-dimensional direction diagram of the first sideband of the scanning azimuth plane at 65 degrees under the four-dimensional array system in Example 2.

Specific implementation mode one

Considering a four-dimensional array of irregular sub-arrays, the size of the array is M×N=16×16, only considering that the irregular sub-array is composed of two array units, so there are 16×16/2=128 sub-arrays in total, and the sub-arrays The antenna units in the array have the same static excitation amplitude, static excitation phase, switch closing start time and switch closing duration. The switch sequence selects the pulse translation sequence. The reference array is a Chebyshev planar array with 16×16=256 units.

Other main parameters are as follows:

d = d _x = d _y = 0.5λ

The first step is to optimize the arrangement of irregular sub-arrays, as shown in Figure 1, an irregular array with a total of 128 sub-arrays is obtained, and the information entropy of this array is H=5.9114, where H _r and H _c are respectively:

Since the values of H _r and H _c are almost the same, it means that the scanning performance of the array in the elevation plane and the azimuth plane is roughly the same. Figure 3-Figure 10 shows the scanning performance of the array arranged under the phased array system situation and the corresponding static excitation amplitude distribution, static excitation phase distribution. It can be seen that the algorithm using information entropy can reasonably allocate degrees of freedom to ensure the scanning performance of the array at various angles.

In the second step, using the differential evolution algorithm switch closure start time and switch closure duration and other information, a directivity pattern with a side lobe of -29.5dB, a directivity coefficient of 22.61dB, and a first sideband of -31.0dB is finally obtained. , as shown in Figure 11-Figure 13. Among them, Figure 13 is a partial switch timing diagram. The array element position corresponding to the sub-array number 1 is (1,1)(2,1), and the array element position corresponding to the sub-array number 2 is (1,2)(1, 3), the array element position corresponding to the number 3 sub-array is (3,10)(3,11), the array element position corresponding to the number 4 sub-array is (3,12)(4,12), and the array element position corresponding to the number 5 The array element position corresponding to the sub-array is (8,8)(9,8), the array element position corresponding to the number 6 sub-array is (8,9)(9,9), and the array element corresponding to the number 7 sub-array The position is (11,5)(12v5), the element position corresponding to the sub-array numbered 8 is (14,4)(14,5), and the element position corresponding to the sub-array numbered 9 is (16,13)( 16,14), the array element position corresponding to the number 10 sub-array is (16,15)(16,16).

For the same array arrangement, optimize the switch closing start time, switch closing duration and static excitation phase distribution, you can get a side lobe of -17.5dB, directivity coefficient of 20dB, first sideband of -22.1dB, scanning The direction diagram at 45 degrees to the D plane is shown in Figure 14-Figure 17. Among them, Figure 17 is a partial switch timing diagram. The array element position corresponding to the sub-array number 1 is (2,9)(2,10), and the array element position corresponding to the sub-array number 2 is (1,0)(1, 1), the array element position corresponding to the number 3 sub-array is (2,5)(2,6), the array element position corresponding to the number 4 sub-array is (3,7)(3,6), and the array element position corresponding to the number 5 The array element position corresponding to the sub-array is (7,4)(8,4), the array element position corresponding to the number 6 sub-array is (7,8)(7,9), and the array element corresponding to the number 7 sub-array The position is (8,12)(8,13), the element position corresponding to the sub-array numbered 8 is (11,1)(11,2), and the element position corresponding to the sub-array numbered 9 is (12,2 )(12,3), the array element position corresponding to the number 10 sub-array is (16,15)(16,16).

Specific implementation mode two

Consider a large four-dimensional array of irregular sub-arrays, the size of the array is M×N=36×36, only considering that the irregular sub-array is composed of two array elements, and the distance between array elements is d=d _x =d _y = 0.5λ, the closing time of the switch is limited to [0.1μs, 1μs].

Through the array synthesis of this scheme, the main performance indicators of the four-dimensional array are: the pitch plane scans to 65°, the side lobe is -19.72dB, the directivity coefficient is 29.51dB, and the first sideband is -26.24dB; the azimuth plane scans to 65°, the side lobe is -20.35dB, the directivity coefficient is 29.52dB, and the first sideband is -26.06dB. The specific direction diagram and arrangement scheme are shown in Figure 18-22.

The foregoing descriptions of the present invention and its embodiments are provided to those skilled in the art of the invention and are to be considered illustrative rather than restrictive. Engineers and technicians can implement specific operations based on the idea in the invention claims combined with specific problems, and naturally can also make a series of changes to the implementation plan according to the above. All of the above should be considered as the scope of the present invention.

Claims (3)

1. A four-dimensional antenna array joint optimization algorithm for irregular sub-array arrangements, characterized in that the definition of information entropy is introduced into the four-dimensional array, the original complex optimization problem is divided into two sub-problems, and then divided into two steps To optimize, the first step is to use the genetic algorithm based on information entropy to optimize the array topology with the largest information entropy value. In the second step, the array arrangement obtained in the first step is regarded as known, and the differential evolution algorithm is used to optimize Non-integer variables, namely switch closure start time, switch closure time, switch closure duration and static excitation phase, are used to suppress sideband and sidelobe levels. 2. four-dimensional antenna array joint optimization algorithm according to claim 1, is characterized in that, described first step is specifically as follows: Among them, R _i represents the phase center of gravity of the i-th row of the sub-array, C _j represents the phase center of gravity of the sub-array at the j-th column, T represents the number of sub-arrays of the array, Indicates the form of the kth sub-array on the (m, n)th unit, and U _ij indicates the unit in the i-th row and j-column. 3. according to the described four-dimensional antenna array joint optimization algorithm of claim 1 or 2, it is characterized in that, described second step is specifically as follows: Where Θ _sidelobe represents the sidelobe area of the normalized field distribution at the center frequency, t _ij represents the initial moment of switch closure, τ _ij represents the switch closure time, and α _ij represents the static excitation phase.