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To lower the peak sidelobe level (PSLL) of sparse concentric ring arrays, a method with multiple design constraints that embed a function model into modified real genetic algorithm (MGA) and select the grid ring radii as optimization individual to synthesize sparse concentric ring arrays is proposed. The multiple constraints include the array aperture, the minimum element spacing, and the number of elements. The proposed method dynamically calculates the ratio of element on each ring, and it has a faster convergence rate than other algorithms. The MGA uses real number to code the optimization variable, and it reduces the complexity of coding and improves the search efficiency. Finally, the results demonstrate the accuracy and effectiveness of the algorithm.

Antenna array plays an important role in technology, including mobile communication, radar system, satellite, and medical treatment. For example, in [

The PSLL is an important criterion to evaluate the performance of the antenna array. Thus, with the multiple design constraints, including the number of elements, the aperture of array, and the minimum spacing of element, it is an important research topic to reduce the PSLL of antenna array in recent years [

Due to the difference of element sparsity degree on each auxiliary ring [

In a planar array, generate a point randomly; the point is selected as centre point, and then generate several circles with different radius and place some elements on each ring; the resulting planar array is a concentric ring array [

Diagram of concentric ring array.

Place an element in the centre of the concentric ring array; the radiation pattern can be described as

For simplicity, we assume that array antenna meets the ideal conditions, including the element that is isotropic and the element that has uniform excitation amplitude and phase shift. The weight in the same ring is equal, and the elements in each ring are uniform distribution. The direction of main beam of the array points to the normal direction of the array, and the array pattern can be described as

If the sparse concentric ring array has multiple constraints, including the number of rings

The flowchart of function model algorithm using MGA is shown in Figure

The flowchart of function model algorithm using MGA.

There is a conclusion in [

The fitting data: element number (

method | PSLL (dB) | | | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|---|---|

Opt | -27.82 | 142 | | 0.76 | 1.36 | 2.09 | 2.99 | 3.78 | 4.70 |

| 9 | 17 | 25 | 31 | 26 | 33 | |||

| |||||||||

| 9 | 17 | 26 | 37 | 47 | 59 | |||

| |||||||||

| 9/9 | 16/16 | 25/26 | 31/37 | 26/47 | 33/59 |

In Table

The function model fits the data in Table

Function model | Model parameter | |||
---|---|---|---|---|

a | b | c | | |

Linear model: | -0.1969 | 0.00228 | 0.6543 | 0.9602 |

Gauss model: | 1.015 | 0.716 | 4.705 | 0.9168 |

Sine model: | 1.054 | 0.2152 | 1.633 | 0.9018 |

Power model: | 1.013 | -0.2878 | 0.6812 | |

Rational model: | 5.468 | 4.315 | 0.7541 | |

Polynomial model: | -0.1331 | 1.166 | 0.8791 |

Plot the fitting data and function model in Figure

Function model diagram.

In the fitting function model, the

Standard genetic algorithm uses 0,1 binary code for individual, and it has a low efficiency. MGA uses real number code for individual directly, and it has a high freedom of search and efficiency. The main steps of MGA include generating initial population, calculating fitness value, selection, crossover, and mutation.

We select ring radii

Bring

If the termination conditions (the number of iterations reaches the limit or the PSLL meets the requirement) are met, output the optimal individual and the minimum PSLL of the current population, end. Otherwise, continue.

Sort the individual according to fitness value.

In order to meet the requirement of minimum element spacing

The precrossover genetic operator is

The premutation genetic operator is

In order to verify the efficiency of proposed method, two simulations were performed. We set some common parameters for two simulations, such as selecting equation (

We set the same parameter values as [

Comparing the optimal result of

method | PSLL (dB) | | | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|---|---|

HGA [ | -22.94 | 201 | | 1.0 | 1.59 | 2.14 | 2.88 | 3.66 | 4.98 | |

| 12 | 19 | 26 | 36 | 45 | 62 | | |||

| ||||||||||

Opt | -25.45 | 201 | | 0.80 | 1.38 | 1.88 | 2.43 | 3.18 | 3.91 | 4.98 |

| 10 | 17 | 22 | 27 | 33 | 40 | 51 | |||

| ||||||||||

MGAFMA | -26.21 | 201 | | 0.72 | 1.22 | 1.72 | 2.39 | 3.18 | 3.93 | 4.98 |

| 9 | 15 | 21 | 28 | 35 | 41 | 51 |

The diagram of element configuration.

Radiation pattern of the optimal result.

The cut of radiation pattern

The convergence characteristics.

According to [

Comparing the optimal result of

method | PSLL (dB) | | | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|---|---|

Opt | -27.82 | 142 | | 0.76 | 1.36 | 2.09 | 2.99 | 3.78 | 4.70 |

| 9 | 17 | 25 | 31 | 26 | 33 | |||

| |||||||||

Opt | -28.07 | 142 | | 0.76 | 1.36 | 2.09 | 2.92 | 3.77 | 4.70 |

| 9 | 16 | 26 | 30 | 27 | 33 | |||

| |||||||||

FMAMGA | -28.19 | 142 | | 0.84 | 1.37 | 2.10 | 2.95 | 3.78 | 4.70 |

| 10 | 17 | 25 | 29 | 29 | 31 |

The diagram of element configuration.

Radiation pattern of the optimal result.

The cut of radiation pattern

The convergence characteristics.

In this paper, a function model that presents the relationship between ring radius and the degree of sparsity is proposed, which is embedded into the process of MGA to synthesize the sparse concentric ring arrays for low PSLL. Comparing the optimal result with other literatures proves that the proposed method is an efficient way to reduce the PSLL and has a faster convergence rate. It is reasonable and efficient to select the element number in the rings according to the function model.

The data of this paper can be accessed for the public; the data have been uploaded to github repository and all the data present in the research are available. The chart, docx data used to support the findings of this study, the result of figure, and the program of this research have been deposited to the github repository; these data can be accessed through

Kesong Chen, Yafei Li, and Jiajia Shi declare that there are no conflicts of interest regarding the publication of this paper.

The research is funded by joint fund for civil aviation (U1233103).