2.2.1 Bent dipole antenna

Dipole antenna, also known as element antenna, is a commonly used microwave antenna. In order to make the antenna structure more compact and miniaturized, a curved structure is used. The radiation direction of the antenna radiates omnidirectionally along the plane perpendicular to the bending axis [23].

2.2.2 Microstrip antenna

Microstrip antennas are another common microwave antenna. The common one is a planar structure, which is simple and easy to integrate, low cost, and excellent in directivity [24]. It can also be made into a conformal antenna, which is easy to form circular polarization. There are many types of microstrip antennas. According to the structure, they can be divided into microstrip patch antennas and microstrip slot antennas; according to the shape, they can be rectangular, triangular, circular, circular, etc.; according to the working principle, they can be divided into resonant type (standing wave Type) and non-resonant type (traveling wave type) microstrip antenna, as shown in Figure 3 [25].

Figure 3: Microstrip antenna structure.

2.2.3 Array antenna

An array antenna is a form of antenna that arranges multiple radiation sources according to a certain rule or randomly, and obtains the best radiation directivity by adjusting different parameters such as feed current, spacing, and electrical length [26]. Common radiation sources are point source and symmetrical array. With the in-depth research of communication technology, new adaptive array antennas are gradually being promoted to achieve omnidirectional coverage.

2.2.3.2 Yagi antenna

The Yagi antenna is an end-fire antenna which is composed of an active vibrator (usually a folded vibrator), a passive reflector and several passive directors arranged in parallel [28]. The Yagi antenna is a typical high-gain directional antenna, which is particularly effective for direction finding and long-distance communication. The antenna installation process needs to ensure that the polarization of the transmitter and receiver is consistent. As shown in Figure 4(b).

Figure 4: Array antenna.

Because the traditional electronic tag antenna design is relatively simple and cannot meet the functional requirements of receiving energy and forwarding signals in a specific direction in the environmental backscatter system [29], it is necessary to design a new type of tag antenna to meet the requirements of the power Internet of Things environment. Backscatter system requirements.

3.2.1 Receiving antenna structure

Considering that the receiving antenna needs to receive signals from the environment approximately omnidirectionally, the receiving antenna first selects a four-element microstrip antenna. The quaternary microstrip antenna belongs to the standing wave patch antenna. It only has a radiating element on one side of the medium. It can be fed by a microstrip line or a coaxial line, but from the characteristics of the patch antenna, it is not an omnidirectional Antenna, and the bandwidth is relatively narrow. Therefore, the structure of the receiving antenna is improved in this design to make it an omnidirectional broadband antenna.

In the first version of the program design, the most basic rectangular patch was selected for simulation, and the coaxial probe was used to feed power.There are many ways to broaden the frequency band of a microstrip antenna. Because the shape of the patch affects the bandwidth, the patch and floor are often grooved or cut to change the shape of the patch. According to formula (1), the width L of the highefficiency rectangular radiation patch is designed.

$L=\frac{c}{2f_0}\frac{1}{\sqrt{\frac{1}{{\epsilon }_e}}}-2\Delta L$ (1)

In addition, the impedance bandwidth conversion formula can calculate the 50Ω input impedance corresponding to the width of the bottom of the microstrip line = 3mm. By cutting off an isosceles triangle on each of the four corners of the rectangular patch, and cutting off a rectangle on each of the top, left and right sides to achieve a gradual effect. In order to extend the bandwidth, the upper two corners of the grounding plate were cut, and two symmetrical rectangular slots were opened on the grounding plate. In addition, two rectangles are cut under the ground plate to reduce the floor space of the ground plate. The broadband microstrip antenna unit model is shown in Figure 5.

Figure 5: Broadband microstrip antenna unit model.

In the antenna design process, by changing the position and size of the cut triangle, the size of the rectangular slot on the ground plate, and the length of the ground plate, the matching of the antenna bandwidth and performance was improved. The improved fourelement patch antenna structure is shown in Figure 6.

Figure 6: Broadband microstrip antenna array model.

3.2.2 Transmitting antenna structure

Because the transmitting antenna is a directional antenna, an endfire antenna such as a log-period dipole antenna is first considered. The log-period dipole antenna (LPDA) is a broadband linearly polarized antenna. In order to make the tag structure more concise, a plane printing structure is adopted to integrate the transceiver antenna on a plane. For the transmitting antenna, the log periodic antenna is a directional end-fire antenna with a wide frequency band. However, in order to cover point-view signals, WIFI, 4G, and 5G signals in the environment as much as possible, the antenna bandwidth needs to be further extended. Therefore, the log-period antenna still has room for improvement.

From the antenna analysis theory, it is known that attaching parasitic patches near the logarithmic period long array is similar to the design of expanding the bandwidth of the Yagi antenna, which can effectively change the resonance mode, thereby broadening the bandwidth of the antenna. The antenna structure is shown in Figure 7. The length of the antenna element is denoted by L_n, and the extension of the end of each antenna element intersects at a point, called a virtual vertex, and the opening angle is α. Denote the vertical distance from the virtual vertex to each antenna element as R_n, the width of the element as W_n, and the distance between two adjacent elements as d_n.

Figure 7: Log-period antenna with parasitic patch.

The geometric structure of the antenna is determined by the geometric factor τ and the spacing factor σ.

$\tau =\frac{R_{n+1}}{R_n}=\frac{L_{n+1}}{L_n}=\frac{d_{n+1}}{d_n}$ (2)

$\sigma =\frac{d_n}{4h_n}$ (3)

The number of antenna elements can be obtained by the following formula:

$N_a=1+\frac{\lg (K_2/K_1)}{\lg \tau }$ (4)

Among them, K1 and K2 are cutoff coefficients.

$K_1=1.01-0.519\tau$ (5)

$K_2=7.10{\tau }^3-21.3{\tau }^2+21.98\tau -7.30\text{ +}\sigma \text{(21}\text{.82}-66\tau +62.12{\tau }^2-18.29{\tau }^3\text{)}$ (6)

In addition, it is also necessary to estimate the width of the vibrator.

$Z_a\approx 120\left\{{\log }_e(h/a)-2.25\right\}$ (7)

LPDA is a directional end-fire antenna, and the maximum radiation direction is from towards the short dipole end. Generally speaking, the larger the value, the greater the number of oscillators in the radiation area, the stronger the directivity of the antenna, and the smaller the half-power angle of the pattern. The length of the longest vibrator and the shortest vibrator of LPDA determines its operating frequency.

LPDA is a linearly polarized antenna. When the vibrator of the LPDA is placed horizontally, it will radiate or receive horizontally polarized waves; when placed vertically, it will radiate or receive vertically polarized waves. Therefore, it is easier to achieve circular polarization with a planar structure.

3.2.3 Antenna structure determination

The final antenna structure consists of a broadband microstrip antenna array and a log-period dipole antenna, as shown in Figure 8. Both antennas are broadband antennas, and the frequency meets the 5G signal requirements. The microstrip antenna array is responsible for receiving signals in the environment and forwarding them through a log-periodic antenna. There are fewer side lobes. Since the feed end of the log periodic antenna is at the short end, it cannot be directly connected. It is necessary to connect the feed network of the microstrip array to the feed end of the log periodic antenna through a coaxial line.

Figure 8: Antenna model.

3.3.1 Multi-objective genetic algorithm

Genetic algorithm is a global algorithm that simulates natural selection and survival of the fittest, and evolves generation by generation to find the optimal solution [30]. The algorithm starts from the initial population of the first generation and evolves from generation to generation to get closer to the optimal solution [31]. In each generation, the fitness function is calculated according to the solved target, sorted and selected according to the fitness from high to low, and one or more points of crossover mutation are performed with the help of genetic operators to generate the progeny population. When the fitness meets the requirements or the number of cycles reaches the set number of iterations, the outstanding individuals of the last generation are the results of the final search [32]. Genetic algorithm has the advantages of not relying on gradient information and strong robustness, so it is widely used in the field of electromagnetic engineering, especially antenna design.

The traditional solution to multi-objective problems is to convert multi-objectives into single objects, such as weighting or constraints, and searching with single-objective solutions. However, the shortcomings are also obvious. The weights of multiple targets need to be set by themselves, and only one solution can be generated per calculation [33]. The MOGA used in this paper can obtain the Pareto solution set of multiple objectives at once.

This paper adopts NSGA-Ⅱ genetic algorithm and introduces the concept of Elitism. On the basis of traditional genetic algorithm, a non-dominant sorting process is added, that is, the parent and offspring are mixed and then sorted and selected to prevent the loss of outstanding individuals from the parent. At the same time, in order to maintain the diversity of the population, density estimation and comparison operators are used in the selection of the binary tournament to effectively prevent local convergence. Therefore, this article makesthe above selection, and the algorithm flow chart is shown in Figure 9.

Figure 9: Multi-objective genetic algorithm graph.

3.3.2 Application of multi-objective genetic algorithm

Since the directional antenna has a greater impact on the physical layer security, and the structure of the log-period dipole antenna is more complicated, the transmitting antenna is used as the optimized antenna. Select the length, width and spacing of the vibrator as the variables to be optimized. In the antenna design process, the gain, bandwidth, and sidelobes of the antenna are important indicators to measure the performance of the antenna, so the functions corresponding to the above three indicators are defined as the objective function.

A multi-objective optimization problem with 3 decision variables and 3 objective functions can be expressed as

$optimal\overline{f}(\overline{x})=[f_1(\overline{x}),f_2(\overline{x}),f_3(\overline{x})]$ (8)

Among them, $\overline{f}(\overline{x})$ represents the objective function vector, $f_1(\overline{x}),f_2(\overline{x}),f_3(\overline{x})$ represents the objective function, $\overline{x}=[L_1,L_2,\mathrm{...}{L}_n,d_1,d_2,\mathrm{...},d_n,w_1,w_2,\mathrm{...},w_n].$ Define X and Z to represent the search space and target space respectively, and use the mapping $\overline{f}:X\to Z$ to indicate that each vector corresponds to the vector $\overline{z}=\overline{f}(\overline{x})\in Z.$

Limit the length of the high-order vibrator to be greater than the length of the low-order vibrator, and take values within a suitable range. According to the physical meaning of the variable, the optimization range L∈[30,200], d∈[0.5,20], w∈[2,7] (unit: mm) is given.