*2.2. Optimal Phase Control for Adaptive WPT*

Due to the imperfection of the manufacturing and experimental setting, the beam may not exactly be directed to the desired direction, which reduces the power received at the receiver. Moreover, in the practical scenarios, the coding metasurface should perform adaptive beam tracking according to the position of the mobile receiving devices. In order to tackle the above-mentioned problem, we propose an optimal phase control scheme allowing us to localize the receiver and focus the power toward that desired position based on the experimental data. The procedure of obtaining the adaptive optimal phase is presented in Figure 3.

**Figure 3.** The block diagram of the proposed adaptive optimal phase control scheme.

Each unit cell in the metasurface can be considered as an antenna element in an array antenna. Therefore, we can mathematically express the system model as below:

$$y = \sum\_{i=1}^{M} h\_i \mathbf{x}\_i + n\_\prime \tag{6}$$

where *M* is the number of unit cells in the metasurface, *n* is the additive white Gaussian noise, and *hi* is the channel corresponding to the *i*th unit cell with the state *xi*.

For adaptive beam focusing, we have to know the channel to obtain the optimal phase at the metasurface. Analogous to the multiple input single output (MISO) system, we can estimate the channel from each unit cell to the receiver using predefined pilots. Recently, researchers in [23–25] attempted to estimate the channels of the intelligent surface by sending data with one unit cell in "ON" state and the others in "OFF" state at a given training time. However, this method would be impractical, especially when it comes to a huge number of unit cells in the metasurface, as the reflected signal from only one "ON" unit cell is too feeble compared to the rest. Consequently, this leads to unfeasible measurement of the change in the received signal at different training times. Therefore, to tackle this problem, we used 256 independent ON/OFF patterns of the metasurface, which is based on the Hadamard matrix, as training pilots. Then, the adaptive optimal phase control scheme is proposed with the following steps:


#### **3. Design of Coding Metasurface**

#### *3.1. Unit Cell Design*

In order to have a good performance coding metasurface, a unit cell should be precisely designed to have particular characteristics. As the ISM (industrial, scientific, and medical) band is free and pervasive, we selected 5.8 GHz which is in the ISM band as the target operating frequency in this work. The final 1-bit unit cell structure is presented in Figure 4. The unit cell is designed on a substrate of Taconic RF-35 with a permittivity of 3.5 and loss tangent of 0.0018. A PIN diode (SMPA1320-079LF-203195B) is integrated with each unit cell to connect the main unit cell with the ground plane through a metal via hole. Thus, it can enable the two states of the unit cell. The operation of the unit cell is ensured by a bias line which is connected to the control board.

**Figure 4.** Unit cell structure.

The equivalent circuit for the two states of the PIN diode is given in Figure 4. As can be seen, in an ON state, the PIN diode behaves as a series circuit of a resistance and an inductance, whereas it acts as a series circuit of a capacitance and an inductance. Under an EM wave illumination, the impedance of the PIN diode can be described as:

$$Z\_{pin}(\omega) = \begin{cases} R + j\omega L & \text{ON state} \\ j\omega L + \frac{1}{j\omega \mathbb{C}} & \text{OFF state} \end{cases} \tag{7}$$

where *R* = 0.9 Ω, *L* = 0.7 nH, and *C* = 0.23 pF. The EM wave will be reflected at the PIN diode and be re-radiated at unit cell surface with the reflection coefficient, which is calculated as:

$$\Gamma(\omega) = \frac{Z\_{\text{pin}}(\omega) - Z\_{\text{R}}}{Z\_{\text{pin}}(\omega) + Z\_{\text{R}}} = |\Gamma| e^{j\phi} \tag{8}$$

where *ZR* is the radiation impedance of the unit cell. One should find the structure which provides an appropriate value of *ZR* to obtain a 180◦ phase change between ON and OFF states at the objective frequency. In order to easily figure out the proper value of radiation impedance and reduce the uncontrolled reflection from the unit cell, the unit cell structure should be designed to resonate at the objective frequency. Normally, a rectangular patch with approximately half wavelength dimensions is used as a resonant structure. However, in this work, we used the fractal structure to achieve compact size (a quarter wavelength) but provided the same performance as the rectangular patch. The detailed dimensions of the unit cell are given in the Table 1.


**Table 1.** The unit cell dimensions.

The unit cell is simulated using commercial software CST studio suite and the simulated reflection magnitude and phase of the unit cell are shown in Figure 5. It is obvious that at 5.8 GHz, while the reflection magnitude is almost identical between the ON and OFF state, the reflection phase between the two cases has 180◦ change. The maximum unit cell loss is around 0.5 dB for the OFF state. It is evident that the proposed 1-bit unit cell is suitable for the coding metasurface. As the phase change between ON/OFF states is relative, we can simply state that a unit cell with an ON state corresponds with a 180◦ phase reflection and one with an OFF state has a 0◦ phase reflection.

**Figure 5.** The simulation results of the unit cell: (**a**) reflection magnitude; (**b**) reflection phase.
