An example of the structure of a 4-element linear array antenna using open-end CPW-fed MSAs is shown in Figure 1. The radiating face is shown in (a), the feeding face is shown in (b), and a cross-section of the part at the dashed line is shown in (c). The patch width W is defined as the length of the patch in the direction perpendicular to the feed line, and the patch length L is defined as the length of the patch in the direction that is parallel to the feed line. The patches are arranged along a straight line, as shown in Figure 1(a). Slots are placed on the back side of the patches, as shown in Figure 1(b). The length of the slots is 100 mm, and the slots are arranged such that their centers are aligned with the centers of the patches. Considering expansion to an adaptive array antenna, we chose a linear array antenna construction for the antenna constituting the fundamental element. Figure 2 shows a conceptual diagram of an adaptive array antenna composed of 16 elements where 4 basic elements are lined up to tilt the beam, in which the basic elements are the 4-element linear array antennas shown in Figure 1. Here, the 4-element linear array antennas are arranged in parallel, and liquid crystal-loaded phase shifters are connected to the feed lines of each one. The tilt of the maximum radiation direction of the main beam in the x-axis direction in Figure 2 can be controlled. For the design of the CPWs, the width of the central conductor is set to a = 1.80 mm, the slit width is set to b = 0.10 mm, and the distance between the centers of neighboring patches is set to the patch pitch d_p so that the characteristic impedance becomes approximately 50 Ω. The printed circuit board has a dielectric thickness of h = 0.50 mm, permittivity of ε_r = 2.60, and conductor thickness of r = 0.018 mm.

In the adaptive array antenna shown in Figure 2, the purpose is controlling the directivity of the main beam through the phase shifters, so we designed the linear array antenna in this investigation such that the maximum radiation direction faces in the direction (z-axis direction) perpendicular to the face in which the linear array antenna is arranged. In the array antenna, the maximum radiation direction is determined by the phase difference of each element, but because the elements in the linear array antenna are arranged on the same feed line, the

element spacing has a large impact on the relative phase between the elements. The equation for the relationship between the element spacing and the maximum radiation direction in the linear array antenna is shown in Equation (1) [11] .

Here, θ represents the offset at the x = 0 face where the z-axis direction is taken to be 0˚, and λ₀ represents the free space wavelength. The maximum radiation direction is designed to be in the z-axis direction, θ = 0, so the effective wavelength on the feed line waveguide λ_g is obtained according to Equation (2).

Based on Equation (2), when making the maximum radiation direction face in the z-axis direction, the element spacing should be set to be equivalent to one wavelength of the radiated electromagnetic wave. Therefore, the element spacing d_p was made to vary within the range 11.00 - 13.50 mm which corresponds to 0.9 λ_g - 1.1 λ_g, and the electromagnetic field simulation software was used to calculate the changes in the maximum radiation direction. As a result of optimizing the size of the patch in the design of one element [10] , we obtained W = 6.90 mm and L = 3.90 mm. In Figure 3, an offset of the maximum radiation direction from the z-axis to the positive y-axis direction is defined to be positive. When the element spacing d_p was 11.00 mm, the offset angle became 0˚. The radiation characteristics for this situation at 20 GHz are shown in Figure 4, and the frequency characteristics of the reflection loss are shown in Figure 5. Figure 4 shows the radiation characteristics for the yz face, for which the effects of the array are significant. The maximum value of the directional gain was 13.70 dBi. In Figure 5, it can be seen that there are several points for which the resonance frequency deviates from the design value of 20 GHz. Verifying the electric field distributions at these resonance points, we determined that the resonance point due to phase resonance based on the design value was at 20.45 GHz. Therefore, we performed optimization on the patch width W and the patch length L so that this resonance point would become 20 GHz. First, to adjust the resonance frequency to 20 GHz, we performed an analysis while varying the patch length L in the range 3.90 - 4.20 mm at intervals of 0.05 mm. The change in the resonance frequency is shown in Figure 6. The resonance frequency becomes f_r = 19.98 GHz when L = 4.05 mm. Therefore, we set L = 4.05 mm, and performed an analysis while varying the patch width W in the range 3.50 - 6.50 mm at intervals of 0.50 mm in order to improve the return loss. The change in the reflection loss is shown in Figure 7. The dotted, dash-dotted, and solid lines show the cases in which W = 6.50 mm, 5.00 mm, and 4.00 mm, respectively. These results show that as the patch width W becomes smaller, the return loss improves and the resonance frequency increases. This is because the effective wavelength changes along with W because of the change in the effective permittivity directly below the patch. Furthermore, given that the maximum radiation direction changed at the same time due to the change in the patch width W, we attempted tore-op- timize the element spacing d_p, patch width W, and patch length L, and obtained a resonance frequency of 20.05 GHz and return loss of −29.59 dB at the resonance frequency when d_p= 11.50 mm, W = 3.90 mm, and L = 4.15 mm. The return loss for this situation is shown in Figure 8, and the frequency characteristics at 20 GHz are shown in Figure 9. Based on the results in Figure 8, it can be

seen that resonance points exist at frequencies other than 20 GHz. The results in Figure 9 show that the maximum value of the directional gain is 13.6 dBi, and the maximum radiation direction is the z-axis direction. The radiation characteristics at the other resonance point, 18.51 GHz, are shown in Figure 10. The maximum radiation direction has changed. Since the radiation direction changes significantly depending on the frequency, it is necessary to suppress undesired resonance points in order to prevent receiving undesired signals. In the next section, we describe a method that uses impedance-matching circuits as a method to suppress undesired resonance points.

The 4-element linear antenna considered in the previous section had multiple resonance points. It was demonstrated that the maximum radiation direction changes for resonance points other than 20 GHz. In this section, we discuss the results of our investigation on placing an impedance-matching circuit on the CPW as a method for solving this problem. Previous studies have reported the creation of filters using short stubs for CPWs [12] . According to reference [12] , the impedance Z_l of the load side separated from the transmission line of line length l can be represented by Equation (3).

To match impedances, the reactance of the parallel stub is represented as j_X, and the designer should connect a circuit with j_X needed to cancel the imaginary part of Z_l shown in Equation (3). Here, the parameters of the stub that can be adjusted include the line length l and stub reactance j_X. Considering the impedance of the stub side as viewed from the feed line, the short stub represents the case where Z_l = 0 in Equation (3), so it can be expressed as shown in Equation (4).

In the 4-element linear array antenna considered here, it is necessary to adjust the impedance-matching circuit to suppress the resonances at frequencies other than the design frequency of 20 GHz. In other words, setting the line length l to λ_g/2 so that Z_l in Equation (4) becomes zero changes the impedance at wavelengths other than λ_g, making it is possible to suppress the undesired resonance points at frequencies other than 20 GHz.

The stub circuit used to load the feed line on the back face of the linear array antenna under consideration is shown in Figure 11. A short stub with a shortened tip is used. The stub length is defined as L_s, and the distance from the feed point to the stub is defined as d_c. The central conductor width and slit width of the stub are a = 1.80 mm and b = 0.10 mm, similar to the feed line. The adjustable parameters of the stub include the stub length and the stub arrangement positions. In this investigation, we set the stub length L_s to λ_g/2 = 6.10 mm, and analyzed the changes in the antenna characteristics with respect to changes in dc using the electromagnetic field simulation software. The return loss S₁₁ at 20 GHz is shown in Figure 12. The largest return loss of −25.22 dB was obtained when d_c = 37.50 mm. Next, we analyzed the changes in the characteristics with respect to changes in the stub length L_s. The changes in return loss at 20 GHz are shown in Figure 13. Because we obtained S₁₁ = −46.5 dB when the stub length was L_s = 5.95 mm, we determined that this is the optimal value. Furthermore, the frequency characteristics of the return loss for this situation are shown in Figure 14, and the radiation characteristics are shown in Figure 15. The solid line shows the return loss frequency characteristics for the case with the stub, and the dotted line shows the characteristics for the case without the stub. Figure 14 shows that the undesired resonances are suppressed well, and that the return loss at the design frequency has been improved. On the other hand, as shown in Figure 15, the gain in the maximum radiation direction decreased.

While the gain was 13.6 dBi without the stub, the gain was 11.2 dBi with the stub. This is believed to be caused by the stub radiating waves from the face with the feed line at the back of the antenna. In addition, the side lobes increased.

In the previous section, we demonstrated that loading with the stub circuit was effective for suppressing undesired resonances, but the gain between the patch face and the opposite face with the feed line increased due to radiation from the stub. Therefore, we attached a stub circuit with a slit as shown in Figure 16. We propose a method for reducing the backward radiation by strengthening the coupling between the stubs. This is done by generating aperture coupling between the stubs by creating slits within the stubs. Since the value of λ_g in the stub circuits may change due to the slits, we performed optimization of the stub length L_s. Figure 17 shows the changes in the return loss with respect to the stub length L_s. When L_s = 5.70 mm, S₁₁ = −42.53 dB, and f_r = 19.99 GHz. This was chosen as the optimal value. The return loss for this situation is shown in Figure 18, and the radiation characteristics are shown in Figure 19. For return loss, the

undesired resonances were suppressed after loading with the stub as well, and no large changes were seen. For radiation characteristics, on the other hand, a gain improvement of 0.5 dBi was seen.