4.1.1 Antenna specifications

For the first example, the considered reflectarray is circular and comprised of 912 unit cells (34 elements in the main axes). The periodicity is 5.36 mm in both axes, which is half a wavelength at the working frequency, 28 GHz, in order to avoid grating lobes [5]. The feed is placed at (�79.3, 0.0, 200.2) mm with regard to the centre of the reflectarray (see Figure 4), and it is modelled as a cos <sup>q</sup> θ function, with q ¼ 20:6, generating an illumination taper of �14.6 dB at the reflectarray edges.

The unit cell shown in Figure 4 is used here. The separation between dipoles is set to Sai ¼ Sbi ¼ 1mm (i ¼ 1, 2), while the width of all dipoles is set to 0.3 mm. Variables Tx and Ty are defined as

$$\begin{aligned} L\_{a\_4} &= T\_{x}; \quad L\_{b\_1} = L\_{b\_3} = 0.63T\_{x}; \quad L\_{b\_2} = 0.93T\_{x} \\ L\_{b\_4} &= 0.95T\_{y}; \quad L\_{a\_1} = L\_{a\_3} = 0.58T\_{y}; \quad L\_{a\_2} = T\_{y}. \end{aligned} \tag{17}$$

reflection coefficient ρxx (the phase shift for polarization Y is the same). After the POS, the synthesized phase shift of Figure 7b is obtained, which generates the desired radiation pattern. Then, by using the procedure summarized in Figure 5,

For polarization X: (a) starting phase distribution (in degrees) obtained with Eq. (15) for the POS and

(b) synthesized phase distribution (in degrees) after the POS with the generalized IA.

Reflectarray Pattern Optimization for Advanced Wireless Communications

DOI: http://dx.doi.org/10.5772/intechopen.88909

The obtained layout was simulated with a MoM-LP [18], and the resulting radiation pattern for polarization X is shown in Figure 8, where the copolar and crosspolar components of the far field are shown in the u v plane for the whole visible region. In this representation, it can be seen the sectored beam is along the v axis for constant u, while along u the squared-cosecant beam reduces the gain of the antenna from a maximum of 19.6 dBi to roughly 5 dB. This represents a dynamic range of almost 15 dB in which the shaped beam has to smoothly decrease over an angular span of 50°, making it challenging pattern to synthesize. In fact, it is very easy to obtain nulls in this region that penalize performance, even in simulations [21], and they have been avoided with success in the present example. Similar

On the other hand, Figure 9 represents the main cuts in elevation and azimuth for both linear polarizations along with the mask requirements. Here, it can be

Radiation pattern in the whole visible region radiated by the reflectarray designed for a 5G base station for polarization X. (a) Copolar component of the far field. (b) Crosspolar component of the far field.

the reflectarray layout is found.

Figure 7.

Figure 8.

63

results were obtained for polarization Y.

The same substrate is used in both layers of the unit cell, with ε<sup>r</sup> ¼ 3:0 and tan δ ¼ 0:0010, which corresponds to the commercially available Rogers R3003. In addition, the bottom layer has a height of hA ¼ 30mil ¼ 0:762mm, while the top layer has a height of hB ¼ 20mil ¼ 0:508mm. Figure 6 presents a unit cell study at central frequency, showing the phase shift produced by the reflectarray element as well as the losses. As it can be seen, the angular stability is good while having low losses better than �0.3 dB. Furthermore, the phase shift provided by the unit cell is more than 720°, which is more than enough for a reflectarray design and subsequent optimization.

Regarding the far field specifications, the chosen pattern for the 5G base station has a 30° sectored beam in azimuth and a squared-cosecant beam in elevation to provide constant power flux in an elevation span of 50°.

### 4.1.2 Results of the antenna design

The starting point for the POS is a pencil beam pointing at ð Þ θ ¼ 10:4°, φ ¼ 0 . This direction corresponds to a region of the specification masks with high gain. To obtain this radiation pattern, the phase-shift distribution calculated with Eq. (15) is employed, and it is shown in Figure 7a for polarization X, that is, for the direct

#### Figure 6.

Unit cell study for the reflectarray for 5G base station at 28 GHz showing the phase shift (left) and the magnitude (right) for several angles of incidence. Unit cell presents a good angular stability with low losses.

Reflectarray Pattern Optimization for Advanced Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.88909

Figure 7. For polarization X: (a) starting phase distribution (in degrees) obtained with Eq. (15) for the POS and (b) synthesized phase distribution (in degrees) after the POS with the generalized IA.

reflection coefficient ρxx (the phase shift for polarization Y is the same). After the POS, the synthesized phase shift of Figure 7b is obtained, which generates the desired radiation pattern. Then, by using the procedure summarized in Figure 5, the reflectarray layout is found.

The obtained layout was simulated with a MoM-LP [18], and the resulting radiation pattern for polarization X is shown in Figure 8, where the copolar and crosspolar components of the far field are shown in the u v plane for the whole visible region. In this representation, it can be seen the sectored beam is along the v axis for constant u, while along u the squared-cosecant beam reduces the gain of the antenna from a maximum of 19.6 dBi to roughly 5 dB. This represents a dynamic range of almost 15 dB in which the shaped beam has to smoothly decrease over an angular span of 50°, making it challenging pattern to synthesize. In fact, it is very easy to obtain nulls in this region that penalize performance, even in simulations [21], and they have been avoided with success in the present example. Similar results were obtained for polarization Y.

On the other hand, Figure 9 represents the main cuts in elevation and azimuth for both linear polarizations along with the mask requirements. Here, it can be

Figure 8.

Radiation pattern in the whole visible region radiated by the reflectarray designed for a 5G base station for polarization X. (a) Copolar component of the far field. (b) Crosspolar component of the far field.

direct-to-home broadcasting in the Ku-band at 12.5 GHz, based on a real mission

For the first example, the considered reflectarray is circular and comprised of 912 unit cells (34 elements in the main axes). The periodicity is 5.36 mm in both axes, which is half a wavelength at the working frequency, 28 GHz, in order to avoid grating lobes [5]. The feed is placed at (�79.3, 0.0, 200.2) mm with regard to the centre of the reflectarray (see Figure 4), and it is modelled as a cos <sup>q</sup> θ function, with q ¼ 20:6, generating an illumination taper of �14.6 dB at the reflectarray

The unit cell shown in Figure 4 is used here. The separation between dipoles is set to Sai ¼ Sbi ¼ 1mm (i ¼ 1, 2), while the width of all dipoles is set to 0.3 mm.

La<sup>4</sup> ¼ Tx; Lb<sup>1</sup> ¼ Lb<sup>3</sup> ¼ 0:63Tx; Lb<sup>2</sup> ¼ 0:93Tx

The same substrate is used in both layers of the unit cell, with ε<sup>r</sup> ¼ 3:0 and tan δ ¼ 0:0010, which corresponds to the commercially available Rogers R3003. In addition, the bottom layer has a height of hA ¼ 30mil ¼ 0:762mm, while the top layer has a height of hB ¼ 20mil ¼ 0:508mm. Figure 6 presents a unit cell study at central frequency, showing the phase shift produced by the reflectarray element as well as the losses. As it can be seen, the angular stability is good while having low losses better than �0.3 dB. Furthermore, the phase shift provided by the unit cell is more than 720°, which is more than enough for a reflectarray design and subse-

Regarding the far field specifications, the chosen pattern for the 5G base station has a 30° sectored beam in azimuth and a squared-cosecant beam in elevation to

The starting point for the POS is a pencil beam pointing at ð Þ θ ¼ 10:4°, φ ¼ 0 . This direction corresponds to a region of the specification masks with high gain. To obtain this radiation pattern, the phase-shift distribution calculated with Eq. (15) is employed, and it is shown in Figure 7a for polarization X, that is, for the direct

Unit cell study for the reflectarray for 5G base station at 28 GHz showing the phase shift (left) and the magnitude (right) for several angles of incidence. Unit cell presents a good angular stability with low losses.

provide constant power flux in an elevation span of 50°.

Lb<sup>4</sup> <sup>¼</sup> <sup>0</sup>:95Ty; La<sup>1</sup> <sup>¼</sup> La<sup>3</sup> <sup>¼</sup> <sup>0</sup>:58Ty; La<sup>2</sup> <sup>¼</sup> Ty: (17)

with Southern Asia coverage.

Advances in Array Optimization

4.1.1 Antenna specifications

edges.

4.1 Reflectarray for 5G base station

Variables Tx and Ty are defined as

quent optimization.

Figure 6.

62

4.1.2 Results of the antenna design

Figure 9.

Main cuts for both linear polarizations in (a) elevation and (b) azimuth with the mask requirements for the reflectarray designed for a 5G base station.

better appreciated how the specifications are met, with side lobes lower than 2 dB, which represent a SLL better than 20 dB for this shaped pattern. In addition, Figure 10 shows the radiation pattern in 3D perspective, along with a sketch of the reflectarray panel.

Thus, a total of 1824 variables will be considered. The copolar requirements are the

After the crosspolar optimization, the radiation pattern shown in Figure 11 was obtained for polarization X. When compared with the far field of Figure 8, it can be seen how the crosspolar pattern maximum value has been considerably reduced while keeping the copolar pattern within specifications. In fact, the maximum copolar gain is now 19.7 dBi and 19.6 dBi for polarizations X and Y, respectively. At the same time, the maximum crosspolar values are 15.7 and 15.4 dBi, with CPmaxXPmax values of 35.4 and 35.0 dB for polarizations X and Y, respectively. This represents an improvement of 9.7 and 8.6 dB for both linear polarizations. This information is summarized in Table 1. Finally, Figure 12 shows the layout of the

For the second example, an elliptical reflectarray with axes 1128mm 1080mm and comprised of 6640 elements, is considered. The reflectarray cells are arranged in a rectangular grid of 94 90 elements for polarization X and 93 89 elements for polarization Y, with a periodicity of 12 mm in both axes. The working frequency

Initial design 19.6 6.12 25.7 19.6 6.84 26.4 Optimized design 19.7 15.75 35.4 19.6 15.40 35.0

For the reflectarray for 5G base station, summary of the performance of the initial and optimized designs regarding the maximum copolar gain (CPmax), the maximum crosspolar gain (XPmax) and the difference

Polarization X Polarization Y CPmax XPmax CPmaxXPmax CPmax XPmax CPmaxXPmax

maximum copolar gain is imposed for both linear polarizations. The goal is to

Radiation pattern in the whole visible region radiated by the reflectarray designed for 5G base station for polarization X after the optimization to improve the cross-polarization performance: (a) copolar component of

max 40 dB below the

same, while for the crosspolar pattern, a constant template Txp

Reflectarray Pattern Optimization for Advanced Wireless Communications

4.2 Reflectarray for direct-to-home satellite application

minimize the crosspolar pattern as much as possible.

the far field and (b) crosspolar component of the far field.

DOI: http://dx.doi.org/10.5772/intechopen.88909

optimized reflectarray for both layers.

CPmax and XPmax are in dBi, while CPmaxXPmax is in dB.

between them (CPmax-XPmax) for both linear polarizations.

4.2.1 Antenna specifications

Table 1.

65

Figure 11.

Regarding the cross-polarization performance, the initial design presents maximum crosspolar values of 6.1 and 6.8 dBi for polarizations X and Y, respectively, while the maximum copolar gain is 19.6 dBi for both polarizations. This gives a maximum copolar gain/maximum crosspolar gain ratio (CPmax/XPmax from here on) of 25.7 and 26.4 dB for polarizations X and Y, respectively. The following step will be to improve the ratio CPmax/XPmax by minimizing the crosspolar component of the far field while keeping the copolar pattern within specifications and maintaining the maximum copolar gain. To this end, a direct optimization layout will be performed using the generalized intersection approach. Now, the optimizing variables will be variables Tx and Ty as defined in Eq. (17), instead of the phases of the reflection coefficients. In addition, since the starting point already complies with the copolar requirements, all variables will be optimized at the same time.

Figure 10. 3D representation of the copolar component of the radiation pattern for a 5G base station.

Reflectarray Pattern Optimization for Advanced Wireless Communications DOI: http://dx.doi.org/10.5772/intechopen.88909

Figure 11.

better appreciated how the specifications are met, with side lobes lower than 2 dB, which represent a SLL better than 20 dB for this shaped pattern. In addition, Figure 10 shows the radiation pattern in 3D perspective, along with a sketch of the

Main cuts for both linear polarizations in (a) elevation and (b) azimuth with the mask requirements for the

Regarding the cross-polarization performance, the initial design presents maximum crosspolar values of 6.1 and 6.8 dBi for polarizations X and Y, respectively, while the maximum copolar gain is 19.6 dBi for both polarizations. This gives a maximum copolar gain/maximum crosspolar gain ratio (CPmax/XPmax from here on) of 25.7 and 26.4 dB for polarizations X and Y, respectively. The following step will be to improve the ratio CPmax/XPmax by minimizing the crosspolar component

of the far field while keeping the copolar pattern within specifications and maintaining the maximum copolar gain. To this end, a direct optimization layout will be performed using the generalized intersection approach. Now, the optimizing variables will be variables Tx and Ty as defined in Eq. (17), instead of the phases of the reflection coefficients. In addition, since the starting point already complies with the copolar requirements, all variables will be optimized at the same time.

3D representation of the copolar component of the radiation pattern for a 5G base station.

reflectarray panel.

reflectarray designed for a 5G base station.

Advances in Array Optimization

Figure 9.

Figure 10.

64

Radiation pattern in the whole visible region radiated by the reflectarray designed for 5G base station for polarization X after the optimization to improve the cross-polarization performance: (a) copolar component of the far field and (b) crosspolar component of the far field.

Thus, a total of 1824 variables will be considered. The copolar requirements are the same, while for the crosspolar pattern, a constant template Txp max 40 dB below the maximum copolar gain is imposed for both linear polarizations. The goal is to minimize the crosspolar pattern as much as possible.

After the crosspolar optimization, the radiation pattern shown in Figure 11 was obtained for polarization X. When compared with the far field of Figure 8, it can be seen how the crosspolar pattern maximum value has been considerably reduced while keeping the copolar pattern within specifications. In fact, the maximum copolar gain is now 19.7 dBi and 19.6 dBi for polarizations X and Y, respectively. At the same time, the maximum crosspolar values are 15.7 and 15.4 dBi, with CPmaxXPmax values of 35.4 and 35.0 dB for polarizations X and Y, respectively. This represents an improvement of 9.7 and 8.6 dB for both linear polarizations. This information is summarized in Table 1. Finally, Figure 12 shows the layout of the optimized reflectarray for both layers.
