4.2.1 Antenna specifications

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


#### Table 1.

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

#### Figure 12.

Layout of the reflectarray designed for 5G base station that generates a radiation pattern with a 30° sectored beam in azimuth and a squared-cosecant beam in elevation: (a) bottom layer and (b) upper layer.

dBW for zone 1 and 48 dBW for zone 2. The EIRP can be converted into gain using

Footprint of the southern Asia coverage for direct-to-home broadcasting application. Zone 1 includes India, Nepal, Bhutan, Bangladesh and Sri Lanka, while zone 2 includes Pakistan and Afghanistan. This coverage mimics the one provided by the SES-12 satellite, placed in geostationary orbit at 95°E. (u,v) coordinates are in

Reflectarray Pattern Optimization for Advanced Wireless Communications

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

where Pt is the power of the transponder. Assuming Pt ¼ 150W, it gives a gain specification of 30 dBi for zone 1 and 26 dBi for zone 2. In addition, the design process will take into account typical pointing errors (0.1° in roll and pitch and 0.5° in yaw). The design will be carried out in dual-linear polarization, imposing the

For the first step, a POS is carried out to obtain the desired copolar pattern in

dual-linear polarization. Figure 15a shows the initial phase shift for the POS

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.

Gð Þ¼ dBi EIRP dBW ð Þ� Ptð Þ dBW , (18)

the following expression:

the satellite coordinate system.

Figure 14.

Figure 15.

67

same specifications in both polarizations.

4.2.2 Results of the antenna design

is 12.5 GHz. The feed is placed at ð Þ �352:9, 0:0, 1061:7 mm with regard to the reflectarray centre and is modeled as a cos <sup>q</sup><sup>θ</sup> with <sup>q</sup> <sup>¼</sup> 18, which generates an illumination taper of �17:9 dB.

A similar unit cell as in the previous example is used with different dimensions and materials. The separation between dipoles is now set to Sai ¼ Sbi ¼ 2:5mm (i ¼ 1, 2), while the width of all dipoles is set to 0.5 mm and Tx and Ty are defined in Eq. (17). Commercial substrates were chosen for both layers, the Arlon AD255C for the top layer, with hA ¼ 2:363mm and ε<sup>r</sup> ¼ 2:17 � j0:0020, and DiClad 880 for the bottom layer, with hB ¼ 1:524mm and ε<sup>r</sup> ¼ 2:55 � j0:0036. Figure 13 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. The phase shift provided by the cell is slightly larger than 600°.

Figure 14 shows the contour requirements for the Southern Asia mission, similar to that provided by the SES-12 satellite. Zone 1 includes India, Nepal, Bhutan, Bangladesh and Sri Lanka, while zone 2 includes Pakistan and Afghanistan. According to the official specifications [22], the satellite provides an EIRP of 52

#### Figure 13.

Unit cell study for the reflectarray for DTH at 12.5 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 while providing more than 600° of linear phase shift.

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

#### Figure 14.

is 12.5 GHz. The feed is placed at ð Þ �352:9, 0:0, 1061:7 mm with regard to the reflectarray centre and is modeled as a cos <sup>q</sup><sup>θ</sup> with <sup>q</sup> <sup>¼</sup> 18, which generates an

Layout of the reflectarray designed for 5G base station that generates a radiation pattern with a 30° sectored beam in azimuth and a squared-cosecant beam in elevation: (a) bottom layer and (b) upper layer.

and materials. The separation between dipoles is now set to Sai ¼ Sbi ¼ 2:5mm (i ¼ 1, 2), while the width of all dipoles is set to 0.5 mm and Tx and Ty are defined in Eq. (17). Commercial substrates were chosen for both layers, the Arlon AD255C for the top layer, with hA ¼ 2:363mm and ε<sup>r</sup> ¼ 2:17 � j0:0020, and DiClad 880 for the bottom layer, with hB ¼ 1:524mm and ε<sup>r</sup> ¼ 2:55 � j0:0036. Figure 13 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. The phase shift provided by the

A similar unit cell as in the previous example is used with different dimensions

Figure 14 shows the contour requirements for the Southern Asia mission, similar to that provided by the SES-12 satellite. Zone 1 includes India, Nepal, Bhutan, Bangladesh and Sri Lanka, while zone 2 includes Pakistan and Afghanistan. According to the official specifications [22], the satellite provides an EIRP of 52

Unit cell study for the reflectarray for DTH at 12.5 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 while providing

illumination taper of �17:9 dB.

Advances in Array Optimization

Figure 12.

Figure 13.

66

more than 600° of linear phase shift.

cell is slightly larger than 600°.

Footprint of the southern Asia coverage for direct-to-home broadcasting application. Zone 1 includes India, Nepal, Bhutan, Bangladesh and Sri Lanka, while zone 2 includes Pakistan and Afghanistan. This coverage mimics the one provided by the SES-12 satellite, placed in geostationary orbit at 95°E. (u,v) coordinates are in the satellite coordinate system.

dBW for zone 1 and 48 dBW for zone 2. The EIRP can be converted into gain using the following expression:

$$\mathbf{G(dBi)} = \mathbf{EIRP(dBW)} - P\_t(\mathbf{dBW}),\tag{18}$$

where Pt is the power of the transponder. Assuming Pt ¼ 150W, it gives a gain specification of 30 dBi for zone 1 and 26 dBi for zone 2. In addition, the design process will take into account typical pointing errors (0.1° in roll and pitch and 0.5° in yaw). The design will be carried out in dual-linear polarization, imposing the same specifications in both polarizations.

#### 4.2.2 Results of the antenna design

For the first step, a POS is carried out to obtain the desired copolar pattern in dual-linear polarization. Figure 15a shows the initial phase shift for the POS

#### Figure 15.

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.

obtained with Eq. (15). It generates a focused beam in the direction ðθ ¼ 16:5°, φ ¼ 0:0°Þ, which corresponds to a high-gain area in India. After the synthesis, the phases shown in Figure 15b were obtained for polarization X. The phases for polarization Y are similar. Once the layout has been obtained, the radiation patterns were computed using a MoM-LP tool. The copolar and crosspolar components for this initial design are shown in Figure 16 for polarization X. In this case, the minimum copolar gain is 31.5 and 28.6 dBi for zones 1 and 2, respectively. Similar results were obtained for polarization Y. Thus, the initial design complies with the requirements in both linear polarizations.

Space missions usually impose very stringent cross-polarization requirements in the form of crosspolar discrimination (XPD) and crosspolar isolation (XPI) for the transmit and receive bands, respectively. Notice that according to the definitions of minimum XPD in Eq. (4) and the XPI in Eq. (5), the XPI is a more stringent parameter than the XPDmin. The first row of Table 2 shows the values of XPDmin and XPI for both coverage zones and polarizations. The initial design presents values of those parameters between 29.5 and 33.0 dB. The goal is thus to improve the cross-polarization performance of this reflectarray by performing a direct optimization of the layout. As in the previous case,Tx and Ty are considered as optimization variables. Thus, a total of 13,097 variables will be considered. In addition, instead of minimizing the crosspolar pattern as in the previous example, now the XPDmin and XPI will be optimized as detailed in [17]. To that end, minimum masks of 37 dB are imposed for both parameters. The goal is to increase as much as possible the XPDmin and XPI while keeping the minimum copolar gain for both coverage zones within specifications.

After the direct layout optimization, the cross-polarization performance of the reflectarray antenna significantly improved. The worst parameter is the XPI for zone 1 and polarization X, which has a value of 37.5 dB. It improved to 8 dB over the value for the initial design. The minimum improvement was 6 dB for the XPI for zone 1 and polarization X and XPDmin for zone 2 and polarization X. At the same time, the copolar minimum gain still complies with the specifications of 30 dBi for zone 1 and 26 dBi for zone 2. A summary of the performance of the initial and optimized layout may be found in Table 2. In addition, Figure 17 shows the copolar and crosspolar pattern for polarization X of the optimized layout. Since the optimization has maximized the cross-polarization performance in the two coverage areas, the maximum crosspolar values are outside both of them.

Zone 1

69

Polarization

CP

31.52

 32.50

 32.08

 31.36

 30.51

 29.56

 28.63

 32.99

 31.13

 28.91

 31.76

 29.87

Initial design Optimized design CP is the minimum copolar gain in dBi in a coverage area, XPDmin is the minimum crosspolar

Table 2. For the reflectarray

 with southern Asia coverage, comparison

 of the performance

 of the initial design after the POS and the optimized layout for improved

 30.07

 38.99

 38.11

 30.04

 39.77

 37.51

discrimination

 in dB, and XPI is the crosspolar isolation in dB.

 29.15

 39.01

 37.53

 29.17

 39.79 cross-polarization

performance.

 38.23

 XPDmin

XPI

 CP

 XPDmin

XPI

 CP

 XPDmin

XPI

 CP

 XPDmin

XPI

 X

Polarization

 Y

Polarization

 X

Polarization

 Y

Reflectarray Pattern Optimization for Advanced Wireless Communications

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

Zone 2

#### Figure 16.

Radiation pattern of the initial layout with southern Asia coverage for polarization X: (a) copolar pattern and (b) crosspolar pattern.


Table 2. For the reflectarray with southern Asia coverage, comparison of the performance of the initial

 design after the POS and the optimized layout for improved

cross-polarization

performance.
