4. Examples of application

Here, we present two examples of application of the optimization framework presented in the previous sections. First, a medium-sized reflectarray is designed to work in a base station for future 5G application in the millimeter band at 28 GHz. The second example is a very large contoured-beam reflectarray for

It has been demonstrated that a properly focused pattern is sufficient for the POS [7]. In that case, the initial phase distribution for the POS may be obtained

� � <sup>¼</sup> <sup>k</sup><sup>0</sup> dl � xl cos <sup>φ</sup><sup>0</sup> <sup>þ</sup> yl sin <sup>φ</sup><sup>0</sup>

exp jϕ<sup>l</sup> xx � �

3.2 Obtaining a reflectarray layout from a phase-shift distribution

The procedure to obtain a reflectarray layout from the two phase-shift distributions obtained after the POS is summarized in the flowchart of Figure 5.

Flowchart of the procedure to obtain a reflectarray layout from the synthesized phase-shift distribution for two

� � sin θ<sup>0</sup>

0

yy � � 1

CA, (16)

� � is the phase of a direct reflection coefficient (ρxx or ρyy, for

linear polarizations X and Y, respectively); dl is the distance from the feed to the lth element (see Figure 4); and θ0, φ<sup>0</sup> ð Þ is the pointing direction of the focused beam. The angle θ0, φ<sup>0</sup> ð Þ is usually selected in a direction where the desired shaped beam

Then, the generalized IA is employed to synthesize the desired pattern. For the POS, the elements are modelled as ideal phase shifters, in which there are no losses (∣ρxx∣ ¼ ∣ρyy∣ ¼ 1) and no cross-polarization (ρxy ¼ ρyx ¼ 0). Thus, the matrix of

0 exp jϕ<sup>l</sup>

where ϕ<sup>l</sup> is the phase of the corresponding reflection coefficient. Thus, the optimizing variables are the phases of the direct coefficients. In addition, the POS is carried out in several steps, gradually increasing the number of optimizing variables as suggested in [14] to further improve the convergence of the algorithm. Once the desired phase-shift distributions are obtained, the following step is to obtain the

� �, (15)

analytically [5]:

where ∠ρ xl, yl

Advances in Array Optimization

has maximum gain.

reflectarray layout.

Figure 5.

60

linear polarizations.

∠ρ xl, yl

reflection coefficients in (11) is simplified to

<sup>R</sup><sup>l</sup> <sup>¼</sup>

0

B@

direct-to-home broadcasting in the Ku-band at 12.5 GHz, based on a real mission with Southern Asia coverage.

### 4.1 Reflectarray for 5G base station
