## 4 Parasitic Layer Design Example  
It is foreseen that a large portion of the initial deployments of the 5G-NR will be concentrated on the Frequency Range 1 (FR1) (sub-6 GHz portion of the spectrum) [49], and special interest is placed in the 3.5 GHz band where moderately large bandwidths up to 100 MHz can be allocated. A particular reconfigurable antenna example for the 3.5 GHz band is presented in this section to illustrate the minimum nonlinearities design method developed in the previous section. The most computationally expensive part of the design process is the initial FWEM simulation to get the 'unloaded' antenna parameters, this simulation must be performed for any candidate value of \(h\) as there is not a straightforward way to reuse simulation results for other \(h\) values. Accordingly, the presented guidelines for determining the optimum \(h\) are intended to greatly reduce the design time. After the fundamental design trade-offs of the reconfigurable parasitic layer are established, an optimum region for the separation between the basic antenna and the PL can be determined based on the compromise that must be made between bandwidth, linearity, and beam-steering. For instance, for 5G applications covering the n78 band at 3.5 GHz, a good starting point should be \(h=\lambda/9-\lambda/12\) that can achieve around  
Figure 13: Design Trade-Offs of a Parasitic Layer (PL) based Reconfigurable Antenna (RA). 12-15% bandwidth, an average 7.3 dB directivity, and a rich beam-steering capability with maximum deviations up to \(55^{\circ}\), joined with average power margins in the range 7-9 dB. However, beyond appropriate region for PL placement, particular indications on how to determine the switch states to achieve the optimum compromise of the objectives are not yet given. The optimum switch states determination is demonstrated by means of a particular design example. In this case, the same topology used to determine the basic trade-offs is employed with some variations, first the basic antenna is modified to resonate at a lower frequency aiming to have a lower cutoff frequency and a richer number of well-matched configurations at the central frequency of 3.5 GHz, also, the pixel size is increased to 14 mm aiming to have finer control of steering. The switch state determination is posed as a multidimensional optimization problem, in which a 3D cost function considering S-parameters, beam pointing and switches power, is defined and explored using Pareto fronts to obtain antenna realizations with an optimum objective compromise. The cost function vector is defined as:  
\[J(k) =\{J_{S}(k),J_{\Delta P}(k),J_{\Delta(\theta,\phi)}(k)\} \tag{19}\] \[J_{S}(k) =\max_{f}\biggl{(}\max_{i,j}\bigl{(}|S_{ij}(k,f)|\bigr{)}\biggr{)}\] \[J_{\Delta P}(k) =-\Delta P(k)\] \[J_{\Delta(\theta,\phi)}(k) =\Delta(\theta,\phi)(k,f_{c},\theta_{0i},\phi_{0i}),\]  
where each component is normalized and mapped to the range \([0,1]\) by the limits _target_\(S_{ij}\in\{-10,0\}\) dB, _target_\(\Delta P\in\{-10,-3\}\) dB, _target_\(\Delta(\theta,\phi)\in\{0^{\circ},10^{\circ}\}\). Imposing requirements on port match and coupling, power margin, and angular deviation from target. The set of desired angles is \((\theta_{0},\phi_{0})=\{(0^{\circ},0^{\circ}),\) and \(\{(40^{\circ},\{0^{\circ},45^{\circ},90^{\circ},135^{\circ},180^{\circ},225^{ \circ},270^{\circ},315^{\circ}\})\}\}\), therefore \(J_{\Delta(\theta,\phi)}(k)\in\mathbb{R}^{9}\). Further restrictions on results are imposed discarding those configurations with \(Dir<6\) dB. After each individual is assigned a cost vector, weak Pareto optimality criterion is used to retain only the better performing configurations for each of the desired modes of operation.