# Wide-Band Wide-Beam Circularly-Polarized Slot-Coupled Antenna for Wide-Angle Beam Scanning Arrays
## 4 Numerical Assessment  
This section is aimed at illustrating the performance of the proposed _WWCS_ antenna model. Towards this end, the synthesis of a _LHCP_-polarized radiator working in the \(f\in\left[2.3,\,2.6\right]\) [GHz] band (\(\Rightarrow f_{0}=2.45\) [GHz] and \(\lambda_{0}=122.44\) [mm] [20]) was addressed. The Rogers RO4350B substrate was chosen for the \(\mathcal{L}=3\) layers (\(\varepsilon_{rl}=3.66\), \(\tan\delta_{l}=0.004\), \(l=1,\ldots,\mathcal{L}\)) with thicknesses set to \(H_{1}=H_{3}=3.04\) [mm] and \(H_{2}=4.56\) [mm]. According to [8], the width of the microstrip feeding line turns out to be \(W_{f}=6.65\) [mm] for \(Z_{0}=50\) [\(\Omega\)], while the analytic guess of the patch radius is set to \(\widetilde{R}_{p}=17.46\) [mm] [33]. The _PSO-OK_/C parameters were chosen by following the literature guidelines to yield a time saving of \(\Delta t_{sav}=86\%\) with respect to a standard optimization based on a bare integration of the global optimizer and the \(FW\) simulator to compute the cost function values in correspondence with each trial antenna layout [32]. More specifically, the swarm size, the number of iterations, the social/cognitive acceleration coefficients, the inertial weight, and the initial training size were set to \(P=9\), \(I=200\), \(C_{1}=C_{2}=2\), \(\omega=0.4\), and \(S_{0}=45\), respectively. Moreover, the numerical evaluation of (3) was performed by sampling into \(Q=3\), \(M=13\), and \(V=4\) samples the frequency, the azimuth, and the elevation range, respectively, while letting \(S_{11}^{th}=-10\) [dB], \(HPBW^{th}=180\) [deg], \(AR^{th}=6\) [dB], and \(XPD^{th}=15\) [dB]. Finally, the optimization bounds were set to \(R_{p}\in\left[0.8,\,1.2\right]\times\widetilde{R}_{p}\), \(L_{f}\in\left[0.1,\,0.9\right]\times\frac{L_{p}}{2}\), \(L_{1}=L_{2}\in\left[0.1,\,0.9\right]\times\frac{L_{p}}{2}\), \(W_{1}=W_{2}\in\left[0.1,\,0.9\right]\times\frac{L_{p}}{2}\), \(D\in\left[0.1,\,1\right]\times\lambda_{0}\), and \(\alpha=\beta\in\left[0.1,\,0.9\right]\). The geometric descriptors of the \(SbD\)-optimized layout are reported in Table 2, while the corresponding layout, modeled in the Ansys _HFSS FW_ simulator [38] and having an overall height of \(T=71.98\) [mm] (\(T=0.59\) [\(\lambda_{0}\)] --Table 1), is shown in Figure 3. Going to the analysis of the antenna performance, Figure 4 shows the simulated reflection coefficient at the antenna input port versus the frequency. As it can be observed, such a radiating element fully complies with the requirement since \(\left|S_{11}^{(dB)}\left(f|\underline{\Omega}^{(opt)}\right)\right|\leq-11.3\) [dB] for \(f\in[f_{\text{min}},\,f_{\text{max}}]\). In more detail, it turns out that \(\left|S_{11}^{(dB)}\left(f|\underline{\Omega}^{(opt)}\right)\right|\leq S_{1 1}^{th}\) for an even wider frequency interval (\(f\in[2.29,\,2.66]\) [GHz]) by assessing the wide-band behavior of the proposed design with an overall fractional bandwidth of \(FBW_{\left|WWCS\right. }=15\%\)[39], while, for instance, the state-of-the-art solution in [20] is limited to \(FBW_{\left|Pan\,2014\right|}=1.2\%\) (Figure 4 and Table 1). As for the radiation features, Figure 5 shows the gain pattern at \(f=f_{0}\), \(G(f_{0},\,\theta,\,\varphi)\), along the two main elevation planes [i.e., \(\varphi=0\) [deg]--Figure 5a and \(\varphi=90\) [deg]--Figure 5b] and the azimuth plane [i.e., \(\theta=90\) [deg]--Figure 5c]. Since the _HPBW_ is equal to \(HPBW(f_{0},\,\varphi=0)=176\) [deg] [Figure 5a] and \(HPBW(f_{0},\,\varphi=90)=189\) [deg] [Figure 5b] on the two vertical cuts, with a good pattern omni-directionality of the whole antenna horizon [Figure 5c], it is reasonable to indicate the proposed antenna such as a wide-beam one suitable for implementing _WASAS_. It is worth noticing that such a feature has been yielded thanks to the constructive combination of the fields radiated by the primary and secondary sources.