# Designing Smart Electromagnetic Environments for Next-Generation Wireless Communications
## 3 Numerical Assessment  
This section is aimed at numerically assessing the effectiveness and the potentialities of the proposed design framework. Towards this goal, an illustrative proof-of-concept is described by considering the benchmark scenario shown in Figure 2.  
The _EM_ environment \(\mathcal{S}\) comprises \(K=3\) electrically-large scatterers (i.e., the maximum edge measures \(L_{\max}=L_{z}=20\)\([\lambda]\), \(\lambda\) being the free-space wavelength at the working frequency) whose size and location is reported in Table 1, while their dielectric characteristics are set to concrete (i.e., relative permittivity \(\varepsilon_{r}=7.0\) and conductivity \(\sigma=0.015\)\([\)S/m\(]\)[23]). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scatterer** & **Size** & **Barycenter** \\ \(k\) & \(\left(\underline{L_{x}^{(k)}},\underline{y_{x}^{(k)}},\underline{L_{z}^{(k)}} \right)\) [\(\lambda\)] & \(\left(\mathbf{x}^{(k)},\mathbf{y}^{(k)},\mathbf{z}^{(k)}\right)\) [\(\lambda\)] \\ \hline \(1\) & (5.0, 2.0, 20.0) & (7.0, 16.0, 0.0) \\ \hline \(2\) & (2.0, 5.0, 20.0) & (7.0, 12.0, 0.0) \\ \hline \(3\) & (5.0, 5.0, 20.0) & (\(-\)5.0, 15.0, 0.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numerical Assessment (\(K=3\), \(N=25\), \(N^{\prime}=64\))—Size and location of the scatterers within \(\mathcal{S}\). As for the incident current distribution, \(\int_{j_{\mu\upsilon}}(t)\), \(t\in\Psi\), it is that of a planar phased array of \(N=(5\times 5)=25\)\(z\)-directed half-wavelength dipole antennas lying on the \((x,\,z)\) plane and centered on the Cartesian axes origin (Figure 2) (Owing to the intrinsic linear polarization of the considered source and without any loss of generality, the scalar \(z\)-component of the electric field has been considered in the following by setting the weights in the cost function equal to \(\gamma_{x}=\gamma_{y}=0.0\) and \(\gamma_{z}=1.0\)). The observation domain \(\Omega\) is a square planar surface of size \(L_{\Omega}=10\)\([\lambda]\) located beyond the scattering environment \(\mathcal{S}\) at a distance \(d_{\Psi\Omega}=20\)\([\lambda]\) from the source (Figure 2). The _EM_ field within \(\Omega\) has been sampled with uniform step along \(x\) and \(z\) directions with probing step \(\Delta_{x}=\Delta_{y}=\frac{\lambda}{2}\), yielding a total number of measurement samples equal to \(M=(21\times 21)=441\). Due to the large scale of the scenario at hand, a ray-tracing numerical solver based on the physical optics tool of Altair FEKO has been adopted to efficiently simulate the _EM_ interactions, including the multipath, between the primary source and the scatterers [24]. Finally, the following parameters have been set to run the optimization: \(P=10\) (number of particles), \(I=10^{4}\) (maximum number of iterations), \(\omega=0.4\) (constant inertial weight), and \(C_{1}=C_{2}=2.0\) (acceleration coefficients) [22]. The goal of the problem at hand is to synthesize a suitable equivalent current distribution \(\int_{Eq}(t)\) within \(\mathcal{S}\) such that the field in \(\Omega\) matches a target distribution corresponding to the field that would be radiated in free-space by a significantly larger aperture comprising \(N^{\prime}=(8\times 8)=64\) dipoles (\(\frac{N^{\prime}}{N}=256\%\)), whose magnitude and phase are reported in Figure 2(a),b, respectively. Figure 3(a) shows the evolution of the cost function \(\frac{\Phi_{i}}{\Phi_{i}}\), \(i=1,\,\dots,\,I,\,\Phi_{1}\) being the value of \(\Phi\) at the initial iteration, in which uniform excitations (i.e., \(w_{n}=1.0\), \(n=1,\,\dots,\,N\)) have been exploited to set an \"initial guess\" for the successive solution space exploration. As it can be observed, the mismatch between the synthesized and the target distributions has been remarkably reduced during the optimization process as pointed out by the final value of the \(\frac{\Phi_{i}}{\Phi_{1}}\) ratio (i.e., \(\frac{\Phi_{i}}{\Phi_{1}}\big{|}_{i=1}=4.6\times 10^{-2}\)--Figure 4).