# Designing Smart Electromagnetic Environments for Next-Generation Wireless Communications

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## Abstract

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## 1. Introduction and Motivation

## 2. Mathematical Formulation

## 3. Numerical Assessment

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Numerical Assessment ($K=3$, $N=25$, ${N}^{\prime}=64$, $M=441$)—Simulated benchmark scenario.

**Figure 3.**Numerical Assessment ($K=3$, $N=25$, ${N}^{\prime}=64$)—(

**a**,

**c**,

**e**) Magnitude and (

**b**,

**d**,

**f**) phase distribution of (

**a**,

**b**) the target field (${N}^{\prime}=64$ dipoles in free-space) and the field radiated towards the complex scattering scenario $\mathcal{S}$ by the planar array of $N=25$ dipoles when exciting the antennas with (

**c**,

**d**) uniform (“initial guess”) and (

**e**,

**f**) the optimized excitation weights ${\underline{w}}_{opt}$.

**Figure 4.**Numerical Assessment ($K=3$, $N=25$, ${N}^{\prime}=64$, $M=441$)—Plot of (

**a**) the evolution of the cost function during the iterations and (

**b**) the amplitude $\left|{w}_{n}^{opt}\right|$, $n=1,\dots ,N$ and phase $\angle {w}_{n}^{opt}$, $n=1,\dots ,N$ values of the optimal excitations vector ${\underline{w}}_{opt}$ (6) obtained by means of the PSO.

**Figure 5.**Numerical Assessment ($K=3$, $N=25$, ${N}^{\prime}=64$, $M=441$) - Error map for $\underline{r}\in \Omega $ between the target distribution and the field radiated by the array of $N=25$ dipoles with (

**a**) uniform [$\Delta {E}_{uni}\left(\underline{r}\right)={E}_{uni}\left(\underline{r}\right)-{E}_{tar}\left(\underline{r}\right)$] and (

**b**) optimized [$\Delta {E}_{opt}\left(\underline{r}\right)={E}_{opt}\left(\underline{r}\right)-{E}_{tar}\left(\underline{r}\right)$] excitations.

**Table 1.**Numerical Assessment ($K=3$, $N=25$, ${N}^{\prime}=64$)—Size and location of the scatterers within $\mathcal{S}$.

Scatterer | Size | Barycenter |
---|---|---|

k | $\left({\mathit{L}}_{\mathit{x}}^{\left(\mathit{k}\right)},\phantom{\rule{0.166667em}{0ex}}{\mathit{L}}_{\mathit{y}}^{\left(\mathit{k}\right)},\phantom{\rule{0.166667em}{0ex}}{\mathit{L}}_{\mathit{z}}^{\left(\mathit{k}\right)}\right)$ [$\mathit{\lambda}$] | $\left({\mathit{x}}^{\left(\mathit{k}\right)},\phantom{\rule{0.166667em}{0ex}}{\mathit{y}}^{\left(\mathit{k}\right)},\phantom{\rule{0.166667em}{0ex}}{\mathit{z}}^{\left(\mathit{k}\right)}\right)$ [$\mathit{\lambda}$] |

1 | $\left(5.0,\phantom{\rule{0.166667em}{0ex}}2.0,\phantom{\rule{0.166667em}{0ex}}20.0\right)$ | $\left(7.0,\phantom{\rule{0.166667em}{0ex}}16.0,\phantom{\rule{0.166667em}{0ex}}0.0\right)$ |

2 | $\left(2.0,\phantom{\rule{0.166667em}{0ex}}5.0,\phantom{\rule{0.166667em}{0ex}}20.0\right)$ | $\left(7.0,\phantom{\rule{0.166667em}{0ex}}12.0,\phantom{\rule{0.166667em}{0ex}}0.0\right)$ |

3 | $\left(5.0,\phantom{\rule{0.166667em}{0ex}}5.0,\phantom{\rule{0.166667em}{0ex}}20.0\right)$ | $\left(-5.0,\phantom{\rule{0.166667em}{0ex}}15.0,\phantom{\rule{0.166667em}{0ex}}0.0\right)$ |

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## Share and Cite

**MDPI and ACS Style**

Massa, A.; Benoni, A.; Da Rù, P.; Goudos, S.K.; Li, B.; Oliveri, G.; Polo, A.; Rocca, P.; Salucci, M.
Designing Smart Electromagnetic Environments for Next-Generation Wireless Communications. *Telecom* **2021**, *2*, 213-221.
https://doi.org/10.3390/telecom2020014

**AMA Style**

Massa A, Benoni A, Da Rù P, Goudos SK, Li B, Oliveri G, Polo A, Rocca P, Salucci M.
Designing Smart Electromagnetic Environments for Next-Generation Wireless Communications. *Telecom*. 2021; 2(2):213-221.
https://doi.org/10.3390/telecom2020014

**Chicago/Turabian Style**

Massa, Andrea, Arianna Benoni, Pietro Da Rù, Sotirios K. Goudos, Baozhu Li, Giacomo Oliveri, Alessandro Polo, Paolo Rocca, and Marco Salucci.
2021. "Designing Smart Electromagnetic Environments for Next-Generation Wireless Communications" *Telecom* 2, no. 2: 213-221.
https://doi.org/10.3390/telecom2020014