# Optimal Design of Aperiodic Reconfigurable Antenna Array Suitable for Broadcasting Applications

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## Abstract

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## 1. Introduction

- (1)
- maximum possible $FG$ at $\theta ={93}^{\circ}$ ($\theta $ is the elevation angle),
- (2)
- null level ≥−20 dB with respect to the main lobe peak inside the service area defined from $\theta ={93}^{\circ}$ to $\theta ={143}^{\circ}$ (a ${50}^{\circ}$ service area),
- (3)
- $SLL\le $$-20$ dB with respect to the main lobe peak outside the service area,
- (4)
- $SWR\le $$1.2$ (S-parameters ≤$-21$ dB) at the inputs of all the array elements.

## 2. Geometry Definition

## 3. PSO with Velocity Mutation

## 4. Optimization Results

## 5. Comparison with Other Optimization Methods

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Normalized radiation pattern versus elevation angle $\theta $ at azimuth angle $\varphi =0$. The maximum value of the normalized radiation pattern (0 dB) corresponds to the actual maximum gain of the AMAA 13.9 dBi at $\theta ={93}^{\circ}$ (main lobe tilting by ${3}^{\circ}$). The red dash-line shows the desired SLL outside the service area, and the green dash-line shows the desired null filling level inside the service area. The optimal radiation pattern should be below the red dash-line and above the green dash-line.

**Figure 4.**S-parameters of the array elements. All S-parameters are ≤−21 dB at 698 MHz (DVB-T channel 49 center frequency) satisfying the optimization goals.

Parameter | Lower Limit | Upper Limit | Parameter | Lower Limit | Upper Limit |
---|---|---|---|---|---|

W | 105 mm | 245 mm | ${t}_{w}$ | 4.2 mm | 16.8 mm |

L | 91 mm | 211 mm | s | 26.5 mm | 61.9 mm |

${d}_{0}$ | 214 mm | 343 mm | g | ${W}_{cur}/40$ | ${W}_{cur}/10$ |

${r}_{i},\phantom{\rule{4pt}{0ex}}i=1,2,3$ | 0 mm | 86 mm | ${A}_{n},\phantom{\rule{4pt}{0ex}}n=1,\cdots ,8$ | 0.1 | 1 |

${t}_{l}$ | 0 mm | 107 mm | ${P}_{n},\phantom{\rule{4pt}{0ex}}n=1,\cdots ,8$ | ${0}^{\circ}$ | ${360}^{\circ}$ |

Parameter | Value (mm) | Parameter | Value (mm) |
---|---|---|---|

W | 170.9 | ${d}_{3}$ | 348.7 |

L | 152.1 | ${t}_{l}$ | 103.6 |

${d}_{0}$ | 256.9 | ${t}_{w}$ | 13.7 |

${d}_{1}$ | 263.9 | s | 37.3 |

${d}_{2}$ | 264.8 | g | 15.8 |

Parameter | Value | Parameter | Value |
---|---|---|---|

${A}_{1}\angle {P}_{1}$ | $0.41\angle 331.{9}^{\circ}$ | ${A}_{5}\angle {P}_{5}$ | $0.53\angle 355.{2}^{\circ}$ |

${A}_{2}\angle {P}_{2}$ | $0.67\angle 333.{1}^{\circ}$ | ${A}_{6}\angle {P}_{6}$ | $0.98\angle 352.{1}^{\circ}$ |

${A}_{3}\angle {P}_{3}$ | $0.61\angle 348.{9}^{\circ}$ | ${A}_{7}\angle {P}_{7}$ | $0.72\angle 58.{5}^{\circ}$ |

${A}_{4}\angle {P}_{4}$ | $0.68\angle 0.{65}^{\circ}$ | ${A}_{8}\angle {P}_{8}$ | $0.15\angle 358.{9}^{\circ}$ |

Parameter | Value | Parameter | Value |
---|---|---|---|

$FG$ | 13.9 dBi | $SW{R}_{3}$ | 1.07 |

Main Lobe Tilting | $3.{0}^{\circ}$ | $SW{R}_{4}$ | 1.05 |

Null level | −20.0 dB | $SW{R}_{5}$ | 1.16 |

$SL{L}_{1}$ | −20.8 dB | $SW{R}_{6}$ | 1.16 |

$SL{L}_{2}$ | −21.0 dB | $SW{R}_{7}$ | 1.20 |

$SW{R}_{1}$ | 1.08 | $SW{R}_{8}$ | 1.20 |

$SW{R}_{2}$ | 1.11 |

Parameter | Value ($\mathbf{\Omega}$) | Parameter | Value ($\mathbf{\Omega}$) |
---|---|---|---|

${Z}_{1}$ | $53.60-j2.14$ | ${Z}_{5}$ | $43.00+j0.90$ |

${Z}_{2}$ | $55.23-j2.42$ | ${Z}_{6}$ | $53.30-j7.10$ |

${Z}_{3}$ | $46.70+j0.45$ | ${Z}_{7}$ | $58.30+j5.40$ |

${Z}_{4}$ | $50.40-j2.70$ | ${Z}_{8}$ | $41.70+j1.20$ |

Alg. | Mainlobe Tilting (${}^{\circ}$) | $\mathbf{FG}$ (dBi) | Null Level (dB) | ${\mathbf{SLL}}_{1}$ (dB) | ${\mathbf{SLL}}_{2}$ (dB) | ${\mathbf{SWR}}_{1}$ | ${\mathbf{SWR}}_{2}$ |
---|---|---|---|---|---|---|---|

PSOvm | $3.2$ | 13.9 | $-20.0$ | $-20.8$ | $-21.0$ | 1.08 | 1.11 |

PSO | $2.2$ | 12.8 | $-17.8$ | $-6.0$ | $-18.3$ | 1.14 | 1.08 |

GA | $0.5$ | 10.5 | $-18.7$ | $-5.7$ | $-15.8$ | 1.06 | 1.13 |

TRF | $3.0$ | 13.9 | $-20.5$ | $-20.8$ | $-21.0$ | 1.10 | 1.12 |

CMAES | $0.5$ | 13.2 | $-23.4$ | $-13.6$ | $-17.3$ | 1.30 | 1.21 |

NMSA | $-0.2$ | 12.8 | $-22.8$ | $-12.6$ | $-12.6$ | 1.22 | 1.17 |

CP | $-0.1$ | 11.5 | $-16.6$ | $-8.8$ | $-13.5$ | 1.09 | 1.15 |

IQN | $-2.0$ | 8.7 | $-16.8$ | $-7.4$ | $-16.6$ | 1.12 | 1.13 |

${\mathbf{SWR}}_{\mathbf{3}}$ | ${\mathbf{SWR}}_{\mathbf{4}}$ | ${\mathbf{SWR}}_{\mathbf{5}}$ | ${\mathbf{SWR}}_{\mathbf{6}}$ | ${\mathbf{SWR}}_{\mathbf{7}}$ | ${\mathbf{SWR}}_{\mathbf{8}}$ | Tot. Time (min) | |

PSOvm | 1.07 | 1.05 | 1.16 | 1.16 | 1.20 | 1.20 | 710 |

PSO | 1.09 | 1.20 | 1.06 | 1.26 | 1.11 | 1.11 | 2000 |

GA | 1.16 | 1.18 | 1.25 | 1.12 | 1.08 | 1.08 | 2000 |

TRF | 1.06 | 1.07 | 1.16 | 1.19 | 1.20 | 1.20 | 900 |

CMAES | 1.12 | 1.20 | 1.48 | 1.25 | 1.15 | 1.05 | 2000 |

NMSA | 1.18 | 1.07 | 1.05 | 1.07 | 1.22 | 1.06 | 2000 |

CP | 1.08 | 1.22 | 1.27 | 1.13 | 1.07 | 1.12 | 2000 |

IQN | 1.35 | 1.19 | 1.22 | 1.20 | 1.32 | 1.12 | 2000 |

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**MDPI and ACS Style**

Gravas, I.P.; Zaharis, Z.D.; Lazaridis, P.I.; Yioultsis, T.V.; Kantartzis, N.V.; Antonopoulos, C.S.; Chochliouros, I.P.; Xenos, T.D.
Optimal Design of Aperiodic Reconfigurable Antenna Array Suitable for Broadcasting Applications. *Electronics* **2020**, *9*, 818.
https://doi.org/10.3390/electronics9050818

**AMA Style**

Gravas IP, Zaharis ZD, Lazaridis PI, Yioultsis TV, Kantartzis NV, Antonopoulos CS, Chochliouros IP, Xenos TD.
Optimal Design of Aperiodic Reconfigurable Antenna Array Suitable for Broadcasting Applications. *Electronics*. 2020; 9(5):818.
https://doi.org/10.3390/electronics9050818

**Chicago/Turabian Style**

Gravas, Ioannis P., Zaharias D. Zaharis, Pavlos I. Lazaridis, Traianos V. Yioultsis, Nikolaos V. Kantartzis, Christos S. Antonopoulos, Ioannis P. Chochliouros, and Thomas D. Xenos.
2020. "Optimal Design of Aperiodic Reconfigurable Antenna Array Suitable for Broadcasting Applications" *Electronics* 9, no. 5: 818.
https://doi.org/10.3390/electronics9050818