# Design of a Multi-Band Microstrip Textile Patch Antenna for LTE and 5G Services with the CRO-SL Ensemble

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## Abstract

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## Featured Application

**A novel textile U-shaped with concentric annular slot antenna prototype for LTE and 5G services has been described. In the ground plane, a meander slot has been introduced to reduce the antenna dimensions. A new multi-method metaheuristic algorithm, the Coral Reefs Optimization with Substrate Layer CRO-SL, has been used to optimize the antenna parameters and improve its performance in the frequency bands of interest.**

## Abstract

## 1. Introduction

## 2. Antenna Model

## 3. Antenna Optimization: the CRO-SL Algorithm

#### 3.1. Substrate Layers Implemented

- HS: Mutation using the Harmony Search procedure. Harmony Search [28] is a well-known meta-heuristic based on the how a music orchestra improvises a melody. HS substrate controls the generation of new larvae in one of the following ways: (i) with a probability HMCR in (0, 1) (Harmony Memory Considering Rate), the value of a component of the new solution is drawn uniformly from the same values of the component in other corals of the current reef; and (ii) with a probability PAR in (0, 1) (Pitch Adjusting Rate), where small adjustments are applied to the values of the current solution.
- DE: Differential Evolution algorithm mutation. This substrate is based on the DE algorithm defined in reference [29]. This approach introduces a differential mechanism for exploring the search space. In this case, new larvae are generated by perturbing the current larva by using a vector of differences between two individuals in the population. This perturbation is defined as x′
_{i}= x^{1}_{i}+ F(x^{2}_{i}− x^{3}_{i}) (where F stands for a weighting the perturbation amplitude, 0.6 in this case). After this perturbation of the current larva, the perturbed vector x′ is in turn combined with an alternative (different) coral in the reef, by means of a classical 2-points crossover, as defined next. - 2Px: Classical two-points crossover. The crossover operator is the most used operator for exploring the search space in evolutionary computation algorithms [30]. It consists of coupling two individuals at random, and then, after choosing two points for the crossover, interchanging the genetic material in between these two points. In the current CRO-SL implementation, one larva to be crossed comes from the 2Px substrate, whereas the other can be chosen from any part of the reef.
- GM: Gaussian Mutation. We consider a traditional Gaussian mutation of the form x′
_{i}= x_{i}+ N_{i}(0, σ^{2}), where N_{i}(0, σ^{2}) is a random number following the Gaussian distribution of 0 mean and variance σ^{2}. We introduce a linear decreasing of σ value during the algorithm, from 0.2(A-B) to 0.02(A-B), where [B,A] is the domain search. Note that this procedure produces a stronger mutation in the beginning of the algorithm, and a fine tuning of the search with smaller displacements nearing the end or the algorithm’s evolution. - SAbM: Strange Attractors-based Mutation. This is a new search operator proposed in reference [31], specifically designed to use fractal geometric patterns in the search of new larvae. Specifically, it is designed to generate structures of non-linear dynamical systems with chaotic behavior [32]. Interested reader may consult reference [31] to obtain more information on this operator.

#### 3.2. Objective Function: Antenna Simulation and Calculation

_{11}antenna parameter, which is calculated by simulation using the CST software, as described in the next subsection. In this case, a discretization in steps of 2 MHz is considered. To calculate f(x), several frequency bands for mobile communication systems (including LTE and 5G) has been considered. For each frequency band, the mathematical formulation of the objective function is the following:

^{−10dB}stands for the number of S

_{11}points in the observation window under −10 dB, M = | mean (S

_{11})|, M

^{∗}= |min(S

_{11})| and f stands for a given selected frequency band. The final objective function value f(x) is obtained by adding the value of ${g}_{f}\left(x\right)$ for all the frequency bands f considered:

_{1}= 791−870 MHz (5G); (2) f

_{2}= 1.7−2.3 GHz (LTE); (3) f

_{3}= 3.3−3.8 GHz (5G). Note that these frequency bands cover the majority of communications services such as 2G/3G/4G and also LTE and 5G bands of ultimate mobile communication systems.

#### Antenna Simulation with CST Software

## 4. Computational Evaluation and Results

_{2}and f

_{3}, associated with LTE and 5G mobile communication systems). In this case, the CRO-SL algorithm is able to obtain a good solution for the problem, within 50 generations, as can be in the S

_{11}antenna parameter obtained (Figure 3), with peaks under −10 dBs in both frequency bands considered. The best solution (antenna) obtained by the CRO-SL is shown in Figure 4 (front and bottom view). In this case, the fitness evolution followed by the CRO-SL is shown in Figure 5. The CRO-SL performance depends on how the different substrates operate for this problem. Figure 6 shows the percentage of best solutions and the number of solutions got into the reef for the different substrates. This is a good indication of the best substrates for this specific optimization problem. In this case, the GM substrate is the most active substrate in the CRO-SL to obtain good solutions for the problem, followed by the SAbM and 2Px operators.

_{11}antenna parameter obtained by the CRO-SL. Note that the solution obtained is extremely good. In Figure 7a, it is possible to visualize three peaks under −25 dBs in the three frequency bands, with a peak under −45 dB in the 5G frequency centered in 3.5 GHz, and good bandwidth associated with all the frequencies considered. In the same way, the results represented in Figure 7b confirm the good performance of the optimized antenna. Please note that the markers on Figure 7b show the center frequency for each service, but not the exact resonant frequency.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Variables description of the proposed antenna. (

**a**) Antenna top view U-shaped variable description; (

**b**) antenna top view the annular patch variable description; (

**c**) detail description of the variables in the top view of the antenna that have been used in the optimization process; (

**d**) antenna ground plane.

**Figure 2.**Hybridization of the CST simulation software with the Coral Reefs Optimization with Substrate Layer (CRO-SL) for optimized the parameters of the proposed antenna.

**Figure 3.**Reflection coefficient of the proposed antenna optimized for f

_{2}and f

_{3}frequency bands.

**Figure 4.**Final antenna layout for the two-frequency bands optimization case, after the optimization process. (

**a**) Front view; (

**b**) bottom view.

**Figure 5.**Evolution of the CRO-SL fitness (Equation (2)) in two frequency bands antenna optimization process.

**Figure 6.**CRO-SL substrate performance metrics for the two-frequencies antenna optimization. (

**a**) Best substrate for larvae generation; (

**b**) best substrate for getting larvae into the reef.

**Figure 7.**Reflection coefficient of the proposed antenna optimized for f

_{1}, f

_{2}and f

_{3}frequency bands. (

**a**) Reflection coefficient in dB; (

**b**) reflection coefficient in Smith Chart.

**Figure 8.**Final antenna layout for the three-frequency bands optimization case, after the optimization process; (

**a**) Front view; (

**b**) Bottom view.

**Figure 9.**Surface current distribution for the antenna obtained in the three-frequency bands optimization case.

**Figure 10.**Final antenna radiation pattern; (

**a**) plane E and plane H at 800 MHz; (

**b**) plane E and plane H at 2.2 GHz; (

**c**) plane E and plane H at 3.5 GHz.

**Figure 11.**Evolution of the CRO-SL fitness (Equation (2)) in the three-frequency bands antenna optimization process.

**Figure 12.**CRO-SL substrate-performance metrics for the two-frequencies antenna optimization; (

**a**) Best substrate for larvae generation; (

**b**) Best substrate for getting larvae into the reef.

**Table 1.**Definition of the variables to optimize in the design of the proposed antenna (see Figure 1 for details).

Variable | Range |
---|---|

Antenna top view | |

U_T | [1,5] |

U_Patch_h | [1,Lp] |

U_Patch_AY | [0.5,(Wp-2Circle_R)/2] |

U_Patch_AX | [0.5,Lp/2-U_Patch_W-Circle_R] |

U_Ah | [1,(Wp-7Mean_A-8Mean_W-2U_T)/2] |

U_L | [0.5,Wp] |

U_Patch_W | [1,5] |

Circle_R | [11,Wp/2] |

Circle_Angle | [0.5,180] |

Circle_S | [3,5] |

Cirlce_CT | [1,5] |

Circle_T | [3,5] |

Lp=60mm; Wp=90mm | |

Antenna ground plane | |

Mean_W | [1,2.7] |

Mean_A | [1,10] |

Mean_h | [1,Lp] |

U_AV | [1,(Lp-Mean_h-2U_T)/2] |

Algorithm Step | Pseudo-Code for the CRO Algorithm |
---|---|

1 | Require: CRO algorithm parameters |

2 | Ensure: An optimal feasible individual (best antenna design) |

3 | Initialize the algorithm and CRO parameters |

4 | for each iteration of the simulation do |

5 | Update values of CRO parameters: predation probability, etc. |

6 | Broadcast spawning and Brooding operators |

7 | Settlement of new corals |

8 | Predation process |

9 | Evaluate the new population in the coral reef |

10 | end for |

11 | Return: the best individual (final solution) from the reef |

**Table 3.**Comparison of the best results obtained by the proposed CRO-SL approaches and an evolutionary algorithm.

Algorithm | Best Fitness |
---|---|

CRO-SL (two frequency bands) | 146.24 |

CRO-SL (three frequency bands) | 155.03 |

Evolutionary Algorithm | 130.05 |

Frequency (GHz) | Gain (dBi) |
---|---|

0.8 | 2.734 |

2.2 | 4.793 |

3.5 | 8.344 |

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**MDPI and ACS Style**

Camacho-Gomez, C.; Sanchez-Montero, R.; Martínez-Villanueva, D.; López-Espí, P.-L.; Salcedo-Sanz, S.
Design of a Multi-Band Microstrip Textile Patch Antenna for LTE and 5G Services with the CRO-SL Ensemble. *Appl. Sci.* **2020**, *10*, 1168.
https://doi.org/10.3390/app10031168

**AMA Style**

Camacho-Gomez C, Sanchez-Montero R, Martínez-Villanueva D, López-Espí P-L, Salcedo-Sanz S.
Design of a Multi-Band Microstrip Textile Patch Antenna for LTE and 5G Services with the CRO-SL Ensemble. *Applied Sciences*. 2020; 10(3):1168.
https://doi.org/10.3390/app10031168

**Chicago/Turabian Style**

Camacho-Gomez, Carlos, Rocio Sanchez-Montero, Diego Martínez-Villanueva, Pablo-Luís López-Espí, and Sancho Salcedo-Sanz.
2020. "Design of a Multi-Band Microstrip Textile Patch Antenna for LTE and 5G Services with the CRO-SL Ensemble" *Applied Sciences* 10, no. 3: 1168.
https://doi.org/10.3390/app10031168