This section explains the design of the proposed H-shaped MPA with experimental results. The performance of the proposed approach is compared with conventional methods to prove its effectiveness of the proposed approach.

## 4.1 Design of H-shaped antenna

For the H-shaped MPA, the parameters are designed as follows. The dielectric constant, resonant frequency, and substrate height are the fixed parameters. The radiation mechanism in MPA is shown in Fig. 4. The proposed inset-fed rectangular MPA is designed using geometric parameters like the patch length (\({\text{L}}_{\text{p}}\)), the patch width (\({\text{W}}_{\text{p}})\), dielectric constant (\({{\epsilon }}_{\text{r}})\), substrate height, and resonant frequency. The independent geometric parameter values such as the dielectric constant, resonant frequency, and substrate height are initialized as 4.4, 13.5 GHz, and 1.6mm respectively for Ku-band applications.

The dataset required to train and test the MLP in the proposed approach is generated using MATLAB 2018a software. The MLP trained with the developed dataset is used to evaluate the fitness value. The proposed RSA-MLP approach is implemented using MATLAB software. The population is initialized as 50 and the total iteration is set as 500. The performance of the proposed approach is compared with other approaches like PSO-SA [15], PSO [6], FA [9], ACO [7], and EHO [8]. Table 1 shows the simulation parameters used for the optimization of antenna.

Table 1

Simulation parameters used for optimization of antenna

Algorithm | Parameters | Values |

**FA** [9] | \(\beta\) | 0.2 |

\(\alpha\) | 0.25 |

\(\gamma\) | 1 |

**PSO** [6] | Weight | 0.2 |

Constant | 2 |

**ACO** [7] | \(\alpha\) | 0.5 |

\(\beta\) | 2.5 |

**EHO** [8] | \(\alpha\) | 0.7 |

\(\beta\) | 0.1 |

**PSO-SA** [15] | Initial temperature, t | 0.1 |

Weight | 0.2 |

Constant | 2 |

**Proposed RSA-MLP** | \(\alpha\) | 0.1 |

\(\beta\) | 0.1 |

## 4.2 Radiation pattern of the Antenna

The radiation pattern is the representation of the antenna radiation. In the far and near-field areas, the power of the antenna will be spread. Figure 5 shows radiation patterns of the proposed MPA with frequencies of 13.5 GHz for the Ku-band. Based on the angular positions and radial positions, the pattern of the radiation of the antenna is represented. Moreover, the function of magnetic and electric fields designed on the logarithmic scale represents the pattern of radiation of the antenna. Depending on the energy radiated direction, the pattern of radiation is determined. On the power patterns and field patterns, the radiation patterns that are designed with the dB scale and logarithmic scale are mentioned.

## 4.3 Return Loss

More signal power will be lost because of the production of reflections by the presence of discontinuities in the transmission line. This power loss is known as return loss and in decibels (dB) it can be represented. This loss can be calculated using Eq. (10).

$$RL\left(dB\right)=10{\text{log}}_{10}\frac{{P}_{IN}}{{P}_{REF}}$$

10

Where Incident power is represented by \({P}_{IN}\) and reflected power is represented by \({P}_{REF}\). Figure 6 shows the return loss for Ku-band applications. The return loss for the Ku-band application is -33.06 dB and resonates at 13.5 GHz. Thus, the return loss of the proposed approach is within the acceptable level.

## 4.4 Antenna Gain

The effectiveness of the radiation of signals from the proposed antenna can be calculated using antenna gain. In the antenna radiation direction, the amount of transmitted power can be determined using the antenna gain. The gain is measured in terms of dB. The radiation pattern used is a broadside pattern. Using the efficiency and the antenna directivity the antenna gain can be calculated as given in Eq. (11).

$$G={{\epsilon }}_{\text{r}}D$$

11

Where directivity is represented by D and relative permeability is represented by \({{\epsilon }}_{\text{r}}\). How much the produced radiation is concentrated in a solitary path is estimated by the directivity and parameter of the receiving wire which is characterized by the directivity. Figure 7 shows the 3D representation of the gain patterns. From conical cuts, this model is developed. Direction-based angles are used to form the model. With the existing approaches like ACO, FA, PSO, PSO-SA, and EHO algorithms, the antenna gain of the proposed RSA approach is compared. From the comparison results, a high gain is attained by the proposed antenna.

## 4.5 Voltage Standing Wave Ratio (VSWR)

For the proper impedance matching indication, at the location of the feed, the VSWR is the important parameter. The ratio of the maximum voltage to the minimum voltage in the antenna defines the VSWR as given in Eq. (12).

$$VSWR=\frac{\left|{V}_{max}\right|}{\left|{V}_{min}\right|}$$

12

Where, \({V}_{max}\) represents the maximum voltage of the antenna and \({V}_{min}\) represents the minimum voltage of the antenna. The efficiency of transformation of radio frequency power of the antenna from the transmission line or source in the channel can be calculated using the VSWR. Figure 8 shows the VSWR of the proposed approach for Ku-band applications. For Ku-band application the VSWR achieved by the proposed approach is 1.074. Thus the VSWR value lies below 2 which are in the acceptable range.

## 4.6 Directivity

The ability of the radiation to focus on the proposed antenna can be calculated using the parameter directivity. For validating the performance of the developed antenna for many antennas, the directivity is the necessary calculation. The ratio of a practical radiator’s radiation intensity to an isotropic radiator is referred to as directivity. It is expressed using Eq. (13).

$$AD=\frac{{R}_{p}}{{R}_{i}}=\frac{4\pi {U}_{p}}{{P}_{rad}}$$

13

Where the practical radiator’s radiation intensity is represented by \({R}_{p}\) and the isotropic radiator’s radiation intensity is represented by \({R}_{i}\). The directivity of the proposed approach is shown in Fig. 9 for Ku-band applications. The proposed approach achieved better directivity and the ability of the radiation to focus on the proposed antenna is higher.

## 4.7 Input impedance

The imaginary reactance and real resistance are denoted as the input impedance. For the essential function of antenna frequency operation, the impedance of the antenna is the necessary function. Figure 10 shows the input impedance vs. frequency response of Ku-band applications. To identify the input impedance of the antenna, the frequency is considered between 11.5 GHz and 13.5 GHz for the Ku-band application. To design the H-shaped MPA, the high input impedance is attained by the proposed antenna.

## 4.8 Comparison with existing techniques

The performance of the RSA technique for MPA is compared with existing techniques like conventional PSO-SA, PSO, ACO, FA, and EHO. Figure 11 shows the return loss comparison for the proposed approach with existing techniques for Ku-band applications. The proposed approach achieved a -33.06 dB return loss. When compared with existing approaches, the return loss achieved by the proposed approach is very less. Figure 12 shows the comparison of the directivity of the proposed approach with existing approaches for Ku-band applications. The proposed approach achieved better directivity. The existing approaches achieved very less directivity when compared with the proposed approach.

Figure 13 shows the comparison of the convergence curve of the proposed approach with existing approaches such as conventional PSO-SA, PSO, ACO, FA, and EHO. The proposed RSA approach has a better convergence rate than the existing approaches. Figure 14 shows the VSWR comparison for the proposed approach with the existing approaches. The VSWR achieved by the proposed approach is 1.07 which is very less compared with existing approaches. Figure 15 displays the gain comparison of the proposed approach with the existing approaches. Using the proposed approach the antenna attains a higher gain of 8.89 dB. The computation time taken by the proposed algorithm is compared with the existing approaches as shown in Fig. 16 (a). The proposed approach took less running time for the RSA algorithm compared with existing approaches. The total computation time taken by the proposed RSA-MLP approach is compared with the existing approaches as shown in Fig. 16 (b). The proposed approach took less time compared with existing approaches.