## 3 Design of Triple-Band Antenna
The geometric centers of the slots are equal to \(x_{1}\) = 0 mm, \(y_{1}\) = \(-\)19.35 mm; \(x_{2}\) = \(-\)7.32 mm, \(y_{2}\) = 0 mm; and \(x_{3}\) = 0 mm, \(y_{3}\) = 19.35 mm, respectively. A general schematic representation of the microstrip patch antenna with triple slots and arc-truncation (MPATSAT) is shown in Figure 1a. \(L\) is the antenna length, \(W\) is the antenna width, \(sL1\) and \(sL2\) are the slot lengths, \(sW1\) and \(sW2\) are the slot widths, and \(r\) is the radius of the arc-truncation in Figure 1a. The sketch of MPATSAT in HFSS is also illustrated in Figure 1b. The inputs of the SVR model are triple-band resonance frequencies \(f_{r1}\), \(f_{r2}\), and \(f_{r3}\) and desired minimum gains at these frequencies \(g_{1}\), \(g_{2}\), and \(g_{3}\). The outputs of the SVR model are slot length and width values (\(sL1\), \(sL2\), \(sW1\), and \(sW2\)) and the radius of arc-truncation (\(r\)) of the MPATSAT. The parametric analysis tool of HFSS was used to create proper training and testing patterns. Parametric analysis is used in HFSS to obtain resonance frequencies and gain values with respect to the slot dimensions and radii of arc-truncations. The sampling procedure for training and testing patterns is given in Table 1. Different values selected in an extensive range are used for constructing training and testing patterns to be able to obtain desired performance characteristics from the antenna. In soft computing methods, the selected dataset must cover all parts of the range that is required to be learned. The range of the slot dimensions and radii of the arc-truncations are selected to ensure that slots and truncation would not coincide with each other, feed point, and edges of the antenna. The step size between the selected samples of the ranges determines the number of samples. Step sizes are selected randomly; however, too-small values are avoided not to increase the computational load of the computer. The number of samples (variants) is limited by the computational power of the computer. Figure 1: Drawings of the proposed antenna: (a) general schematic representation of MPATSAT; (b) sketch of MPATSAT in HFSS. After parametric analysis, the whole HFFS' parametric analysis data are imported to MATLAB. Some of the elements of the data set are reserved as test samples, and the remaining ones are used to train the SVR model in MATLAB. Desired kernel function is selected and created in MATLAB via the required parameters (\(a\) for the Mexican-hat wavelet kernel). The dual form of the regression problem with linear constraints is written in MATLAB with related parameters (kernel function, \(C\), \(\varepsilon\)). The dual form has a convex objective function with linear constraints; therefore, a global solution to the problem is guaranteed. The optimal solution of the dual problem can be achieved via employing a quadratic programming solver, and the Lagrange multipliers are obtained. \"quadprog\" function of MATLAB is used as a quadratic programming solver in this study. \(\beta\) and \(\lambda\) are obtained via a quadratic programming solver, and \(w\) values are updated. Bias (\(b\)) values are updated with respect to the difference between the output of the training pattern values and weight values. The regression problem of (2) is solved by obtaining \(\lambda\), \(b\) and using the kernel function. In this way, a trained SVR model is obtained. This model can be used to compute the testing error, which gives the accuracy of the model. SVR model parameters related to the Mexican-hat wavelet kernel function are given in Table 2.  
HFSS simulation of training and testing patterns with a total of 1249 samples took 2 h and 36 min using a computer that has 3.2 GHz CPU and 16 GB RAM. In total, 1100 training samples were used to train the SVR model, applying related parameters given in Table 2 via MATLAB [54]. The SVR parameters that yielded the best performance were selected. Training time was 2.8 s. Mean accuracy was acquired as 98.35% via testing with the remaining 149 test samples.