Antenna design simulation and characterization

The antenna designed in this paper is shown in Fig. 1. It is printed on the FR4 substrate and consists of a hexagonal radiating patch, a stepped microstrip feedline, and a DGS structure.

Figure 1.

Structure of the UWB antenna: (a) top view and (b) bottom view.

The microstrip line of the antenna is a stepped feedline with 50-Ω impedance. The impedance of 50-Ω can reduce reflections, signal loss, and signal distortion. The microstrip line characteristic impedance can be computed by

(1)\begin{equation} {\varepsilon _{re}} = \frac{{{\varepsilon_{r}} + 1}}{2} + \frac{{{\varepsilon_{r}} - 1}}{2}\left(1 + 12\frac{h}{W} \right)^{-\frac{1}{2}}, \end{equation}

(2)\begin{equation} {Z_0} = \frac{{120{\pi}}}{{\sqrt {{\varepsilon _{re}}} \left[ {\frac{W}{h} + 1.393 + 0.667\ln (\frac{W}{h} + 1.444)} \right]}}, \end{equation}

where W denotes the width of the microstrip line and h represents the height of the dielectric substrate. ɛ_r is the relative permittivity of the dielectric substrate. ${{\varepsilon _{re}}}$ represents the effective relative permittivity of the microstrip line, and Z ₀ represents the characteristic impedance of the microstrip line. After the above calculations, we can estimate the microstrip line width. Other structural parameters of the antenna are shown in Table 1.

Table 1.

Dimensions of the antenna

The design evolution of the antenna structure is shown in Fig. 2. The antenna is simulated by using HFSS to measure the return loss of the antenna, which is calculated by

(3)\begin{equation} \Gamma = \frac{{{Z_o} - {Z_{in}}}}{{{Z_o} + {Z_{in}}}}, \end{equation}

(4)\begin{equation} RL = -20log(|\Gamma |). \end{equation}

Z_o and Z_in represent the characteristic impedance of the transmission line and the input impedance of the feedline, respectively. Γ is the reflection coefficient of the antenna. The smaller the reflection coefficient is, the better the impedance matching will be. The return loss is a method of representing the reflection coefficient in logarithmic form (dB), and $ \left\lvert {S_{11}} \right\rvert \lt -10\ \mathrm{dB}$ is usually used as a criterion for antenna bandwidth in engineering applications [Reference Qin, Wei and Guo19].

Figure 2.

The design evolution of the antenna structure: (a) structure 1, (b) structure 2, (c) structure 3, and (d) structure 4.

The reflection coefficient of the four antenna configurations is shown in Fig. 3. As we can see, the bandwidth of Structure 1 is 3.3–8.7 GHz. Quarter-circle slots are cut in the corners of the ground plate of Structure 1, which are used to build Structure 2. Invert convex shape slots are cut in the middle of Structure 2, and we can get Structure 3. In these ways, the antenna surface current path is enlarged and the impedance matching characteristics are improved [Reference Singh, Dwivedi, Singh and Yadav20]. The antenna’s bandwidth increased to 3.2–9.2 GHz and 3.2–20 GHz, respectively. Finally, the rectangular microstrip feedline in Structure 3 is changed to a stepped shape. This modification further increases the antenna’s bandwidth and enables it to satisfy the UWB standard in the low-frequency band. The low frequency of Structure 4 is 2.95 GHz.

Figure 3.

The S11 parameters of four antenna structures.

The bandwidth covered by UWB antennas ranges from 3.1 GHz to 10.6 GHz. Within this range, there are narrowband commercial frequency bands such as WiMAX (3.3–3.8 GHz), C-band satellite communication (3.7–4.4 GHz), and digital microwave communication (4.3–4.5 GHz), which may interfere with the frequency bands of UWB antennas. To address the issue of frequency reuse, enhance spectrum efficiency, and minimize costs wherever possible, we have designed UWB antennas with band-notched properties within the WiMAX frequency band. Cut slots in the radiating patch enable the antenna to achieve band-notched characteristics. The band notch is implemented by using the following formulas [Reference Sharma and Bhatia21]:

(5)\begin{equation} {f_n} = \frac{c}{{2{L_s}\sqrt {{{\varepsilon }_{re}}} }}, \end{equation}

(6)\begin{equation} {{\varepsilon }_{re}} = \frac{{{{\varepsilon }_{r}} + 1}}{2}, \end{equation}

where f_n is the resonant frequency and L_s is the length of the slot.

The inner perimeter length of the slot required to produce a notch at 3.6 GHz can be estimated using (5) and (6). A bent slot is made on the radiating patch to facilitate the opening of the slot inside the hexagonal radiating patch and increase the adjustment space. The bent slot enables the work current to be concentrated at the edge of the thin slot, so the nearby currents have the same amplitude and opposite direction. As a result, the radiated electromagnetic energies counteract each other in the far-field region and form the band-rejected characteristic. Figure 4 shows the reflection coefficients corresponding to different inner perimeters of the bent slot.

Figure 4.

Input reflection coefficients corresponding to different lengths of antenna bent slot.

From Fig. 4, it can be seen that the size of the antenna bent slot parameter affects the range of the notched band. By optimizing the structural parameters, we can achieve the band-notched characteristic in WiMAX (3.3–3.8 GHz) of the antenna. However, using HFSS for antenna parameter optimization consumes a significant amount of resources and needs high computational costs. Fortunately, the neural network can get a nonlinear relationship between input and output in a short time after the training is completed. This approach can significantly reduce design time. Based on this, the following 1DCNN-IPS model is set up to optimize the UWB antenna.

Improved one-dimensional convolutional neural network

The traditional method for optimizing antenna structures relies on the optimization function of electromagnetic simulation software, but each optimization process consumes a great deal of time. Compared with traditional methods, 1DCNN can automatically learn features and show better performance when processing large-scale data.

1DCNN

CNN [Reference Staszewski, Jaworski, Cao and Rutkowski22–Reference Cheng, Xie, Shi and Xiong24] structure has been widely used in recent years. Its structure consists of multiple layers like the convolutional layer, pooling layer, and fully connected layers, as shown in Fig. 5, which is the network structure of a 1DCNN. Compared to heuristic optimization techniques such as genetic algorithms and particle swarm optimization, ANNs possess powerful learning capabilities and excellent nonlinear mapping abilities. Once the relationship between antenna structural parameters and reflection coefficient is established, even minor adjustments to the antenna structure can immediately yield the corresponding antenna performance without the need for additional inference calculations.

Figure 5.

1DCNN architecture.

Convolutional layers

The convolutional layer can extract edge features and deeper feature information from the image. It consists of multiple layers of convolutional kernels of the same size. In the antenna modeling process, the structural parameters of the antenna can be abstracted as a one-dimensional image and then processed with the convolutional layer. The operation of the convolutional layer is evaluated by

(7)\begin{equation} {O^l} = \sum\limits_{i = 1}^n {\sum\limits_{j = 1}^m {I_{i,j}^{l - 1} \times K_{i,j}^l + {b^l}} }, \end{equation}

where $I^{l-1}$ represents the input of the convolutional layer in layer l − 1. O ^l represents the output of the convolutional layer in layer l. K ^l represents the convolutional kernel in layer l, and b ^l is the bias of the convolutional kernel in layer l.

Pooling layer

The main role of the pooling layer is to reduce the dimensionality of the data by downsampling the input data and to retain the key information from the input data. The max pooling layer and average pooling layer are commonly used for pooling in CNN and can be expressed as

(8)\begin{equation} ({s_j})_\mathrm{max} = \mathop {\max }\limits_{i \in {R_j}} {a_i}, \end{equation}

(9)\begin{equation} ({s_j})_\mathrm{avg} = \frac{1}{{\left| {{R_j}} \right|}}\sum\limits_{i \in {R_j}} {{a_i}}, \end{equation}

where ${a_i}$ is the i-th element in the j-th region ${R_j}$.

Fully connected layer

The fully connected layer can synthesize all the extracted features and then map them to labels for regression prediction. The operation of the fully connected layer can be written as

(10)\begin{equation} {y^r} = f({w^r} \bullet {y^{r - 1}} + {b^r}), \end{equation}

where ${y^r}$ is the output of the r-th fully connected layer and ${w^r}$ is the weight matrix. ${b^r}$ is the bias entry.

Loss function

The loss function represents the extent to which the prediction falls short of the actual data. Through a backpropagation algorithm, CNN can calculate the gradient errors of the loss function with the model’s parameters. These gradients are used to update the parameters and optimize the model. The loss function can be expressed as

(11)\begin{align} {E_{Loss}} = \frac{1}{n}\sum\limits_{i = 1}^n {{{({t_i} - {y_i})}^2}}, \end{align}

where ${t_i}$ is the target output and ${y_i}$ is the network’s prediction of the response i.

Batch normalization algorithm

The BN algorithm can compute the mean and variance of each neuron and then utilize these statistical values to normalize their inputs. This process allows each neuron in the network to adapt to the training data better, so it can accelerate the convergence rate of the network training. The calculation can be described as

(12)\begin{equation} {\hat x^{(k)}} = \frac{{{x^{(k)}} - E[{x^{(k)}}]}}{{\sqrt {Var[{x^{(k)}}]} }}, \end{equation}

where ${\hat x^{(k)}} = Wh + {b}$ is the input of the neurons in the network. W is the weight of the current layer. h is the output of the previous layer, and b is the bias term.

The output changes the learned feature distribution after normalization, and the BN algorithm configures learnable reconstruction parameters with

(13)\begin{equation} {y^{(k)}} = {\gamma ^{(k)}}{\hat x^{(k)}} + {\beta ^{(k)}}. \end{equation}

When ${\gamma ^{(k)}} = \sqrt {Var[{x^{(k)}}]}$ and ${\beta ^{(k)}} = E[{x^{(k)}}]$, the network can recover the original learned features by the reconstruction transformation.

Improved 1DCNN

Traditional neural networks, such as Back Propagation (BP) networks, are computationally fast, but their fitting accuracy is low. Although it is possible to optimize the neural network by machine learning to improve accuracy, it increases the training time of the network. In addition, the traditional method to design antennas by neural networks needs to use the structural parameters of the antenna as network inputs. However, the antenna parameters have low feature dimensions and the neural network extracts the features to reduce the dimensions of the feature mapping after forward propagation, which is unsuitable for deeper learning. To address these problems, a 1DCNN-IPS model is proposed in this paper. 1DCNN-IPS improves the propagation structure of the network by using padding in the convolutional layers in such a way that the inputs to the deeper convolutional layers remain sufficiently informative. The network concludes with three convolutional layers, a max pooling layer, and a fully connected layer. Compared to the standard CNN model, the 1DCNN-IPS model scheme is as follows:

1. (i) Padding is added to the convolutional layer to mitigate the problem of the network losing information during forward propagation. The same padding is calculated as [Reference Simonyan and Zisserman25]

   (14)\begin{equation} N = \frac{{W - F + 2P}}{S} + 1, \end{equation}

   where N represents the output dimension and W represents the dimension of the input features. F represents the dimension of the convolution kernel. S represents the step size, and P represents the number of padding layers;

2. (ii) The BN layer is added after each convolutional layer to adjust the distribution of the output of the convolutional layer;

3. (iii) The ReLU activation function between convolutional layers is explored instead of the Sigmoid function. It gives the neurons sparse activation and alleviates the vanishing gradient problem. The ReLU activation function is expressed as follows:

   (15)\begin{equation} {f_{\mathrm{ReLU} }}(x) = \max (0,x). \end{equation}

   The function returns 0 if it receives any negative input but returns it back for any positive value x.

The 1DCNN-IPS model concludes with three convolutional layers with a convolutional kernel size of two and a max pooling layer to extract features. Padding is added to the convolutional layers, and the BN layer is added after each convolutional layer. The ReLU activation function accelerates the model training, alleviating the problem of training overfitting and enhancing the model robustness. The structure of the 1DCNN-IPS model is shown in Fig. 6.

Figure 6.

Structure of 1DCNN-IPS.

The network architecture and parameter count of the 1DCNN-IPS model designed in this paper are presented in Table 2. The model has approximately 5.5K computational parameters. In the case of optimal prediction performance, the parameter counts for 1DCNN, MLP, and 1DLeNet-5 networks are 5.6K, 5.8K, and 6.4K, respectively. Compared to these models, the model designed in this paper has fewer parameters.

Table 2.

The structure and parameter count of the 1DCNN-IPD model

Optimized design of UWB antennas by 1DCNN-IPS

Figure 4 shows that the structural parameters of the antenna’s bent slot greatly impact the reflection coefficient. Optimizing with electromagnetic simulation software usually requires multiple simulation calculations, and each calculation takes a certain amount of time. Specifically for complex antenna structures, the time required for simulation calculations may be very long. In contrast, CNN can evaluate and optimize plenty of design schemes quickly. Upon completion of the training process, CNNs can promptly predict the performance of new design schemes, thereby leading to a significant reduction in the optimization cycle. Consequently, we use the 1DCNN-IPS model to optimize the antenna design. The 1DCNN-IPS optimized UWB antenna design flowchart is shown in Fig. 7.

Figure 7.

The 1DCNN-IPS optimized UWB antenna design flowchart.

The process consists of the HFSS simulation part and the 1DCNN-IPS network-based antenna bent slot optimization part. The HFSS simulation part mainly performs the following two functions:

1. (i) During the HFSS simulation, the antenna’s structural parameters and reflection coefficients are obtained, providing a dataset for the subsequent training of the 1DCNN-IPS network.

2. (ii) Verify the accuracy of the antenna reflection coefficients output by the 1DCNN-IPS network.

The antenna bent slot optimization process based on the 1DCNN-IPS network primarily includes the following:

1. (i) Training the 1DCNN-IPS model using the dataset derived from the HFSS simulation part. The training procedure focuses on adjusting the model’s parameters to accurately predict the relationship between the antenna’s reflection coefficients and the structural parameters of the bent slot.

2. (ii) Once the network training is completed, the antenna parameters to be tested are imported, and the 1DCNN-IPS model is used for final performance prediction and verification. Subsequently, the optimal structural parameters of the bent slot are determined based on the reflection coefficient results.

It is important to note that HFSS simulations require significant computational time after modifying the antenna’s structural parameters. However, once the 1DCNN-IPS network is trained, the corresponding reflection coefficient results can be immediately obtained by inputting the structural parameters of the bent slot into the network. Based on these reflection coefficient results, the structural parameters of the bent slot can be optimized, thereby saving the calculation time of using the HFSS software.

The detailed steps for optimizing the antenna’s bent slot structure using 1DCNN-IPS are as follows.

1. (i) The antenna model is built using HFSS software, and the reflection coefficient parameters of the antenna are extracted by finite element method simulation. The output data are divided into training samples and testing samples with a ratio of 9:1. The structural parameters of the antenna are shown in Table 3.

   Table 3.

   Structural parameter range of the antenna

   

2. (ii) The dataset is normalized, enabling equal scaling of the original data and unifying each parameter’s specification. The normalization calculation can be expressed as

   (16)\begin{equation} {X_{norm}} = \frac{{X - {X_{min} }}}{{{X_{max} } - {X_{min} }}}, \end{equation}

   where ${X_{norm}}$ is the normalized output. ${X_{max}}$ and ${X_{min}}$ are the maximum and minimum values of X, respectively.

3. (iii) Build the 1DCNN-IPS model. The network contains three convolutional layers, and padding has been added to improve the network structure. The BN layer is added after each convolutional layer to normalize its inputs and enhance the robustness of the network. The last convolutional layer connects the max pooling layer to speed up the computation.

4. (iv) Initialize the hyperparameters such as 1DCNN-IPS model weights ${w^l}$, bias ${b^l}$, loss function, training batch size, learning rate, etc.

5. (v) Train the 1DCNN-IPS model. The dataset obtained in Step (ii) is sent into the model. Once the model is trained well, it will calculate the error in the forward propagation phase and adjust the weight matrix in the backward propagation phase to optimize the network.

6. (vi) Optimization of the structural parameters of the bent slot. The trained model is employed to substitute the time-consuming electromagnetic simulation software for the optimization of the structural parameters of the bent slot. In contrast to the relatively long simulation time required by electromagnetic simulation software, the 1DCNN-IPS model can quickly establish the relationship between inputs and outputs. When the structural parameters of the bent slot are input into the model, the antenna’s reflection coefficient is immediately output. If a notch exists in the reflection coefficient of the antenna within the WiMAX frequency band, and the antenna’s frequency band meets the UWB design requirements, the structural parameters of the bent slot are recorded. If the results do not meet the design specifications, new parameters are selected for further testing.

7. (vii) Verification is performed using HFSS simulation. If the results do not meet the design requirements, the process returns to step (vi). If the requirements are met, the optimization of the antenna bent slot design is completed.

Experiments and analysis of results

This experiment was conducted in MATLAB R2022a to realize the construction and training of the five network models. The antenna designed in this paper was simulated using HFSS software, and the sweep range was set to 1–10.6 GHz with a step size of 0.3 GHz to derive the antenna reflection coefficient dataset. The 1DCNN-IPS model, 1DCNN model, MLP model, 1DLeNet-5 model, and Jellyfish Search-Optimized BP Neural Network JS-BP model were trained using the obtained dataset. After the training had been completed, the test set was used to verify the test effect of the five models.

As shown in Fig. 8, we compared the S11 prediction results of the 1DCNN-IPS model with the other four models. This figure shows that in the frequency band of 3.1–4.6 GHz, the 1DCNN model and and the 1DLeNet-5 model differ from the actual simulation results. In the frequency band 5.5–7 GHz, only the 1DCNN-IPS model can be fitted with the HFSS simulation results. As shown in the root mean squared error (RMSE) results in Fig. 9, the IDCNN-IPS model works better than the other four models.

Figure 8.

Prediction curves of the five models fitted to the HFSS simulation curves.

Figure 9.

RMSE for five networks.

The mean squared error (MSE) and running time of the five models are shown in Table 4. It can be seen that the MSE value of the 1DCNN-IPS model is 0.4342. The prediction accuracy of the 1DCNN-IPS model is improved by 22.49 $\%$, 27.67 $\%$, 19.87 $\%$, and 34.06 $\%$ than the 1DCNN model, MLP model, 1DLeNet-5 model, and JS-BP model, respectively. In terms of training time, the 1DCNN-IPS model is 9.17 $\%$ faster than the 1DLeNet-5 model. So the 1DCNN-IPS model has lower MSE but faster computing speed.

Table 4.

Comparison of mse and computation time of different models

The antenna structural parameters were optimized by using the trained 1DCNN-IPS model. The model inputs the structural parameters of the antenna and outputs the reflection coefficient of the antenna. As shown in Fig. 10, if the lengths of L4, W4, W5, and Wd are 4 mm, 3.6 mm, 2.9 mm, and 0.4 mm respectively, the antenna’s notched band will be 3.55–4.15 GHz, which does not satisfy the design requirements. If the four structural parameters are 4 mm, 4 mm, 3 mm, and 0.5 mm, respectively, the antenna’s notched band is 3.3–3.9 GHz, which covers the work band of WiMAX. The antenna has an impedance bandwidth ( $ \left\lvert {S_{11}} \right\rvert \lt -10\ \mathrm{ dB}$) from 2.8 to 14 GHz, which covers the entire UWB frequency band. Finally, after HFSS verification, the structural parameters of the antenna bent slot are set as L4 = 4 mm, W4 = 4 mm, W5 = 3 mm, and Wd = 0.5 mm.

Figure 10.

Effectiveness of 1DCNN-IPS fitting.

According to the antenna band-notched principle, the antenna is further analyzed to determine the relationship between the bent slot and the corresponding notched band. By simulation, we obtain the antenna surface current distribution at the notch center with 3.6 GHz, as shown in Fig. 11. It can be seen that the current mainly gathers near the bent slot. A notched band is generated since the energy is pooled at the bent slot and cannot be radiated outward.

Figure 11.

Antenna surface current distribution at 3.6 GHz.

The physical diagram of the antenna is shown in Fig. 12. The antenna is manufactured on the FR4 substrate having dielectric constant $\varepsilon _\mathrm{r} = 4.4$ and height $h = 1.5\,\mathrm{mm}$. After soldering the Radio Frequency (RF) coaxial connector (SubMiniature version A, SMA) joints, it was tested by using a vector network analyzer, and the results are shown in Fig. 13. Due to the errors in the fabrication process and the errors in soldering the SMA connector, etc., the simulated and measured results deviate from each other. From the measured waveforms, it can be seen that the antenna realizes the band-notched characteristic in the frequency band from 3.35 to 4 GHz. Except for the notched band, the reflection coefficient of the antenna is less than $-10 $ dB, which can meet the UWB system’s operation requirements.

Figure 12.

Prototype of the antenna. (a) Top view. (b) Bottom view.

Figure 13.

The simulation and measurement comparison of S11.

Figure 14 shows the measured and simulated gain of the antenna in the WiMAX frequency band. As depicted in the figure, the antenna exhibits a noticeable decrease in gain in the WiMAX frequency band, effectively suppressing interference and impacts on narrowband communication bands.

Figure 14.

The measured and simulated gains of the antenna.

The radiation characteristics of the band-notched UWB antenna are analyzed at 4.5 GHz and 9 GHz. Due to manufacturing errors in the antenna production process and the influence of the antenna testing environment, discrepancies occur between the testing and simulated results of the antenna. Simulated and measured Radiation Pattern for phi = 0 and phi = 90 are shown in Fig. 15. It is clear from Fig. 15 that the radiation pattern at lower frequency is omnidirectional while a little distortion at higher frequency is observed.

Figure 15.

The radiation patterns of the antenna. (a) Radiation pattern at 4.5 GHz. (b) Radiation pattern at 9 GHz.

Table 5 presents the similarities and differences in various performances such as dimensions, bandwidth, notch band, and gain between the UWB notch antenna in this paper and the antennas in the references.

Table 5.

Table of comparison between designed antenna and published work

As shown in the table, the antenna designed in this study offers a wide bandwidth and exceptional notch characteristics. With its performance parameters, it is well-suited for a wide range of UWB applications. Compared with the works in the references, the proposed antenna demonstrates superior bandwidth, higher gain, and notch filtering capabilities. The antenna covers a frequency range from 3.1 to 13 GHz, with a notch band from 3.35 to 4 GHz, making it suitable for various UWB communication scenarios.