Structural layout of antenna

Different views/components of designed two-port aerial are shown in Fig. 1 and the sizes of various parameters of designed aerial is listed in Table 1. Alumina-based ceramic (ε_r = 9.8) is used as radiator and placed on the FR4 substrate (ε_r = 4.4). The thickness of substrate is 1.6 mm. Cross-formed slot has been etched from the substrate and created as a feed for ceramic. Printed line is placed in the lower part of substrate and used to feed the cross slot. Metasurface is based on single-sided FR4 substrate with a thickness of 1.6 mm.

Figure 4.

(a) |S₁₁| variation with various alteration in shape of slots and (b) axial ratio variation with various alteration in shape of slots.

Table 1.

Optimal sizes of various parameters of designed aerial

Figure 5.

Axial ratio variation with different change in L_1.

Figure 6.

S-parameter alteration for two-port radiator with change in aperture placement.

Figure 7.

|S₁₁|/|S₁₂| alteration of designed unit cell.

Figure 8.

Effective permittivity and permeability of designed unit cell.

Figure 9.

|S₁₁|/|S₁₂| variation of dual port aerial with and without MS.

Figure 10.

Axial ratio variation of dual port aerial with and without MS.

Figure 11.

Broadsided gain variation of dual port aerial with and without MS.

Figure 12.

Gain variation with change in H_M.

Antenna analysis

This segment provides a detailed investigation on proposed two-port ceramic aerial with the assistance of HFSS software. Analysis has been started with one-port radiator. Figure 2 presents the |S₁₁| alteration for single-port aerial with and without alumina ceramic. One significant reflection found from Fig. 2 that the complete working spectrum is because of alumina ceramic. In the working spectrum, two resonances are visible at 7.58 GHz and 8.1 GHz. Vectored E-field lines are plotted in Fig. 3 at 7.58 GHz and 8.1 GHz. It can be perceived from Fig. 3 that dual orthogonal hybrid mode i.e. ${\text{HEM}}_{11{{\delta }}}^{\text{x}}$ and ${\text{HEM}}_{11{{\delta }}}^{\text{y}}$ at 7.58 GHz and 8.1 GHz correspondingly [Reference Kajfez, Glisson and James24]. Numerically, the resonance frequency of fundamental hybrid mode is given as follows [Reference Sharma, Das and Gangwar25]:

\begin{equation*}{{\text{f}}_{{\text{r}},HE{M_{11\delta }}}} = \frac{{6.321{\text{c}}}}{{{{\pi D}}\sqrt {{{{\varepsilon }}_{\text{r}}} + 2} }}\left[ {0.27 + 0.36\left( {\frac{{\text{D}}}{{4{\text{H}}}}} \right) + 0.02{{\left( {\frac{{\text{D}}}{{4{\text{H}}}}} \right)}^2}} \right]{\text{ }}\left( 1 \right)\end{equation*}

In eqn. (1), ‘“c,” “D,” and “H” denote speed of light, diameter, and height of dielectric rod, respectively. From above equation, the resonant frequency is found to be 7.85 GHz, which is closer to resonance obtained in HFSS software.

For finding out the reason of taking cross slot with unequal arm length, Fig. 4(a) and Fig. 4(b) plot the |S₁₁| and axial ratio alteration with three different cases: (i) rectangular slot linked ceramic; (b) X-slot with identical arm size-linked ceramic; and (iii) X-slot with uneven arm size-linked ceramic. Two significant remarks found from Fig. 4: (a) in case three, two resonant peaks occurred, which is due to orthogonal mode; and (b) X-slot with uneven arm size supports CP waves from 7.42 to 7.8 GHz. A variation in the size of one arm of the X-aperture produces a 90° phase difference between the orthogonal modes, and the cross slot aids in the production of twin orthogonal modes within the DRA. Thus, the suggested aperture provides a dual orthogonal mode inside the ceramic with 90° phase changes, which is a prerequisite for the formation of circular polarization [Reference Balanis26]. Figure 5 presents the axial ratio alteration with change in dimension L₁. It can be seen from Fig. 5 that the optimized AR bandwidth is obtained when L₁ = 14.0 mm.

Table 2.

Comparing every model using S11 performance metrics

Table 3.

Comparing every model using axial ratio performance metrics

Single port aerial is converted in dual port with parallel placing of antenna ports. However, the aperture orientation is taken as two ways: (i) same slot placement; and (ii) mirror slot placement. Figure 6 shows the alteration of S-parameter with aforementioned two cases. It can be seen from Fig. 6 that |S₁₁| parameter is approx. same in both cases, while the mutual coupling is reduced to less than −25 dB within the working spectrum in case of mirror slot placement. This is because of the polarization diversity concept [Reference Varshney, Singh, Pandey and Yaduvanshi5]. Polarization diversity means that the one port supports left-handed CP (LHCP) wave, while other port supports right-handed CP (RHCP).

Figure 13.

Comparison of the estimated and actual values: (a) decision tree_|s₁₁|, (b) random forest_|s₁₁|, (c) decision tree_axial ratio, and (d) random forest_axial ratio.

Figure 14.

Fabricated prototype of designed aerial (a) feed layout (b) metasurface design (c) adjacent view.

Figure 15.

Pictures of measuring setup (a) VNA and (b) anechoic chamber.

Figure 16.

Measured/simulated/forecasted s-parameter of designed aerial.

A MS is suspended over the two-port ceramic radiator. This metasurface is made up of periodic arrangement of unit cell. Figure 7 shows the |S₁₁|/|S₁₂| variation for unit cell. It can be seen from Fig. 7 that |S₁₁| is well below to −10 dB, while |S₁₂| is near to 0 dB with in the working spectrum. This confirms that the unit cell allows the EM waves passes through it. In order to extract the effective dielectric constant and permeability of unit cell, the following equations are utilized [Reference Numan and Sharawi27]:

(2)\begin{equation}{\text{Z = \pm }}{\left[ {\frac{{{{{\text{(1 + }}{{\text{S}}_{{\text{11}}}}{\text{)}}}^{\text{2}}}{\text{ - S}}_{{\text{21}}}^{\text{2}}}}{{{{{\text{(1 - }}{{\text{S}}_{{\text{11}}}}{\text{)}}}^{\text{2}}}{\text{ - S}}_{{\text{21}}}^{\text{2}}}}} \right]^{{\text{0}}{\text{.5}}}}\end{equation}

(3)\begin{equation}{e^{j\eta {k_0}d}} = \frac{{{S_{21}}}}{{1 - {S_{11}}\frac{{Z - 1}}{{Z + 1}}}}\end{equation}

(4)\begin{equation}\varepsilon = \frac{\eta }{Z}{\text{ }}\end{equation}

(5)\begin{equation}\mu = \eta *Z\end{equation}

In the above equations, “Z,” “d,” “k₀,” and “η” indicate the input impedance, width of substrate, wave number, and intrinsic impedance, respectively. “S₁₁” and “S₁₂” denote reflection coefficient and mutual coupling, respectively. “ $ \varepsilon $” and “ $\mu $” denotes effective permittivity and permeability, respectively. With the assistance of above equations, effective permittivity and permeability is plotted within the working spectrum and shown in Fig. 8. It can be perceived from Fig. 8 that both permeability and permittivity is negative within the working spectrum. This means that unit cell behaves as double negative material.

Figure 17.

Measured/simulated/forecasted axial ratio alteration of designed aerial.

Figure 18.

Measured/simulated LHCP and RHCP pattern at 7.6 ghz (a) port-1 (b) port-2.

Figure 19.

Measured/simulated gain alteration of designed aerial.

Figure 9 presents the S-parameter alteration with and without suspension of MS over the two-port aerial. It can be detected from Fig. 9 that |S₁₁| is approximately same in both circumstances. The mutual coupling level is also same with and without MS. Figure 10 shows the axial ratio variation with and without MS. It is observed from Fig. 10 that the axial ratio curve is also not much effected by placing MS. Broadsided gain variation is shown in Fig. 11 with and without MS. It can be seen from Fig. 11 that the broadsided gain is enhanced to more than 11 dBi after placing MS. Double negative unit cell’s made MS improves the directivity, which in turn improves the antenna’s gain [Reference Samantaray and Bhattacharyya28].

Figure 12 shows the gain variation with different changes in the gap between antenna and MS. It can be seen from Fig. 12 that the optimized gain is obtained at 10.0 mm.

Prediction of s-parameter using ML algorithms

Two different ML methods are applied in this section to predict the planned radiator’s axial ratio and reflection coefficient (S11). Decision Tree and Random Forest (RF), are the ML methods that have been used for that purpose [Reference Ranjan, Maurya, Gupta, Yadav and Sharma21]. A RF voting mechanism selects the main tree as the ultimate output after several trees vote for the outcomes. In ML, decision trees are frequently used to generate and predict results using input data. The architecture resembles a tree, with every inner node testing a property, every branch representing a feature value, and each leaf node representing the ultimate choice or forecast. The main advantage of these two algorithms is to get better accuracy even for smaller data set. After training process, these algorithms are utilized to predict the reflection coefficient and axial ratio value of proposed antenna by simply provides the sizes of various antenna parameters [Reference Bhavani, Raviteja and Shanmuganantham29, Reference Praveena, Umamaheswari, Rai and Ranjan30]. Collections of data are generated by changing D (13.0–17.0 mm in 0.25 incremental step), H (5.0–10.0 mm in 0.25 incremental step), L₁ (12.0–16.0 mm in 0.25 incremental step), L₂ (8.0–12.0 mm in 0.25 incremental step), H_M (8.0–12.0 mm in 0.25 incremental step), L_F (27.0–32.0 mm in 0.25 incremental step), L₄ (3.0–7.0 mm in 0.25 incremental step), and L₃ (10.0–15.0 mm in 0.25 incremental step) with a frequency sweep from 7.0 GHz to 8.4 GHz with 51 points in between the mentioned range after the proposed antenna is designed with the assistance of HFSS. There were 25,041 dataset points in the entire created dataset. Thirty percent (7513) of the complete dataset are utilized for testing, while the remaining seventy percent (17,528) are used for training. A variety of loss parameters features, including as mean squared error (MSE), R-squared loss, and mean absolute error (MAE), are used to assess how well the planned antenna models perform [Reference Ranjan, Maurya, Gupta, Yadav and Sharma21]. Here, the four remaining antenna parameters – D, H, L₁, L₂, H_M, L_F, L₃, L₄, and frequency – are regarded as input features, while S11 and axial ratio are taken as goal variables. Every ML method is trained, and then a validation dataset is used to evaluate every model. All of the outcomes produced by the various ML methods employed for S11 and axial ratio are compared in Tables 2 and 3, respectively. It can be shown from Tables 2 and 3 that random forest has the lowest mean error and the highest R² Score. Therefore, RF outperforms decision tree in performance prediction.

The anticipated vs. real outcomes graph for RF and Decision Tree on the test dataset for |S11| and axial ratio is shown in Fig. 13. The optimal scenario for regression issues is Y = X. Therefore, a higher density in the vicinity of the Y = X line indicates superior algorithmic performance. It can be shown from Fig. 13 that the random forest forecast is more accurate. For larger negative values of |S11|, the predicted value differed further from the real one.

Figure 20.

ECC and DG alteration of planned aerial.

Experimental verification

This section focuses on validating optimized simulated/forecasted machine learning outcomes with empirically acquired results. The designed aerial prototype is made and evaluated for this reason. In Fig. 14, it is displayed. Figure 15 shows the pictures of measuring set up i.e. vector network analyser (VNA) and anechoic chamber. Keysight’s E5071C VNA is used to measure the S-parameter. The frequency range for Anechoic Chamber is from 1 to 18 GHz. The designed aerial’s simulated, predicted, and measured S-parameter is shown in Fig. 16. There is good agreement among forecasted, simulated, and practically obtained S-parameter. The designed aerial works effectively in 7.21–8.2 GHz with the separation level more than 25 dB. Slight variance is obtained owing to the influence adhesive substance for adhering the ceramic over substrate. Addition of adhesive creates the small air gap between alumina ceramic and substrate. Due to this, there is reduction in impedance matching as well as shifting in the resonance peak [Reference Faiz, Gogosh, Khan and Shafique31].

Figure 17 presents the comparison of simulated/forecasted and experimentally attained axial ratio alteration for designed aerial. It is measured inside the anechoic chamber with the technique of dual linear far-field measurement [Reference Stutzman and Thiele32]. It can be seen from Fig. 17 that there is good correlation among simulated, forecasted, and experimentally gained axial ratio. The designed aerial supports CP waves in between 7.35 and 7.8 GHz. Figure 18 shows the 2D measured/simulated LHCP and RHCP pattern at 7.6 GHz. Good corelation is obtained between experimental and simulated LHCP and RHCP pattern. In case of port-1, the LHCP is more dominant as compare to RHCP. That means, the port-1 supports LHCP waves from ceramic. Similarly, port-2 supports RHCP waves. Because of this, polarization diversity concept is supported by designed aerial. Broadsided far-field confirms the HEM_11δ mode inside the ceramic material. Figure 19 presents the experimental and simulated gain alteration of designed aerial. It is measured using two antenna technique [Reference Stutzman and Thiele32]. Due to directive pattern, the maximum gain of designed aerial is approx. 11.5 dBi.

Table 4 compares the performance of designed aerial with published two-port aerials on the basis of working range, aerial’s gain and utilization of ML technique. The designed aerial provides wider impedance as well as axial ratio bandwidth. Aerial gain and isolation level between the ports of designed radiator is also quite high in comparison to published radiator. Last and important analysis for designed aerial is MIMO parameters, i.e. Envelop Correlation Coefficient (ECC) and diversity gain (DG). ECC talks about likeness among the antenna ports. It should be as low as (less than 0.2) possible for effective multi-port aerial. DG is directly related to ECC and talks about multi-port gain in fading situation [Reference Sharawi1]. There are well known formulas for calculating ECC and DG [Reference Sharawi1]. Figure 20 presents the simulated and experimental ECC and DG alteration for designed aerial. It can be seen from Fig. 20 that EEC is much lower than the standard, i.e. 0.2, while DG is approx. 10.0 within the working spectrum. This confirms the effectiveness of designed multi-port ceramic aerial.

Table 4.

Comparing the designed twin band aerial’s performance to published CP multiport ceramic aerials