Quarter mode substrate integrated waveguide (QMSIW)

Figure 1 illustrates the design evaluation of the proposed design to achieve the size reduction and Fig. 1a shows the circular-shaped SIW cavity-backed antenna. It can be split into two parts either horizontally or vertically for size reduction as named as circular half-mode SIW (CHMSIW) represented in Fig. 1b and further split into two parts named as circular Quarter Mode SIW (CQMSIW) antenna represented in Fig. 1c. The material used for developing proposed design is FR-4 with a dielectric constant of 4.4 with a thickness of 1.6 mm. The electromagnetic tool is used employed to assess the antenna performance in terms of S₁₁, gain, surface current, voltage standing wave ratio (VSWR), and far-field radiation pattern

Figure 13. S₁₁ for different values of octagonal slot width (W₂).

Figure 14. S₁₁ for different values of second side circle slot width (W₃).

Figure 15. S₁₁ for different values of bottom rectangular slot width (W_s).

The Fig. 2 represents the design evaluation of the proposed antenna and their design steps are as follows

The Fig. 3 shows a parametric representation of the proposed design where the left side indicates the top view and the right side indicates the bottom view. The microstrip feed line used in this design and has 50ohms characteristics impedance. In the top view, two circle slots are loaded in the middle of the substrate and an octagonal slot is loaded in between two circular slot and rectangular slots are loaded in the back side of the proposed antenna and their dimension is 27 × 33.5 × 1.6 mm³. The Fig. 4 represents the printed prototype in which the right side belongs to the bottom view and the left side belongs to the top view. Table 1 intensifies the parameters used in this design.

Figure 16. S₁₁ for different values of extended substrate width (W_x).

Table 1. Parameters used in this antenna

Figure 17. S₁₁ for different values of extended substrate length (W_y).

Figure 18. S₁₁ for different microstrip feed length (L_f) feed.

Figure 19. S₁₁ for different microstrip feed width (W_f).

The SIW cavity is cylindrical in nature, so the design frequency and working principle can be calculated from the solution of the wave equation in a cylindrical cavity with few modifications due to the discontinuous sidewall. If we neglect the leakage of the sidewall, the resonant frequency of the TM_npq mode of a cylindrical cavity, having radius (a) and height (d), is represented in eq. 1 [Reference Sehrai, Asif, Shoaib, Ibrar, Jan, Alibakhshikenari, Lalbakhsh and Limiti18].

(1)\begin{equation}{f_r} = \frac{C}{{2\Pi \sqrt {{\mu _r}{\varepsilon _r}} }}{\text{ }}\sqrt {{{\left( {\frac{{{X_{np}}}}{a}} \right)}^2} + {{\left( {\frac{{{q_\Pi }}}{d}} \right)}^2}} \end{equation}

Figure 20. S₁₁ for different back slot width (W_b).

Figure 21. Surface Current. A. 3.57 GHz b. 4.41 GHz. C. 5.43 GHz.

where X_np tells the P_th zero of the n_th order Bessel function of the first kind. For the fundamental TM₀₁₀ mode, in the context of a circular SIW cavity, the resonant frequency can be articulated as

(2)\begin{equation}{f_{010}} = \frac{{2.405C}}{{2\Pi a\sqrt {{\mu _r}{\varepsilon _r}} }}\end{equation}

The frequency of resonance achieved is calculated to be 3.2 GHz when the parameter a (representing the radius of the cavity) is assigned a value of 18.15 mm. The diameter (d) and spacing (s) between the adjacent metallic via are two key parameters of the SIW of the metallic via is represented in eq. 3 [Reference Niu and Tan2, Reference Kumar and Shanmuganantham8].

(3)\begin{equation}d \leqslant \frac{{{\lambda _g}}}{5}{\text{ and }}s \leqslant 2d\end{equation}

Figure 22. Comparison of S₁₁ measured, simulation results.

Figure 23. 1 × 2 MIMO antenna.

Figure 24. Fabricated Prototype.

Figure 25. Measurement of proposed design using VNA and anechoic chamber.

The reflection coefficient of the proposed design for different stages is represented in Fig. 5 over the frequency range 3 to 6 GHz. Final proposed antenna as good accuracy comparing with all the stages and resonates at 3.57 GHz, 4.41 GHz and 5.43 GHz respectively. The S₁₁ of the proposed antenna is shown in Fig. 6 over the frequency range 3 to 6 GHz and it is operated in three frequencies i.e. 3.57 GHz, 4.41 GHz, 5.43 GHz and their S₁₁ values are − 23.66 dB − 25.44 dB, − 16.10 dB. The operating bandwidth of the proposed design is 110 MHz at 3.57 GHz resonant frequency (3.52 GHz to 3.63 GHz), 100 MHz at 4.41 GHz resonant frequency (4.36 GHz to 4.46 GHz), 150 MHz at 5.43 GHz resonant frequency (5.35 to 5.50 GHz) concerning − 10 dB baseline and well suited to operate in WLAN, Wi-MAX, Wi-Fi, radar systems and sub-GHz 5 G Applications.

The Fig. 7 represents the VSWR of the proposed design and produces three resonant frequencies 3.57 GHz, 4.41 GHz and 5.43 GHz respectively, has VSWR of 1.141, 1.118 and 1.367. The VSWR results (2:1 ratio) matched with S₁₁ result. The parametric variation of SIW Width S₁₁ result is revealed in Fig. 8 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 20.5 mm, 21 mm, 21.5 mm, represented by green, red and blue colours. The change in SIW width will affect the accuracy and resonant frequency. The best value chosen is 21 mm and has better accuracy and operated in three frequencies 3.57 GHz, 4.41 GHz and 5.43 GHz.

Figure 26. S- Parameters results.

The parametric variation of bottom side rectangular slot width S₁₁ result is revealed in Fig. 9 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 0.4 mm, 0.5 mm, 0.6 mm, represented by green, red and blue colours. The change in bottom side rectangular slot width will affect the change in second resonant frequency. The best value chosen is 0.5 mm.

Figure 27. S₂₁ values for different values of G_p.

The parametric variation of strip length (L_s) S₁₁ result is revealed in Fig. 10 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 4.1 mm, 4.3 mm, 4.5 mm, represented by green, red and blue colours. The accuracy was found to be varied by changing L_s were observed at all three resonant frequencies and the best value chosen is 4.3 mm. The parametric variation of substrate width (W) S₁₁ result is revealed in Fig. 11 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 26 mm, 27 mm, 28 mm, represented by green, red and blue colours. There is a drastic change in the accuracy, resonant frequencies while changing the width of SIW(W) and also found that increasing the W will increase the accuracy as well as resonant frequency moving toward left that is decreasing the resonant frequencies and the best value chosen is 27 mm.

Figure 28. Comparison of S₁₁/S₂₁ results.

Figure 29. Co and Cross polarization.

The parametric variation of first circle width (W₁) S₁₁ result is revealed in Fig. 12 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 0.4 mm, 0.5 mm, 0.6 mm, represented by green, red and blue colours. The accuracy was found to be varied by changing W₁ were observed at all three resonant frequencies and also found variations in first resonant frequency. The best value chosen is 0.5 mm.

Figure 30. Surface Current of 1 × 2 MIMO antenna.

Figure 31. Gian in dB.

The parametric variation of octagonal circle width (W₂) S₁₁ result is revealed in Fig. 13 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 0.4 mm, 0.5 mm, 0.6 mm, represented by green, red and blue colours. The accuracy was found to be varied by changing W₂ were observed at all three resonant frequencies and the best value chosen is 0.5 mm. The parametric variation of second circle slot width S₁₁ result is revealed in Fig. 14 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 0.4 mm, 0.5 mm, 0.6 mm, represented by green, red and blue colours. The accuracy was found to be varied by changing W₃ were observed at all three resonant frequencies and the best value chosen is 0.5 mm.

Figure 32. Efficiencies of the antenna.

The parametric variation of insert feed width S₁₁ result is revealed in Fig. 15 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 0.7 mm, 0.75 mm, 0.8 mm, represented by green, red and blue colours. The accuracy was found to be varied by changing Ws were observed at all three resonant frequencies and the best value chosen is 0.75 mm.

Figure 33. 1 × 2 MIMO antenna with decoupling stub.

Figure 34. Frequency versus S₁₂/S_21.

Figure 35. Frequency Vs ECC.

The parametric variation of extended substrate width (W_x) width S₁₁ result is revealed in Fig. 16 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 2.5 mm, 3.0 mm, 3.5 mm, represented by green, red and blue colours. The accuracy was found to be varied by changing W_x were observed at all three resonant frequencies and also observed variations in third resonant frequency and the best value chosen is 3.0 mm.

Figure 36. Frequency Vs Diversity Gain (DG).

The parametric variation of extended substrate width (W_y) width S₁₁ result is revealed in Fig. 17 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 0.5 mm, 1.0 mm, 1.5 mm, represented by green, red and blue colours. The accuracy was found to be varied by changing W_y were observed at all three resonant frequencies and also observed variations in second and third resonant frequency and the best value chosen is 1.0 mm.

Figure 37. Frequency Vs MEG.

The parametric variation of microstrip feed length S₁₁ result is revealed in Fig. 18 over the range of frequencies 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 11 mm,11.5 mm, 12 mm, represented by green, red and blue colours. The accuracy was found to be increased by the feed length with few variations were observed at second and third resonant frequency and the best value chosen is 11.5 mm.

Figure 38. Frequency Vs CCL.

The parametric variation of the microstrip feed width S₁₁ result is revealed in Fig. 19 over the range 3 to 6 GHz. The three values are taken for analysing the performance of the S₁₁ and those are 1.5 mm,1.6 mm, 1.7 mm, represented using different colours those are green, red and blue colour. The accuracy was found to be increased by the feed width with few variations observed at the first and second resonant frequency and the best value chosen is 1.6 mm.

The reflection coefficient for different values of back side slot width (W_b) is shown in Fig. 20 and three values are chosen to fix the best value of W_b which are 17 mm, 17.5 mm and 18 mm respectively. The change in W_b will affect the antennas second resonant frequency and also accuracy of the first and third resonant frequency. As W_b is increasing second frequency moving to left side and it is improving reflection coefficient. Hence, the optimistic value chosen W_b is 17.5 mm. The surface current of the antenna is shown in Fig. 21 where Fig. 21a, 21b and 21c portray the surface current of the antenna operated at 3.57 GHz, 4.41 GHz and 5.43 GHz respectively. At, 3.57 GHz the current is more on the patch, at 4.41 GHz the current is more at the octagonal slot and at 5.43 GHz, the surface current is more at the octagonal slot and outer circular slot. In all three frequencies, the current flow is high at the top of the feed point.

The Fig. 22 shows that the comparison of S₁₁ in terms of simulated and measured results and as observed compromised results. There is a slight deviation at resonant frequency at 5.6 GHz due to little bit deviations occurred while etching, filling the copper in the holes of the antenna. The measured antenna resonates at 3.57 GHz, 4.41 GHz and 5.6 GHz and their S₁₁ values are − 23 dB, − 26 dB and − 15 dB.

1 X 2 MIMO antenna

A 1 × 2 MIMO antenna was realized by co-locating a CQMSIW loaded with quarter part octagonal, two-quarter circle on the dielectric substrate. The two radiating elements were arranged in 180^. phase differences as shown in Fig. 23 with a gap distance of G_p where the left side structure describes the top view and right-side structure describes bottom view of the structure. The top and bottom views of the fabricated prototype are shown in Fig. 24, and their dimensions are 54 mm x 33.5 mm x 1.6 mm. The Fig. 25 shows the measured photographs of the antenna where left side indicates VNA setup and right side indicates anechoic chamber.

The S-Parameter of the 1 × 2 MIMO antenna is shown in Fig. 26 over the frequency range 3 to 6 GHz. The 1 × 2 is arranged in a symmetric Configuration hence, the S₁₁ and S₂₂, S₁₂ and S₂₁ result are equal. The isolation between the ports is less than (< −15 dB) in simulation results.

The S₁₂ result for different values of G_p are reported in Fig. 27. The three different values are chosen to evaluate the best isolation value of the 1 × 2 array. It is observed that increasing G_P will give better isolation results affecting the accuracy of the reflection coefficient. From the iteration, the best value chosen is 0 mm.

The comparison of simulation measured S₁₁/S₁₂ results are revealed in Fig. 28. The S₁₁ results are observed that almost same results in-terms of simulation, measured results except third resonant frequency with respect to −10 dB reference line. The small result fluctuations occurred due to etching the slot. Copper filled in the vias during the fabrication process. There is a compromised results observed in isolation between the ports and the values is less than −15 dB in all the operating frequency band. The Fig. 29 represents the comparison of simulation, measured results in terms of cross and co polarization of the proposed antenna. The Fig. 29a, Fig. 29b and Fig. 29c shows that E-field and H-field pattern of the proposed antenna at three frequencies those are 3.57 GHz, 4.41 GHz and 5.5 GHz respectively. There is close match between the patterns is observed and radiates bi-directional radiation pattern and well suited the all-commercial wireless applications.

The surface current of the 1 × 2 MIMO antenna is shown in Fig. 30, which portrays the antenna surface current operated at 3.57 GHz, 4.41 GHz and 5.43 GHz respectively. At 3.57 GHz, the current is more on patch in the port1 and port2; at 4.41 GHz the current is more at the octagonal slot in the port1 and port2 and at 5.43 GHz the surface current is more at the octagonal slot and outer circular slot in the port1 and port2. In all three frequencies, the current flow is high at the top of the feed point. The Fig. 31 shows the comparison of gain results where blue colour indicates simulated results and red colour indicate measured results. The simulated, measured gain values are 4.98dBi, 5.092 dBi, at 3.57 GHz resonant frequency, 4.6dBi, 4.51dBi at 4.41 GHz resonant frequency and 3.06dBi, 3.075dBi at 5.5 GHz resonant frequency. The average gain value is around 4.5dBi in both cases that is simulation, measured results and well suited operate the applications like WLAN, WiMAX, Sub 6-GHz, Wi-Fi and fixed wireless access etc.,

The efficiencies of the proposed antenna are represented in Fig. 32 and the blue colour, red colour are indicating radiation and total efficiency. The radiation, total efficiency values are 78%, 76% at 3.57 resonant frequency, 81.02%, 71.5% at 4.41 GHz resonant frequency and 74.1%, 72.89% at 5.43 GHz resonant frequency. This is well suited to operate a wireless application like sub 6 GHz 5 G Applications.

MIMO Parameters

The ECC, DG and MEG parameters are general parameters to validate the MIMO antenna and their measured result is discussed in preceding sections

Envelope correlation coefficient (Ecc)

The quantity of similarity between the antenna ports with respect to radiated signals is notated as ECC. It computes the similarity or correlation and similarity of the signal envelopes other than the magnitude or phase of signals themselves [Reference Dhananjeyan, Ramesh and Kumar14–Reference Nayak and Manjunathachari16].

The ECC value is represented in equation 4 and the ideal value is zero but in practical situations, the tolerable value of ECC is below 0.5. The comparison of simulation measured 1 × 2 MIMO array ECC is shown in Fig. 35 and observed close match at operating frequency band. From the Fig. 35, observed that ECC value is less than 0.0001 for all the operating frequencies with respect to simulation, measured results.

(4)\begin{equation}ECC = \frac{{{{\left| {S_{11}^{\text{*}}{S_{12}} + {S_{22}}S_{21}^{\text{*}}} \right|}^2}}}{{\left( {1 - {{\left| {{S_{12}}} \right|}^2} - {{\left| {{S_{22}}} \right|}^2}} \right){\text{ }}\left( {1 - {{\left| {{S_{12}}} \right|}^2} - {{\left| {{S_{22}}} \right|}^2}} \right)}}\end{equation}

Diversity gain (Dg)

DG is another essential feature to evaluate the performance of the MIMO antenna and is expressed in terms of ECC as represented in the equation 5 [Reference Dhananjeyan, Ramesh and Kumar14–Reference Nayak and Manjunathachari16]. If the DG is 10 dB, the SNR or BER will increase by tenfold equated to a single-antenna system. Figure 36 represent the 1 × 2 HM-SIW based MIMO antenna simulation, measured results and observed close match between simulation, measured results. The DG value is more than 9.995 dB across the operating frequency band.

The proposed antenna has been proven to be effective in combating fading, with less interference and other impairments, reliability, leading to improved signal quality, and overall system performance. The DG and ECC are correlated to each other in an inversely proportional relation, indicating that and that indicates decreasing ECC will increase the value of diversity gain [Reference Bing and Yan10, Reference Malviya and Chouhan11].

(5)\begin{equation}DG = 10\sqrt {1 - ECC} \end{equation}

Mean effective gain (meg)

This is used to measure the gain of the antenna in a desired direction ranging from − 3 dB ≤ MEG ≤ −12 dB [Reference Dhananjeyan, Ramesh and Kumar14–Reference Nayak and Manjunathachari16]. The formula is used to find the MEG is in equation 6. Figure 37 represents the MEG between the ports and observed that it lies under the value −3 dB to −4 dB over the operating frequency band and also observed close match between simulation, measured results at every operating frequency. The ratio of MEG1/MEG2 is equal to 1 due to symmetry deign used in the proposed MIMO design (S₁₁ = S₂₂ & S₂₁ = S₁₂).

(6)\begin{equation}ME{G_{\text{i}}} = 0.5\left( {1 - {{\left| {{S_{{\text{ii}}}}} \right|}^2} - {{\left| {{S_{ij}}} \right|}^2}} \right)\end{equation}

Channel capacity loss (Ccl)

Another parameter of to evaluate the performance of MIMO antenna, which tells us the loss occurred during channel. The acceptable value is less than 0.4bits/sec and the equation 7 represents the formulae of CCL

(7)\begin{equation}CCL = - {\log _2}\det \left( {{\varphi ^R}} \right){\text{ }}\end{equation}

Where,

(8)\begin{equation}{\varphi ^R} = \left( {\begin{array}{*{20}{c}} {{\varphi _{ii}}}&{{\varphi _{ij}}} \nonumber \\ {{\varphi _{ji}}}&{{\varphi _{jj}}} \end{array}} \right)\end{equation}

(9)\begin{equation}{\varphi _{ii}} = 1 - \left( {{{\left| {{S_{ii}}} \right|}^2} + {{\left| {{S_{ij}}} \right|}^2}} \right)\end{equation}

(10)\begin{equation}{\varphi _{jj}} = 1 - \left( {{{\left| {{S_{jj}}} \right|}^2} + {{\left| {{S_{ji}}} \right|}^2}} \right)\end{equation}

(11)\begin{equation}{\varphi _{ji}} = 1 - \left( {{S_{jj}}*{S_{ji}} + {S_{ij}}*{S_{jj}}} \right)\end{equation}

(12)\begin{equation}{\varphi _{ij}} = 1 - \left( {{S_{ii}}*{S_{ij}} + {S_{ji}}*{S_{ii}}} \right)\end{equation}

The comparison of simulation measured results of CCL as shown in Fig. 38 and observed close match results at every operating frequency. The CCL value is less than 0.3 bits/sec at every operating frequency.

Table 2 represents the comparison of the proposed 1 × 2 MIMO QMSIW antenna with similar literature in terms of size, technique used in the design, operating bands, number of elements, gain in dBi, efficiency, ECC, DG. The results show that the proposed antenna has achieved moderate gain, size miniaturization, broad bandwidth and good efficiency as compared to existing literature and also observed acceptable MIMO parameters for better isolation.

Table 2. Comparison of the proposed work with similar literature