Band gap determination

To further validate the band gap characteristic of EBG structure, the proposed EBG structure 5 × 4 lattice of EBG structure is simulated using an FR4 substrate with ɛ_r = 4.4 with the height of 1.6 mm. The bandwidth of the band gap of the EBG structure is computed by using the suspended microstrip transmission line method presented in Fig. 3. In the presence of the EBG periodic structure, the transmission responses (S ₂₁) between the two ports are analyzed to obtain the band gap properties. Figure 4 shows three band gaps as 0.4 GHz (3.3–3.7 GHz), 1 GHz (5.15–5.85 GHz), and 1.4 GHz (7.2–8.6 GHz); the minimum S ₂₁ value is about −37 dB for the triple band gaps.

Fig. 3.

Transmission line over modified EBG structure.

Fig. 4.

Transmission coefficient for modified EBG structure.

Equivalent circuit model

The equivalent circuit of the suggested structure is depicted in Fig. 5. The arrangement of inductor (L), capacitor (C), and resistance (R) is used to demonstrate the port of 50 Ω load, feed line, and radiating patch [Reference Malviya, Panigrahi and Kartikeyan11]. The fed lines and radiating patch are symbolized by the series and parallel arrangement of L1, C1, R1, and L7, C7… LN, CN, respectively. The parallel arrangement of L6 and C6 use to denote the mutual coupling among ports 1–2, and ports 1–4. Similarly, the parallel arrangement of L5 and C5 is used to symbolize isolation between ports 1–3. The modified EBG structure is equivalent to three resonant circuits denoted by parallel combination L2 and C2, L3 and C3, and L4 and C4.

Fig. 5.

Equivalent circuit.

Voltage standing wave ratio (VSWR) and S parameters

Figure 6 illustrates the simulated VSWR curve with and without the EBG structure. From the simulated result, it is observed that the UWB MIMO antenna with EBG structure function in the entire UWB range except for WiMAX, WLAN, and X-band. The VSWR parameter of the suggested antenna is illustrated in Fig. 7 and it show that the VSWR value at rejecting bands is more than 2; therefore, it is clear that no radiation is taking place at the rejecting frequencies 3.5, 5.5, and 7.7 GHz.

Fig. 6.

Deviation of VSWR with frequency.

Fig. 7.

Variation of VSWR with the frequency of different ports.

However, Fig. 8 shows the tested and simulated VSWR curve of the structure. The difference in the tested and simulated results is because of the various losses like conduction loss, dielectric loss, mismatch loss, SubMiniature version A (SMA) soldering, fabrication error, measurement error, and orientation problems when the proposed structure is connected to the vector network analyzer [Reference Thakur, Jaglan and Gupta12].

Fig. 8.

Variation of measured and simulated VSWR.

Figure 9 demonstrates the isolation of the suggested antenna. The mutual coupling among the patch antenna is considerably minimized by using T-shaped stubs on the ground plane. A slot is etched on the ground plane to enhance the isolation. It can be seen from Fig. 10 that mutual coupling is below −15 dB for the whole frequency band. The measured curves confirm good resemblance with simulated curves.

Fig. 9.

Deviation of mutual coupling with frequency.

Fig. 10.

Variation of mutual coupling with frequency.

Radiation pattern

Figure 11 indicates the simulated and tested radiation plot at 4, 6.3, and 7.6 GHz at both E plane and H plane. It is seen that the suggested structure shows a ring-shaped radiation pattern in the H plane and rotation symmetry at the E plane. Figure 12 illustrates that the gain of the suggested antenna is varied from −9.5 to 7.5 dB for the entire UWB range.

Fig. 11.

(a) Normalized radiation plot at 4 GHz. (b) Normalized radiation plot at 6.3 GHz. (c) Normalized radiation plot at 7.6 GHz.

Fig. 12.

Deviation of gain with frequency.

MIMO characteristics

The significant factors to analyze and validate the MIMO characteristics are envelope correlation coefficient (ECC), diversity gain (DG), total active reflection coefficient (TARC) [Reference Chae, Oh and Park13], and mean effective gain (MEG) [Reference Karaboikis, Papamichael, Tsachtsiris, Soras and Makios14]. During the analysis of the MIMO antenna, the ECC is considered as a valuable parameter to evaluate the degree of signal fading or diversity skill of the MIMO antenna. Correlation is commonly used to measure the difference between the radiation patterns. ECC and DG can be determined using S parameters [Reference Chae, Oh and Park13] and radiation pattern [Reference Karaboikis, Papamichael, Tsachtsiris, Soras and Makios14]. The mathematical formula to evaluate the ECC in terms of scattering parameters and radiations pattern can be given by [Reference Chandel, Gautam and Rambabu15]

(1)$$ECC( \rho _{ij}) = \displaystyle{{{\vert {S_{ii}^\ast S_{ij} + S_{\,ji}^\ast S_{\,jj}} \vert }^2} \over {( {1-{\vert {S_{ii}} \vert }^2-{\vert {S_{\,ji}} \vert }^2} ) ( {1-{\vert {S_{\,jj}} \vert }^2-{\vert {S_{ij}} \vert }^2} ) }}$$

For four elements:

(2)$$ECC( \rho _{12}) = \displaystyle{{{\vert {S_{11}^\ast S_{12} + S_{21}^\ast S_{22}} \vert }^2} \over {( {1-{\vert {S_{11}} \vert }^2-{\vert {S_{21}} \vert }^2} ) ( {1-{\vert {S_{22}} \vert }^2-{\vert {S_{12}} \vert }^2} ) }}$$

(3)$$ECC( \rho _{13}) = \displaystyle{{{\vert {S_{11}^\ast S_{13} + S_{31}^\ast S_{33}} \vert }^2} \over {( {1-{\vert {S_{11}} \vert }^2-{\vert {S_{31}} \vert }^2} ) ( {1-{\vert {S_{33}} \vert }^2-{\vert {S_{13}} \vert }^2} ) }}$$

(4)$$ECC( \rho _{14}) = \displaystyle{{{\vert {S_{11}^\ast S_{14} + S_{41}^\ast S_{44}} \vert }^2} \over {( {1-{\vert {S_{11}} \vert }^2-{\vert {S_{41}} \vert }^2} ) ( {1-{\vert {S_{44}} \vert }^2-{\vert {S_{14}} \vert }^2} ) }}$$

where S ₁₁, S ₂₂, S ₃₃, and S ₄₄ are the reflection coefficients. S ₁₂, S ₂₁, S ₃₁, S ₁₃, S ₄₁, and S ₁₄ are coupling between the ports:

(5)$$ECC = \displaystyle{{{\left\vert {\int {{}_\Omega [ {XPR\cdot E_{\theta_i}E_{\theta_j}^\ast P_\theta + E_{\phi_i}E_{\theta_j}^\ast P_\phi } ] } d\Omega } \right\vert }^2} \over {\int {{}_\Omega [ {XPR\cdot E_{\theta_i}E_{\theta_i}^\ast P_\theta + E_{\phi_i}E_{\phi_i}^\ast P_\phi } ] } d\Omega X\int {{}_\Omega [ {XPR\cdot E_{\theta_j}E_{\theta_j}^\ast P_\theta + E_{_{\theta_j} }E_{_{\theta_j} }^\ast P_\phi } ] } d\Omega }}$$

XPR is the cross-polarization rate of the incident field:

(6)$$XPR = \displaystyle{{P_V} \over {P_H}}$$

where P_V and P_H are the average power along elevation (θ) and azimuthal angle (ϕ). DG is an efficient parameter used to measure the enactment level of diversity systems. The DG defined as the slant of the error probability plot of the received SNR DG is related to ECC by the below equation [Reference Kumar, Kumar, Kumar Vishwakarma and Srivastava16]

(7)$$DG = 10\sqrt {1-ECC^2} $$

The RE and BW of an MIMO antenna are not accurately characterized by return loss. Therefore, rather than using return loss, TARC can be used so that it accounts for both coupling and random signal combination. Thus, TARC delivers a more significant measure of MIMO efficiency.

Figure 13 shows the simulated ECC and DG measured using S parameters. Ideally, ECC must be 0 but practically it should be beneath 0.5 and DG must be around 10 dB. The ECC and DG for different antenna elements are within 0.02 and 9.92 dB, respectively. The radiation efficiency and bandwidth of an MIMO antenna are not accurately characterized by return loss. Therefore, rather than using return loss, TARC can be used so that it accounts for both coupling and random signal combination. TARC is a significant factor that denotes the mutual coupling of the ports. For the four-port UWB MIMO antenna, the TARC can be calculated using below equation [Reference Blanch, Romeu and Corbella17]:

(8)$$TARC = \sqrt {\displaystyle{{{( S_{11} + S_{12} + S_{13} + S_{14}) }^2 + {( S_{21} + S_{22} + S_{23} + S_{24}) }^2 + {( S_{31} + S_{32} + S_{33} + S_{34}) }^2 + {( S_{41} + S_{42} + S_{43} + S_{44}) }^2} \over 4}} $$

Figure 14 illustrates the TARC of the suggested antenna. Ideally, for an MIMO system, the TARC should be less than 0 dB. It is clear from Fig. 14 that the TARC is below −2.5 dB for the complete band with the triple rejected bands.

Fig. 13.

Deviation of ECC and DG with frequency.

Fig. 14.

Variation of TARC with frequency.

MEG is one of the significant factors and is defined as the relation given below [Reference Tang, Zhan, Wu, Xu, Chen and Hu18]:

(9)$$MEG_i = 0.5\mu _{irad} = 0.5\left({1-\sum\limits_{\,j = 1}^N {{\vert {S_{ij}} \vert }^2} } \right)$$

where N is the number of patches and μ_irad is the efficiency. In this case N = 4:

(10)$$MEG_1 = 0.5[ {1-{\vert {S_{11}} \vert }^2-{\vert {S_{12}} \vert }^2-{\vert {S_{13}} \vert }^2-{\vert {S_{14}} \vert }^2} ] $$

(11)$$MEG_2 = 0.5[ {1-{\vert {S_{21}} \vert }^2-{\vert {S_{22}} \vert }^2-{\vert {S_{23}} \vert }^2-{\vert {S_{24}} \vert }^2} ] $$

(12)$$MEG_3 = 0.5[ {1-{\vert {S_{31}} \vert }^2-{\vert {S_{32}} \vert }^2-{\vert {S_{33}} \vert }^2-{\vert {S_{34}} \vert }^2} ] $$

(13)$$MEG_4 = 0.5[ {1-{\vert {S_{41}} \vert }^2-{\vert {S_{42}} \vert }^2-{\vert {S_{43}} \vert }^2-{\vert {S_{44}} \vert }^2} ] $$

For better diversity performance, the range of MEG should be |MEG _i − MEG _j| < −3 dB. The simulated MEG of the suggested four-port UWB MIMO is shown in Fig. 15. The value of MEG's for all the four elements is within the desired limit. The performance evaluation of the suggested UWB MIMO antenna with those recent antennas in the publication is presented in Table 2.

Fig. 15.

Variation of MEG with frequency.

Table 2.

Comparison table of the proposed antenna with other antennas