Realization of the diversity configuration

The diversity configuration as depicted in Fig. 1(c) is attained by an orthogonal combination of PPM1 and PPM2 maintaining a compact inert-element separation of 8 mm (0.13λ ₀ at 3.1 GHz). The mutually perpendicular location of radiating monopoles is chosen to acquire high non-pairing as a result of polarization diversity. The individual monopoles are fed by a P ₂ × P ₉ 50 Ω microstrip line. PPM1 and PPM2 have a common rectangular ground plane with identical width of G ₂ but dissimilar lengths of W _S and L _S, respectively, and are placed behind the substrate. For attaining higher impedance matching (in terms of S₂₂) near the lower (3.8 GHz) and upper edges (9–18 GHz) of the UWB spectrum, an L-shaped slot with a dimension of G ₅ × G ₃ and G ₄ × G ₆ is carved from the top of the common ground structure. To attain wideband impedance matching as well as high and wideband isolation amidst the radiating monopoles, a couple of rectangular extended ground stubs of identical dimensions is deployed as shown in Fig. 1(a). Stub 1 is positioned side by side with PPM1 and the 2nd stub is positioned side by side in the company of PPM2. The optimized extent of the UWB diversity radiator is given in Fig. 1.

Effects of introducing Cayley tree fractal NL

To attain bandwidth enhancement (by constructing a substitutive resonance near 3.8 GHz), additional decoupling (between 3 and 7 GHz by more than 5 dB), and impedance matching (between 9 and 18 GHz), a Cayley fractal neutralization line (CFNL) is connected to the peak impedance zone of the radiating monopole (near the excitation zone of the monopoles) as presented in Fig. 1(a) and (c) [Reference Wang and Du18]. Fig. 2(a), (b), and (c) depict the improvement of S₁₁, S₁₂, and S₂₂ with the introduction of the CFNL respectively.

The length of the NL is initiated at 0.5λ ₀ at 3.1 GHz (lowest resonant frequency) and is gradually tuned to obtain an optimum level of impedance matching as well as isolation [Reference Banerjee, Gorai and Ghatak37]. The value of λ ₀ at 3.1 GHz = 96.8 mm and the overall length of the CFNL is measured to be 50.7 mm. The theoretical and actual measure of the length of the fractal NL are in close agreement and thus justify the design methodology. According to paper [Reference Wang and Du18], the suspended link acts as a NL by providing a counter-phase current to counter the original coupling current. Besides, the inductive and capacitive behaviors of the NL are specified by its length and width, respectively. The NL is used to connect both monopoles close to their feeding to draw maximum current. The simple 2nd-order Cayley fractal tree geometry is chosen for designing the NL to reduce the design complexity and ease the realization as well as manufacturing process. This process of isolation improvement utilizing NL does not eliminate the basic pairing among the radiators, nevertheless improves the inter-port non-pairing [Reference Wang and Du17].

Figure 2. Analysis of S-parameter with an application of CFNL. (a) Comparison of S11, (b) S12, and (c) S22 after the application of CFNL and (d) comparison between application of fractal and non-fractal NL for impedance matching and isolation improvement.

The Cayley tree fractal-inspired NL is a Y-formed assembly (the 1st-order fractal, N = 1, Fig. 3) of three microstrip-line branches spaced apart from each other by 120° rotation angle. The length and breadth of an individual branch are uniform, i.e., L_{N 1} = 5.36 mm and W_{N 1} = W_{N 2} = 0.25 mm, respectively. The fractal NL formation is proportionate across the y–z plane. The construction of the Cayley tree is by straightforward iterative function. The geometry is generated from an equilateral Y shape. Upon each iteration, two new branches are added to each terminal branch. The angle between each branch is kept constant (at θ = 120°), maintaining a threefold rotational symmetry [Reference Gottheim, Zhang, Govorov and Halas38]. The number of tips in a Cayley tree of order N = 3 × 2^{N −1}. The Cayley tree is a kind of dendrimer, also known as Bethe lattice. The construction procedure of the Cayley tree (C_{s, t}) (s ≥ 3, t ≥ 0) consists of t iterations. S is the number of nodes in the 1st iteration. C_s,0, for t = 0, consists of only a central vertex. For t > 1, the Cayley tree C_{s, t} is obtained from C_{s, t−1}. In ${C_{s,t}}$, the pendent vertices are $s{(s - 1)^{n - 1}}$and the s-degree vertices are [Reference Imran, Baig and Khalid39]:

(2)\begin{equation}2\sum\limits_{i = 1}^t {{{(s - 1)}^{i - 1}} - {{(s - 1)}^{n - 1}}}.\end{equation}

(3)\begin{align}& {\text{The cardinality of vertex and edges in}}\;{{\text{C}}_{s, t}}\;{\text{is}}\;\;\nonumber\\ & \qquad 2\sum\limits_{i = 1}^t {{{(s - 1)}^{i - 1}}} + {{{(s - 1)}^t}} \;{\text{and}}\;s\sum\limits_{i = 1}^t {(s - 1} {)^{i - 1}}\end{align}

L_{N 1} = 5.36 mm, W_{N 1} = W_{N 2} = 0.25 mm, L_{N 2} = 2.68 mm.

Figure 3. First two iterations (N) of the Cayley tree fractal curves.

respectively [Reference Imran, Baig and Khalid39]. To attain miniaturization of the isolation improvement structure and to strengthen the despairing of the MIMO system with increasing iterations, a fractal-shaped NL is introduced in this layout. On top of each repetition, a pair of additional arms is added per terminating branch. The angle among every branch and the branch widths are identical to that of level 1 but the length of the arms (for N = 2) is shortened equally to N_{L 6} = 2.68 mm. The overall length of the CFNL is found to be ≈λ ₀/2 at 3.1 GHz. The use of 2nd-order Cayley tree fractal geometry for designing the NL aids to escalate the effective electrical path length, thereby allowing the monopole to resonate at a low frequency of 3.8 GHz (see Fig. 2(a)). The incorporation of the CFNL improves the decoupling level drastically (by a minimum enhancement of 5 dB) between 3 and 7 GHz (see Fig. 2(b)). Figure 2(c) shows the improvement of S22 (among 10–20 GHz). Consequently, a wideband isolation enhancement can be attained due to modification in the surface current spread on the radiating monopoles, leading to modification in the impedance properties of the antenna [Reference Wang and Du17]. It is evident from Fig. 2(d) that as compared to the non-fractal counterpart, the 2nd-order CFNL provides a higher isolation enhancement (between 3 and 8 GHz). Thus, the CFNL aids to improve both the impedance matching and the non-pairing among PPM1 and PPM2. It was also observed that with the increase in iterations of the CFNL, the isolation among the radiating elements increases as well as the complexity of the design also increases. To attain minimum design complexity, we orderly inspect elementary branching fractal formation, the Cayley tree.

Effects of introducing ground stubs and L-shaped defect in common ground plane

It was noticed from Fig. 4(a) and (b) that high currents move among the pair of monopole elements via the common ground plane. Also, the currents along the shared ground structure pass straight to port 2 through the ground corner. It is evident from Fig. 4(a) and (b) that the extended ground stubs are behaving as a reflector to minimize EM pairing [Reference Tang, Zhan, Wu, Xi and Wu32]. The ground stubs can minimize the current over the ground structure moving among the PPM1 and PPM2. To examine the outcome of a pair of ground stubs on the scattering performance of the MIMO antenna, the simulated S₁₁, S₂₁, and S₂₂ with and without the presence of stubs are plotted in Fig. 5(a) and (b) respectively. It is noticed from Fig. 5(a) and (b) that the inception of the ground stubs enhances the impedance bandwidth of the antenna in terms of S₁₁ between 3.8 and 5 GHz and in terms of S₂₂ between 3.8 and 7 GHz as well as between 12.6 and 18 GHz respectively. The addition of the ground stubs also strengthen the isolation (S₁₂/S₂₁) between 4.3 and 7 GHz as well as between 11 and 16.7 GHz. So, it can be concluded that in agreement with paper [Reference Sohi and Kaur27], the extended ground stubs improve both impedances matching as well as isolation of the diversity system. Next, an L-shaped slot is created by utilizing the corner of the common ground structure and the extended ground stub (as depicted in Fig. 1 [STEP 4]). Due to the elongation of the effective path length of the induced current (as depicted in Fig. 6(a)) on the ground structure [Reference See, Abd-Alhameed, Abidin, McEwan and Excell16], the impedance traits (S₂₂) of the radiator are modified, thereby allowing the radiator to possess a lower S₂₂ cutoff frequency of 3.3 GHz instead of 3.9 GHz. A significant improvement of the S₂₂ (especially near 3.5 GHz, 9 GHz, and 12–18 GHz) is noticed (see Fig. 6(b)). The parametric investigations have shown the negligible influence of the L-slot on the S₁₁ and S₁₂ characteristics of the antenna.

Figure 4. The surface current spread over the radiator at (a) 4.3 GHz without the ground stubs, (b) 4.3 GHz with ground stubs, (c) 13.1 GHz without extended ground stubs, and (d) at 13.1 GHz with extended ground stubs.

Figure 5. Scattering parameters of the radiator in the presence and absence of the extended ground stubs. (a) Comparison among S11 and S12 for STEP 2 and 3 and (b) comparison among S22 for STEP 2 and STEP 3.

Figure 6. The surface current spread over the radiator at (a) 3.7 GHz without the L-shaped slot, (b) 3.7 GHz with the L-shaped slot, and (c) comparison of S₂₂ with and without the L-slot up on the ground structure.

Introduction of hybrid fractal parasitic elements for isolation enhancements

A set of three hybrids (Koch–Koch) fractal parasitic elements are introduced among the radiating monopoles to attain wideband isolation enhancement (between the lower 2.7–4.7 GHz and the upper 7–16.7 GHz bands) as depicted in Fig. 7a. The hybrid fractal parasitic strips artificially produce a reverse field linking trace to nullify the primary field linking thereby enhancing isolation among the radiating monopoles [Reference Banerjee, Gorai and Ghatak40]. The use of fractal parasitic elements provides better isolation (S₁₂/S₂₁) enhancement between 3.3 and 4.7 GHz as well as between 5.9 and 11.5 GHz and among 12.7 and 18 GHz as compared to non-fractal counterparts (see Fig. 7(b)). The length, position, and separation among the three parasitic elements are optimized by a series of parametric studies. Figure 7(c) indicates that the introduction of hybrid fractal parasitic elements allows the antenna to resonate near 3.1 GHz, thereby covering the complete UWB bandwidth. The use of fractal geometry for designing the parasitic elements provides miniaturization of the isolation improvement and impedance matching structures [Reference Banerjee, Gorai and Ghatak40].

Figure 7. Improvement of isolation (a) with the addition of hybrid (Koch–Koch) fractal parasitic elements, (b) comparison of isolation improvement in the absence of parasitic elements, by non-fractal, and hybrid fractal counterparts respectively, along with the (c) comparison of S₁₁ and S₂₂ characteristics with and without parasitic elements.

Band rejection using hybrid fractal slots

A pair of hybrids (Koch–Minkowski) fractal slots (as shown in Fig. 8(a) and (b)) is carved out from PPM1 and PPM2 for attaining band rejection characteristics across the WLAN band (5.15–5.825 GHz). Minkowski along with Koch’s fractal geometries are used as generator curves to obtain the final structure, which contains the 14 segments. The resonant frequency of the band notch slot can be evaluated by using Equation (4):

(4)\begin{equation}{f_{notch}} = \frac{c}{{2{L_{Total}}\sqrt {{\varepsilon _{eff}}} }}.\end{equation}

Figure 8. Comparison of (a) S₁₁, (b) S₂₂ with the introduction of the hybrid fractal slots, and (c) oppositely directed surface currents on either wall of the hybrid fractal slot (at 5.5 GHz).

Here, c stands for the speed of light across empty space, L_Total stands for the gross extent of the slot, with ε_eff = ε_r + 1/2. The overall stretch of the hybrid fractal opening is found to be ≈λ ₀/2 (along 5.5 GHz). The radiator’s S-parameter post-insertion of the hybrid fractal slots is depicted by Fig. 8(a) and (b). The hybrid fractal slot behaves like an inductor and a capacitor in series with the antenna and causes refusal in the WLAN band [Reference Zheng, Chu and Tu41]. Additionally, the current distribution shown in Fig. 8(c) suggests that the current in either wall of the hybrid fractal slot is oppositely directed. So current in one wall cancels the current in the other wall and thus provides band stop attributes. The parametric variations in the background have depicted that the stretch, breadth, and location of the slots are vital parameters in tuning the band rejection at the WLAN band.

Impedance aspects and radiation performance

The realized archetype for the recommended diversity radiator is shown in the inset of Fig. 9(b) along with its S-parameters validated by employing Rhode and Schwarz ZVA 40 VNA. Figure 9(a), as well as Fig. 9(b), illustrates that the measured functional bandwidth stretches from 3 to 18 GHz (S₁₁ ≤ −10 dB) and S₂₂ ≤ −10 dB (covering a super-wide bandwidth including the UWB spectrum) sharply excluding a pre-assigned narrow band among 5.15–5.825 GHz (WLAN). Figure 9(c) depicts that the |S₂₁| is below −20dB between 4 and 18 GHz showing high and wideband isolation. However, the |S₁₂|is found to attain lesser values (between −13 and −18 dB) between 3.1 and 4 GHz. Figure 9(d) depicts the comparison between the S-parameters received by simulation, empirical, and equivalent circuit (the circuit is depicted in Fig. 10) investigations of the suggested antenna. Figure 9 shows a good accord between the simulation and the empirical results. Some variations amidst the numerical as well as the experimental results are noticed because of variabilities of dielectric constant and loss tangent of the substrate. Figure 10 illustrates the equivalent circuit setup drawn out for the suggested super-wideband diversity antenna. The equivalent circuit is modeled by analyzing the S-parameter of the suggested antenna. The parallel resonant circuit at 3.1 GHz is modeled by employing L1, C1, and R1. The second resonance frequency is specified by implementing L3, C3, and R3 in the form of a parallel resonant circuit. Likewise, the third resonant frequency (at 10.2 GHz) is configured by utilizing L4, C4, and R4. The fourth resonant frequency is modeled by a parallel resonant circuit C5, L5, and R5. The fifth resonant frequency at 17 GHz is modeled by using C6, L6, and R6. It is evident from Fig. 9(d) that a band refusal is extended at 5.5 GHz. This observation suggests that the band refusal trait at 5.5 GHz (due to the hybrid fractal slots) could be configured by utilizing a parallel resonant circuitry comprising L2, R2, and C2. The isolation improvement provided by the CFNL is modeled by utilizing a T-network of L7, C7, and C8.

Figure 9. Numerical as well as empirical (a) S₁₁, (b) S₂₂ (inset realized antenna), (c) S₁₂, and (d) S-parameters from equivalent circuit model.

Figure 10. Equivalent circuit of the proposed antenna.

Figure 11 portrays the normalized numerical and empirical two-dimensional radiation patterns of the recommended radiator. The two-dimensional radiation pattern for each antenna element is examined along with two sets of planes (the X–Z plane together with the X–Y plane). The examination is executed for three sets of frequency bands located at 3.3 GHz, 7 GHz, and 15 GHz. During the evaluation, port 1 is solely excited, during that time the second port is discontinued employing a 50 Ω load. Figure 11(a)–(c) reveal that the two-dimensional radiation patterns across the X–Y plane (H-plane) are low on directional radiation (at the bottom end of the UWB spectrum [at 3.3 GHz]) as compared to the patterns at the top verge (at 7 GHz). The patterns at the higher verge of the UWB are close to omnidirectional accompanying multiple lobes. Monopole-like patterns are noticed in the X–Z plane (E-plane). The nearing omnidirectionality of the radiation patterns across the X–Y plane ensures the enclosure of a uniform along with a broad range for utilization in the UWB system.

Figure 11. Radiation patterns of the suggested super-wideband diversity radiator (with the radiator aligned in the y–z plane) at (a) 3.3 GHz, (b) 7 GHz, and (c) 15 GHz.

Next, Fig. 12 presents the maximum empirical gain along with the total radiation efficiency for the suggested radiator. The empirical gain is found to fluctuate between 1.06 and 5.1 dBi, excluding an elimination band centered at 5.5 GHz. The real radiation efficiency (empirical value) spans between 50 and 76%. Figure 12 also depicts a deep drop in realized gain (drops to −1.03 dBi) and efficiency (drops to 22.5%) at 5.5 GHz, providing firm evidence of effective interference suppression at WLAN frequencies.

Figure 12. Simulated and measured realized gain as well as radiation efficiency of the suggested antenna.

For increasing the spectral efficiency of MIMO systems, spatial multiplexing is important [Reference Sharawi42]. A metric for estimating the diversity radiator’s functioning in the form of spatial multiplexing is the multiplexing efficiency. A closed-form expression of multiplexing efficiency is reported in paper [Reference Banerjee, Gorai and Ghatak40] and is given by Equation (5)

(5)\begin{equation}{\eta _{MUX}} = \sqrt {(1 - {{\left| {{\rho _C}} \right|}^2}){\eta _1}{\eta _2}}.\end{equation}

Here, ρ_C represents the complex correlation coefficient amid a couple of monopoles, whereas envelope correlation coefficient (ECC) ≈ |ρ_C|², as well as η_n, is the overall effectiveness for the nth radiator. The multiplexing efficiency of the recommended radiator and its likeness to the total efficiency plot can be observed from Fig. 12 across the intended UWB bandwidth, as a result of low ECC.

Diversity performance

To demonstrate the diversity features for the proposed diversity arrangement, the ECC is computed utilizing Equations (6) and (7) [Reference Sharawi42]. As Equation (7) takes into account both coupling from antenna ports as well as coupling due to the radiated fields, we use Equation (7) to compute the ECC. The far-field method of ECC measurement was utilized (i.e., Equation (7)) as the one reported using Equation (6) requires the antenna to be lossless and single-mode antenna [Reference Sharawi42]. For improving the reliability of detection (of the identical samples of individual information), the diversity gain (DG) is computed [Reference Sharawi42]. The DG is calculated using Equation (8), and individually these outcomes are plotted in Fig. 13:

(6)\begin{equation}{\rho _e} = \frac{{{{\left| {S_{11}^ * {S_{12}} + S_{21}^ * {S_{22}}} \right|}^2}}}{{\sqrt {(1 - {{\left| {{S_{11}}} \right|}^2} - {{\left| {{S_{21}}} \right|}^2})(1 - {{\left| {{S_{22}}} \right|}^2} - {{\left| {{S_{12}}} \right|}^2}){\eta _{rad1}}{\eta _{rad2}}} }}\end{equation}

(7)\begin{equation}{\rho _e} = \frac{{\left| {\iint {\left[ {{E_1}\left( {\theta ,\varphi } \right) * {E_2}} \right.\left. {\left( {\theta ,\varphi } \right)} \right]d{\Omega ^2}}} \right|}}{{\iint\limits_{4\pi } {{{\left| {{E_1}\left( {\theta ,\varphi } \right)} \right|}^2}d\Omega \iint\limits_{4\pi } {{{\left| {{E_2}\left( {\theta ,\varphi } \right)} \right|}^2}d\Omega }}}}\end{equation}

(8)\begin{equation}DG = 10\sqrt {1 - {{\left| {{\rho _e}} \right|}^2}}.\end{equation}

Figure 13. Measured ECC and DG of the recommended antenna.

The ECC value in Fig. 13 is found to be lower than the experimental margin of 0.5 [Reference Zheng, Chu and Tu41], and the DG is found to be well above 9.5 dB, depicting desirable diversity characteristics.

Mean effective gain (MEG)

To inspect the influence of the surrounding on the radiation traits of the antenna as well as to determine the correlative mean power among the signals offered by the individual radiator, the MEG is employed. The MIMO realization along with the channel aspects of the radiator is bound to be high, if the proportion of MEG (|MEG1/MEG2|) of the pair of monopoles is under ±3 dB [Reference Gurjar, Upadhyay, Kanaujia and Sharma43]. The steadiness of MEG is noticeable in Fig. 14. It is also perceived that the proportion of MEG is well under the reasonable margin of ±3 dB in the entire UWB bandwidth and beyond (up to 20 GHz).

Figure 14. Measured (a) mean effective gain of the suggested antenna and (b) TARC.

Total active reflection coefficient (TARC)

The S-parameter alone of a diversity system cannot be satisfactorily specified, the efficiency and bandwidth

(9)\begin{equation}TARC = \sqrt {\frac{{{{({S_{11}} + {S_{12}})}^2} + {{({S_{21}} + {S_{22}})}^2}}}{2}}.\end{equation}

For the implicit estimation of a radiating system with diversity, the TARC is utilized. The investigation of the TARC also aids in examining the results of phase changes among the pair of ports on the resonance response of the radiator. The TARC of a bi-port diversity system [Reference Chae, Oh and Park44] is discovered using Equation (9). The TARC for a diversity antenna system must be restricted to <0 dB [Reference Thomas and Sreenivasan36]. Fig. 14b conveys that the recommended antenna manifests a TARC below −24.5 dB for the entire super-wide bandwidth (3.1–18 GHz).

A comparative study amid the recommended radiator and already proclaimed UWB MIMO radiators in papers [Reference See, Abd-Alhameed, Abidin, McEwan and Excell16, Reference Liu and Tu22–Reference Sohi and Kaur34] is listed in Table 1. The analogy outlines the newness of the recommended radiator in comparison to the UWB diversity radiators reported in the recent past.

The design and investigation of super-wideband MIMO antennas with polarization diversity as well as common ground plane remains minimally explored in the reported literature and thus is a significant novelty of the suggested work. The suggested antenna is found to be smaller than all the antennas enlisted in the comparison Table 1 except paper [Reference See, Abd-Alhameed, Abidin, McEwan and Excell16]. The suggested antenna covers a much wider impedance bandwidth as compared to all the designs enlisted in Table 1. Additionally, the reported antenna covers the same impedance bandwidth (ranging from 3 to 18 GHz with an isolation of >20 dB) as suggested by paper [Reference Tang, Zhan, Wu, Xi and Wu32] but is realized in a smaller footprint and has attained a larger peak gain. The wideband isolation as compared to paper [Reference Tang, Zhan, Wu, Xi and Wu32] is realized with a comparatively lower inter-element spacing of 8 mm. The suggested radiator attains a higher realized gain as compared to the related works reported in Table 1, considering its realization over the low cost FR4 substrate.

Table 1. Comparison of the recommended antenna with formerly reported UWB MIMO antennas