Space Efficient Meta-Grid Lines for Mutual Coupling Reduction in Two-Port Planar Monopole and DRA Array

Traditionally used mutual coupling (MC) reduction techniques such as electromagnetic bandgap structures, isolators and neutralization lines require extra space between radiators. Besides, metamaterial-based techniques require multi-layer arrangements. However, the proposed meta-grid lines overcomes the above demerits by integrating meta-grid lines in the ground plane itself. As a proof-of-concept, two-port CPW-fed monopole antenna array (TPCFMAA) and two-port DRA array (TPDRAA) are designed, fabricated and tested. It has been observed that the TPCFMAA has mutual coupling below −20 dB for frequency between 2.6 to 4.4 GHz. The envelope correlation coefficient reduces from 0.072 to 0.026 by integrating meta-grid lines in the ground plane of the TPCFMAA. At 3.5 GHz, the inter-element distance between the antennas is noted to be <inline-formula> <tex-math notation="LaTeX">${0.015}\lambda _{\mathrm {h}}$ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$\lambda _{\mathrm {h}}\,\,=$ </tex-math></inline-formula> highest operating wavelength). The TPDRAA’s operating frequency can be tuned by changing the parameters of the annular ring slot in the excitation patch. The bandwidth of TPDRAA can be further increased by merging the two resonances of the two annular ring slots in the excitation patch. For TPDRAA, the measured −10 dB impedance bandwidth is from 5.65 to 6.55 GHz. The mutual coupling between the antenna elements is seen to be below −16 dB for an inter-element spacing of 4.8 mm, which is <inline-formula> <tex-math notation="LaTeX">$0.090\lambda _{\mathrm {h}}$ </tex-math></inline-formula>. The measured gain of TPDRAA within the bandwidth is from 4.17 dBi to 5.2 dBi. The TPCFMAA can be used in 3.5 GHz Internet of Vehicles (IoV) multi-user MIMO service, whereas the TPDRAA can be used for satellite communication in the 5.925 to 6.425 GHz frequency band, WiMAX in the 5.7 to 5.85 GHz band, ISM in the 5.725 to 5.85 GHz band, and WLAN in the 5.8 GHz band.


I. INTRODUCTION
Multiple-input-multiple-output (MIMO) communication system fulfills the demand for higher data rate and better quality of service in modern communication systems. MIMO system's channel capacity increases linearly with the number of the antenna elements for rich Rayleigh scattering environments [1], [2]. Compact MIMO communication systems generally deploy closely spaced multiple The associate editor coordinating the review of this manuscript and approving it for publication was Giorgio Montisci . antennas at the transmitter and receiver sides. However, this results in an undesired mutual coupling (MC) effect, which is inversely proportional to the distance between the antenna array elements [3]. Therefore, designing a compact MIMO antenna with small inter-element spacing and low mutual coupling between antenna array elements is challenging.
In the literature, several methods have been proposed to reduce the MC between planar and dielectric resonator antenna (DRA) elements. For MC reduction in planar antennas, electromagnetic band gap (EBG) [4] structures in [5]- [9] VOLUME 10,2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ and isolators in [10] and [11] are used. Neutralization Lines (NLs) are used for isolation enhancement in [12] and [13] for planar monopole antennas. However, EBG structures, isolators and NLs require extra space between the antenna elements and therefore increase the inter-element spacing between them. Mushroom type EBG unit cells used for MC reduction in [5], are spread on 13.5 mm × 48.5 mm space. EBG surface composed of short-circuited microstrips is used in [6] for MC reduction and occupies two times more area than that of the single radiating patch. Uniplanar compact EBG structure of 13.2 mm × 72.6 mm size is used in [7] for MC reduction in another layer that also increases the vertical profile of the two-port antenna by 1.27 mm. In [8], EBG unit cells occupy 33.3 % of the total antenna area. EBG based fractal isolator is used for MC reduction in [9], which takes a size of 16 mm × 23 mm while the single radiating patch occupies a space of 23 mm × 23 mm. Similarly, NLs and isolators also occupy area which increase the edge-to-edge spacing between antenna elements. A ring-shaped defected ground structure is demonstrated to suppress the MC between two cylindrical DRAs (CDRAs) in [14]. In [15], mushroomshaped DRAs are arranged orthogonally to reduce the MC between them. Triple-port, two-element CDRA with orthogonal modes for MIMO applications is presented in [16]. Twoport low MC antenna array comprising two A-shaped DRAs are excited by means of conformal strip for wideband applications in [17]. Three decoupled modes in a single rectangular DRA are excited using three separate ports to achieve low inter-port coupling in [18]. Metal strips are printed on the dielectric block (DB) in [19] and vias are inserted in the DBs in [20] for enhancing the decoupling. Exotic properties of metamaterials have been exploited for MC reduction [21]- [25]. Waveguide metamaterial (MTM) is placed in the same layer as that of patches for reduction of MC in [21] but this decoupling structure uses extra space between the antennas. Double layer MTM mushroom wall in [22] and polarization-rotator wall in [23] are used for MC reduction in planar antennas and DRAs respectively though these methods increase the height and therefore vertical profile of the antenna array. Capacitively loaded loop based MTM superstrate and metasurface (MS)-based decoupling techniques are used for isolation enhancement in [24] and [25]. The decoupling in [26] is realized by adding a pure DB above the coupled array, and a ceramic superstrate in [27]. All these four designs have decoupling structures between or above the antenna elements, which significantly increase the antenna footprint. It is noted that the array antenna-decoupling surfaces (ADSs) or superstrates enable the partially reflected signal to interact out of phase with the coupled signal and hence nullify the effect of the latter thus ensuring better isolation. Intuitively, the height of the ADS above the antenna determines the phase of the partially reflected wave and the size of the metal reflection patches on the ADS controls the intensity of the partial reflected wave [28]. Therefore, ADSs or superstrates [29] are placed at some height above the antenna array that increase the overall height of the antenna.
In this paper, a novel single negative (SNG: µ and are of opposite signs) meta-grid line (MGL) structure is presented, which is used for the following two low MC MIMO antenna configurations: 1. Two-port coplanar waveguide (CPW)-fed monopole antenna array (TPCFMAA) 2. Two-port DRA array (TPDRAA) The novel aspect presented in this article is the use of meta-grid lines (MGLs) integrated with the ground plane for suppression of the surface wave linkage between the antenna elements and hence achieve a satisfactory isolation level. Unlike EBGs, isolators or NLs for MC reduction, this approach obviates the need for any extra space between antennas to accommodate the decoupling unit. Also, integration of MGLs in the ground plane does not require any additional layers unlike ADSs or superstrates that increase the height of the antenna. Therefore, integration of MGLs in the ground plane helps to realize compact design and TPCFMAA has a minimal (0.015λ h ) edge-to-edge spacing between the antenna elements.
It is noted that for TPCFMAA, the unit cell periodicity (p) of MGL structure is 6.35 mm, guided wavelength (λ g ) is 57.7 mm whereas, for TPDRAA, p is 6 mm, λ g is 34.85 mm at 5.8 GHz. Hence, p is much smaller than the guided wavelength λ g of the propagating wave (i.e. p λ g ) [30], [31], so that fields are averaged across the unit cells and see the structure as a homogenous medium at a macroscopic scale. Also, from the extracted permittivity and permeability curves of MGLs for TPCFMAA and TPDRAA, it is noted that the MGLs shows wideband SNG behaviour. Therefore, although the presented structure bears resemblance to a DGS (both being etched copper patterns on the ground plane), due to the characteristic properties discussed above, the former is significantly different from a DGS that uses slot (of length comparable to the guided wavelength [32], [33] or half of the guided wavelength [34]).
It may also be noted that most of the MC reduction techniques employing EBG and superstrates do not generally show portability or interoperability among different types of radiators (patch antenna↔DRA). This means that EBG and superstrates for MC reduction in patch antennas are generally very difficult to be employable in DRAs without major modifications in their structures and vice-versa. However, this is not the case with presented technique because in TPDRAA, the dielectric blocks are excited by means of microstrip patch feed which are printed over an MGL (with wideband SNG characteristics) backed substrate. Therefore, MGLs effectively deal with the MC in both printed and dielectric resonator antennas. One may also note that an important feature of this decoupling structure is that by varying its geometric parameter, it is possible to make the TPCFMAA resonate over a wide range of frequencies while ensuring minimal offset between the return loss and mutual coupling i.e. the antenna resonating frequency can be positioned at any value lying from 2.6 to 4.4 GHz keeping the MC performance undisturbed. In the TPDRAA design as well, the resonating frequency can be made to lie at any value between 5.78 and 6.55 GHz by changing the dimensions of annular ring slots in the patch which excites the DRA. Even in the TPDRAA, the MC performance is preserved with varying antenna resonating frequency.
Section II presents the unit cell analysis of the proposed MGL structure. Section III contains the TPCFMAA, Section IV discusses the TPDRAA. Conclusions are drawn in Section V.

II. UNIT CELL ANALYSIS
An isolated unit cell (single unit cell) of MGLs integrated with the ground plane is shown in Fig. 1(a). The MGLs are printed on the back of Rogers RT-Duroid 5870 with r = 2.33 and tan(δ) = 0.0012. The simulation set-up illustrating wave-guide ports and boundary conditions for extracting the real parts of the complex permeability and permittivity of such a unit cell is shown in Fig. 1(b). Permeability and permittivity curves are plotted in Fig. 2(a) and Fig. 2(b) using parameter retrieval option in CST Microwave Studio Suite 2018.
From Fig. 2(a) and Fig. 2(b), it can be seen that the unit cell shows the behavior of SNG MTM ( -negative). Refractive index (n = √ µ ) becomes imaginary if µ and are of opposite sign. Electromagnetic waves can not propagate in such mediums, and therefore can be used for the isolation     bottom layer consists of a MGL structure (5 × 4 unit cells). The photographs of the top view and the bottom view of the fabricated prototype of TPCFMAA are shown in Fig. 4(a) and Fig. 4(b), respectively. All simulation results are generated using High-frequency structure simulator (HFSS) 14.0. To understand the contribution of the proposed MGL structure in MC reduction, the S-parameters without and with this structure are plotted in Fig. 5. It is apparent from these plots that integrating the MGLs in the ground plane at 3.5 GHz reduces the MC by 20 dB. MGLs reduces MC at the expense of reduction in antenna bandwidth. Two important design parameters (M and G as in Fig. 3) are found to be vital in positioning the antenna resonating frequency. In case of G as shown in Fig. 6, increasing or decreasing the values of G shift the frequency upward or downward respectively. However, in case of M as shown in Fig. 7, it is reversed, i.e. increasing or decreasing the values of M shift the frequency downward or upward respectively. In both the cases, the MC performance remains intact. Retaining the MC performance with varied resonating frequencies is one of the novel aspects of proposed two-port antenna. For M = 6.85 mm and G = 5 mm, the antenna can be designed for 3.5 GHz WiMAX application.    . It is seen that by selecting the proper combination of these parameters, optimum mutual coupling performance can be obtained and the antenna can be designed to resonate at any frequency from 2.6 GHz to 4.4 GHz. For example, using Combination B (M = 11.85, G = 7, r = 0.9) isolation close to −45 dB can be achieved. For Combination A, the MC is below −17.27 dB while for rest of the combinations, the MC is noted to be below −20 dB. Table 1 shows that the proposed TPCFMAA has the minimum inter-element spacing (λ h ) except that in [25]    but [25] occupies 64 times more volume (in λ 3 h ) than TPCFMAA. The TPCFMAA has broader percentage bandwidth than [24], comparable percentage bandwidth with [7] but lesser percentage bandwidth than [8], [9], [25], [26] and [27]. However, excellent bandwidth improvements will be shown for TPDRAA employing meta-grid lines in the ground plane as discussed in section IV. The TPCFMAA is a very low profile antenna which occupies 48.6, 3.95, 44, 101.6, 64, 236 and 205 times lower volume than that of [7]- [9], [24]- [27], respectively. In fact, elements of this highly compact MIMO antenna satisfy criterion (ka < 1) for electrically small antennas [35]. Furthermore, the TPCF-MAA design is simple, compact and especially, does not have a multi-layer arrangement contrary to the antennas of [7], [24]- [27] that add excess heights to these antenna profiles.
Normalized radiation patterns at 3.5 GHz (Combination D) for φ = 0 0 plane and φ = 90 0 plane are plotted in Fig. 9. The peak gain is noted to be lying from 1.53 dBi to 1.68 dBi within the antenna bandwidth from 3.46 GHz to 3.56 GHz (Fig. 10).
It can be observed that the measured gain slightly deviates from the simulated gain which may be due to fabrication tolerances.
The ECC is a measure of isolation and correlation between communication channels and is an important performance metric to be considered in MIMO communication. The ECC between the antenna ports is calculated using equation (1) from [36] and plotted in Fig. 10.
Here, F i (θ, φ) is simulated 3-D radiation field corresponding to the i th antenna element and is the solid angle. It is obvious from Fig. 10 that the ECC is significantly reduced from 0.072 to 0.026 over the entire operation band when MGLs are integrated in the ground plane. The ECC for the TPCFMAA is found to be below 0.026 within the operational bandwidth. The antenna correlation coefficient (ACC) is approximately equal to the square root of the ECC [37]. Hence, the ACC matrix of this two-element MIMO antenna is 1 0.161 0.161 1 . The channel capacity loss (CCL) [38] for point-to-point N × N MIMO system is where R Rx and R Tx are the ACC matrix of the MIMO antenna deployed at the transmitter and the receiver respectively. For a 2 × 2 MIMO system deploying two-element MIMO antenna of Fig. 3 at the transmitter as well as at the receiver, the CCL is calculated to be just 0.0758 b/s/Hz. Such a low CCL is a desirable characteristic of MIMO antenna. Since the ACC matrix for this MIMO antenna is full rank (rank = 2), 2 × 2 MIMO system deploying the TPCFMAA will achieve maximum diversity gain of 4.
Considering the practical deployment of this antenna and to understand the effect of the large ground plane on antenna performance, simulation with an extended ground plane (50 mm in the +Y axis, +X axis and -X axis direction as per Fig. 3) in the plane containing the bottom layer of the antenna is carried out. It is noted that the cross-polarization discrimination (XPD) performance and antenna gain both improve with the usage of extended ground plane. Another simulation is carried out with a large ground plane (50 mm VOLUME 10, 2022 in the +Y axis, +X axis and -X axis direction as per Fig. 3), which is placed 10 mm below the plane containing the bottom layer of the TPCFMAA. It is seen that the gain improves from 1.65 dBi to 2.91 dBi. However, the XPD does not improve. In both the cases, impedance matching and isolation performances remain almost unaffected.
The TPCFMAA can be mounted over a vehicle roof where it can utilize the large metallic roof of the vehicle as extended large ground plane or as a reflector below the antenna. Therefore, this antenna can be used for the 3.5 GHz Internet of Vehicles (IoV) multi-user MIMO service.

IV. 2-PORT DRA ARRAY USING SNG META-GRID LINES
This section contains the TPDRAA as shown in Fig. 11. It uses two CDRA blocks of r = 25 as radiating elements. These dielectric blocks are excited by means of two concentric annular rings in the circular patches placed above the substrate (Rogers RT-Duroid 5870 with r = 2.33 and tan(δ) = 0.0012). These circular patches are connected to the microstrip line through which signal is fed to the antenna elements. The ground plane (in maroon) has an MGL structure (7 × 4 unit cells) integrated between two uniform rectangular sections of dimensions L g × W at its two ends. The values of all the geometrical dimensions (in mm) corresponding to Using equations (3) and (4) from [39], resonating frequency of the circular patch of radius a = 5.2 mm is calculated to be 9.8 GHz which is much higher than the frequency range of the proposed antenna. Therefore, it is concluded that the non-radiating patches with annular ring slots are used for exciting the HEM 12δ mode in the cylindrical dielectric blocks.  Here, h and a are in cm and f r is the resonant frequency of the circular patch.
Without annular ring slots, the bandwidth of the antenna is noted to be very less (refer Fig. 12). This is mainly because of high dielectric constant of CDRA blocks i.e. 25. Therefore, attempts are made to increase the bandwidth of the antenna by employing the annular ring slots in the circular patch to excite the CDRA blocks.
It is clearly shown in [40] that increasing the radius of the feeding slot decreases the resonating frequency and viceversa. The same is noted in the S-parameters of the antenna with only the outer annular ring slot (OARS) and only the inner annular ring slot (IARS) by varying the radius of the slots, which are plotted in Fig. 13 and Fig. 14 respectively. It has been observed that by varying the radius of OARS and IARS, the resonance can be adjusted in the lower frequency region and higher frequency region respectively. By choosing the radius of the OARS as 3.8 mm and IARS as 2.2 mm, the bandwidth of the antenna can be significantly increased when compared to the excitation of the DRA blocks without the annular slots in the circular patch. It can be inferred from Fig. 12 that the lower resonance occurring at 5.78 GHz is because of the OARS and the higher resonance at 6.5 GHz is because of the IARS. When both the IARS and the OARS are used together, these two resonances merge and lead to a wider bandwidth from 5.68 GHz to 6.7 GHz as shown in Fig. 12.
The dimensions of the circular dielectric block to excite the HEM 12δ at the 5.8 GHz, is calculated using equation (5) from [41] and turn out to be H = 3.8 mm where, , f is the resonating frequency and r is the relative permittivity of DRA.
From Fig. 13, it is observed that the mutual coupling curves have valleys just below the resonance for the OARS and same is observed for the IARS in Fig. 14. This is mainly because of the integration of the MGLs in the ground plane.
Electric field patterns at 5.78 GHz are shown in Fig. 15 and confirms the excitation of HEM 12δ mode [42].
The simulated and measured S-parameters versus frequency of the fabricated prototype (as depicted in Fig. 16) are plotted in Fig. 17. The measured impedance bandwidth of the antenna is observed to lie from 5.65 GHz to 6.55 GHz, whereas the simulated bandwidth is from 5.68 GHz to 6.7 GHz. The slight difference in the measured and simulated   bandwidth of this antenna is because of various tolerances such as imperfections in the cutting of DRA blocks and PCB fabrication. The measured isolation between the antenna elements is found to be more than 16 dB for the entire bandwidth and the maximum isolation is noted to be 38.6 dB.
The measured and simulated co-polar and cross-polar radiation patterns for φ = 0 0 and φ = 90 0 planes at 5.8 GHz are plotted in Fig. 18. During pattern measurements, port P 1 is excited whereas port P 2 is terminated with a matched load. The measured cross-polarization discrimination (XPD) in the broadside direction is greater than 11.5 dB in both planes. The difference in the cross polarized results between simulation and experiment could be due to the detector sensitivity. The measured and the simulated gain with respect to frequency are plotted in Fig. 19. Peak measured gain is noted to be from 4.17 dBi to 5.2 dBi, while the simulated gain is observed to lie between 3.97 dBi and 5.4 dBi. The ECC as a function of the frequency is plotted in Fig. 19 and its value is noted to be < 0.046 in the entire operating frequency range of the antenna array. Hence, the ACC matrix of this two-element MIMO antenna is 1 0.214 0.214 1 . For a 2 × 2 MIMO system deploying two-element MIMO antenna of Fig. 11, the CCL is calculated to be 0.1727 b/s/Hz, which is low and desirable. The ACC matrix of this MIMO antenna is full rank (rank = 2) and hence 2 × 2 MIMO system employing the TPDRAA will achieve maximum diversity gain of 4. The comparison of the proposed work (TPDRAA) with other contemporary works is listed in Table 2. It has been observed that MIMO antennas in [16], [18]- [20] occupy 3, 34.8, 23 and 6.1 times more volumes than the TPDRAA, respectively. Moreover, the TPDRAA has the largest percentage bandwidth except [16] and the lowest inter-element spacing (in terms of λ h ).

V. CONCLUSION
In this paper, meta-grid lines are integrated in the ground plane for effectively reducing the MC in a TPCFMAA which is further extended for MC reduction in case of a TPDRAA as well. The proposed MC reduction approach does not add any extra foot print to the TPCFMAA and the TPDRAA profile. The TPCFMAA and the TPDRAA are fabricated and tested as proofs-of-concept. For the TPCFMAA, at 3.5 GHz center frequency (bandwidth from 3.46 GHz to 3.56 GHz), the MC is -28 dB and the ECC is below 0.026. Therefore, the TPCFMAA is a suitable candidate for 2-port MIMO WiMAX application. The MC in the TPDRAA, is noted to be less than -16 dB with the ECC less than 0.046, therefore satisfying the criteria of low correlation, making this compact TPDRAA a suitable candidate for MIMO application in the operating frequency range from 5.65 GHz to 6.55 GHz that covers 5.925 to 6.425 GHz frequency band for satellite communication, 5.7 to 5.85 GHz for WiMAX, 5.725 to 5.85 GHz for ISM band and 5.8 GHz for WLAN application.

ACKNOWLEDGMENT
Mohit Mishra, Sumantra Chaudhuri, and Rakhesh Singh Kshetrimayum are thankful to Dr. Nemai Chandra Karmakar from Monash University, Australia, for his valuable comments and Rakhesh Singh Kshetrimayum is also grateful to Dr. Nasimuddin from I2R, A-STAR, Singapore, for some of his insightful comments. The authors are also grateful to the anonymous reviewers for their insightful comments and thoughtful suggestions, which helped them improve the quality of the article significantly.