Mutual Coupling Reduction in Microstrip Patch Antenna Arrays Using Simple Microstrip Resonator

In this paper a novel ladder resonator is introduced to reduce mutual coupling effect in the patch antenna array structure. Applied patch antennas are operating at 2.45 GHz frequency, which specially used for MIMO (multiple input multiple output) systems. The edge-to-edge distance between two microstrip patch antennas is 0.05 λ. The proposed ladder resonator impressively blocks the surface current between two patch antennas at the operating frequency, which results in mutual effect reduction. The designed configuration has been analyzed, simulated and measured. Scattering parameters with and without of proposed resonator has been investigated. The result shows that, the proposed configuration increases isolation between two microstrip patch antennas about 44 dB.


Introduction
Patch antennas are important components, which have been widely used in recently communication systems. Patch antennas are used for compact designs applications and have several advantages such as: easy fabrication process, light weight and high efficiency, but high mutual coupling effects is the main drawback of microstrip patch antennas, when used as array antennas [1][2][3][4][5][6][7][8][9]. In antenna arrays, when the array elements are very close together, the radiation power of one antenna will be absorbed by another one [2], which called mutual coupling effects.
Recently, various approaches are introduced to overcome the mutual coupling effects in the antenna array. The idea of using SCSRR (slotted complementary split ring resonator) is introduced in [10]. The reported SCSRR element is reduced mutual coupling effect about the 10 dB. In this technique, a resonator or structure is etched on the ground plane, which is undesirable for fabrication process [11]. A simple slot structure between the microstrip 1 3 antenna elements is presented in [12]. Inserting slots between the extremely close microstrip patches partially improved isolation. In [13] a simple U-shaped microstrip unit is applied to decrease mutual coupling effect [13], but the isolation improvement level in this design is not so high. In [14], a meandered line resonator is introduced to decrease the mutual coupling effect. This resonator sandwiched between patch antenna elements, which works as a filter and used as a decoupling unit. But, in this design, the isolation parameter has not decreased significantly. Modified serpentine structure (MSS) is introduced as isolation enhancement method in [15]. Reported MSS inserted between two antennas and reduced the mutual coupling effect. In [16] sub-wavelength resonator effects on suppressing mutual coupling is investigated. With placing open slot SRR (OSSRR) and complementary SRR (CSRR) in ground plane, the coupling effect is reduced [16]. In [17,18], latticed resonator and C-shaped resonators are applied in the MIMO antennas structure, respectively to reduce the antennas coupling effect, but the significant amount of reductions have not been achieved in these two works.
The EBG (electromagnetic band gap) technique is introduced to decrease the coupling effect between antenna arrays in [34]. Electromagnetic band gap structures prevent wave propagation in a specific direction and frequency. Therefore, it can block surface wave propagation and reduce mutual coupling effect. In [34] six EBG cells are inserted between two radiating elements, which reduced mutual coupling effect. The DGS (defected ground structure) technique is also applied to decrease coupling effect in [35,36]. Unfortunately, both of the EBG and DGS techniques are undesirable method because of complex fabrication process [37,38].
In this work a novel ladder resonator, which work as decoupling unit, is proposed. The presented decoupling unit is located between two antennas. The main frequency of the proposed configuration is 2.45 GHz. The proposed resonator acts as band-reject filter that prevents surface currents from one patch antenna to another patch antenna.

Design Process
The layout of the proposed ladder-shaped resonator, which is incorporated between two antenna cells, is depicted in Fig. 1. The distance between antenna array is considered equal to 6 mm (0.05 λ).
The layout of the designed resonator with detailed view is depicted in the Fig. 2. The proposed resonator, consist of two separated part, which symmetrically arranged. The physical dimensions of the applied ladder-shaped resonator are given in Table 1. The presented resonator acts as decoupling units between two antenna cells at 2.45 GHz frequency. In the proposed resonator, like a band-stop filter, the surface current is rejected from one patch antenna cell to another patch antennas cell. The frequency resonance of the proposed decoupling unit is controlled by the length of the Ls.
The proposed ladder-shaped resonator, shows a desirable rejection response at operating frequency of 2.45 GHz with the length of L s = 33.85 mm. In addition, to investigate the effects of the L s (length of the ladder resonator) on the frequency response, simulations done for several length of L s as shown in the Fig. 3.   The resonant frequency is shifted by changing the length of L s . As results shown, increasing the length of L s decreases the resonant frequency.
The proposed LC circuit of the main resonator cell is shown in Fig. 4. In the LC circuit, the middle dashed line shows the symmetry of the proposed resonator cell circuit. Upper and lower parts of the middle dashed line are connected in parallel. Therefore, the values of 2R = 100 Ω are considered at the end of each part. The seen impedances of Z 1 , Z 2 , Z 3 , Z 4 and Z 5 are defined in Eqs. (1)(2)(3)(4)(5)(6)(7)(8) The value of Z 2 impedance is defined in Eq. (2) Impedances of Z 3 and Z 4 can be obtained using the same procedure as defined in Eqs. (3) and (4) where σ 1 is defined in Eq. (5) as follows. (1) The LC circuit of the main resonator cell

Port2
The impedance of Z 4 and C 12 /2 are connected in parallel, so the final value of Z 5 can be calculated as written in Eq. (6) where the parameters of σ 2 and σ 3 , used in Eq. (6), are defined in Eqs. (7) and (8). Finally, by equating the value of Z 5 to 2R the resonance frequency of the resonator1 can be calculated. After designing of the resonator circuit, the transmission line realization of the resonator can be extracted from the proposed LC circuit. Two resonators named resona-tor1 and resonator2 are extracted based on the proposed LC circuit. The extracted layouts of resonator1 (Res1) and resonator2 (Res2) are depicted in Fig. 5. As seen, the desired numbers of resonator1 and resonator2 can be used in series structure to obtained the best results.
The values of circuit parameters used in LC circuit of resonator1 is listed in Table 2. The LC circuit and layout frequency responses of the resonator1 are shown in Fig. 6. Res1 As seen, the resonance frequency of the proposed resonator1 is high, so the desired numbers of resonator1 and resonator2 can be used in series structure to obtained the optimum resonance frequency.
To investigate the performance of the ladder-shaped resonator, a standard 31 mil RO-4003C substrate is used. The simulation has done with advanced design system (ADS) simulator. The proposed configuration (two patch antennas and ladder resonator) is designed, simulated and fabricated. The measurement and simulation results of S 11 with proposed ladder resonator and without resonator are shown in Fig. 7. The measurement and simulation results show that, device correctly works at 2.45 GHz and there is negligible difference between results.
The simulated S 11 and S 12 parameters of two patch antennas array without resonator is depicted in Fig. 8. As seen, the simulated value of S 21 at main frequency of 2.45 GHz is − 9 dB. And the operating bandwidth of 22 MHz from 2440 up to 24,462 MHz is obtained for the designed antenna array.  The simulated S 11 and S 12 parameters of two patch antennas array with resonator is shown in Fig. 9. As seen, the simulated value of S 21 at main frequency of 2.45 GHz is − 53 dB, which shows 44 dB improvement in reducing mutual coupling. Also, the operating bandwidth of 30 MHz from 2442 up to 2472 MHz is obtained for the designed antenna array, which shows 36% of bandwidth improvement.

Antenna Design and Fabrications
To determine the mutual coupling effect and reduce it, two-element antenna arrays are constructed. The distance space between patch antennas and applied resonator play an important role in coupling effect. In this construction the antennas located at distance of 6 mm (0.05 λ g ). The presented patch antennas have dimensions of 42.2 mm × 33.85 mm.
The applied patch antenna correctly, radiates at frequency of 2.45 GHz (f r ). Due to the operating frequency and applied substrate, W and L obtained as follows [39]: where ΔL and L eff are the extended length and effective length respectively. The ΔL parameters can be obtained as follows [39]: , L eff = L + 2ΔL where ε reff called effective dielectric constant of substrate and represented as [39]: In order to realize the value of isolation improvement between two patch antennas, the simulated and measured isolation characteristics (S 21 ) of patch antennas, with and without proposed resonator are depicted in Fig. 10. Results show the effective role of the proposed resonator on the mutual coupling reduction. The simulation result shows that, the value of the S 21 parameter without resonator is about − 9 dB at operating frequency of 2.45 GHz. With applied ladder resonator this parameter is about − 53 dB. As result show, the proposed ladder resonator improved isolation about 44 dB. Also, the measured value of 48 dB is obtained for the S 21 parameter of the fabricated antenna array with the presented resonator at the main frequency.
The applied ladder-shaped resonator, located between antenna elements, improved the mutual coupling effect and has negligible effect on the characteristics of the patch antennas. The proposed resonator with special structure helps in trapping surface current toward it. This specification can be determined by analyzing surface current through the whole structure (two patch antennas and applied resonator). Distribution of the surface current structure is depicted in Fig. 11. The results clearly show that the ladder shaped resonator sufficiently decreases the mutual coupling.
The far-field characteristics, with and without resonator are depicted in Fig. 12. The radiation pattern of the proposed antenna array with proposed ladder resonator and regular antenna array without resonator are demonstrated in Fig. 12. The radiation patterns are provided at two elevation angle of Phi = 0° and Phi = 90°. According to the results, the applied resonator between the antenna array has very little effects on the radiation characteristics of the antenna array. Also, it can be seen that the resonator has slightly improved the gain of the antenna. It is very clear from this figure that, applied ladder resonator has a little effect on cross polarization and gain ratio.
In order to investigate and analyze the role of the presented ladder-shaped resonator on reduction of the antennas coupling effect, the proposed patch antennas with and without presented ladder shaped-resonator are simulated and constructed. The fabricated configuration is show in Fig. 13.
A comparison between performance of the proposed structure and similar designs, is presented in Table 3. It is clear from Table 3, that the proposed resonator with simple  The proposed structure radiation characteristics with and without ladder resonator method, helps to improve the isolation in the patch antenna arrays with less edge-to-edge spacing. Moreover, the presented technique has the best improvement in mutual coupling reduction effect among the all cited references in Table 3. Therefore, the proposed structure is good candidate for compact antenna design.

Conclusion
In this paper an impressive technique with simple method is proposed to decrease the coupling effects in the antenna array structure. By adding the proposed ladder-shaped resonator between patch antennas, the coupling effect is reduced about 44 dB. The proposed decoupling unit has simple structure and impressively improved isolation level in microstrip patch antenna arrays, which leads to design of a miniaturized antenna with better isolation, which is suitable for MIMO applications.  Data Availability Enquiries about data availability should be directed to the authors.

Declarations
Conflict of interest The authors declare that they have no conflict of interests in this paper.