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Compact Quad-band MIMO Antenna Array with Low Mutual Coupling for Mobile Terminal Mohit Mishra Department of Electronics and Electrical Engineering IIT Guwahati Guwahati, India [email protected] Rakhesh Singh Kshetrimayum Department of Electronics and Electrical Engineering IIT Guwahati Guwahati, India [email protected] Abstract—A low mutual coupling multiband two element antenna array for the mobile terminal is proposed. This array consists of two symmetrical antenna elements with grounded branches and a slot in between the microstrip feed lines in the ground plane. The working mechanism is explained by analysing the S-parameter and surface current plots. The measured -10 dB impedance bandwidth of a fabricated prototype covers from 824-894 MHz (GSM850), 1427.9-1495.9 MHz (LTE1500), 1575.42 MHz (GPS-L1), 1710-1880 MHz (GSM1800), 1850-1990 MHz (GSM 1900), 1921-2170 MHz (UMTS), 3400-3600 MHz (LTE- 42), 3550- 3700 MHz (CBRS-citizen broadband radio services), 3600-3800 MHz (LTE-43), 4800-5000 MHz (proposed for 5G), 5725-5875 MHz (WLAN-5.8 GHz) and 5855-5925 MHz (V2X) band. Mutual coupling in all the frequency bands is found to be less than -16 dB while maintaining 27 mm (0.076 times free space wavelength at 850 MHz) edge to edge inter-element spacing. The measured S-parameters and radiation patterns are found to be matching with the simulated results. Index Terms—MIMO antenna, low mutual coupling, antenna array I. I NTRODUCTION The ever growing high data rate demand can be met by the long-term evolution (LTE) and 5G standard. These tech- nologies rely on the antenna array and multiple input multiple output (MIMO) system to improve the quality and capacity of the communication [1]. The realisation of MIMO requires the development of multiple element antenna arrays with high isolation. However, when antenna elements are placed in near surrounding of each other, mutual coupling comes into the picture and degrades the MIMO performance [2]. In addition, modern mobile handsets need to be operated at various fre- quency bands. So there is a need for the development of the multiple-band antenna array with low mutual coupling to meet the requirements of the modern communication system. Simpler fabrication, low expenses and good performance make the monopole antenna a good candidate to be used in a wide range of applications. MIMO systems need very low mutual coupling antenna arrays to ensure the quality and high capacity communication. One way of reducing the mutual coupling is to place the antennas at 0.5 λ 0 (free space wavelength) distance from each other. However, with respect to GSM850 or LTE700 band, this idea cannot be realised because of the space constraints in mobile handsets. Fig. 1. Array design and specifications (mm) In literature [3]-[10], various methods have been used to mitigate the mutual coupling. In [3], a defected ground structure (DGS) as a slot in between the patches in the ground plane has been used for the WLAN MIMO application. In [4], two planar inverted F antennas are decoupled using a T-shaped slot (DGS) at WLAN and WiMAX bands. Similarly, in [5], grounded branches have been introduced to get the low mutual coupling in dual-band diversity antenna at UMTS and WLAN bands. A T-shaped grounded branch is used to suppress the coupling between the two orthogonal monopole antennas for a wider range of frequency covering GSM850/900, DCS, PCS, UMTS and LTE2500 bands [6]. Two PIFAs have been decoupled by using neutralisation line (NL) technique at the UMTS and DCS1800 bands [7]. Neutralisation lines (NLs) are used to decouple two 3-D radiating elements in [8] for LTE700 and GSM850/900 bands. Three NLs are used in [9] for mutual coupling reduction for the wideband application which covers GSM 1800/1900, UMTS, LTE2300, LTE2500, 2.4 GHz WLAN. Grounded branch and neutralisation line (NL) techniques have been used together in [10] to decouple the printed monopole antennas for a wider frequency range which covers GSM 1800/1900, UMTS, LTE2300, LTE2500 and 2.4 GHz-WLAN bands. In this communication, a two element printed monopole antenna array is reported which uses the grounded branches and a slot in between the feedline at the bottom layer to

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Page 1: Compact Quad-band MIMO Antenna Array with Low Mutual ... · responsible for the 6 GHz band which covers (WLAN-5.8 GHz) and 5855-5925 MHz (V2X). To make the antenna elements sufficiently

Compact Quad-band MIMO Antenna Array withLow Mutual Coupling for Mobile Terminal

Mohit MishraDepartment of Electronics and Electrical Engineering

IIT GuwahatiGuwahati, India

[email protected]

Rakhesh Singh KshetrimayumDepartment of Electronics and Electrical Engineering

IIT GuwahatiGuwahati, India

[email protected]

Abstract—A low mutual coupling multiband two elementantenna array for the mobile terminal is proposed. This arrayconsists of two symmetrical antenna elements with groundedbranches and a slot in between the microstrip feed lines in theground plane. The working mechanism is explained by analysingthe S-parameter and surface current plots. The measured -10dB impedance bandwidth of a fabricated prototype covers from824-894 MHz (GSM850), 1427.9-1495.9 MHz (LTE1500), 1575.42MHz (GPS-L1), 1710-1880 MHz (GSM1800), 1850-1990 MHz(GSM 1900), 1921-2170 MHz (UMTS), 3400-3600 MHz (LTE-42), 3550- 3700 MHz (CBRS-citizen broadband radio services),3600-3800 MHz (LTE-43), 4800-5000 MHz (proposed for 5G),5725-5875 MHz (WLAN-5.8 GHz) and 5855-5925 MHz (V2X)band. Mutual coupling in all the frequency bands is found to beless than -16 dB while maintaining 27 mm (0.076 times free spacewavelength at 850 MHz) edge to edge inter-element spacing. Themeasured S-parameters and radiation patterns are found to bematching with the simulated results.

Index Terms—MIMO antenna, low mutual coupling, antennaarray

I. INTRODUCTION

The ever growing high data rate demand can be met bythe long-term evolution (LTE) and 5G standard. These tech-nologies rely on the antenna array and multiple input multipleoutput (MIMO) system to improve the quality and capacityof the communication [1]. The realisation of MIMO requiresthe development of multiple element antenna arrays with highisolation. However, when antenna elements are placed in nearsurrounding of each other, mutual coupling comes into thepicture and degrades the MIMO performance [2]. In addition,modern mobile handsets need to be operated at various fre-quency bands. So there is a need for the development of themultiple-band antenna array with low mutual coupling to meetthe requirements of the modern communication system.

Simpler fabrication, low expenses and good performancemake the monopole antenna a good candidate to be usedin a wide range of applications. MIMO systems need verylow mutual coupling antenna arrays to ensure the qualityand high capacity communication. One way of reducing themutual coupling is to place the antennas at 0.5 λ0 (free spacewavelength) distance from each other. However, with respectto GSM850 or LTE700 band, this idea cannot be realisedbecause of the space constraints in mobile handsets.

Fig. 1. Array design and specifications (mm)

In literature [3]-[10], various methods have been usedto mitigate the mutual coupling. In [3], a defected groundstructure (DGS) as a slot in between the patches in the groundplane has been used for the WLAN MIMO application. In [4],two planar inverted F antennas are decoupled using a T-shapedslot (DGS) at WLAN and WiMAX bands. Similarly, in [5],grounded branches have been introduced to get the low mutualcoupling in dual-band diversity antenna at UMTS and WLANbands. A T-shaped grounded branch is used to suppress thecoupling between the two orthogonal monopole antennas fora wider range of frequency covering GSM850/900, DCS,PCS, UMTS and LTE2500 bands [6]. Two PIFAs have beendecoupled by using neutralisation line (NL) technique at theUMTS and DCS1800 bands [7]. Neutralisation lines (NLs)are used to decouple two 3-D radiating elements in [8] forLTE700 and GSM850/900 bands. Three NLs are used in [9]for mutual coupling reduction for the wideband applicationwhich covers GSM 1800/1900, UMTS, LTE2300, LTE2500,2.4 GHz WLAN. Grounded branch and neutralisation line(NL) techniques have been used together in [10] to decouplethe printed monopole antennas for a wider frequency rangewhich covers GSM 1800/1900, UMTS, LTE2300, LTE2500and 2.4 GHz-WLAN bands.

In this communication, a two element printed monopoleantenna array is reported which uses the grounded branchesand a slot in between the feedline at the bottom layer to

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TABLE IBRIEF SUMMARY OF THE PROPOSED WORK AND STATE OF THE ART

Reference Bandwidth covers the following fre-quency bands

Bandwidth criteria Substrate size in terms of freespace wavelength (λ0)

Element spacing in λ0 inthe lowermost band

[6] GSM850/900, DCS, PCS, UMTS, LTE2500 -6 dB 0.283 λ0×0.354 λ0 0.1 λ0[9] GSM1800/1900, UMTS, LTE2300,

LTE2500, 2.4 GHz-WLAN-10 dB 0.599 λ0×0.359 λ0 0.09 λ0

[10] GSM1800/1900, UMTS, LTE2300,LTE2500 and 2.4 GHz-WLAN

-10 dB 0.359 λ0×0.479 λ0 0.132 λ0

[This work] GSM850, GSM1800/1900, GPS-L1 Band,UMTS, CBRS, LTE3500, V2X, LTE-42,LTE-43, 4.8-5GHz (5G), 5.8 GHz-WLAN

-10 dB 0.258 λ0×0.255 λ0 0.076 λ0

enhance the isolation level. As compared to the state ofthe art given in Table I, this antenna array works at muchreduced inter-element spacing and has a wider frequency rangecovering multiple bands which are being used or will be usedin the near future. Table I signifies that the proposed work hasa minimum inter-element spacing in terms of the free spacewavelength ( λ0) i.e. 0.076 λ0 at the lowermost frequency band(GSM850). Mutual coupling is measured and found to be lessthan -16 dB in all the bands. Section II explains the antennastructure and Section III contains the working mechanism.Section IV contains the results and conclusions are given inSection V.

II. ANTENNA GEOMETRY AND DESIGN

Array design and geometrical specifications of the proposedantenna array are explained in Fig. 1. This antenna array isprinted on an FR-4 substrate of relative permittivity 4.4 andloss tangent of 0.02. This array consists of two symmetric F-shaped monopole antennas [11] with an extra L shaped branchA-B-C as shown in Fig. 1. Each antenna element consists of 3branches named as A-B-C, A-D-E and A-F-G. Branches P-Q-R and S-T-U are extended in the bottom layer from the groundplane around antenna-A and antenna-B respectively. Thesebranches are termed as grounded branches (GBs). Antennasare fed through two 50-Ω microstrip lines using port-1 andport-2. A slot is created in between the microstrip feedlinesat the bottom layer (ground plane). The inter-element spacingbetween antenna elements is 27 mm or 0.076 λ0 at 850 MHz.

III. WORKING MECHANISM

Small edge to edge inter-element spacing and use of com-mon ground layer are few important reasons for the high inter-action between the antenna elements in printed antenna arrays.To increase the isolation between array-elements, groundedbranches (GBs) around the antennas and a slot in between the50-Ω microstrip feedlines have been used. To understand thecontribution of various branches in the design, surface currentdistribution at various frequencies are plotted in Fig. 2 and theresults of the parametric study are given in Fig. 3.

Part B-C of branch A-B-C is 41.75 mm which is veryclose to 42 mm (λg/4 at 850 MHz) and is responsible forthe resonance at GSM 850 band. From |S11| plot in Fig.3(a) and Fig. 3(b), it is clear that the length of branch A-B does not affect the resonance at 850 MHz and resonance

(a) (b)

(c) (d)

Fig. 2. Surface current distribution (a) 850 MHz and (b) 1.8 GHz (c) 3.6GHz and (d) 4.8 GHz

at GSM850 band can be adjusted by varying the length ofbranch B-C. Branch A-D-E is 10 mm which is close to9.75 mm (λg/4 at 3600 MHz) and provides the resonancesfor the frequency band which cover LTE-42, LTE-43, 3550-3700 MHz (CBRS- citizen broadband radio services) bands.Branch F-G also affects the resonance in 3400-3600 MHz banddue to its loading effect on branch A-D-E. The same can beendorsed by the surface current distribution in Fig. 2(c) and|S11| parameters in Fig. 3(c) and Fig. 3(d). The primary mode(λg/4 resonance) because of branch A-B is responsible for thewide range of frequencies which covers 1427.9-1495.9 MHz(LTE1500), 1710-1880 MHz (GSM1800), 1850-1990 MHz(GSM 1900), 1921-2170 MHz (UMTS) bands, this can beseen from the surface current distribution plot at 1.8 GHz inFig. 2(a). From Fig. 3(d), it is clear that minor adjustment inthis band can be done by adjusting the length of the branchF-G. The third mode (3λg/4 resonance) of branch A-B isresponsible for the 6 GHz band which covers (WLAN-5.8GHz) and 5855-5925 MHz (V2X).

To make the antenna elements sufficiently decoupled,grounded branches around both the antenna elements anda slot to disconnect the ground plane is used. |S11| and|S21| comparison between various design stages is plotted inFig. 4. From Fig. 4(a), it is clear that insertion of grounded

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branches leads to an extra resonance that covers 4800-5000MHz (proposed for 5G) band.

(a)

(b)

(c)

(d)

Fig. 3. Variation of |S11| with length of branch (a) AB (b) BC (c) DE (d)FG

Grounded branches reduce the mutual coupling at 3400-3600 MHz (LTE3500), 3550-3700 MHz (CBRS) and GSM850and are able to reduce the antenna elements interaction below-16 dB in these bands but the antenna element interaction inGSM 850 band could not be reduced below -15 dB. Thecommon ground plane is one of the important reason forhigh interaction level between elements of printed antennaarrays. Keeping the same fact into consideration, an attempt ofdisconnecting the ground plane by creating a slot in betweenthe microstrip feed line at the bottom layer is done. This slot inthe bottom layer is capable of reducing the antenna elementsinteraction below -16 dB at GSM850 band too. The same canbe interpreted by studying the variation of the |S21| parameterwith various design stages in Fig. 4(b). By observing thesurface current distribution plot in Fig. 5, the contribution ofgrounded branches and slot in isolation enhancement can be

(a)

(b)

Fig. 4. Variation of (a) |S11| & (b) |S21| for various design stages

(a) (b)

(c) (d)

Fig. 5. Surface current plot (a) without decoupling units & (b) with groundedbranches at 3.6 GHz; (c) with only grounded branches & (d) with bothgrounded branches and slot at 850 MHz when only antenna-B is excited

understood in a better way. Figures 5(a) and 5(b) reveals thatthe grounded branches help in suppressing the surface currentlinkage between antennas at 3.6 GHz. Similarly, Fig. 5(c) and5(d) shows the contribution of the slot in the reduction ofsurface current linkage between array elements at 850 MHz,thus help in improving the isolation.

IV. RESULTS AND DISCUSSIONS

This section contains the important results correspondingto a fabricated prototype design as shown in the Fig. 6(a)& Fig. 6(b) and is divided into 3 sub-sections. Sub-sectionIV-A contains the scattering parameter results, the far-fieldradiation pattern are plotted in sub-section IV-B and diversityperformance is evaluated in sub-section IV-C.

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(a) (b)

(c) (d)

Fig. 6. Fabricated prototype (a) top layer (b) bottom layer and correspondingS-parameters (c) |S11| (d) |S21|

A. S-Parameters

The experiment is performed to measure the scattering pa-rameters of a fabricated prototype and results are plotted withthe simulated scattering parameters in Fig. 6(c) and 6(d). Themeasured -10 dB impedance bandwidth is found to be from779-903 MHz, 1452-2374 MHz, 3400-3813 MHz, 4652-5273MHz, 5729-6400 MHz and covers several frequency bands ofimportance. Measured results are found to be matching withthe simulated parameters. Mutual coupling (S21) across all thefrequency bands is noted to be below -16 dB.

B. Radiation pattern

Measured and simulated radiation pattern corresponding to850 MHz, 1.8 GHz, 3.6 GHz and 4.8 GHz are plotted in XOZand YOZ plane for antenna-A and antenna-B in Fig. 7 to Fig.10 respectively. At a time, only one antenna is fed and thesecond one is terminated with the 50-Ω matched load. At850 MHz, the omnidirectional radiation pattern is observedin both the XOZ and YOZ plane. Radiation patterns at 1.8GHz and 2 GHz are found to be similar thus plotted onlyfor 1.8 GHz. Radiation patterns in XOZ plane at 3.6 and 4.8GHz is found to be almost omnidirectional. Radiation patternsin the XOZ plane for both the antennas are observed to beidentical because of the symmetry. The simulated peak gainat 850 MHz, 1.8 GHz, 3.6 GHz and 4.8 GHz is noted to be-0.865 dBi, 2.12 dBi, 5.46 dBi and 4.24 dBi respectively.

C. Diversity performance

The envelope correlation coefficient (ECC) provides anidea about the correlation between the antenna elements anddiversity gain can also be calculated based on it. ECC can becalculated by using the equation (1) as suggested in [6]. Mean

(a) (b)

(c) (d)

Fig. 7. Radiation patterns at 850 MHz (a), (b) antenna-A; (c), (d) antenna-B

(a) (b)

(c) (d)

Fig. 8. Radiation patterns at 1.8 GHz (a), (b) antenna-A; (c), (d) antenna-B

(a) (b)

(c) (d)

Fig. 9. Radiation patterns at 3.6 GHz (a), (b) antenna-A; (c), (d) antenna-B

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TABLE IIPARAMETERS FOR DIVERSITY PERFORMANCE

Frequency XPD(dB) MEG1(dB) MEG2(dB) ECC Diversity Gain(dB)

850 MHz 0 -6.9610 -6.97642.7688× 10−4 106 -8.6671 -8.6929

1.8 GHz 0 -3.9512 -3.98941.0405× 10−4 106 -5.5239 -5.5786

3.6 GHz 0 -7.8210 -7.90629.1173× 10−5 106 -9.2933 -9.3410

4.8 GHz 0 -4.4013 -4.48461.5027× 10−4 106 -6.0124 -6.0812

(a) (b)

(c) (d)

Fig. 10. Radiation patterns at 4.8 GHz (a), (b) antenna-A; (c), (d) antenna-B

effective gain provides an idea of the averaged received powerwith the variation in the channel condition and it is evaluatedbased on the assumptions proposed in [12] by using equation(2).

ECC = [|S∗11S12 + S∗

21S22|2]/[1− [(|S11|2)][1− [(|S22|2)](1)

MEGi = (1/2π)

∫ 2π

0

[[XPD/1 +XPD]Gθi(π/2, φ).+

[1/1 +XPD]GΦi(π/2, φ)]dφ(2)

Here, Sij are the scattering parameters and XPD is crosspolar discrimination. Gθi and Gφi denotes the power gainof the i-th antenna element in the θ and φ directions. Meaneffective gains are calculated considering the XPD of 0 dBfor indoor environment and 6 dB for the urban environment[13]. Diversity gain (DG) is calculated based on ECC. TableII contains the ECC, MEG and DGs for the proposed array.The DG is 10dB, ECC is less than 2.7688×10−4 and MEGis less than -3.9844 dB at all the four operational frequenciesof the quad-band MIMO antenna array. Hence, this antennaarray can be employed for closely spaced quad-band MIMOantenna arrays.

V. CONCLUSION

In this communication, a multiband antenna array consistingof two symmetrical elements separated by 0.076 λ0 edge

to edge inter-element spacing is investigated. The fabricatedprototype has a -10 dB impedance bandwidth which covers824-894 MHz (GSM 850), 1427.9-1495.9 MHz (LTE-1500),1575.42 MHz (GPS-L1 Band), 1710-1880 MHz (GSM 1800),1850-1990 MHz (GSM 1900), 1921-2170 MHz (UMTS),3400-3600 MHz (LTE-42), 3550-3700 MHz (CBRS), 3600-3800 MHz (LTE-43), 4800-5000 MHz (proposed for 5G),5725-5875 MHz (WLAN-5.8 GHz) and 5855-5925 MHz(V2X). Grounded branches and a slot are used for isolationenhancement. Mutual coupling is measured and found to beless than -16 dB across all the frequency bands. S-parametersand radiation patterns are measured and found to be matchingwith the simulated results. ECC value is calculated and foundto be less than 0.5 thus satisfying the requirement of lowcorrelation. Variation in MEG for XPD of 0 dB and 6 dB isnoted to be less than -3 dB [12] for both the antenna elements.The diversity gain is found to be 10 dB.

REFERENCES

[1] M. A. Jensen and J. W. Wallace, “A review of antennas and propagationfor MIMO wireless communications,” in IEEE Transactions on Antennasand Propagation, vol. 52, no. 11, pp. 2810-2824, Nov. 2004.

[2] X. Chen, S. Zhang and Q. Li, “A Review of Mutual Coupling in MIMOSystems,” in IEEE Access, vol. 6, pp. 24706-24719, 2018.

[3] J. OuYang, F. Yang and Z. M. Wang, “Reducing Mutual Coupling ofClosely Spaced Microstrip MIMO Antennas for WLAN Application,” inIEEE Antennas and Wireless Propagation Letters, vol. 10, pp. 310-313,2011.

[4] S. Zhang, B. K. Lau, Y. Tan, Z. Ying and S. He, “Mutual CouplingReduction of Two PIFAs With a T-Shape Slot Impedance Transformerfor MIMO Mobile Terminals,” in IEEE Transactions on Antennas andPropagation, vol. 60, no. 3, pp. 1521-1531, March 2012.

[5] Y. Ding, Z. Du, K. Gong and Z. Feng, “A Novel Dual-Band PrintedDiversity Antenna for Mobile Terminals,” in IEEE Transactions onAntennas and Propagation, vol. 55, no. 7, pp. 2088-2096, July 2007.

[6] Cheng Yang, Yuan Yao, Junsheng Yu, and Xiaodong Chen, “Novel Com-pact Multiband MIMO Antenna for Mobile Terminal,” in InternationalJournal of Antennas and Propagation, vol. 2012, Article ID 691681, 9pages, 2012.

[7] A. Diallo, C. Luxey, P. Le Thuc, R. Staraj and G. Kossiavas, “Study andReduction of the Mutual Coupling Between Two Mobile Phone PIFAsOperating in the DCS1800 and UMTS Bands,” in IEEE Transactions onAntennas and Propagation, vol. 54, no. 11, pp. 3063-3074, Nov. 2006.

[8] A. Cihangir, F. Ferrero, G. Jacquemod, P. Brachat and C. Luxey, “Neutral-ized Coupling Elements for MIMO Operation in 4G Mobile Terminals,”in IEEE Antennas and Wireless Propagation Letters, vol. 13, pp. 141-144,2014.

[9] Y. Wang and Z. Du, “A Wideband Printed Dual-Antenna With ThreeNeutralization Lines for Mobile Terminals,” in IEEE Transactions onAntennas and Propagation, vol. 62, no. 3, pp. 1495-1500, March 2014.

[10] Y. Wang and Z. Du, “A Wideband Printed Dual-Antenna System With aNovel Neutralization Line for Mobile Terminals,” in IEEE Antennas andWireless Propagation Letters, vol. 12, pp. 1428-1431, 2013.

Page 6: Compact Quad-band MIMO Antenna Array with Low Mutual ... · responsible for the 6 GHz band which covers (WLAN-5.8 GHz) and 5855-5925 MHz (V2X). To make the antenna elements sufficiently

[11] J.R. Panda, R.S. Kshetrimayum, “An F shaped printed monopole antennafor dual-band RFID and WLAN applications,” in Microwave and OpticalTechnology Letter, 53, pp. 1478-1481, 2011.

[12] S. C. K. Ko and R. D. Murch, “Compact integrated diversity antennafor wireless communications,” in IEEE Transactions on Antennas andPropagation, vol. 49, no. 6, pp. 954-960, June 2001.

[13] R. G. Vaughan and J. B. Andersen, “Antenna diversity in mobilecommunications,” in IEEE Transactions on Vehicular Technology, vol.36, no. 4, pp. 149-172, Nov. 1987.