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A Novel T-shaped Slot PIFA for MIMO Applications Mian Abdul Razzaq 1 , Prof., Joong-Geun Rhee 2 , Prof., Sung-Il Yang 2 , Muhammad Shoaib Khalid 1 1 Electronic, Electrical, Control and Instrumentation Engineering Dept., Hanyang University, 426-791, South Korea 2 Faculty of Electronics & Communication Engineering, Hanyang University, 426-791, South Kor ea Mian.abdulrazzaq@yahoo.com, HL1AQQ@hanyang.ac.kr, Syang@hanyang.ac.kr,Shoaibusmani@yahoo.com AbstractBecause of rapidly increasing demand for high capacity communication services compact antennas have become center of research interest nowadays and this reduction of siz e becomes much more important especially when we want to use the multiple-input multiple-output (MIMO) technology; to increase channel capacity, in modern compact devices. Microstrip antennas are an attractive option due to low cost, and small siz e. However to fulfill need for more compact and miniaturiz ed devices; a dual feed dual element planar inverted-F antenna (PIFA) at 2.45GHz has been proposed on a very small PCB (60 mm × 20 mm × 0.8 mm), to be used for ISM 2.45 GHz band. While total volume occupied by two antennas is 10 mm × 20 mm × 2.5 mm. -10 dB return loss or VSWR=2 criterion for required bandwidth has been satisfied, only with help of designing a novel radiation structure. To miniaturiz e siz e of PIFA a novel T-shaped slot has been employed in radiation structure. Overall siz e is compact than small MIMO antennas, available in open literature. As the proposed design is suitable for different feeding environments, it can be used in different small siz e PCB devices, for different applications. Results show satisfactory bandwidth, and omnidirectional radiation pattern. I. INTRODUCTION To increase the wireless channel capacity, multiple-input multiple-output (MIMO) systems have attracted a considerable research interest. Theoretical as well as practical inv estigations show substantial improvements in data throughput and reliability, in rich scattering environments; when multiple transmitter and receiv er antennas are utilized [1]-[3]. MIMO communication protocols are one such development along the path, and have demonstrated significant data communication capacity improvements by exploiting multiple independent channels. While going to use MIMO technology important aspect is that size and compactness of device should not be affected. In case of cellular communication, for example, size of transmitter is not a big problem so it can be designed easily, but the receiver side, e.g. cell phone, we have limitation for size and there is a lot of research going on for more compact receiver modules. With recent advances in solid state devices, construction of high performance miniaturized modules especially receivers have become realizable. These modules together with miniaturized sensors and transducers have found numerous applications in industry, medicine and military. As significant efforts have been devoted towards achieving miniaturized electronics and RF components; issues related to design and fabrication of efficient, miniaturized, and easily itegrable antennas for MIMO applications are as well important and need to be addressed for smart and compact future applications, and this is our motivation for current research work. Internal antennas or planar internal antennas are essential candidates for modern thin profile MIMO applications. The planar monopole antenna has simple structure but relativ ely large volume. Microstrip antennas being small in size and low profile are being used for size reduction but in case of multiple antennas we need smaller structures, and, for this Planer Inverted-F antenna (PIFA) looks a suitable candidate for MIMO antenna design, to be used for applications using MIMO technology. PIFA are smaller, cheaper and low profile than microstrip antenna. PIFA is basically inverted L antenna, which actually originates from a monopole with a bend, such that the most of the arm is parallel to the ground plane. It can also be treated as an Inverted-F antenna (IFA), with the wire radiator element replaced by a plate to expand the bandwidth, where IFA is well known for its ability to provide flexibility in impedance matching, without using any external circuitry. In addition, IFA and so as PIFA can produce both vertically and horizontally polarized electric fields, a feature desirable for indoor environments. On the other hand PIFA can be considered as a microstrip antenna modified with a shorting pin that reduces its size from λ/2 to λ/4, at the cost of reduced impedance bandwidth [4], [5]. There are several shorting mechanisms such as use of shorting pins [6], a shorting plate, or a shorting wall [7]. PIFA antenna can also be considered a microstrip antenna, modified with a shorting pin. This is basically λ/4 structure and various techniques have been used to accommodate this structure at small available PCB plane. Folding one side of antenna and making a slit or slot can reduce the size of PIFA effectively, along with introducing multiple frequency bands. Researchers have applied these techniques to minimize the size of PIFA, but with above mentioned techniques reduction in size of antenna is smaller than our proposed design. The distance or separation between two antenna elements is small in case of modern compact receivers and this is most critical parameter affecting mutual coupling. Studies have shown that for little or no mutual coupling the distance between typical antenna elements needs to be at least half wavelength [8]. However, in case of small available space, in modern compact devices, different techniques have been investigated; to reduce mutual coupling and to increase the electrical separation between two antennas; including orientation of the two antennas in space as in [9]. 978-1-4244-4873-9/09/$25.00 ©2009 IEEE
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Page 1: [IEEE 2009 IEEE 13th International Multitopic Conference (INMIC) - Islamabad, Pakistan (2009.12.14-2009.12.15)] 2009 IEEE 13th International Multitopic Conference - A novel T-shaped

A Novel T-shaped Slot PIFA for MIMO Applications

Mian Abdul Razzaq1, Prof., Joong-Geun Rhee 2, Prof., Sung-Il Yang2, Muhammad Shoaib Khalid1

1 Electronic, Electrical, Control and Instrumentation Engineering Dept., Hanyang University, 426-791, South Korea 2 Faculty of Electronics & Communication Engineering, Hanyang University, 426-791, South Korea

[email protected], [email protected], [email protected],[email protected]

Abstract—Because of rapidly increasing demand for high capacity communication services compact antennas have become center of research interest nowadays and this reduction of size becomes much more important especially when we want to use the multiple-input multiple-output (MIMO) technology; to increase channel capacity, in modern compact devices. Microstrip antennas are an attractive option due to low cost, and small size. However to fulfill need for more compact and miniaturized devices; a dual feed dual element planar inverted-F antenna (PIFA) at 2.45GHz has been proposed on a very small PCB (60 mm × 20 mm × 0.8 mm), to be used for ISM 2.45 GHz band. While total volume occupied by two antennas is 10 mm × 20 mm × 2.5 mm. -10 dB return loss or VSWR=2 criterion for required bandwidth has been satisfied, only with help of designing a novel radiation structure. To miniaturize size of PIFA a novel T-shaped slot has been employed in radiation structure. Overall size is compact than small MIMO antennas, available in open literature. As the proposed design is suitable for different feeding environments, it can be used in different small size PCB devices, for different applications. Results show satisfactory bandwidth, and omnidirectional radiation pattern.

I. INTRODUCTION

To increase the wireless channel capacity, multiple-input multiple-output (MIMO) systems have attracted a considerable research interest. Theoretical as well as practical investigations show substantial improvements in data throughput and reliability, in rich scattering environments; when multiple transmitter and receiver antennas are utilized [1]-[3]. MIMO communication protocols are one such development along the path, and have demonstrated significant data communication capacity improvements by exploiting multiple independent channels. While going to use MIMO technology important aspect is that size and compactness of device should not be affected. In case of cellular communication, for example, size of transmitter is not a big problem so it can be designed easily, but the receiver side, e.g. cell phone, we have limitation for size and there is a lot of research going on for more compact receiver modules. With recent advances in solid state devices, construction of high performance miniaturized modules especially receivers have become realizable. These modules together with miniaturized sensors and transducers have found numerous applications in industry, medicine and military.

As significant efforts have been devoted towards achieving miniaturized electronics and RF components; issues related to design and fabrication of efficient, miniaturized, and easily itegrable antennas for MIMO applications are as well important

and need to be addressed for smart and compact future applications, and this is our motivation for current research work.

Internal antennas or planar internal antennas are essential candidates for modern thin profile MIMO applications. The planar monopole antenna has simple structure but relatively large volume. Microstrip antennas being small in size and low profile are being used for size reduction but in case of multiple antennas we need smaller structures, and, for this Planer Inverted-F antenna (PIFA) looks a suitable candidate for MIMO antenna design, to be used for applications using MIMO technology. PIFA are smaller, cheaper and low profile than microstrip antenna. PIFA is basically inverted L antenna, which actually originates from a monopole with a bend, such that the most of the arm is parallel to the ground plane. It can also be treated as an Inverted-F antenna (IFA), with the wire radiator element replaced by a plate to expand the bandwidth, where IFA is well known for its ability to provide flexibility in impedance matching, without using any external circuitry. In addition, IFA and so as PIFA can produce both vertically and horizontally polarized electric fields, a feature desirable for indoor environments. On the other hand PIFA can be considered as a microstrip antenna modified with a shorting pin that reduces its size from λ/2 to λ/4, at the cost of reduced impedance bandwidth [4], [5]. There are several shorting mechanisms such as use of shorting pins [6], a shorting plate, or a shorting wall [7]. PIFA antenna can also be considered a microstrip antenna, modified with a shorting pin. This is basically λ/4 structure and various techniques have been used to accommodate this structure at small available PCB plane. Folding one side of antenna and making a slit or slot can reduce the size of PIFA effectively, along with introducing multiple frequency bands. Researchers have applied these techniques to minimize the size of PIFA, but with above mentioned techniques reduction in size of antenna is smaller than our proposed design.

The distance or separation between two antenna elements is small in case of modern compact receivers and this is most critical parameter affecting mutual coupling. Studies have shown that for little or no mutual coupling the distance between typical antenna elements needs to be at least half wavelength [8]. However, in case of small available space, in modern compact devices, different techniques have been investigated; to reduce mutual coupling and to increase the electrical separation between two antennas; including orientation of the two antennas in space as in [9].

978-1-4244-4873-9/09/$25.00 ©2009 IEEE

Page 2: [IEEE 2009 IEEE 13th International Multitopic Conference (INMIC) - Islamabad, Pakistan (2009.12.14-2009.12.15)] 2009 IEEE 13th International Multitopic Conference - A novel T-shaped

A miniaturized dual element dual feed PIFA design for MIMO applications has been proposed in this paper. For satisfactory performance and bandwidth requirements, -13db return loss and about -9dB mutual coupling has been achieved; only by designing a novel structure. The introduction of a novel T-shaped slot in radiating patch helped to reduce the size drastically, without any modification in PCB; keeping PCB structure simple for cheaper design.

II. DESIGN OF PIFA ANTENNA

A. Single element PIFA Design

PIFA is basically a microstrip antenna modified with a shorting pin that reduces its size from λ/2 to λ/4 [10]. Conventional PIFA size is determined by (1)

/ 4.L h λ+ = (1)

i.e. height of antenna plus length of radiating element [10]. In case of using Bluetooth band (2402~2483.4MHz.), with center frequency fc=2.45 GHz, λ/4 is 30.6mm whereas the resonant frequency is given by

.4( )

cc

fW L

=+

(2)

Where, W and L are width and length of radiating element of PIFA antenna.

Various techniques have been research interest; to reduce the size of, single PIFA antenna element, and hence to minimize the overall size of MIMO antenna array; and we have proposed a much smaller size by introducing a novel T-shaped slot in antenna structure.

Along with planar dimensions (length and width) of PIFA antenna, height is also a very important parameter for designing PIFA antenna. Conventional internal antennas usually show a high profile of about 6 to 10 mm above the system ground plane. This causes limitation on their applications in the modern thin profile applications, and when the distance or thickness between the radiating strip and the ground plane is reduced, the operating Band width of traditional PIFA is decreased [11]. Therefore, there is always a tradeoff between height of PIFA radiation structure above ground plane of PCB, and achieved bandwidth.

As the design limit for height was very small (only 2.5 mm in our requirement), so this problem was addressed by using ground plane of bottom side of PCB instead of top side. This technique effectively increased the bandwidth of antenna to satisfactory level. Since there are two ways to increase the bandwidth of Antenna; either by increasing the height of antenna, or by increasing the dielectric constant of antenna; to make thin profile design, we had to choose second option, i.e., to increase the dielectric constant, by using FR-4 epoxy material and by using the bottom side of PCB as ground plane.

Moreover when, available size for antenna ground plane decreases, its bandwidth also decreases. As discussed by M. C.

Huynh and W. Stutzman in [12], for obtaining bandwidth of 8 % or more we need at least 0.8λ ground plane which is about 100 mm for ISM 2.45GHz, or Bluetooth frequency band, and this size exceeds our available PCB Size. Therefore achieved bandwidth is comparatively low (although still good for small applications in this band) due to very small size of PCB used for proposed design.

As total size of PCB, and total space available for antenna volume, for design, are very small, so electrical length was needed to be increased by using various techniques.Previously researchers have introduced L-shaped slot in PIFA structure along with folding and meandering the PIFA antenna to reduce its size as mentioned already. However the size achieved by above mentioned techniques, as proposed in [11], [13], [14], [15], is much bigger than our proposed design. A novel T-shaped slot in radiating element has been proposed in this design, which has increased electrical length of antenna; and it helped to reduce overall size drastically. For further reduction of size, folded loop technique has also been employed, to increase electrical size of radiating element. To miniaturize size of single element, parametric study was performed, by using Ansoft’s High Frequency Structure Simulator (HFSS) simulation tool for best size and positions of shorting plate and feed plate.

Optimized simulation model was fabricated using FR-4 epoxy material, as PCB, and 0.2 mm thick copper, as radiation element. Fabricated model has been shown in Fig.1, which shows proposed miniaturized single element PIFA with a T-shaped slot to be used for MIMO applications. Size and accuracy of design is visible in isometric view. In Fig.2, front view shows very simple feeding mechanism where 50 Ω BNC connector has been soldered directly to the feed plate. Top view, in Fig. 3, provides idea about actual size of PIFA. Moreover, in top view width of single element can be seen clearly, which is 7 mm only.

.

Fig. 1. Miniaturized PIFA with T-shaped slot ( Isometric View).

Page 3: [IEEE 2009 IEEE 13th International Multitopic Conference (INMIC) - Islamabad, Pakistan (2009.12.14-2009.12.15)] 2009 IEEE 13th International Multitopic Conference - A novel T-shaped

Fig. 2. Miniaturized PIFA with T-shaped slot (Front view).

Fig. 3. Miniaturized PIFA with T-shaped slot (Top view).

Fig. 4. Frequency vs. Return Loss (PIFA with T-shaped slot).

To verify the simulation accuracy, PIFA sample, as shown in Fig. 1, was first simulated using HFSS ver. 11, by Ansoft; and it was fabricated and measured using vector network analyzer (VNA). Fig. 4. shows simulated results as compared with measured results, at resonant frequency 2.45 GHz, obtained by VNA (HP/Agilent, Model: 8753D). Measurement results in Fig. 4, shows that the fabricated PIFA is resonant at a frequency little lower than center frequency, which is due to small manufacturing errors, but it covers, entire Bluetooth band. Simulation results were found close enough to justify the simulation accuracy for proposed MIMO design.

B. Dual element PIFA design for MIMO applications Antennas should not only exhibit low port-to-port signal

correlation, but should exhibit isolation from one another so that signals being broadcast or received from one feed port don’t appear at the opposite port or feed. The isolation is typically measured at the antenna terminals by using the commonly derived s-parameters. Isolation figures typically given in decibels and are designated as S12 or S21 depending on, whether the measurement is from antenna 1 to 2 or vice versa. If the isolation is poor, the source antenna will deliver substantial power into the adjacent antenna’s termination impedance (typically 50 Ω resistive), with a corresponding reduction of the overall radiation efficiency. Since the antenna near field coupling is related to the far-field pattern, it is possible to approximately express the correlation coefficient in terms of s-parameters measured at each antenna terminal. This is given by [16].

( ) ( )

11 12 21 22

11 21 22 12

* *

1/2 1/22 2 2 2

1 1

S S S S

s

S S S S

ρ

+

=

− + − +⎛ ⎞⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎝ ⎠

(3)

After successful simulation and fabrication of single element PIFA, dual element PIFA for MIMO applications was simulated.

To reduce mutual coupling parametric study was performed for best size and positions of shorting plates and feed plates. As distance between shorting plate and feed plate is important parameter, so it also, has been optimized for best performance.

As shown in Fig. 3, 0.8 mm thick FR4 Substrate on copper ground plane has been employed for cheap design. Single element volume is 10 mm × 7 mm × 2.5 mm, whereas space occupied by dual element MIMO PIFA is 10 mm × 20 mm × 2.5 mm; over total ground plane size of 20 mm × 60 mm, PCB.

Final optimized model of MIMO PIFA, using HFSS, has been shown in Fig. 5, whereas, parameterized dimensions have been summarized in Table 1.

Page 4: [IEEE 2009 IEEE 13th International Multitopic Conference (INMIC) - Islamabad, Pakistan (2009.12.14-2009.12.15)] 2009 IEEE 13th International Multitopic Conference - A novel T-shaped

Fig. 5. MIMO Antenna array of two elements.

Fig. 6. Frequency vs. S Parameters (S11 & S12 for proposed design).

Page 5: [IEEE 2009 IEEE 13th International Multitopic Conference (INMIC) - Islamabad, Pakistan (2009.12.14-2009.12.15)] 2009 IEEE 13th International Multitopic Conference - A novel T-shaped

TABLE 1

PROPOSED PIFA DIMENSIONS

Entity Dimensions

Length (mm) Width (mm) Height (mm)

Fold1 0.2 2 1.5

Fold2 0.2 7 1

Fold3 2.2 7 0.2

T(Arm1) 4.5 0.5 0.2

*T(Arm2) 4.5 5 0.2

PCB 20 60 0.8

a. Dimension of T Slot Are Mentioned As 2 Different Parts, Arm 1 & Arm2.

III. RESULTS

Fig. 6, shows frequency vs. return loss graph of our proposed design, obtained by HFSS, which shows the bandwidth requirement of -10 dB (or VSWR = 2) return loss is satisfied. In fact, -13 dB return loss value is good and can easily compensate the small reduction in return loss due to manufacturing errors. As marked in Fig. 6, -10 dB impedance bandwidth, marked by m4 and m5, on S11 plot, is about 2.5 %.

In fact it was observed during simulations that improving the S11 parameter is easy with help of some additional slot in ground plane but it affects mutual coupling S12, badly. So the change in the geometry of design was concentrated mainly and a novel T-shaped slot was introduced in the radiating element which helped to reduce the size to required level along with minimizing the mutual coupling affect to -8 dB design requirement.

(a) E Plane (φ = 0)

(b) H Plane (φ = 90)

Fig. 7. Radiation Pattern of proposed MIMO array.

Fig. 7, above shows the radiation pattern at 2.45 GHz frequency, for proposed design. As shown in figure, radiation pattern is almost omnidirectional, which is required feature for many of common PIFA applications. Gain is about 1.8 dB and radiation pattern is almost omni-directional. PIFA antennas have small bandwidth inherently and here achieved bandwidth is about 2.5%, which can be improved to some extent, as a tradeoff of mutual coupling, by using slots in ground plane, according to design requirements.

IV. CONCLUSION AND FUTURE WORK

Miniaturized MIMO antenna has been proposed in this paper. Return loss, -13dB, fulfills -10dB requirement and can be improved easily, but at the cost of mutual coupling by using slots in the ground plane. Achieved mutual coupling is around -9 dB without using any external element or change in PCB design, only with the help of design optimization of radiating element. Overall size is compact than available compact MIMO antennas available in open literature. Single element size for proposed model is 10 mm × 7 mm × 2.5 mm whereas space occupied by dual element MIMO PIFA is 10 mm × 20 mm × 2.5 mm. When compared with [17], having single element dimensions, 15.6 mm × 10.4 mm ×4 mm or; with [18], having dimensions, 30.5 mm × 10 mm ×8.5 mm, our proposed model is clearly smaller. When compared with printed MIMO PIFA as proposed in [11], having dimensions 15 mm × 31 mm or by [19] having dimensions 20 mm × 46.6 mm our model still proposes smaller dimensions of length and width (height is not comparable in case of printed PIFA). As the proposed design is suitable for different feeding environments, it can be used in different small size PCB devices, for different applications. As future work electromagnetic band gap (EBG) structures are to be employed, to improve mutual coupling effects further.

Page 6: [IEEE 2009 IEEE 13th International Multitopic Conference (INMIC) - Islamabad, Pakistan (2009.12.14-2009.12.15)] 2009 IEEE 13th International Multitopic Conference - A novel T-shaped

ACKNOWLEDGMENT

This research work is sponsored by ‘Higher Education Commission (HEC), Govt. of Pakistan’ under the scholarship program titled: MS Level Training in Korean Universities/Industry.

I am special thankful to Mr., Y. H. Kim, Eugene Rhee, Kim Jin Bok and Mr. J. H. Kim, along with ANTRF lab, at Seoul campus, for their co-operation in my work as well as in communication problems during my stay in Korea. I am also thankful to David Ryu for his practical and moral, co-operation throughout this work.

REFERENCES

[1] Y. Gao, X. Chen, Z. Ying and C. Parini, “Design and Performance investigation of a Dual-Element PIFA Array at 2.5 GHz for MIMO Terminal,” IEEE Transactions On Antenna and Propagation, Vol. 5, NO. 12, December 2007.

[2] G. Foschini, “Layered space time architecture for wireless communication in a fading environment when using multi element antennas,” Bell labs Tech. J., vol. 1, no. 2, pp. 41-59, 1996.

[3] J. Wallace, M. Jensen, A. Swindlehurst, and B. Jeffs, “Experimental characterization of the MIMO wireless channel: Data acquisition and Analysis,” IEEE Trans. Wireless Commun., vol. 2, no. 2, pp. 335-343, Mar.2003.

[4] H. M. Chen, Y. F. Lin, P. S. Cheong, H.H. Lin, CTP Song, and P. S. Hall, “Parametric Study on the characteristics of Planar Inverted-F Antenna,” .Proc. Int. Elect. Eng. Microwave. Antennas and Propagation, vol. 152, no. 6, Dec. 2005.

[5] Z. N. Chen, K. Hirasawa, K. W. Leung, and K. M. Luk, “A New Inverted F antenna with a ring Dielectric Resonator,” IEEE Trans. on vehicular Technology, VT-48, pp. 1029-1032, July 1999.

[6] W. C. Mok, R. Chair, and K. F. Lee, “Wideband quarter-wave patch antenna with shorting pin,” Proc. Int. Elect. Eng. Microwave. Antennas and Propagation, vol. 150, pp 56-60, 2003.

[7] C. L. Mak, R. Chair, K. F. Lee, K.M. Luk, and A. A. Kishk, “Half U-slot patch antenna with shorting wall,” Electron. Lett. , vol. 39, pp 1779-1780, 2003.

[8] W. L. Stutzman and G. A. Thiele, “Antenna Theory and Design,” John Wiley & Sons, 2nd Edition, 1998.

[9] J. Thaysen, “ Mutual Coupling between Identical Planar Inverted-F Antenna,” In IEEE Antennas Propag. Society Int. Symp., San Antonio, TX, Jun. 2002, pp. 504-507.

[10] Kazuhiro Hirasawa, Analysis, Design, and Measurement of small and Low profile antennas, Artech House London: Clarendon, 1891, pp.1611-180.

[11] Chin-Hua Chang, Kin-Lu Wong, “Printed λ/8-PIFA for Penta band WWAN Operation in the Mobile Phone,” IEEE Transactions on Antenna and Propagation, Vol.57, NO. 5, May 2009.

[12] M. C. Huynh and W. Stutzman, “Ground Plane effects on Planar Inverted-F antenna (PIFA) Performance,” IEE.Proc. Microw. Antennas Propag. Vol., 150, No.46, August 2003.

[13] G. P. Karakoussis, A. I. Kostaridis, C. G. Biniaris, and D. I. Kaklamani,”A dual band inverted –F antenna printed on a PC Card for the ISM and UNNI bands,”Proc. IEEE WCNC 2003, vol. 1, pp. 88-92,Mar.2003.

[14] I. Ang, Y. X. Guo, and Y. W. Chia, “Compact internal quad-band antenna for mobile phones,” Microw. Opt. Technol. Lett., vol. 38, no. 3,pp. 217–223, Aug. 2003.

[15] C. R. Rowell and R. D. Murch, “A compact PIFA suitable for dualfrequency 900/1800-MHz operation,” IEEE Trans. Antennas Propag., vol. 46, no. 4, pp. 596–598, Apr. 1998.

[16] S. Blanch, J. Romeu, and I. Corbella, “Exact representation of antenna system diversity performance from input parameter

description,”Electronics, Letters, 1 May 2003, Volume 39, Issue 9, p. 705-707.

[17] M . Manteghi, and Y. Rahmat-Samii, A novel miniaturized triband PIFA for MIMO applications,” Microwave Opt. Technol. Lett., vol. 49, pp. 724-731, Mar. 2007.

[18] A. Diallo , C. Luxey , P. Le Thuc , R. Staraj and G. Kossiavas “Study and reduction of the mutual coupling between two mobile phone PIFAs operating in the DCS1800 and UMTS bands,” IEEE Trans. Antennas Propag., vol. 54, pp. 3063, Nov. 2006 .

[19] M. Karaboikis , C. Soras , G. Tsachtsiris and V. Makios “Compact dual-printed inverted-F antenna diversity systems for portable wireless devices,” IEEE Antennas Wireless Propag. Lett., vol. 3, pp. 9, 2004.


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