IEICE Communications Express, Vol.4, No.12, 387–392

Design of matching networks
based on image impedances
for near ﬁeld MIMOKazuki Ishiia), Naoki Honma, and Yoshitaka Tsunekawa
Graduate School of Engineering, Iwate University,
4–3–5 Ueda, Morioka 020–8551, Japana) t2314002@iwate-u.ac.jp

Abstract: This paper proposes matching method based on image impedances for near ﬁeld MIMO. In this letter, matching method, which canrealize matching of all port at the same time by extending image impedances
theory, is proposed. Numerical analysis and experimental results demonstrate
the proposed matching method is effective in enhancing the channel capacityof the near ﬁeld MIMO, where facing antennas strongly couple to each other.
Keywords: matching network, near ﬁeld MIMO, conjugate image impedancesClassiﬁcation: Antennas and Propagation
References© IEICE 2015
DOI: 10.1587/comex.2015XBL0150
Received October 30, 2015
Accepted November 24, 2015
Published December 22, 2015[1] J.-S. Jiang and M. A. Ingram, “Spherical-wave model for short-range MIMO,”IEEE Trans. Commun., vol. 53, no. 9, pp. 1534–1541, Sep. 2005. DOI:
10.1109/TCOMM.2005.852842[2] N. Honma, K. Nishimori, T. Seki, and M. Mizoguchi, “Short range MIMOcommunication,” Proc. 3rd EuCaP, pp. 1763–1767, Mar. 2009.
[3] D. Kwon, “Reactive near-ﬁeld multiplexing and reliable diversity communication method,” 2010 Proc. of the Fourth European Conference on Antennas
and Propagation (EuCAP), 2010.
[4] M. A. Nikravan, D. Kwon, H. G. Schantz, and A. H. Unden, “Near-ﬁeld
MIMO communication utilizing both electric and magnetic ﬁeld components,”
2014 IEEE International Symposium on Antennas and Propagation and USNCURSI Radio Science Meeting (AP-S 2014), pp. 474–475, Jul. 2014. DOI:
10.1109/APS.2014.6904568[5] K. Shishido, K. Nishimori, and N. Honma, “Decoupling method for compact
MIMO antenna utilizing MISO channel response on neighboring antennas,”
Proc. International Symposium on Antenna and Propagation (ISAP) 2011,
Session FrP2-20, Oct. 2011.
[6] S. Roberts, “Conjugate-image impedances,” Proc. IRE, vol. 34, pp. 198–204,
Apr. 1946. DOI:10.1109/JRPROC.1946.234242[7] N. Inagaki and S. Hori, “Fundamentals of wireless connections with near ﬁeld
coupled antennas,” IEICE Trans. Commun., vol. J94-B, no. 3, pp. 436–443,Mar. 2011.
[8] K. Ishii, N. Honma, and Y. Tsunekawa, “Matching method based on image
impedances for near ﬁeld MIMO,” 2014 IEEE International Symposium on
Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S2014), vol. 3, pp. 1119–1120, Jul. 2014. DOI:10.1109/APS.2014.6904886

387

IEICE Communications Express, Vol.4, No.12, 387–392[9] K. Ishii, N. Honma, and Y. Tsunekawa, “Experimental evaluation of matching
method based on image impedances for near ﬁeld MIMO,” 2014 International
Symposium on Antennas and Propagation (ISAP 2014), TH4C, pp. 411–412,Dec. 2014. DOI:10.1109/ISANP.2014.7026704[10] U.-M. Jow and M. Ghovanloo, “Design and optimization of printed spiral coils
for efﬁcient transcutaneous inductive power transmission,” IEEE Trans.
Biomed. Circuits Syst., vol. 1, no. 3, pp. 193–202, Sep. 2007. DOI:10.1109/
TBCAS.2007.913130

1Introduction

Recently, noncontact short range communication attracts attentions. Also, with therapid spread of compact terminal including smartphone, high speed data transmission in short range is required.
A short range MIMO (Multiple-Input Multiple-Output) [1, 2] has been proposed for extending the data-rate of the short range wireless communication, where
the channel capacity is enhanced by increasing the number of antennas at thetransmitting and receiving antenna. When the distance between the transmitting andreceiving array antennas is sufﬁciently short, the channel has low spatial correlation
characteristics even with line-of-sight (LOS) situation. As a result, the short range
MIMO offers a higher channel capacity than conventional MIMO does. In manystudies, the short range MIMO has been evaluated at a high frequency band such asa millimeter wave band since larger bandwidth is available. However, the propagation loss is serious in such high frequency band.
The near ﬁeld MIMO offers less propagation loss and high energy efﬁciency
due to near ﬁeld electromagnetic coupling since the distance between transmitting
and receiving antennas is shorter than the wavelength [3, 4]. However, theimpedances of the antennas are seriously affected by other antennas as well as
their feed networks in the near ﬁeld situation. Therefore, near ﬁeld MIMO cannot
use the conventional matching method based on only one side impedance ofantenna. The feed networks for near ﬁeld MIMO need to be designed iteratively
since it is necessary to consider the effect of feed network, which is connected tothe facing antenna [5]. Image impedance theory [6, 7] offers matching condition for
SISO (Single-Input Single-Output) considering effect of other antennas. However,further extension of the theory is needed for near ﬁeld MIMO.
In this letter, matching method, which can achieve matching of all port at thesame time by using image impedances theory, are proposed [8, 9]. Numericalanalysis and experimental results demonstrate the proposed matching method iseffective in enhancing the channel capacity of near ﬁeld MIMO. Also, it is foundthat the mutual coupling among the non-facing antennas does not affect the channel
capacity, which has not been well considered in [9].
2© IEICE 2015
DOI: 10.1587/comex.2015XBL0150
Received October 30, 2015
Accepted November 24, 2015
Published December 22, 2015

Matching method based on image impedance for near ﬁeld MIMO

Fig. 1 shows equivalent circuit of 2  2 near ﬁeld MIMO array. 2  2 near ﬁeld
MIMO array antenna system is treated as four port network. The signals transmitted388

IEICE Communications Express, Vol.4, No.12, 387–392

Fig. 1. The concept of the proposed methodfrom port 1 and 2 are received by port 3 and 4. In this ﬁgure, Z and Y represent
impedance and admittance matrices of antenna system, respectively. Zi1 and Zi3
represent the image impedances for designing matching network (MN) of port 1and 3, respectively. When we assume neighboring ports have a sufﬁciently low
mutual coupling with the exception of two facing antenna ports, MNs can be
designed using image impedance theory by focusing only on two facing antennas.
For example, when port 2 and 4 are terminated by Z0 represented reference forS-parameter, Zi1 and Zi3 are calculated byZi1 ¼1
G11 ðg þ jb Þ  jB11ð1Þ

Zi3 ¼

1
G33 ðg þ jb Þ  jB33

ð2Þ

where g , b are deﬁned asﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
s
ﬃ
G213
B213
1þ
g ¼
1þ
G11 G33
G11 G33

ð3Þ

Gpq ¼ ReðYpq Þ

G13 B13G11 B33
ðp ¼ 1; 2; 3; 4;

q ¼ 1; 2; 3; 4Þ

ð5Þ

Bpq ¼ ImðYpq Þðp ¼ 1; 2; 3; 4;

q ¼ 1; 2; 3; 4Þ

ð6Þ

b ¼

ð4Þ

where Ypq represents the element of Y. When input and terminate impedances ofport 1 and 3 are in the complex conjugate relation, matching can be achieved. Also
the matching conditions for ports 2 and 4 can be determined in the same manner.
Nevertheless, the MN design satisfying the above condition needs to be considered
as follows.
As shown in Fig. 1, MNs for two facing coupled ports are designed byneglecting other two facing ports because the terminated non-facing ports little
affect the matching condition due to small mutual coupling among them. When we
focus on one certain antenna port, the observed reﬂection coefﬁcient at the port isexpressed as¼© IEICE 2015
DOI: 10.1587/comex.2015XBL0150Received October 30, 2015
Accepted November 24, 2015
Published December 22, 2015

Zi  Z0Zi þ Z0ð7Þ

where Zi represent conjugate complex of the image impedance Zi . The facing ports
are assumed to be terminated by the image impedance element, and all other ports
are terminated by Z0 . When the MN is designed using Γ, S-parameter of the MN isdeﬁned as389

IEICE Communications Express, Vol.4, No.12, 387–392

SM ¼SM11SM12

SM21SM22!
:ð8Þ

The reﬂection coefﬁcient through the MN becomes
Sref ¼ SM11 þ SM12 ð1  SM22 Þ1 SM21 ¼ 0:

ð9ÞAlso, the design condition of MN is given by
SM22 ¼  :

ð10Þ

Additionally, the lossless MN satisﬁes
SM  SH
M ¼ I

ð11Þ

where the operation, fgH , is the complex conjugate transpose. From (9)∼(11), Sparameter of MN is calculated by
SM22 ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
SM12 ¼ 1  jSM22 j2 ejð12Þ

SM21 ¼ SM12

ð14Þ

SM11 ¼ SM12 ð

1

ð13Þ

1

 SM22 Þ SM21

ð15Þ

where θ is arbitrary value.
3Simulation(a)Simulation Model(b) S-parameters

Fig. 2.

© IEICE 2015
DOI: 10.1587/comex.2015XBL0150
Received October 30, 2015
Accepted November 24, 2015
Published December 22, 2015(c) Channel Capacity

Simulation results

Fig. 2(a) shows the antenna model in the simulation. An antenna system consists offour planar spiral antennas. This antenna element [10] is the square shaped spiralantenna printed on FR-4 substrate and the center frequency is set to 150 MHz. FR-4
substrate’s relative dielectric constant is 4.4. In this ﬁgure, element spacing d is
65 mm, and distance between transmitting and receiving antennas is D. S-parameterof this model is analyzed by the method of moments. The signals transmitted from
#1 and #2 are received by #3 and #4, respectively. Fig. 2(b) shows S-parameters of
this model by the numerical analysis when D is 10 mm. In the ﬁgure, solid lines andbroken lines represent the S-parameters with and without MNs respectively. The
conjugate image impedances were!
!
Zi1 Zi2
94:16 þ j201:5 94:14 þ j201:5¼;
ð16Þ
Zi3 Zi4
97:44 þ j204:0 97:66 þ j203:8390

IEICE Communications Express, Vol.4, No.12, 387–392

in this model. From this result, it can be seen that the proposed matching method
improves S11 signiﬁcantly and transmitting power S31 by 5 dB. Moreover, themutual coupling, S21 , is even lower than transmission between facing antennas, S31 .
Fig. 2(c) plots the channel capacity versus distance between transmitting andreceiving antennas. In this ﬁgure, solid line shows the channel capacity with theMN optimized for every distance, i.e. the MN is changed depending on D, dottedline shows the channel capacity with the MN designed only for D ¼ 10 mm, anddashed line shows the channel capacity without MN. The transmitting power is set
to 0 dBm, and noise power is −90 dBm. From this result, it can be seen the MN
improves channel capacity by 12 bits/s/Hz at maximum since SNR (Signal toNoise Ratio) is improved thanks to the MNs at all port. Also, it is found that MN
designed for 10 mm offers higher capacity than that without MN.
4Experiment(a) Experimental Model(b) S-parameter(Reflection S11 )(c) S-parameters(Transmission andcoupling)(d) Channel Capacity

Fig. 3.

© IEICE 2015
DOI: 10.1587/comex.2015XBL0150
Received October 30, 2015
Accepted November 24, 2015
Published December 22, 2015

Experiment results

Fig. 3(a) shows the photos of fabricated antennas and MN based on the proposed
matching method. Conﬁguration of the antenna system and antenna element forexperiment is same as condition of simulation. MNs were fabricated on FR-4
substrate, and consist of chip capacitors and inductors. The conjugate image
impedances of all ports are calculated by using the measured S-parameter of thefabricated antennas. The calculated image impedances were!
!
68:58 þ j123:6 86:16 þ j173:0
Zi1 Zi2¼
ð17Þ
Zi3 Zi4
57:44 þ j128:3 50:22 þ j133:1
and the MNs were designed from this result.
391

IEICE Communications Express, Vol.4, No.12, 387–392

Fig. 3(b) shows that the frequency characteristics of the measured reﬂection
characteristic S11 when D is 8.4 mm. In this result, reﬂection characteristics S11 areless than −10 dB at the center frequency when the MNs are used. Reﬂectioncharacteristics of other ports are also improved.
Fig. 3(c) shows that the experimental result of transmission and coupling
characteristics. This result indicates MN improves transmission, S31 . Moreover,the mutual coupling, S21 , is even lower than transmission, S31 , as with simulation
results.
Fig. 3(d) plots the channel capacity versus frequency between transmitting andreceiving antennas. The condition of calculating channel capacity is the same asthat of the simulation. From this result, it is found the proposed MNs improve thechannel capacity by 1.54 bits/s/Hz at the center frequency since reﬂection characteristics are improved.
5Conclusion

This paper has proposed matching method based on image impedances suitable fornear ﬁeld MIMO. Simulations and experiments showed that the proposed matching
method improves the channel capacity since reﬂection characteristics of all ports
are improved at the same time. Both simulation and experiment results demonstrated that the proposed method is effective in enhancing channel capacity of nearﬁeld MIMO.
Acknowledgments
This research was partially supported by JSPS KAKENHI (25709030).

© IEICE 2015
DOI: 10.1587/comex.2015XBL0150
Received October 30, 2015
Accepted November 24, 2015
Published December 22, 2015

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