IEICE TRANS. COMMUN., VOL.E100–B, NO.2 FEBRUARY 2017219

PAPER Special Section on Antenna and Propagation Technologies Contributing to Realization of Next Generation Wireless Systems

Wavelength Analysis Using Equivalent Circuits in a Fast and SlowWave Waffle-Iron Ridge Guide

Hideki KIRINO†a), Kazuhiro HONDA†, Members, Kun LI†, Student Member, and Koichi OGAWA†, Member

SUMMARY In this paper we use equivalent circuits to analyze the wave-lengths in a Fast and Slow wave Waffle-iron Ridge Guide (FS-WRG). Anequivalent circuit for the transverse direction is employed and the transverseresonance method is used to determine the fast wave wavelength. Anotherequivalent circuit, for the inserted series reactance in the waveguide, is em-ployed for the fast and slow wave wavelength. We also discuss the physicalsystem that determines the wavelengths and the accuracy of this analysis bycomparing the wavelengths with those calculated by EM-simulation. Fur-thermore, we demonstrate use of the results obtained in designing an arrayantenna.key words: waffle-iron, ridge, waveguide, fast wave, slow wave, wavelength,array antenna

1. Introduction

Our designation for a waveguide combining waffle-iron andridge structures, presented by us in references [1] and [2], isa Waffle-iron Ridge Guide (WRG). This is the same as theGap Ridge Waveguide (GRW) presented by other researchers[3]–[5]. The WRG, or GRW, has two metal plates. On oneof the plates, there are two-dimensional periodic arrays ofmetal rods on either side of the central ridge. The other metalplate has a flat surface, and is positioned such that there isan air gap between the two plates.

Feeding the circuits of array antennas, and guiding anddistributing RF signals to each antenna element are essentialfunctions, and these have typically been accomplished byemploying hollow waveguides and micro strip lines. How-ever, at frequencies around 100 GHz, hollow waveguides areunsuitable because many screws are needed to fix the upperand lower plates, and micro strip lines are unsuitable becauseof the dielectric loss and radiation from the waveguide. TheWRG (or GRW) has advantages in such frequency bands be-cause there is no contact between the upper and lower metalplates and the absence of a dielectric.

The fast and slow wave waffle-iron ridge guide (FS-WRG) uses a novel technique, in that it has periodic steps onthe ridge in order to shorten the wavelength in the WRG.

Generally, a rectangular hollow tube is used to rep-resent a waveguide, where the fundamental wavelength inthe waveguide is defined by the boundary conditions at thewaveguide walls. These days, EM-simulators are employedto accurately and very easily predict the outcome when de-

Manuscript received May 18, 2016.Manuscript revised September 20, 2016.†The authors are with University of Toyama, Toyama-shi, 930-

8555 Japan.a) E-mail: kirino.hideki@m.ieice.org

DOI: 10.1587/transcom.2016WSP0003

signing microwave and millimeter-wave devices includingwaveguides. On the other hand, before the advent of EM-simulators, scientists and engineers used many different the-oretical methods and formulas to optimize the configurationsof waveguides. An example, given in reference [6], is cal-culating the wavelength in a periodic structure similar to theWRG, where the transverse resonance method is employed.The authors point out that the accuracy of the calculation inthis case is determined by the formulas used to describe theperiodic structure. They also mention that, even with carefulselection of the formulas, the size and type of periodic struc-ture that can be analyzed may be limited. As stated above,EM-simulation is superior to theoretical methods such asthe transverse resonance method as it can be more easily andgenerally applied.

In this paper, we adopt the transverse resonance methodto analyze the wavelengths of the WRG and the FS-WRGin order to reveal the physical basis for the wavelengths.Although, the accuracy of the results is not guaranteed, weplan to use the results to predict variations that we can maketo the WRG and the FS-WRG, such as modulating the heightand arrangement of the waffle-iron rods, in order to widenthe frequency band or have dual frequency bands.

Furthermore, we use the results obtained to design anarray antenna. Even state of the art EM-simulators need aninitial configuration to begin the calculations. We demon-strate the design of an array antenna using the results ob-tained from the wavelength analysis to define the initial con-figuration, and then evaluate the result. The EM-simulatorused in this paper is Femtet from Murata Software.

2. Configuration of the FS-WRG

Figure 1 shows the configuration of a FS-WRG [7]–[9].There are waffle-iron regions on both sides of the ridge. Theheight of the waffle-iron rod is λ/4, where λ is wavelengthin free space. The upper and lower plates are not in contactand are separated by a gap of λ/8, which is determined bythe essential condition of preventing parallel plate propaga-tion in the waffle-iron region. By preventing propagationin the waffle-iron region, the RF signals propagate only onthe ridge. The waffle-iron rod sizes and the spaces betweenadjacent rods in the x- and y-directions are both λ/8. Thereare trenches on each side of the ridge of depth D from thetop of the ridge, and there are periodic steps of depth d onthe ridge that generate the slow wave.

There are no cut off frequencies in a WRG or a FS-WRG

Copyright © 2017 The Institute of Electronics, Information and Communication Engineers

220IEICE TRANS. COMMUN., VOL.E100–B, NO.2 FEBRUARY 2017

Fig. 1 Configuration of the FS-WRG.

Fig. 2 Set up for measuring the isolation between two parallel WRGswith N waffle-iron lines between them.

Table 1 Isolation between two WRGs arranged in parallel with N waffle-iron lines between them defined for ω/ωo = 0.83 to 1.1.

as there are in hollow waveguides. As described in the liter-ature [2], the propagation frequency band and the preventionof parallel plate mode characteristics can be evaluated byisolating two WRGs arranged in parallel with N waffle-ironlines between them. The set up for measuring the isolationis shown in Fig. 2, where a TEM wave is input in the normaldirection to the ridge and leaked to the other ridge. Theisolation with respect to N is given in Table 1.

3. Analysis of the Fast Wave

As mentioned in the previous section the periodic steps inFig. 1 are for generating the slow wave, so here we consider aconfiguration with d = 0, which is for the fast wave analysis ina WRG. As is generally known, the fast wave is the motionof the wavefront of a TEM wave tilted from the directionof the waveguide. A well-known conventional method for

Fig. 3 Relationships in transverse resonance and the equivalent circuit.

analyzing the fast wave is the transverse resonance method,which has also been employed in periodic structures [6].The left hand side of Fig. 3 shows the relationship betweenthe wavelength of the TEM wave, λ, and the wavelength ofthe fast wave, λ f , and an equivalent circuit for the WRGin transverse resonance. As shown in Fig. 3, there is anEquivalent Magnetic Boundary (EMB) on each side of theridge formed by waffle-iron rods with height λ/4. The phaseϕ is the only parameter used to evaluate the wavelength. InFig. 3, to make it easier to understand transverse resonancein a WRG, we introduce an Equivalent Short Wall (ESW),where the ESW is a virtual wall with phase shift π (or −π),the same as in a hollow waveguide. The relationship betweenthe wavelength and the distance between the EMB walls isthen given by

1λ2 =

1(λ + 2a)2 +

1λ2f

(1)

λ: Wavelength in free spaceλ f : Wavelength of the fast wavea: Distance between the EMB wallsEMB: Equivalent Magnetic BoundaryESW: Equivalent Short Wallϕ: Reflection phase of TEM wave in the transverse

directionZt : Equivalent impedance looking in the transverse di-

rectionZo: Signal source impedance for the TEM waveθ: Angle between the TEM wave and the waveguide

axiswhere all the parameters mentioned above correspond tothose in Fig. 3.

In Fig. 3, ϕ is the phase generated by the round tripbetween ESW and the centre of the ridge, where the TEMwave has been injected in the transverse direction from thecentre of the ridge. When we make the phase shift at theESW π rather than −π, and use β = 2π/λ, the phase ϕ isgiven by

ϕ = π − 2β(λ

4+

a2

)= −2π

aλ

(2)

where the range of ϕ is −2π < ϕ < 0. Having a phase shift

KIRINO et al.: WAVELENGTH ANALYSIS USING EQUIVALENT CIRCUITS IN A FAST AND SLOW WAVE WAFFLE-IRON RIDGE GUIDE221

Fig. 4 Field approximation in the WRG.

π at the ESW means the phase shift at the EMB is zero.Substituting a from Eq. (2) into Eq. (1), we obtain the

wavelength ratio λ f /λ in terms of ϕ as follows:

λ f

λ=

√√ 1

1 −(

ππ−ϕ

)2 (3)

The right hand side of Fig. 3 shows an equivalent circuit foranalyzing the fast wave. When the input impedance in thedirection of the transverse resonance at the centre of the ridgeis Zt as shown in the figure, the reflection phase ϕ can bewritten in another form as follows:

ϕ = Ang(Γ) (4)

Γ =Zt/Zo − 1Zt/Zo + 1

(5)

where Zo is the characteristic impedance of the parallel platewaveguide between the ridge and the upper plate, for whichthe width is infinite and the height is λ/8.

In order to obtain Zt , we use an approximation for thefield distribution in the WRG. Fig. 4 shows an illustration ofthe field in the WRG and an approximation to the field wherethe region S has been replaced by metal, with field lines nor-mal to the metal surface. Comparing Fig. 4(a) and Fig. 4(b),we find that the field distributions are similar because thereis almost no field in the region S and also no field in theregion S’, which justifies the use of this approximation.

To find Zt , we use this approximation to develop theequivalent circuit shown in Fig. 5. In Fig. 5, all the char-acteristic impedances of the transmission lines in each parthave the same value Zo because all the lines have the samedimensions when viewed as a parallel plate waveguide. Animportant point for obtaining Zt is how many waffle-ironlines are included in the equivalent circuit. In order to evalu-ate the effect of the number of waffle-iron lines, we analyzedthree equivalent circuits having open-ends at positions P1,P2 and P3 as shown in Fig. 5, where the boundary conditionexpressed by the reflection coefficient at P1 to P3 is “1”.

Fig. 5 Equivalent circuit in the transverse resonance direction.

Table 2 Parasitic reactance on the Ridge and the Waffle-iron.

Fig. 6 Wavelengths of the fast wave obtained using the equivalent circuitswhere the number of waffle-iron lines is three for EM-simulation.

In addition, we evaluated the effect of the parasitic reac-tance at the corners of the ridge and waffle-iron rods as shownin Fig. 5. The parasitic reactance values can be obtained fromthe simple equations given in Sect. 6.1 of Chapter 6 in refer-ence [10]. The values obtained for the dimensions in Fig. 1are given in Table 2.

Figure 6 shows the calculated wavelength ratio λ f /λusing the equivalent circuit in Fig. 5 as a function of trenchdepth D. As shown in Fig. 6, the curves calculated fromthe equivalent circuits tend to converge as the number ofwaffle-iron lines increases. In Fig. 6, the wavelength ratiodetermined by EM-simulation is also displayed. We can seefrom Fig. 6 that the wavelength ratio curves calculated fromthe equivalent circuits and that by EM-simulation have simi-lar trends. This result indicates that the transverse resonancemethod is effective for inferring the variations in the wave-

222IEICE TRANS. COMMUN., VOL.E100–B, NO.2 FEBRUARY 2017

length characteristics of the WRG when its size or shape ischanged. Moreover, the result means that the wavelengthcharacteristics can be predicted just by analyzing the reflec-tion characteristics in the transverse direction of the WRG.Understanding this is very important for our future workwhere we plan to propose new WRG variations in order, forexample, to widen the frequency band or have dual frequencybands.

The difference of the values to the EM-simulation isaround +15%. We consider that this difference is causedby rough approximations and adopting simple formulas forthe complex WRG structure. However, this accuracy is suf-ficient to apply to an initial design of EM-simulation. Thecurve when P3 is open-ended can be written in the followingpolynomial form.

λ f

λ= −49.23

(Dλ

)3+ 53.61

(Dλ

)2− 20.37

(Dλ

)+ 3.84

(6)

4. Analysis of the Fast and Slow Waves

Basically, propagation in the WRG is by the fast wave. Theslow wave function must be added to the WRG, and theanalysis of the slow wave is based on that of the fast wave.

In general, the slow wave effect can be obtained from aperiodic structure, which increases the equivalent length ofthe waveguide by inserting a series of inductances or shuntcapacitances into the waveguide. Fig. 7 shows cross sectionsand equivalent circuits of the FS-WRG, where Fig. 7(a) isfor d = 0 and Fig. 7(b) is for d , 0. As shown in Fig. 7(b),a periodic step with depth d (refer to Fig. 1) is equivalent toa line of impedance Zp terminated by a short. Therefore,under the condition that the parasitic reactance producedat a corner of the step shown in Fig. 7(b) is small enoughand d < λ/4, the equivalent reactance of the periodic stepbecomes inductive which generates a slow wave effect.

By focusing on the difference between the distributedreactance for d = 0 and d , 0, the wavelength ratio betweenthem can be expressed in terms of the distributed reactanceas follows:

λ f s

λ f=

√L f Cf

L f sCf s(7)

where λ f , L f and Cf are the wavelength, the distributedseries inductance and the distributed shunt capacitance perunit length for d = 0, respectively, while λ f s , L f s and Cf s

are those for d , 0. The distributed reactance due to L f s andCf s in Eq. (7) can be substituted by the average reactance inthe period T in Fig. 7. In order to determine the average reac-tance of the period T , the equivalent circuit is approximatedby that shown in Fig. 8. In Fig. 8 ZEL is the impedance of theperiodic step when looking in the −z direction from the topof the ridge and ZEC is the impedance for the approximationfrom Fig. 8(a) to Fig. 8(b). Using the approximate equivalent

Fig. 7 Cross sections and equivalent circuits of the FS-WRG.

Fig. 8 Approximate equivalent circuit for the periodic steps.

circuit in Fig. 8(b), Eq. (7) can be rewritten as follows:

λ f s

λ f=

√√√√√√ ∆L∆C(∆L2+

ZEL

jω

) (∆C2+

1jωZEC

) (8)

KIRINO et al.: WAVELENGTH ANALYSIS USING EQUIVALENT CIRCUITS IN A FAST AND SLOW WAVE WAFFLE-IRON RIDGE GUIDE223

where ∆C and ∆L are fragments of the distributed reactanceL f and Cf in a period of the periodic step T .

Equation (8) means that the wavelength ratio of the fastand slow waves to the fast wave λ f s/λ f , can be obtainedfrom ∆C, ∆L, ZEL and ZEC . From Eqs. (6) and (8), thewavelength ratio λ f s/λ is given by

λ f s

λ=λ f s

λ f·λ f

λ(9)

∆C and ∆L can be obtained as follows. We make an-other approximation that most of the electric field is confinedto the region G as shown in the upper-right hand side of Fig. 7.Using this approximation, ∆C is equal to the parallel platecapacitance of a λ/8 cube, which is given by

∆C = ε(λ/8)2

λ/8= ελ

8(10)

ε: permittivity of the air

The characteristic impedance, Z f , for the fast wave inFig. 7(a) is given by

Z f =

√∆L∆C

(11)

The height and width of the cross section in region Gare the same, and we can introduce a virtual initial value forZ f of Z f o = 120π which is the characteristic impedance ofa TEM wave propagating in the direction of the ridge. In theactual fast wave, however, the TEM wave propagates at anangle θ as shown in Fig. 3. Hence the magnetic field normalto the ridge, H ′, is given by

H ′ = H sin θ (12)

where H is the magnetic field of the TEM wave in free space.This means that Z f can be expressed in terms of the ratiobetween the wavelength of the fast wave and that in freespace as follows:

Z f =EH ′=

EH

1sin θ

= Z f o

λ f

λ= 120π

λ f

λ(13)

where E is the electric field of the TEM wave in free space.From Eqs. (10), (11) and (13) ∆L is given by

∆L = ελ

8

(120π

λ f

λ

)2(14)

We can obtain ∆C and ∆L from Eqs. (10) and (14).ZEL and ZEC in Eq. (8) can be obtained from the fol-

lowing considerations. The equivalent circuit of the periodicstep is a shorted transmission line in the −z direction withthe parasitic reactance as shown in Fig. 7(b) and Fig. 8. Wedenote the characteristic impedance of the shorted transmis-sion line of the periodic step by ZP . The cross section of theshorted transmission line is square with side length λ/8 andhas no metal sidewall. Therefore, the TEM wave propagatesin the shorted transmission line and Zp = 120π. In order to

Table 3 Parasitic reactance of the periodic steps on the ridge.

Fig. 9 Wavelength of the Fast and Slow wave, where the number ofwaffle-iron lines is three for the EM-simulation.

obtain the parasitic reactance, we employ an approximationZ f = ZP which is based on the fact that the dimensions ofthe cross sections are similar. With these considerations, theparasitic reactance values are obtained as shown in Table 3from equations given in reference [10].

Now we have Zp , d and the parasitic reactance inFig. 8(b), ZEL and ZEC can be calculated. Finally, the wave-length ratio λ f s/λ f can be calculated from Eq. (8) using thevalues of ∆C, ∆L, ZEL , ZEC and the parasitic reactance.

Figure 9 shows the wavelength ratio of the fast and slowwaves obtained using Eqs. (6), (8) and (9) as a function of thedepth of the periodic steps d. In Fig. 9, the wavelength ratiodetermined by EM-simulation is also displayed. The wave-length ratio curves calculated from the equivalent circuitsand by EM-simulation have similar trends, which verifiesthat the analysis using the equivalent circuits in Figs. 5 and 8is effective in order for us enough to predict the way in whichthe wavelength characteristics change with the shape of theridge surface in the FS-WRG. This is also important for ourfuture work on proposing new FS-WRG variations. In thecase of D = 0.25λ, the difference of the calculated valuesto the EM-simulation is between −5% and +7% which isimproved from that in the fast wave. We consider the reasonfor this improvement is that, the influence of rough approxi-mations and adopting simple formulas for the complex WRGstructure canceled each other between the calculations of thefast wave and the fast and slow wave.

In Fig. 9, we selected the curve for D = 0.25λ to usein our array antenna design in the following section. Theselected curve can be written in the following polynomialform.

224IEICE TRANS. COMMUN., VOL.E100–B, NO.2 FEBRUARY 2017

λ f s

λ= −61.33

(dλ

)3+ 11.03

(dλ

)2− 2.41

(dλ

)+ 1.13

(15)

5. Application to Array Antenna Design

In this section, as an example, we demonstrate the use ofEqs. (6) and (15) in designing an array antenna. If onlyin-phase excitation over a big aperture is needed, a longpyramidal horn is the best solution. A benefit of the arrayantenna is to reduce the thickness of the antenna. The greaterthe number employed in the array for the same aperture thethinner the antenna becomes. Increasing the number in thearray for the same aperture is equivalent to shortening thedistance between the element ports, which requires a shorterwavelength on the feed line. As mentioned in the abovediscussion, the benefit of a FS-WRG is its ability to shortenthe wavelength compared to that without trenches or periodicsteps. Therefore, we select a shorter element distance ofλ f s = λ rather than λ f by which the benefit of the arrayantenna is used.

In this paper, we demonstrate an example of an arrayantenna with two elements in series in which the aperture is2λ. The initial configuration of the feeding circuit for EM-simulation calculated using Eqs. (6) and (15) is shown in

Fig. 10 An example of an array antenna with two elements in series andthe initial configuration of the feeding circuit for EM-simulation calculatedusing Eqs. (6) and (15).

Fig. 10, in which D = 0.25λ and d = 0.06λ. The pyramidalhorns are outlined in Fig. 10. Therefore, the EM-simulationmodel used to obtain just the distribution characteristics tothe element ports can be represented by the structure with-out the lines showing the pyramidal horns. As shown inFig. 10, the shape of element ports in the model to obtain thedistribution characteristics are straight slots.

Figure 11 shows an equivalent circuit of the designgoal of an array antenna with two elements in series. Asshown in Fig. 11, the elements in the design goal are λ-length line sources in phase and of the same magnitude,which corresponds to the prepared initial configuration. Theimpedance has no reactance, such as for long pyramidalhorns, and the space between the elements is λ, which is thesame as in the initial configuration. The dashed line in Fig. 11encompasses the distribution circuit, which corresponds tothe EM-simulation model used to obtain the distributioncharacteristics, as explained above.

First, we calculated the distribution characteristics byEM-simulation as two vectors, one from the Input Port toElement Port 1 and the other from the Input Port to ElementPort 2. The vector of Element Port 1 is normalized by thevector of Element Port 2. The normalized vector is comparedto that of the Design Goal in Table 4.

Next we calculated the whole antenna configuration inFig. 10. In Fig. 12, two directivity curves are plotted. DesignGoal is the product of an array factor and an element factorin which the array factor is in-phase and the same magnitudeand the element factor is the directivity of a λ-length linesource. Whole Antenna directivity is the result of an EM-simulation of the whole antenna structure in Fig. 10 includingthe horns.

Fig. 11 Equivalent circuit of the Design Goal in the example application.

Table 4 Distribution difference of Element Port relative to Port 2 of thefeeding circuit without radiation elements.

KIRINO et al.: WAVELENGTH ANALYSIS USING EQUIVALENT CIRCUITS IN A FAST AND SLOW WAVE WAFFLE-IRON RIDGE GUIDE225

Fig. 12 Directivities of the Design Goal in Fig. 11 and the whole antennamodel in Fig. 10.

It can be surmised that the difference between the WholeAntenna directivity and the Design Goal directivity is gen-erated by the following effects.

i) The coupling reactance between the ridge and the horns.ii) The phase difference at the aperture of the short pyra-

midal horn.

As shown in Fig. 12, the difference between the direc-tion of the main lobe in the Whole Antenna directivity andthat of the Design Goal is around 5 degrees. This resultmeans that the remaining work for the designer is to adjustthe trench depth D and the periodic step depth d to approachthe Design Goal.

6. Conclusion

We proposed a new method using equivalent circuits foranalyzing the wavelengths in a WRG and a FS-WRG. Thetraditional transverse resonance method was also employedfor the fast wave. From this analysis we obtained informationsufficient for us to predict how the wavelength characteris-tics change when the shapes of the WRG or FS-WRG arechanged. This information will be very important for ourfuture work in which we intend to design new WRGs andFS-WRGs with, for example, wider or dual frequency bands.

We demonstrated the use of the results obtained in defin-ing an initial configuration for an array antenna design withtwo elements in series. This method makes the design workfor WRGs and FS-WRGs easier and faster.

References

[1] H. Kirino and K. Ogawa, “A 76 GHz phased array antenna usinga waffle-iron ridge waveguide,” EuCAP2010, C32P2-2, Barcelona,Spain, April 2010.

[2] H. Kirino and K. Ogawa, “A 76 GHz multi-layered phased arrayantenna using a non-metal contact metamaterial waveguide,” IEEETrans. Antennas Propag., vol.60, no.2, pp.840–853, Feb. 2012.

[3] P.-S. Kildal, E. Alfonso, A. Valero, and E. Rajo, “Local metamaterial-based waveguides in gaps between parallel metal plates,” IEEE An-tennas Propag. Lett., vol.8, pp.84–87, Sept. 2009.

[4] E. Pucci, A.U. Zaman, E. Rajo-Iglesias, P.-S. Kildal, and A. Kishk,“Losses in ridge gap waveguide compared with rectangular waveg-uides and microstrip transmission lines,” EuCAP2010, C32P1-5,

Barcelona, Spain, April 2010.[5] A.A. Brazález, E. Rajo-Iglesias, J.L. Vázquez-Roy, A. Vosoogh, and

P.-S Kildal, “Design and validation of microstrip gap waveguides andtheir transitions to rectangular waveguide, for millimeter-wave appli-cations,” IEEE Trans. Microw Theory Tech., vol.63, no.12, pp.4035–4050, Dec. 2015.

[6] A.A. Oliner and W. Rotman, “Periodic structures in trough wave-guide,” IRE Trans. MTT, vol.7, Issue 1, pp.134–142, 1959.

[7] H. Kirino and K. Ogawa, “Metamaterial ridged waveguides withwavelength control for array antenna applications,” ISAP Intl. Symp.4E2-1, Digest, 2012.

[8] H. Kirino and K. Ogawa, “A fast and slow wave combined-modemetamaterial ridged waveguide for array antenna applications,” Eu-CAP2013, CA02a.5, Gothenburg, Sweden, April 2013.

[9] H. Kirino and K. Ogawa, “Simplified wavelength calculations for fastand slow wave metamaterial ridged waveguides and their applicationto array antenna design,” ISAP2013, pp.597–600, 2013.

[10] N. Marcuvitz, Waveguide Handbook, McGraw-Hill, 1951.

Hideki Kirino received the B.S. degreesin electronic engineering from the University ofElectro-Communications in 1985. In 1985, hejoined Panasonic, where he was engaged in re-search and development on microwave and mil-limetre wave devices. From 1988 to 1998, he wasa research student in the University of Electro-Communications doing research on waveguides.He received the Paper Award from the Interna-tional Symposium on Antenna and Propagation2007, and also received the Best Paper Award

from the Institute of Electronics, Information and Communication Engi-neers (IEICE) Transactions of Japan, in Sep., 2009. He is a member of theIEICE and the IEEE. He is now a doctoral candidate in the University ofToyama.

Kazuhiro Honda received the M.E. andPh.D. degrees in electrical engineering from To-yama University, Toyama, Japan, in 1998 and2016, respectively. Dr. Honda is currently amember of the technical staff at Toyama Univer-sity, Toyama, Japan. His research interests in-clude compact antennas, diversity, adaptive, andMIMO antennas for mobile communication sys-tems, electromagnetic interaction between an-tennas and the human body. His research alsoincludes over-the-air testing for evaluating high-

speed communication systems and other related areas of radio propagation.He is a member of the IEICE and IEEE.

226IEICE TRANS. COMMUN., VOL.E100–B, NO.2 FEBRUARY 2017

Kun Li received his B.E. degree in Commu-nication Engineering from Nanjing University ofPosts and Telecommunications in 2011, and anM.E. degree in Electrical and Electronic Engi-neering from Toyama University, Toyama, Japan,in 2014. He is currently a D.E. student at ToyamaUniversity, where he is studying an over-the-airtesting methodology for body-area networks andMIMO systems. His studies also include hu-man vicinity polarization behavior and wearableantenna design for on-body radio link enhance-

ment. Mr. Li was the recipient of the IEEE AP-S Japan Student Award in2015. He is a student member of the IEEE and IEICE.

Koichi Ogawa received his M.S. degreein Electrical Engineering from Shizuoka Uni-versity in 1981. He received a Ph.D. degreein Electrical Engineering from the Tokyo Insti-tute of Technology in 2000. In 2005, he was aVisiting Professor with the Antennas and Prop-agation Division, Aalborg University, Denmark.Dr. Ogawa is currently a Professor at ToyamaUniversity, Japan.