IEICE TRANS. COMMUN., VOL.E99–B, NO.8 AUGUST 2016

1846

PAPER

Simultaneous Decoupling and Matching Technique for Short-Range
MIMO
Kentaro MURATA†a) , Naoki HONMA†† , Members, Kentaro NISHIMORI††† , Senior Member,
Naobumi MICHISHITA† , Member, and Hisashi MORISHITA† , Fellow

SUMMARY This paper presents a novel simultaneous decoupling andmatching technique for transmitting (Tx) and receiving (Rx) ports in shortrange multiple-input multiple-output (SR-MIMO) systems. The principal
diﬀerence with conventional decoupling and matching network (DMN) approaches is that the proposed technique considers strong mutual coupling
between closely-positioned Tx/Rx arrays, and the S-parameter variation
due to the presence of each other’s array. This technique has two stages;
first, 180-degree hybrid couplers are connected to both Tx/Rx ports ofa plane-symmetrical MIMO system. This decouples both Tx/Rx ports,
and moreover, channels between them are orthogonalized. That is, theMIMO system is transformed into multi orthogonalized single-input singleoutput (SISO) systems. Second, Tx/Rx ports of each orthogonalized SISO
system are simultaneously matched based on conjugate matching theory.
Consequently, the transmission power of the short-range MIMO system ismaximized. Numerical results show that the proposed technique realizes
higher channel capacity than the conventional DMN; indeed it achieves thetheoretically possible capacity. In addition to theoretical analyses, we provide an example for microstrip line (MSL) circuit implementation. This
MSL model oﬀers good simultaneous decoupling and matching performance yielding channel capacity comparable to that of an ideally-designed
circuit model. This validates the implementation feasibility of the proposed
technique.
key words: short-range MIMO, decoupling and matching network

1.

Introduction

Short-range communication is playing a key role in therealization of seamless connectivity, and data transfer between mobile and stationary devices is envisioned as one of
the main applications. In order to deal with Gbit/s-orderlarge-volume data sets such as movies and images, ultra
wide band (UWB) and millimeter-wave technologies areused that can increase the transmission capacity per unitof time [1]. A diﬀerent approach to enhancing frequency
utilization eﬃciency is short-range multiple-input multipleoutput (SR-MIMO) communication [2]–[4].
Literally, “short-range MIMO” is a MIMO techniqueintended for short-range communication wherein Tx/Rx arrays face to each other with line-of-sight (LOS) links. Its
usage scenarios include wall-the-through repeaters [5] andManuscript received October 29, 2015.
Manuscript revised March 19, 2016.
†
The authors are with Graduate School of Science and Engineering, National Defense Academy, Yokosuka-shi, 239-8686
Japan.
††
The author is with Faculty of Engineering, Iwate University,
Morioka-shi, 020-8551 Japan.
†††
The author is with Faculty of Engineering, Niigata University,
Niigata-shi, 950-2181 Japan.
a) E-mail: kentaro.murata@m.ieice.org
DOI: 10.1587/transcom.2015EBP3463

peer-to-peer communication between digital KIOSK andmobile terminals [6].
In our previous work, we focused on the characteristics of SR-MIMO, its propagation channels are uniquelydetermined due to its LOS configuration, and proposed ananalog-beamforming-based eigenmode transmission technique [7]–[9]. In this technique, by connecting 180-degreehybrid couplers (HCs) to both Tx/Rx sides of a planesymmetrical SR-MIMO system, the MIMO channels are orthogonalized into multi independent streams using only analog passive networks which greatly reduces hardware complexity.
However, while the channel characteristics of SRMIMO have been well analyzed, antenna characteristic
problems such as reflection and mutual coupling, all ofwhich can degrade channel capacity, have not been addressed. Solving these problems allows the maximum channel capacity of a SR-MIMO system to be realized.
A typical approach to improve the radiation eﬃciency
and envelope correlation of a MIMO array is the use of decoupling and matching networks (DMN) [10]–[16]. These
conventional DMN approaches assume that Tx/Rx arrays
exist in non-LOS (NLOS) and far field configurations asshown in Fig. 1(a). In such a case, the Tx/Rx S-parameters

Fig. 1

Assumed situations for conventional and proposed approaches.

c 2016 The Institute of Electronics, Information and Communication Engineers
Copyright ⃝MURATA et al.: SIMULTANEOUS DECOUPLING AND MATCHING TECHNIQUE FOR SHORT-RANGE MIMO

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are independent of the existence of the array on the otherside. Thus, Tx/Rx DMNs can be designed independently
based on only the Tx/Rx S-parameters, respectively. However, in short range communication, undoubtedly near field
as shown in Fig. 1(b), the Tx/Rx S-parameters are influenced by the strong mutual coupling between proximallypositioned Tx/Rx arrays. Hence, a conventional DMN
preliminarily-designed for each array does not work effectively, if anything, it may worsen performance due thematching condition on the other side. Such interaction between Tx/Rx arrays makes it diﬃcult to satisfy decoupling
and matching conditions on both sides simultaneously.
On the other hand, Roberts established the theory of
conjugate-image impedances, which allows simultaneous
matching at both Tx/Rx sides in the presence of mutual coupling [17] (A similar approach can be seen in [18] but witha diﬀerent mathematical presentation.) For reference, Inagaki applied this theory to wireless power transfer (WPT)
between inductively coupled coils to maximize transfer eﬃciency [19]. However, this concept is valid only for a twoport network, i.e. single-input single-output (SISO) systems, so it cannot be extended to MIMO systems directly.
In order to provide a comprehensive solution to theabove problems, we proposed the bidirectional matching
technique for SR-MIMO [20] by combining the aforementioned conventional ideas. This technique has two stages;
first, the SR-MIMO system is orthogonalized into several
SISO systems by HCs. Second, Tx/Rx ports are simultaneously matched by applying the conjugate image impedancetheory to each orthogonalized SISO system individually. Finally, the whole SR-MIMO system is fully matched.
As possible target scenarios of the proposed technique,we envision its application to the SR-MIMO systems operated in wireless data transfer and video streaming involving
mobile devices as shown in Fig. 2(a) and (b), respectively[21]. The proposed technique can overcome the following
negative factors faced in such applications, (i) strong mutual
coupling between multi-antennas closely packed in the mobile device and (ii) mismatching caused by the proximity of
the Tx/Rx MIMO arrays. As a consequence, it unleashes thepotential of SR-MIMO performance.

practical implementation were not mentioned.
This paper proposes an extended simultaneous decoupling and matching technique for SR-MIMO based on an
S-parameter analysis; the S-parameter-based approach iseﬃcient and simple to apply to the analysis of cascadeconnected networks [22]. Furthermore, insights on an extension to, at most, 8×8 SR-MIMO is given. Finally, an example of practical circuit implementation using microstriplines (MSLs) is presented to validate the feasibility of the
proposed technique.
Section 2 focuses on the theoretical aspects of the proposed technique. In Sect. 3, some numerical results are presented for a performance comparison between the proposedand conventional DMN techniques in terms of (i) simultaneous decoupling and matching eﬀects and (ii) channel capacity improvement. Section 4 concludes the paper withapplication prospects and challenges posed by the proposed
technique.
2. Theory of Proposed Technique
The proposed method is implemented in two steps: “portdecoupling and channel orthogonalization” and “simultaneous matching”. In this section, the theory of the proposed
method is explained step-by-step.
2.1 Port Decoupling and Channel Orthogonalization
In order to explain the basic theory, the 2×2 SR-MIMO system shown in Fig. 3(a) is considered for simplicity. In the
MIMO system, the ports from #1 to #2 and from #3 to #4

However, [20] considers only the theoretical aspect for
2×2 SR-MIMO, while extensions to more than 2×2 andFig. 2

Target scenarios of the proposed technique.

Fig. 3

Conceptual diagram of the S-parameter on each stage.

IEICE TRANS. COMMUN., VOL.E99–B, NO.8 AUGUST 20161848

are Tx/Rx ports, respectively. Here, we define Tx-Rx portpairs of #1 and #3, and #2 and #4, and the channel between
each port pair is defined as the “signal channel”, while thechannel between the non-corresponding ports is defined as
the “interference channel”. The S-parameter of the system
is defined as][
STT STRSMIMO =
(1)
SRT SRR S 11 S 12 S 13 S 14 
 S
S 22 S 23 S 24 =  21
 S 31 S 32 S 33 S 34 
S 41 S 42 S 43 S 44
where STT and SRR represent reflections and couplings at
Tx/Rx ports, respectively. STR and SRT , which represent thechannel matrices between Tx/Rx ports, are the transpose ofeach other. If the SR-MIMO array is configured symmetrically with respect to the reference plane that divides the array into two pairs of Tx/Rx antennas, submatrices STT , STR ,SRT and SRR in (1) become symmetrical. With regard to Tx
ports, reflections at ports #1, S 11 , and #2, S 22 , are equal andit is obvious that the couplings between them, S 12 and S 21 ,are equal because of the reciprocity of the S-parameter. Thatis also true for Rx ports. Furthermore, signal channels between facing ports #1 and #3, S 31 , and between #2 and #4,
S 42 , are equal as are the interference channels between diagonal ports #1 and #4, S 41 , and between #2 and #3, S 32 .
Taking these matters into consideration, all submatrices in(1) can be expressed in the form of
[
]
α β
(2)
β α
where α and β are complex constants.
Next, HCs are connected to both Tx/Rx ports of the
SR-MIMO system as shown in Fig. 3(b). The S-parameterof an HC, SHC , is expressed as[]
SHC,ii SHC,oi
SHC =
(3)
SHC,io SHC,oo
where index “i” and “o” denote “input” and “output”, respectively. Since neither reflection nor mutual coupling occurs at either the input or output of an ideal HC,
SHC,ii = SHC,oo = O2

(4)

where On denotes an nth-order zero matrix. The transmission matrices between inputs and outputs are
[
]
j
1 1
SHC,io = SHC,oi = − √(5)
2 1 −1
where the first and second column (or row) vectors correspond even and odd modes, respectively, and such matrix inthe brackets is known as the second-order Hadamard matrix.
When HCs connected to both Tx/Rx sides, the S-parameterof the whole MIMO system including HCs, S′MIMO , is expressed as

S′MIMO =[SHC,io STT SHC,oi
SHC,oi SRT SHC,oi

SHC,io STR SHC,io
SHC,oi SRR SHC,io

]
.

(6)

The derivation of the above equation is explained in Appendix A in the end of the paper. As a result, all submatrices in (6) are expressed as the product of the matrices having
the symmetric form of (2) and the transmission matrices ofTx/Rx HCs (given as (5)) in the form of
[
] [
]
[
]
j
j
1 1
α β
1 1
·
·−√
−√
(7)
β α
2 1 −12 1 −1
[
]
α+β
0
=−
0
α−β
and diagonalized. That means that both Tx/Rx ports are decoupled [14], and moreover, interference channels are canceled out [7]. Consequently, S′MIMO has regular sparsenessthat is expressed as ′
′
0 S 130 
 S 11
 0 S ′′ 
0 S 24 22
S′MIMO =  ′(8)′
0 S 330 
 S 31′′
0 S 420 S 44
where diagonal components in each ruled-oﬀ submatrix are
given by (8). From (8), it is found that light- and darkcolored parts form independent SISO systems between corresponding Tx-Rx port pairs. These first and second diagonal SISO systems correspond to even and odd modes of theHC, respectively. In this way, the first stage transforms the
MIMO system into two orthogonalized SISO systems.
This process seemingly has a negative impact, reducing channel capacity, since some channel components are′
eliminated. Moreover, S 41
is given as the subtraction between two constants in (8). However, the Frobenius normof the channel matrix, i.e. total transmission power, is actually constant before and after the process. This is because
the transmission matrix of HC, given as (5), is unitary, andso channel capacity is never changed by the process; that isproven in Appendix B.
2.2 Simultaneous Matching
Now that the two orthogonalized SISO systems are obtained, the conventional simultaneous matching theory canbe applied to each individually.
According to [23], when the reflection coeﬃcients of
Tx/Rx MNs that have their inputs or outputs terminated withreference impedances Z0 , are equal to the conjugates of thereflection coeﬃcients looking into an arbitrary SISO systemfrom the Tx side, ΓTx , and looking back at the Rx side, ΓRx ,respectively, as shown in Fig. 4, conjugate matching conditions are simultaneously satisfied at both Tx/Rx sides. In[23], if the S-parameter of a SISO system, SSISO , is definedas[]
S TT S TR
SSISO =
(9),
S RT S RR
equivalent reflection coeﬃcients ΓTx and ΓRx are given as

MURATA et al.: SIMULTANEOUS DECOUPLING AND MATCHING TECHNIQUE FOR SHORT-RANGE MIMO

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Condition of simultaneous matching for a SISO system.

Fig. 4√∗ B ± B2 − 4 |C |2 
Tx 
Tx

 Tx
ΓTx = 


2CTx

√
∗

 B ± B2 − 4 |C |2 
Rx 
Rx

 Rx
ΓRx = 


2CRx


(10)

where
BTx = 1 + |S TT |2 − |S RR |2 − |∆|2
BRx = 1 + |S RR |2 − |S TT |2 − |∆|2∗
CTx = S TT − ∆S RR∗
CRx = S RR − ∆S TT

.

(11)

In the above equations, A∗ and |A| denote conjugate and absolute of complex number A, respectively, and ∆ is the determinant of SSISO . Note that, in (10), the appropriate sign must
be chosen so that the absolute of each coeﬃcient falls in therange of 0 to 1. Furthermore, [23] discusses the maximum
gain, Gmax , when both Tx- and Rx-port mismatch losses arecompensated; it is expressed as
Gmax =

1
1 − Γ∗Tx

2|S TR |

2

1 − Γ∗Rx

2.

where reflections, mutual couplings and interference channels are completely eliminated, and only signal channels exist as shown in Fig. 3(c) and are maximized as expressed in
(12).

(12)

Next, the design method of MN that realizes the maximum gain in (12) is detailed. Here, let the S-parameter of
MN, SMN , be expressed as[]
S MN,ii S MN,oi
SMN =
.
(13)
S MN,io S MN,oo
Basically, there are two conditions that MN must satisfy.
The first is the above-mentioned conjugate matching condition, and the S-parameter components S MN,oo and S MN,ii ofTx/Rx MNs are given as
S MN,oo = Γ∗Tx for Tx MN.
S MN,ii = Γ∗Rx for Rx MN(14)

The second is a unitary condition that is expressed as
H
SMN
SMN = I2

on the above theory and then cascade-connecting them. The
S-parameter of the whole MIMO system, including HCs and
MNs, S′′MIMO , is expressed as


′′
S 13
0 


O2

′′
0 S 24 S′′MIMO = 
(16)
′′
0
 S 31
O
2′′
0 S 42

2.3 Extension to 4×4 and 8×8 SR-MIMO

2

1 − S RR Γ∗Rx

Fig. 5 Some practical configurations for application of the proposed
technique.

(15)

In Sect. 2, we discussed the basic theory of the proposed
technique for a 2×2 SR-MIMO case that is symmetrical respect to a certain plane as shown in Fig. 5(a). The above
discussion indicates that, if a SR-MIMO system can be divided into multiple orthogonalized SISO systems by HCs, it
is possible to apply the simultaneous matching process. In[7], it was proven that a rectangularly configured 4×4 SRMIMO system (as shown in Fig. 5(b)) that is symmetricalwith respect to vertical and horizontal reference planes canbe orthogonalized using four cascade-connected HCs forming a fourth-order-Hadamard-matrix weight. Furthermore,from the geometrical perspective, it is possible to orthogonalize, at most, an 8×8 SR-MIMO system having a cuboidal
configuration and three symmetry planes, in which Tx/Rxarrays are interwoven. Therefore, the proposed technique
can be extended, at most, to 8×8 SR-MIMO systems.
3. Numerical Results

H

where A denotes the Hermitian transpose of matrix A and
In is an nth-order identity matrix, and (15) indicates that the
MN is lossless. By satisfying (14) and (15), the amplitudesof all components in (13) are uniquely determined, also theirphases are related to each other having one degree of freedom [24].
In this way, each orthogonalized SISO system is simultaneously matched by designing the MNs individually based

A 2×2 SR-MIMO system consisting of very thin halfwavelength dipoles, see Fig. 5(a), is simulated wherein
Tx/Rx arrays face each other in complete LOS. Antennas
Tx/Rx1-2 correspond to Tx ports #1-#2 and Rx ports #3-#4,
respectively. For S-parameter calculation of the SR-MIMO
array, NEC2 is used [25].
In the rest of this paper, the structural symmetry of

IEICE TRANS. COMMUN., VOL.E99–B, NO.8 AUGUST 20161850

the system is assumed, and some S-parameters components
bearing a symmetrical relationship may not be mentioned to
avoid repetitive statements.
3.1
3.1.1

Frequency Responses
Simulation Condition

In this subsection, frequency characteristics are discussed.
In the simulation, center frequency fc is set to 2.5 GHz.
The analysis frequency range is ±0.5% from the normalized center frequency, so the analysis bandwidth, BW, is
25 MHz. As for array parameters, antenna spacing d andTx-Rx distance D are set to 0.1 λ and 0.25 λ, respectively. λis the wavelength of fc in free-space. For comparison, theS-parameter of only a single array, S, at fc without the otheris calculated as follows.
[]−6.28∠41.5 −11.2∠−82.0
S=dB∠deg.
(17)−11.2∠−82.0 −6.28∠41.5
3.1.2

Four Analysis Cases

To evaluate the simultaneous decoupling and matching effects yielded by the proposed technique, the following fourcases are examined.
(i) Without DMN: The first case, defined as “w/o DMN”,
applies neither decoupling nor matching technique. In theabove condition, the S-parameter submatrices of the SRMIMO system at fc are calculated as[]−5.38∠72.3 −15.9∠−65.2
STT =dB∠deg (18)−15.9∠−65.2 −5.38∠72.3[]−5.50∠−35.4 −21.4∠−112.1
STR =dB∠deg. (19)−21.4∠−112.1 −5.50∠−35.4
The most important point is that STT is varied from (17) due
to the presence of the Rx array.
(ii) With conventional DMN: The second case, definedas “Conv.”, applies conventional multiport-conjugate-match(MCM) DMN [10]–[12]; basically, the MCM-based approach can be universally applied to any MIMO antennas
without specific requirements.
The DMN is designed based on the S-parameter of onlya single array expressed as (17). In this paper, we use a typical DMN configuration consisting of susceptances as shownin Fig. 6(a) [13]. Although there should originally be twomore susceptances between inputs and between outputs (indicated by the dotted lines), they can be eliminated by optimization; in fact, the MCM approach provides infinite degrees of freedom in terms of circuit design. The values ofsusceptances B1 ∼B8 are shown in Table 1; a capacitor isused if the susceptance is positive, while an inductor is used
if it is negative. For port correspondence, OUT1 and OUT2of the DMN are connected to antennas Tx1 and Tx2, respectively. Its IN1 and IN2 correspond to Tx ports #1 andFig. 6

Table 1

Conventional DMN.

Susceptances of conventional DMN in mS.

B1

B2

B3

B4

B5

B6

B7

B8

9.44

9.44

13.7

−13.7

7.16

−14.4

−20.3

−32.6

#2, respectively. Likewise, the same DMN is also connectedto the Rx array. The S-parameter characteristics when the
DMN is used are shown in Fig. 6(b). Note that only the Tx
array is considered in the simulation. From the figure, theDMN enables perfect decoupling and matching at fc .
(iii) With proposed DMN with ideal implementation: The
third case, defined as “Ideal”, employs the proposed technique implemented with ideal circuit design as shown in
Fig. 7.
The transmission-line (TL) rat-race HC (Fig. 7(a)) operates ideally as expressed (4) and (5) at fc . However, it
is frequency-dependent due to the fixed √TL length while its
characteristic impedance is constant at 2Z0 (Z0 is 50 Ω).
Taking the Tx side as an example, OUT1 and OUT2 of the
HC are connected to antennas Tx1 and Tx2, respectively. Its
IN1 and IN2 correspond to even and odd modes of the hybrid, and diﬀerent MNs are individually designed for eachmode.
As the simplest MN configuration, the L-section
inductor-capacity (LC) MN (Fig. 7(b)) is used. The values

MURATA et al.: SIMULTANEOUS DECOUPLING AND MATCHING TECHNIQUE FOR SHORT-RANGE MIMO

1851

Fig. 7

Ideal circuit model.

of inductor L and capacitor C of the even- and odd-mode
MNs are determined to satisfy the simultaneous matchingcondition as explained in Sect. 2.2 and listed in Table 2(a).
The inputs of the even- and odd-mode MNs correspond to
Tx ports #1 and #2, respectively. While inputs and outputsof the HC are reversible due to the symmetrical circuit configuration, attention should be paid to the orientation of the
MN at the Rx side; should we follow the connection ruleshown in Fig. 4, IN and OUT of the MN shown in Fig. 7(b)must be switched on the Rx side.
(iv) With proposed DMN with practical implementation:
The fourth case, defined as “Prac.”, also employs the proposed technique but a more practical MSL circuit arrangement is used as shown in Fig. 8.
Figure 8(a) and (b) show a MSL rat-race HC andsingle-shunt MN, respectively. They are individually assumed to exist on an infinite dielectric substrate with thickness of 1.56 mm, permittivity of 2.2 and dielectric tangentof 0.0008. For MSL analysis, IE3D is used [26] and circuit
parameters are optimized. The width and length of the ratrace ring are as shown in the figure, and design parametersof the MN are shown in Table 2(b). For comparison with theideal HC, the S-parameter submatrices, S′HC,ii and S′HC,io , ofthe practical one at fc are as follows.
[]−38.8∠87.9 −57.3∠39.1′
SHC,ii =dB∠deg(20)−57.3∠39.1 −44.2∠128.8[]−3.14∠0−3.12∠0.24
S′HC,io =dB∠deg (21)−3.12∠0.07 −3.13∠179.9
where the phases in (21) are normalized by that of the upperleft element. The above equations indicate that reflections
and mutual coupling at inputs are suﬃciently reduced. Also,
the transmission matrix of (5) is realized with slight loss
and phase error. However, the S-parameter submatrices of
the SR-MIMO system cannot be strictly diagonalized as expressed in (8) by the practical HC. In the practical model, thesimultaneous matching conditions are derived without consideration of the slightly-remaining mutual coupling and interference channel components between the diﬀerent-mode
SISO systems.
To evaluate the design accuracy of the practical MNs,
the following two parameters are defined, see also Table 3.
ρ=′
S MN,ooΓ∗TxPractical circuit model.

Fig. 8(22)

Design parameters of MNs.

Table 2(a) Ideal LC MN.

Even
Odd

(b) Practical MSL MN.

L [nH]

C [pF]

Unit: mm

w

l1

l2

l3

3.06
5.40

0.924
1.22

Even
Odd

5.40
4.21

11.2
11.9

8.05
14.4

3.04
3.85

MSL MN characteristics at center frequency.

Table 3

Even
Odd

Ploss = 1 −ρ [dB∠deg]

Ploss [dB]

−0.02∠0.05
0.03∠−0.15

−19.1
−21.0

1 ′ 2
S
2 MN F(23)′
where S MN,oo
is an element of the S-parameter matrix, S′MN ,of the practical MN, and || A||F is the Frobenius norm of matrix A. The first parameter ρ indicates how much the simultaneous matching condition of (14) is satisfied. When ρ = 1(antilog), the condition is perfectly satisfied. The second parameter Ploss indicates losses generated by the practical MN
but does not include mismatching loss. The factor 1/2 isfor normalization. Ploss = 0 (antilog) means that the unitarycondition given as (15) is satisfied, i.e. the MN is lossless.
From the table, both even- and odd-mode MNs can be designed with high accuracy and small loss.

Regarding the second, third and fourth cases, the Sparameter of the whole SR-MIMO system including the circuit part is rigorously computed by cascade-connecting theTx/Rx arrays and the circuits in post-processing based on(A· 2) as detailed in Appendix A.

3.1.3 S-Parameter Characteristics
Figures 9(a), (b), (c) and (d) show the frequency responsesof mutual coupling, interference channel, reflection and signal channel, respectively. In the figures, the aforementioned
four-case characteristics are displayed with diﬀerent line
types. For quantitative understanding, those at fc are organized in Table 4.
First, mutual coupling, S 12 , and interference channel,
S 41 , characteristics are considered. From the figures, thoseof the ideal model are completely suppressed at fc as ex-

IEICE TRANS. COMMUN., VOL.E99–B, NO.8 AUGUST 2016

1852

Fig. 9

Table 4

Fig. 9(a)
(b)
(c)
(d)

Frequency responses of S-parameter.

S-parameter components at center frequency.

Unit: dB

w/o DMN

Conv.

Prac.

Ideal

Theor.

S 12
S 41
S 11
S 22
S 31
S 42

−15.9
−21.4
−5.38
−5.38
−5.50
−5.50

−∞
−∞
−11.4
−6.63
−4.76
−4.37

−48.9
−47.2
−36.1
−33.7
−4.28
−2.57

−∞
−∞
−∞
−∞
−3.72
−1.64

−∞
−∞
−∞
−∞
−3.72
−1.64

pressed in (8). Although those of the practical model cannot
be completely reduced due to the design error of the MSL
HC, they remained below −40 dB or so over the analysis
range of frequencies. Other interesting point is that conventional model also allows perfect decoupling and interference
channel suppression despite the S-parameter variation due tothe presence of the opposite array. This can be interpreted
as follows; turning back to the conventional DMN configuration shown in Fig. 6, if a current is imposed on IN1, it
is equally distributed to OUT1 and OUT2 in phase because
susceptances B1 and B2 are equal as shown in Table 1. On
the other hand, if a current is imposed on IN2, out-of-phasecurrents are observed at the outputs because B4 has opposite
sign to B3 causing a 180-degree phase delay. In this way, thetwo orthogonal excitation weights are formed by the DMN,
i.e., the same principle as eigenmode decoupling [14] andchannel orthogonalization is realized by using HC [7].
We turn to the reflection characteristics. The figure
clarifies the defining diﬀerence between conventional andideal models; while the conventional model does not work
properly, the ideal model oﬀers perfect matching. This, theprimary feature of the proposed technique, is due to the presence of the opposite array. The practical model also reducesreflections to under −30 dB at fc . However, the matching eﬀect by the proposed technique is noticeably degradedwith frequency shift. Such severe frequency dependency
is considered to be due to the high Q factor of the array
resulting from the proximity of multi-antennas, which canbe only mitigated by increasing antenna spacing or reducing number of antennas [27]. In particular, it is found thatthe matching bandwidth of S 22 is narrower than that of S 11 .
As mentioned before, the Tx ports #1 and #2 correspondto even and odd modes of the connected HC. According to[28], odd-mode excitation naturally has high-Q characteristic causing a narrow bandwidth due to the relationship ofQ ∝ 1/BW [29]. However, the practical model holds reflections lower than those without DMN over the bandwidth of
1%; the bandwidth is comparable to a channel width specified in IEEE 802.11n (20 MHz at 2.4 GHz band), one of thecurrent WLAN standards [30].
Next, we discuss signal channel characteristics. At fc ,the ideal model exactly matches the theoretical values of theMURATA et al.: SIMULTANEOUS DECOUPLING AND MATCHING TECHNIQUE FOR SHORT-RANGE MIMO

1853

maximum gains expressed in (12) (plotted with star marker
as “Theor.”). Because of the design error and losses of MSL
HCs and MNs, S 31 and S 42 of the practical model are degraded by −0.56 dB and −0.93 dB, respectively, comparedto the ideal model. Yet, they are still 1.22-dB and 2.93dB larger than those without DMN and also surpass thoseachieved by the conventional DMN.
The above results verify the simultaneous decoupling
and matching eﬀects oﬀered by the proposed techniques.
3.1.4

Channel Capacity

This subsection evaluates channel capacity characteristics.
Channel capacity C ( f ) per unit frequency at f is calculated
based on Shannon’s theorem as
C ( f ) = log2 I NRx +S NR
SRT ( f ) SRT ( f )H .
NTx

(24)

where channel matrix SRT ( f ) is a function of frequency f ,and | A| is a determinant of matrix A. In the above equation,
both Tx/Rx port numbers NTx and NRx are 2, and the signal
to noise ratio, S NR, is 20 dB. Channel capacity with bandwidth BW is calculated by integrating (24) over the analysis
frequency range as∫
CBW =C ( f ) d f.
(25)
BW

Figure 10 plots channel capacity characteristics versus
normalized frequency. Table 5 shows channel capacities atthe center frequency, C( fc ), and with bandwidth, CBW . From
the table, C( fc ) of the ideal model completely matches thetheoretical value calculated from maximum gains expressedby (12). These capacities are 21.8-% higher than that without DMN. As previous results showed, the practical modelcannot match the ideal model’s performance, but it yields

15.8-% and 8.61-% larger capacities than without DMN andwith conventional DMN, respectively. From the bandwidth
evaluation, the capacity of the practical model exceeds those
without DMN and with conventional DMN by 11.5% and4.41%, respectively; this superiority of the practical modelover the conventional DMN model is expected to increase
given the latter’s lossy factors. These results prove the effectiveness of the proposed technique in terms of channel
capacity improvement. Consequently, the practical implementation feasibility of the proposed technique has been
demonstrated.
Although we only dealt with the simple L-shape MNs
in this paper, there are much more options considering thefollowing factors;• the arbitrarily-settable phase in the S-parameter of the
MN mentioned in Sect. 2.2• the network topology, e.g. configuration types such as
T- and π-shape, and connection types such as serial andparallel
The frequency characteristic might be improved by optimizing these factors.
3.2 Array Parameter Characteristics
This subsection evaluates performances at fc versus somearray parameters for all models. In the following analyses, conventional DMN is optimally constructed for a single array with arbitrary antenna spacing. Also, for the ideal
model, optimal circuit parameters of MN are adaptively chosen depending on both antenna spacing and Tx-Rx distance.
On the other hand, the practical model uses the same fixed
networks as shown in Fig. 8 designed for d = 0.25 λ and
D = 0.1 λ; these values are defined as reference spacing anddistance, respectively.
3.2.1 Impact of Antenna Spacing

Fig. 10Channel capacity versus normalized frequency.

Table 5C ( fc ) [bit/s/Hz]
CBW [Mbit/s]

Channel capacity.

w/o DMN

Conv.

Prac.

Ideal

Theor.

7.90
197

8.42
210

9.14
219

9.62
226

9.62
-

First, channel capacity versus antenna spacing is plotted inFig. 11. In the simulation, antenna spacing d is changed
from 0.01 λ to 2.0 λ while Tx-Rx distance D is fixed at 0.1 λ.
The figure shows that the ideal model always realizes
the capacity equivalent to the theoretical value, and outperforms the others over the whole analysis range. In particular, it is noteworthy that, although the capacity without
DMN drops as antenna spacing becomes smaller than approximately 0.25 λ, that of the ideal model increases, a stark
contrast. The other interesting characteristic is that capacities periodically fluctuate and finally converge on certain
values. This can be explained by referencing the eigenmodecharacteristics of the channel matrix as shown in Fig. 12,
where bold and dot lines indicate even and odd modes, respectively. This figure shows the following three key points.
• When antenna spacing is extremely small, strong mutual coupling and mismatching arise at Tx/Rx arrays
resulting in eigenvalue degradation. Also, channel

IEICE TRANS. COMMUN., VOL.E99–B, NO.8 AUGUST 2016

1854

Fig. 11

Channel capacity versus antenna spacing.

Fig. 13Channel capacity versus Tx-Rx distance.

the best in term of SNR.
• In such LOS MIMO communication, a full-rank
MIMO channel with two identical eigenvalues can begenerated by optimizing array parameters as proven in[32]–[34]. In fact, such points can be found in the
figure and capacity peaks appear near these optimal
points.

Fig. 12

Eigenvalue versus antenna spacing.

components are highly correlated leading to a rankdeficient MIMO channel, all of which limit MIMO performance.
On the other hand, the eigenvalues of the ideal model(especially the odd mode) contrastingly increase as antenna spacing approaches zero; it can be regarded as the“supergain”, or “superdirectivity”, phenomenon that
accomplishes much higher gain than that based on theclassic array theory when antenna spacing is infinitesimally small and adjacent antennas have oppositely directed currents [31].
In the proposed technique, such out-of-phase current
distribution is induced by odd-mode excitation using
the HC. Though such a small spacing incurs high mutual coupling, the HC can actually isolate the antenna
ports, and they are fully matched by the MN. In thisway, the ideal model theoretically satisfies the aforementioned condition, and maximizes channel capacity
by counteracting the strong mutual coupling and mismatch.
• When antenna spacing is suﬃciently large, the MIMO
system can be regarded as two independent SISO systems between facing Tx/Rx pairs. Hence, the two
eigenvalues finally become equal and channel capacity converges to twice the capacity of one SISO link.
However, cross channel components are completely diminished so infinite antenna spacing is not necessarily

Focusing on the practical model, it keeps the capacity
improvement eﬀect to some extent and outperforms the conventional DMN in the range between 0.09 λ and 0.57 λ evenwith the fixed network configuration. However, while it iscomparable to the conventional DMN for wider spacing, its
performance deteriorates sharply when antenna spacing is
extremely small since the S-parameter of the array rapidlychanges in this region.
3.2.2 Impact of Tx-Rx Distance
Channel capacity versus Tx-Rx distance is plotted in Fig. 13.
In the simulation, D is varied from 0.01 λ to 0.5 λ while d isfixed to 0.25 λ.
As the previous result shows, the ideal model has perfect agreement with the theoretical values. In contrast, thecapacity with conventional DMN drops below that without DMN when D is smaller than 0.1 λ. This is because the Tx/Rx antennas are already strongly-coupled andsuﬃciently-separated SISO links are established even without any decoupling countermeasure. However, when D islarger than approximately 0.25 λ, capacities of the ideal andconventional DMN models become equal. In this region,
coupling between Tx/Rx arrays are negligibly, and it becomes unnecessary to consider the presence of the opposite
array when designing the DMN.
From these results, the proposed technique is eﬀective when antenna spacing and Tx-Rx distance are less thanquarter-wavelength, i.e. near field communication (NFC)
applications.
Finally, focusing on the practical model, its eﬀective
range where “Prac.” outperforms “Conv.” and “w/o DMN”
is more limited between 0.06 λ and 0.13 λ; it is an unavoidable barrier for the passive networks.

MURATA et al.: SIMULTANEOUS DECOUPLING AND MATCHING TECHNIQUE FOR SHORT-RANGE MIMO

1855

In the proposed technique, the first process using theHCs is valid regardless of the array parameters such as antenna spacing and Tx-Rx distance under the condition thewhole SR-MIMO configuration is plane-symmetrical [7].
However, the problem lies in the second process using the
MNs, which is influenced by the variations of the array parameters. As a promising solution for this problem, automatic matching control using variable circuit elements that
responds to the array parameter variations is recommended
for greater practicality [35].
4.

Conclusion

This paper proposed a simultaneous decoupling and matching technique for Tx/Rx ports of SR-MIMO systems. The
first process establishes parallel SISO links using hybrids
and the second oﬀers simultaneous matching in each SISO
link which maximizes channel capacity. In the sense thatthe proposed technique fulfills both requirements, signaland-power separation and eﬃciency enhancement, this idea
is also applicable to simultaneous wireless information andpower transfer [36].
Numerical analyses of 2 × 2 SR-MIMO were introduced to investigate the proposed and conventional DMN
approaches in terms of (i) simultaneous decoupling andmatching eﬀects and (ii) channel capacity improvement.
The results confirmed the advantage of the proposed technique given very close arrays as are common in NFC applications. Also, the successful capacity enhancement by the
MSL model indicates the implementation feasibility of the
proposed technique.
Experimental evaluations are required as the next stepin verifying its eﬀectiveness with more realistic RF hardware configurations in actual environments. Last but notleast, the proposed technique is very sensitive to the positional error and highly frequency-dependent, so its robustness against such factors especially needs to be evaluated;these issues will be tackled in our future research.
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Appendix A:

Derivation of (6)This appendix derives the S-parameter expression ofcascade-connected networks given as (6). We assume thatthree arbitrary networks A, B and C, and their S-parameters
are expressed as[]
SX,ii SX,io
SX =(A· 1)
SX,oi SX,oo
where index “X” is replaced A, B or C indicating network
sign.
When networks A and B are cascade-connected asshown in Fig. A· 1(a), the complete S-parameter is given as(A· 2) at the bottom of this page. Equation (A· 2) is a modified version of the expression shown in [22] (the original
expression is somewhat complicated due to confusing port
definition.) Also, same expressions can be seen in [10] and[11].
Specifically, in the case that network A has neither reflection nor coupling at its inputs and outputs, i.e. SA,ii andSA,oo are zero matrices, (A· 2) can be expressed more simplyas[]SA,io SB,ii SA,oi SA,io SB,ioS=(A· 3).
SB,oi SA,oi
SB,ooFrom the above equation, the rules of the cascadeconnection in this situation are summarized as follows.
[
S=

(
)
SA,ii + SA,io I − SB,ii SA,oo −1 SB,ii SA,oi()−1
SB,oi I − SA,oo SB,ii SA,oi

Fig. A· 1

Cascade-connected multiple networks.

With regard to the S-parameter of the cascadeconnected networks,• the reflection-and-coupling submatrix at the ports
with the matched-and-decoupled network connected issandwiched by its transmission matrices from both left
and right sides.
• the reflection-and-coupling submatrix at the other ports
remains unaltered.
• the transmission submatrices between inputs and outputs of the whole system are expressed by multiplexing the transmission matrices of the two networks. The
order of matrix multiplication depends on from whichside the matched-and-decoupled network is connected.
Based on the above rules, when three networks A, B,
and C are cascade-connected as shown in Fig. A· 1(b), andnetworks A and C have neither reflection nor mutual coupling, the complete S-parameter of the whole system isgiven as[]SA,io SB,ii SA,oi SA,io SB,io SC,ioS=.
(A· 4)
SCoi SB,oi SA,oi SC,oi SB,oo SC,io
Again, the ports of the ideal hybrid are perfectly
matched and decoupled. Thus, (6) is justified in the proposed technique.
Appendix B:

Channel Capacity with Ideal HCs

The channel matrix when the HCs are connected to Tx/Rx
sides, S′RT , is expressed as
S′RT = SHC,oi SRT SHC,oi(A· 5)

as derived in Appendix A.
Based on Shannon’s theorem, the channel capacity of
the 2×2 MIMO system after the HCs are connected is calculated as]()
SA,io I − SB,io SA,oo −1 SB,io()−1.
SB,oo + SB,oi I − SA,oo SB,ii SA,oo SB,io(A· 2)MURATA et al.: SIMULTANEOUS DECOUPLING AND MATCHING TECHNIQUE FOR SHORT-RANGE MIMO1857

S NR ′ ′H(A· 6)S S
2 RT RTS NR
H
H H= log2 I2 +SHC,oi SRT SHC,oi SHC,oi
SRT
SHC,oi .
2

C = log2 I2 +H
Remember that SHC,oi is unitary, i.e. SHC,oi SHC,oi= I2 . Thus,
the above equation is rewritten as

S NR
H
H H
C = log2 SHC,oi SHC,oi+
SHC,oi SRT SRT
SHC,oi (A· 7)
2
(
)
S NR
H
H
= log2 SHC,oi I2 +SRT SRT
SHC,oi.
2

Naoki Honma
received the B.E., M.E., andPh.D. degrees in electrical engineering from Tohoku University, Sendai, Japan in 1996, 1998,
and 2005, respectively. In 1998, he joined the
NTT Radio Communication Systems Laboratories, Nippon Telegraph and Telephone Corporation (NTT), in Japan. He is now working for
Iwate University. He received the Young Engineers Award from the IEICE of Japan in 2003,
the APMC Best Paper Award in 2003, the Best
Paper Award of IEICE Communication Society
in 2006, and the APMC Best Paper Award in 2014, respectively. His current research interest is MIMO antennas for high-speed wireless communication systems.

Further, by the use of following two fundamental theoremsof determinants;• the determinant of the product is equal to the productof the determinants, i.e. | AB| = | A| |B|• the product of the determinants is commutative, i.e.
| A| |B| = |B| | A|
where A and B are square matrices of the same order, (A·7)
is factorized as
S NR
HH
SRT SRT
SHC,oi2S NR
H
H= log2 SHC,oi SHC,oi
SRT SRT.
I2 +2

C = log2 SHC,oi I2 +(A· 8)H
Again, SHC,oi SHC,oi= I2 , so the first determinant term in theabove equation becomes one. Finally, we obtainC = log2 I2 +S NR
HSRT SRT,2(A· 9)

which is exactly the same as the channel capacity of the 2×2
MIMO system before the HCs are connected. Hence, channel capacity is constant before and after the HCs are connected.

Kentaro Murata
received the B.E. and M.E.
degrees in electrical and electronics engineeringfrom Iwate University, Morioka, Japan in 2011
and 2014, respectively. He is currently working
toward the Ph.D. degree with Graduate Schoolof Science and Engineering, National Defense
Academy of Japan, Yokosuka, Japan. His current research interests include feeding methods
for multiple-input-multiple-output antenna systems.

Kentaro Nishimori
received the B.E., M.E.
and Ph.D. degrees in electrical and computer engineering form Nagoya Institute of Technology,
Nagoya, Japan in 1994, 1996 and 2003, respectively. In 1996, he joined the NTT Wireless Systems Laboratories, Nippon Telegraph and Telephone Corporation (NTT), in Japan. He was senior research engineer on NTT Network Innovation Laboratories. He is now associate professor in Niigata University. He was a visiting
researcher at the Center for Teleinfrastructure(CTIF), Aalborg University, Aalborg, Denmark from Feb. 2006 to Jan.
2007. He was an Associate Editor for the Transactions on Communications for the IEICE Communications Society from May 2007 to May 2010
and Assistant Secretary of Technical Committee on Antennas and Propagation of IEICE from June 2008 to May 2010. He received the Young
Engineers Award from the IEICE of Japan in 2001, Young Engineer Award
from IEEE AP-S Japan Chapter in 2001, Best Paper Award of SoftwareRadio Society in 2007 and Distinguished Service Award from the IEICE
Communications Society in 2005, 2008 and 2010. His main interests are
spatial signal processing including MIMO systems and interference management techniques in heterogeneous networks. He is a member of IEEEand IEICE. He received IEICE Best Paper Award in 2010.

Naobumi Michishita
received the B.E.,
M.E. and D.E. degrees in electrical and computer engineering from Yokohama National
University, Yokohama, Japan, in 1999, 2001,
and 2004, respectively. In 2004, he was a research associate at the Department of Electrical and Electronic Engineering, National Defense Academy, Kanagawa, Japan, where he iscurrently an associate professor. From 2006 to
2007, he was a visiting scholar at the Universityof California, Los Angeles. His current researchinterests include metamaterial antenna and electromagnetic analysis. He
is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), Japan. He is also members of the Japan Society
for Simulation Technology and the Institute of Electrical and Electronics
Engineers (IEEE). He was the recipient of the Young Engineer Award presented by the IEEE Antennas and Propagation Society Japan Chapter andthe IEICE, Japan (2004 and 2005). He received the best paper award andthe best tutorial paper award from the IEICE Communication Society in2013 and 2014, respectively.

IEICE TRANS. COMMUN., VOL.E99–B, NO.8 AUGUST 2016

1858

Hisashi Morishita
received the B.S. degree in Electrical Engineering from National
Defense Academy of Japan in 1980, the M.S.
and Ph.D. degrees from University of Tsukuba
in 1987 and 1990, respectively. From 1990 to
1992, he worked as a research and developmentoﬃcer at Air Research and Development Command of Japan Air Self-Defense Force (JASDF).
Since 1992, he has been with National Defense
Academy and is currently a Professor in the Department of Electrical and Electronic Engineering. From 1996 to 1997, he was a Visiting Researcher at the Communications Research Laboratory, McMaster University, Canada. His research isconcerned with mobile communication and small antennas. He is a fellowof IEICE and a senior member of IEEE.