IEICE TRANS. COMMUN., VOL.E97–B, NO.3 MARCH 2014

620

PAPER

Analog Decoding Method for Simplified Short-Range MIMO
Transmission
Ryochi KATAOKA† , Student Member, Kentaro NISHIMORI†a) , Senior Member, Takefumi HIRAGURI†† ,Naoki HONMA††† , Members, Tomohiro SEKI†††† , Senior Member, Ken HIRAGA†††† ,and Hideo MAKINO† , Members

SUMMARY
A novel analog decoding method using only 90-degree
phase shifters is proposed to simplify the decoding method for short-range
multiple-input multiple-output (MIMO) transmission. In a short-range
MIMO transmission, an optimal element spacing that maximizes the channel capacity exists for a given transmit distance between the transmitter andreceiver. We focus on the fact that the weight matrix by zero forcing (ZF)
at the optimal element spacing can be obtained by using dividers and 90degree phase shifters because it can be expressed by a unitary matrix. The
channel capacity by the proposed method is next derived for the evaluationof the exact limitation of the channel capacity. Moreover, it is shown thatan optimal weight when using directional antennas can be expressed by using only dividers, 90-degree phase shifters, and attenuators, regardless ofthe beam width of the directional antenna. Finally, bit error rate and channel capacity evaluations by both simulation and measurement confirm theeﬀectiveness of the proposed method.
key words: short-range MIMO transmission, zero forcing, unitary matrix,
90-degree phase shifter, optimal element spacing

1.

Introduction

Because of the recent popularity of smartphones and wireless local area network (WLAN), ultimate high-speed data
communication at speeds over 10 Gbps is essential in future wireless communication systems [1]–[3]. Multipleinput-multiple-output (MIMO) systems have attracted significant attention because they can improve the transmission rate within a limited frequency band [4], [5]. Moreover,they have already been commercialized in latest cellular and
WLAN systems [6], [7].
Multipath-rich environments are generally consideredfor MIMO systems, and independent and identically distributed (i.i.d.) channels are usually assumed to explain suchenvironments in a simple manner [4], [5]. Paulaj et al. indicated that the channel capacity in a specific channel exceeds
the ergodic capacity of an i.i.d. channel, even when the Rician factor is infinite [5]. Recently, the existence of optimal
element spacing has been confirmed such that the channel
Manuscript received June 12, 2013.
Manuscript revised November 8, 2013.
†
The authors are with the Faculty of Engineering, Niigata University, Niigata-shi, 950-2102 Japan.
††
The author is with the Department of Electrical and Electronics Engineering, Nippon Institute of Technology, Saitama-ken,
345-8501 Japan.
†††
The author is with the Faculty of Engineering, Iwate University, Morioka-shi, 020-8551 Japan.
††††
The authors are with the NTT Network Innovation Laboratories, NTT Corporation, Yokosuka-shi, 239-0847 Japan.
a) E-mail: nishimori@ie.niigata-u.ac.jp
DOI: 10.1587/transcom.E97.B.620

capacity is maximized for a given signal-to-noise power ratio (SNR), even when a line-of-sight (LOS) environment is
considered [8]–[10]. The relationship between the optimal
element spacing and transmit distance is theoretically derived in the closed form when considering the linear array[9] and rectangular array [10]. However, there is an issue on
complexity of signal processing in the conventional MIMO
system.
Short-range communications have been also attracted
much attention [11]–[13], because they can realize the very
high speed communication by using broadband signals.
For ultimate high-speed data communication at speeds over
10 Gbps, the combination of MIMO transmission and shortrange communication is eﬀective. This concept is called
short range MIMO (SR-MIMO) [14] and it is clarified thatthe concept of LOS-MIMO can be applicable in SR-MIMO[15].
As concrete applications on SR-MIMO transmission,
there are wireless repeater which connects networks througha wall [15] and communication between chips [16], and soon. Although very high-speed communication is requiredin such applications, the variation on the propagation channel is assumed to be very small: The static propagation environment is realized. Hence, weights by obtained MIMO
transmission or decoding method can be fixed and conventional MIMO signal processing is not required when considering the burden on signal processing part. Although there
are studies regarding SR-MIMO transmission [17]–[20], thesimplification on signal processing part have not been evaluated in [17]–[20].
It was clarified that the channel capacity when using
Zero Forcing (ZF) [21] is the same as that using Eigenmodebeamforming (EM-BF) [22], [23] when considering the optimal element spacing in the SR-MIMO [24]. However, thecomputational complexity of the ZF method is still large because the calculation of channel inversion is required in the
ZF method.
We proposed the decoding method using a simple analog circuit to simplify the decoding method in an SR-MIMO
transmission [25]. This method utilizes the fact that thechannel matrix becomes a unitary matrix by properly adjusting the phase diﬀerences among transmit and receive antennas with optimal element spacing. The weights produced by
ZF with optimal element spacing are approximated by using
90-degree phase shifters and dividers. This circuit realizes
MIMO decoding that has the same ability as the ZF method

c 2014 The Institute of Electronics, Information and Communication Engineers
Copyright KATAOKA et al.: ANALOG DECODING METHOD FOR SIMPLIFIED SHORT-RANGE MIMO TRANSMISSION

621

without any digital signal processing. By the evaluation of
the bit error rate, it was found that BER by the proposed
method is not degraded compared to the ZF method when
considering the optimal element spacing.
This manuscript contains a significantly broadened
treatment of the proposed approach. In particular:• The optimal condition in SR-MIMO transmission is
described in greater detail. The relationship among
eigenvalues, spatial correlation, and the unitary condition is explained in Sect. 2.
• We theoretically derive the channel capacity when considering the simple decoding method. Although only
BER evaluation is employed in [25], the theoretical upper bound by the proposed method is evaluated via thechannel capacity evaluation.
• Because planar arrays between the transmitters and receivers should face each other for short-range communication, the use of a directional antenna such as a microstrip antenna (MSA) is essential. In this paper, theoptimal weight when considering the directional antennas is derived.
• We investigate the measurements to verify the eﬀectiveness of our theory. Moreover, frequency characteristics, which are a very important factor in broadband
communications, are also evaluated.
The remainder of this paper is organized as follows.
Section 2 shows the optimal weight for SR-MIMO. It isshown that this condition can be derived by the unitary matrix that is obtained from the antenna arrangement with optimal element spacing. A configuration that realizes a simple decoding method using analog devices is proposed in
Sect. 3. In Sect. 3, the channel capacity of the simple decoding method is derived, and the optimal condition whenusing a directional antenna is exhibited. Section 4 evaluates
the channel capacity and BER performance in order to show
the eﬀectiveness of the proposed analog decoding method.
The experimental results by the proposed method are shownin Sect. 5 to show the validity of our theory and simulation
results.
2.

Weight and Channel Matrices for Optimal Element
Spacing in SR-MIMO

2.1 Optimal Element Spacing in SR-MIMO
We consider the channel capacity versus array element spacing, d, to show the optimal condition in SR-MIMO. The
simulation condition is shown hereafter. The transmit distance between transmit and receive antennas is set to be
D = 2λ0 . Here, λ0 denotes the wavelength of the transmitted signal. Two identical array antennas that face eachother, each of which is a dipole array with a spacing of d, areplaced parallel to each other and separated by D. All antennas have vertical polarization for simplicity. The SNR per
antenna is 20 dB. The simulation considers the free space
between the array antennas. In this simulation, we adopt theFig. 1Channel capacity versus element spacing (2×2 MIMO, D = 2λ0 ).

geometrical optics approximation for the propagation channel in the SR-MIMO.
Figure 1 shows the channel capacity versus element
spacing, d. Ergodic channel capacity in the i.i.d. channel
and the upper bound, at which all the eigenvalues with thegiven SNR are identical, are plotted in this figure. As can beseen in Fig. 1, the channel capacity by using EM-BF / ZF isidentical to that of the upper bound when d = 1.0 λ0 . This
result confirms the existence of the optimal element spacing, dopt , when the EM-BF and ZF is adopted [24]. It canbe also seen that the capacity with dopt by using EM-BF or
ZF is higher than the ergodic capacity in the i.i.d. channel,
which is commonly used as the channel model in conventional MIMO transmission. Moreover, the channel capacity
using ZF is almost the same as that using EM-BF, when considering dopt .
It is shown that the maximum value of the channel capacity is small when the transmit distance, D, is increased[24]. In addition, the optimal element spacing, dopt , ischanged when D is given, and the value of dopt is wider when
D is increased [24].
2.2 Zero Forcing Algorithm
The ZF method is well known as a simple decoding algorithm in a MIMO system because only receivers employ
signal processing, unlike EM-BF. The weight matrix, W Z F ,is calculated by using the channel inversion, which is obtained by channel estimation at the receivers in the ZF algorithm. Our aim is to realize the simple decoding method,as the computational complexity by the ZF algorithm is stilllarge because of the calculation of the channel inversion. As
shown in Fig. 1, the channel capacity using ZF is almost thesame as that using EM-BF, when considering dopt in the SRMIMO system. We focus on the condition of the weightmatrix, W Z F , which is obtained by the ZF algorithm. We realize a fixed weight, WS , that can be configured by an analog
circuit. The detailed scheme is shown in Sect. 3.
Here, the basic principle of ZF is described. When
H0 is the weight matrix for the channel, H0 with an M ×

IEICE TRANS. COMMUN., VOL.E97–B, NO.3 MARCH 2014622

M MIMO channel is denoted as⎡⎤⎢⎢⎢ h11 h12 · · · h1M ⎥⎥⎥⎢⎢⎢ h⎥⎢⎢⎢ 21 h22 · · · h2M ⎥⎥⎥⎥⎥
H0 = ⎢⎢⎢ .
..
.. ⎥⎥⎥ ,..
⎢⎢⎢ ..
.
.
. ⎥⎥⎥
⎣
⎦
h M1 h M2 · · · h MM

(1)where hi j is the channel response for the j-th and i-th transmit and receive antennas. The receive signal vector, y(t) =[y1 (t), · · · , y M (t)]T is denoted asy(t) = H0 s(t) + n(t),(2)

where s(t) = [s1 (t) · · · , s M (t)]T and n(t) = [n1 (t), · · · , n M (t)]Tdenote the receive signal and noise vectors, respectively.
Here, T is the transpose operation on the vector.
The weight matrix of ZF, W Z F , is represented as
W Z F = H0 −1 .

Fig. 2

Amplitude ratio versus array element spacing.

Fig. 3Phase diﬀerence versus array element spacing.

(3)

Hence, the decoding signal vector, y (t), is denoted asy (t) = W Z F y(t)= W Z F H0 s(t) + W Z F n(t).

(4)

In the next subsection, we analyze how the elements of
W Z F are changed when changing the element spacing in the
SR-MIMO system.
2.3 Weight of ZF with Optimal Element Spacing
For the following explanation, the element spacings thatfirstly and secondly maximize the channel capacity in Fig. 1
are defined as dopt,1 and dopt,2 , respectively. In order to examine the characteristics of W Z F , W Z F is normalized by w11
as

WZ F
w11 /w11 w12 /w11
=
,
(5)
w
w11
21 /w11 w22 /w11

algorithm. As can be seen in Fig. 3, θW at the element
spacing that maximizes the channel capacity in Fig. 1 is expressed aswhere w22 = w11 , and w12 = w21 because of the symmetricproperty of the array configuration. We focus on the weightmatrix created by ZF when d = dopt,1 in Fig. 1. When dopt,1
is given, W Z F /w11 is calculated asWZ F
1−0.04 + 0.89 j=.
−0.04 + 0.89 j
1
w11
(6)

Hence, W Z F and channel matrix H0 when considering dopt,1
can be approximated by

WZ F
1 j

,
(8)
j 1
w11

H0
1 −j

.
(9)
−j 1
h11

As shown in Eq. (6), the ratio of |w21 /w11 | (|w12 /w22 |) is 0.91,
and tan−1 (w21 /w11 ) (tan−1 (w12 /w22 )) is approximately 90 degrees. Note that this condition in the optimal element spacing is constant even if the transmit distance, D, is changed.
Figure 2 shows the amplitude ratio (|w11 /w21 |) versus
the element spacing when using the ZF algorithm. As can beseen in Fig. 2, the amplitude ratio when d = dopt,1 is approximately 1.1, and the amplitude ratio increases in proportion
to the element spacing, d.
Figure 3 denotes the phase diﬀerence, θW (tan−1(w11 /w21 )), versus the element spacing when using the ZF

θW (dopt,1 ) = . . . = θW (dopt,2n+1 )  90◦
θW (dopt,2 ) = . . . = θW (dopt,2n )  −90◦

(7)

When considering the above condition, the following relationship is obtained.
W Z F = H0 −1 = H0 H .

(10)As a result, it is shown that the weight matrix of ZF canbe approximated by a unitary matrix when considering the
optimal element spacing in the SR-MIMO system.
2.4 Channel Matrices and Unitary Matrix for Optimal Element Spacing
Let us assume a unitary matrix, U. A unitary matrix has theKATAOKA et al.: ANALOG DECODING METHOD FOR SIMPLIFIED SHORT-RANGE MIMO TRANSMISSION

623∝ Rs(t) + W s n(t).

following property:
UU H = U H U = I,

(11)

where I is the identity matrix. Hence, U H = U−1 [26]. As
shown in the previous subsection, W Z F and H0 are approximated by the unitary matrix. Hence, W Z F H0 , which is thechannel matrix after multiplying the weight matrix, is denoted as
W Z F H0 = H0 −1 H0 = H0 H H0 = I.

(12)

When considering the above condition, all the eigenvalues
are identical, and the spatial correlation is zero [24]. This is
an optimal condition in MIMO transmission: the maximum
channel capacity is obtained for the given SNR.
3.

Analog Beamforming Circuit Using Condition on
Optimal Element Spacing

3.1 Analog Beamforming Circuit
As mentioned in 2.3, W Z F /w11 in a 2×2 MIMO system considering the optimal element spacing can be approximated
by

W
H0 H
1 j

 H .
(13)
j 1
w11
h11
We propose an analog decoding method by utilizing thefact that the propagation channel is not changed in the SRMIMO when Eq. (13) is obtained. The condition in Eq. (13)can be configured by using only simple analog devices withdividers and 90-degree phase shifters. Figure 4 shows the
proposed analog beamforming circuit. As shown in Fig. 4,
because two pairs of weights can be multiplied with the received signals, the inter-steam interference can be automatically canceled at the output signals, y1 and y2 : MIMO transmission is realized without any decoding scheme such as
channel inversion in the digital signal processor.
The decoding signal vector y (t) using analog weightW s is denoted asy (t) = W s H0 s(t) + W s n(14)

When an M × M MIMO channel is considered for R in
Eq. (14), R is expressed as⎡⎤⎢⎢⎢ a11 a12 · · · a1M ⎥⎥⎥⎢⎢⎢⎢ a21 a22 · · · a2M ⎥⎥⎥⎥⎥
R = ⎢⎢⎢⎢⎢ .
(15)..
.. ⎥⎥⎥⎥ .
..
⎢⎢⎢ ..
.
.
. ⎥⎥⎥
⎣
⎦
a M1 a M2 · · · a MM
Because W s with 2×2 MIMO is the unitary matrix, R in
Eq. (14) is approximated as

R
1 0
=
= I.
(16)
0 1
a11
Hence, the inter-stream interference can be canceled, andthe desired signals can be decoded by the proposed circuit.
Although the proposed decoding in a 2×2 MIMO system can be realized by using the circuit in Fig. 4, the idea
for the proposed method can be applicable for a larger number of antennas. Let us assume a 4×4 MIMO system withsquarely arranged antennas at the transmitter and receiver.
Figure 5 shows the 4×4 MIMO system with squarely arranged antennas at the transmitter and receiver. When considering this antenna arrangement, W Z F (a, b)/w11 (a, b =1 ∼ 4) can be calculated as
W Z F (k, k)/w11 = 1(k = 1 ∼ 4)
W Z F (i, j)/w11 = −0.09 + 0.89 j(i = 2, 3, j = 1, 4)
W Z F (m, n)/w11 = −0.09 + 0.89 j(m = 1, 4, n = 2, 3)
W Z F (5 − l, l)/w11 = −0.78 − 0.04 j(l = 1 ∼ 4).

(17)
(18)
(19)
(20)

We approximate the above matrix to realize a simple decoding method with an analog circuit that uses only dividers and
90 and 180-degree phase shifters. The approximated matrix,
W s,4×4 , is expressed as⎡⎤jj −1 ⎥⎥
⎢⎢⎢ 1
⎥
⎢⎢⎢ j
1 −1 j ⎥⎥⎥⎥⎥,
W s,4×4 = ⎢⎢⎢⎢
(21)j ⎥⎥⎥⎥⎢⎢⎣ j −1 1
⎦
−1
j
j
1
where W s is the unitary matrix because W s,4×4W s,4×4 H is theFig. 4

Proposed analog beamforming circuit.

Fig. 5 4×4 MIMO system with squarely arranged antennas at thetransmitter and receiver.

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Fig. 7 Schematic of the eﬀect of the radiation pattern and the antenna
directivity.
MC=

log2 1+k=1

Fig. 6 Amplitude ratio and phase diﬀerence at the optimal element
spacing of each D.

identity matrix.
Although the optimal element spacing itself is changed
when the transmit distance, D, is changed, the weight forthe simple decoding method is not changed. Figure 6 shows
the amplitude ratio and phase diﬀerence of W Z F at the optimal element spacing when D is changed. As can be seenin Fig. 6, the amplitude ratio is increased when D is wider.
The adjustment of amplitude can be used by the attenuator.
Furthermore, the phase diﬀerence is approximately 90◦ as a90-degree phase shifter is used. Hence, the simple decoding
method can be realized by the analog weight circuit with the
optimal element spacing when D is determined.
3.2 Derivation of Channel Capacity
The performance by the proposed method is degraded because the approximation of the weights by using the unitarycondition is adopted. In this subsection, the channel capacity by the proposed method is derived in an exact expression
to accurately evaluate the upper bound of the channel capacity by the proposed method.
Here, we introduce a new parameter, bki (k = 1 ∼M, i = 1 ∼ M, i  k). bki is defined as
aki
bki =
(k = 1 ∼ M, i = 1 ∼ M, i  k).
(22)
akk|bki | is approximated by 0 at the optimal element spacing.
On the other hand, |bki | is large when the channel capacity is low. Hence, bki can be treated as the influence of theinter-steam interference. Thus, the signal-to-interferenceand-noise power ratio (SINR) for the k-th received antennaby the proposed method is denoted as
S INR(k) =E|sk (t)|2 .

M|bki | E|si (t)|  + E|nk (t)| 2

22ik,i=1(23)
Here, E· is expectation value. Hence, the channel capacity,
C, using the proposed method is expressed as

1
S INR(k) .
M(24)

3.3 Analog Weight for Directional Antenna
Figure 7 shows the definition of the 3-dB beamwidth (BW)when using a directional antenna. θBW is the half-power
beamwidth (HPBW). The antenna pattern from the directional antenna is generally approximated by cosn (n: positive value). Hence, the response of the directional antennain the direction of θ, FθBW (θ) is expressed as
FθBW (θ) = cosn (θ).
Here, n is calculated by θBW as
θ 
1
BW
cosn
= √
2
2
1
  .
n=−
2 log2 {cos θBW
2 }

(25)

(26)
(27)

When using the directional antennas, W Z F /w11 in
2×2 SR-MIMO with the optimal element spacing can be approximated by

H0 H
W
1 jα

 H ,
(28)
jα 1
w11
h11
where we define α as the weight factor. Figure 8 shows thecharacteristics of α and the phase diﬀerence, tan−1 (w21 /w11 )or tan−1 (w12 /w22 ), at the optimal element spacing when D ischanged. Here, the HPBW is set to be 80 degrees. As shownin Fig. 8, α is increased when D is wider, but α is saturated.
On the other hand, it is shown that the phase diﬀerence isapproximately 90 degrees.
Figure 9 shows the characteristics of α and the phase
diﬀerence, tan−1 (w21 /w11 ) or tan−1 (w12 /w22 ), at the optimal
element spacing when the HPBW is changed. D is set tobe 5λ0 . As can be seen in Fig. 9, α is increased when the
HPBW is wider, but α is saturated. Hence, an attenuator isrequired to realize the weights with the analog circuit. On
the other hand, the phase diﬀerence is approximately 90 degrees, regardless of the HPBW.
From the results in Figs. 8 and 9, it was found that theanalog weight can be realized by using a divider, 90-degree
phase shifter, and attenuator when using the directional antennas. Figure 10 shows the proposed analog beamformingKATAOKA et al.: ANALOG DECODING METHOD FOR SIMPLIFIED SHORT-RANGE MIMO TRANSMISSION

625

circuit when using the directional antenna. The condition
in Eq. (28) can be configured by using only simple analog
devices with dividers, 90-degree phase shifters, and attenuators.

4.

Basic Performance of the Simple Decoding Method

To verify the basic performance of the proposed method, theBER and the channel capacity using the proposed method
are evaluated.
4.1 Simulation Conditions

Fig. 8 Weight factor α and the phase diﬀerence at the optimal element
spacing at each D.

In the simulation, the channel matrix, H0 , is calculated by
the geometrical optics approximation [24]. Although a mutual coupling eﬀect cannot be reflected by using geometrical
optics approximation, we have already confirmed that thechannel capacity obtained by geometrical optics approximation is almost same with that by Moment of Method analyses
which considers the mutual coupling eﬀect between antennas [24]. Hence, we adopted the geometrical optics approximation in this section. The results in which the mutual coupling eﬀect is considered are shown in Sect. 5. The antenna
distance, D, is set to be 2λ0 . The modulation scheme is
16 QAM and number of data streams is equal to the numberof transmit antennas. One million bits are totally transmitted by the transmit antennas in order to evaluate the BER
characteristic which is equal to 10−5 . We assume that theweight matrix given in Eq. (9) can be ideally obtained withthe analog circuit using the proposed method. The issue ofphase errors caused by the phase shifter remains and will be
evaluated in future work.
4.2 BER Characteristics

Fig. 9 Weight factor α and phase diﬀerence at the optimal element
spacing when D = 5λ0 .

Fig. 10 Proposed analog beamforming circuit when using the directional
antenna.

Figure 11 shows the BER versus the array element spacing, d, when a 2×2 MIMO system is considered. Prop. in
Fig. 11 denotes the proposed simple decoding method, andthe results using the proposed method and ZF are plotted inthis figure. The SNR per antenna is 20 dB at the optimal
element spacing. Although the BER by proposed method is
6 × 10−4 while the BER is less than 10−5 by the ZF at theFig. 11

BER versus element spacing (2×2 MIMO, D = 2λ0 ).

IEICE TRANS. COMMUN., VOL.E97–B, NO.3 MARCH 2014

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Fig. 12BER versus SNR (2×2 MIMO, D = 2λ0 ).
Fig. 142λ0 ).

Channel capacity versus element spacing (2×2 MIMO, D =ered. The other simulation conditions are the same as thosein Fig. 12. As can be seen in Fig. 13, compared to ZF, 2.5 dBof degradation exists at BER=10−3 when using the proposed
method with dopt . On the other hand, the BER using the proposed method is not improved versus the SNR when considering that d is 1.5λ0 . Therefore, it is clarified that a simple
decoding method is applicable for 4×4 MIMO if we utilize
the optimal element spacing.
4.3 Channel Capacity Characteristics

Fig. 13

BER versus SNR (4×4 MIMO, D = 2λ0 ).

optimal element spacing (d = 1.0λ0 ), the BER can be actually zero when the error coding scheme is employed. On theother hand, the BER using the proposed method is greatly
degraded at all other element spacings except for the optimal element spacing. Hence, it is shown that the use of the
optimal element spacing is essential in the proposed circuit
for the given the transmit distance.
Figure 12 shows the BER versus the SNR when 2×2
MIMO transmission is employed. The array element spacing, d, is set to be dopt (= 1.0λ0 ) and 1.5λ0 , respectively,
in Fig. 12. The results using the simple decoding method,
Prop., and ZF are plotted in this figure. As can be seen in
Fig. 12, only 1 dB of degradation exists when the BER=10−3
compared to ZF, when using the proposed method with dopt .
On the other hand, the BER using the proposed method is
not improved versus the SNR, whereas the BER using the
ZF is improved at SNRs over 20 dB when d is 1.5λ0 .
Next, we evaluate the eﬀectiveness of the proposed
method when 4×4 MIMO is applied. We assume that theweight matrix W s,4×4 given in Eq. (21) can be ideally obtained in the proposed method. Figure 13 shows the BER
versus the SNR when 4×4 MIMO with a square antennaarrangement at both the transmitter and receiver is consid-

To confirm the validity of our derivation of the channel capacity, the channel capacity versus array element spacing, d,
is plotted when 2×2 MIMO is considered. Prop. in Fig. 14
denotes the proposed simple decoding method, and the results using the proposed method and ZF are plotted in thisfigure. The SNR per antenna is 20 dB. As can be seen in
Fig. 14, Prop. has almost the same performance as ZF andthe upper bound [24] at the optimal element spacing. Moreover, because the tendency regarding channel capacity versus d in Fig. 14 is similar to that in Fig. 11, the corresponding values of the optimal and worst element spacings in eachfigure are equivalent. Hence, it is clarified that our derivation of the channel capacity is eﬀective for evaluating theupper bound on the transmission performance.
5.

Eﬀectiveness of the Proposed Method Using Measured Propagation Channel

To verify the eﬀectiveness of the proposed method in a realpropagation environment, the channel matrix is measured
when considering the environment in the SR-MIMO transmission.
5.1 Measurement Environment
Figure 15 shows the measurement environment. We conducted the measurement in an anechoic chamber. In order to obtain pure channel responses between the transmit

KATAOKA et al.: ANALOG DECODING METHOD FOR SIMPLIFIED SHORT-RANGE MIMO TRANSMISSION

627

Fig. 15

Measurement environment.
Fig. 17 Eigenvalues versus element spacing (2×2 MIMO, SNR = 20 dB,
D = 5λ0 ).

Fig. 16

Radiation patterns of MSA.

and received antennas, channel matrix H0 with 2×2 MIMO
was obtained by using a vector network analyzer. The center frequency is 5.0 GHz, and the bandwidth is 100 MHz inthis measurement. For antenna elements, MSAs are used.
The radiation patterns are plotted in Fig. 16. The measured
HPBW is approximately 80 degrees. Hence, the HPBW is
set to be 80 degrees in the simulation, and the antenna response is approximated by a cosn pattern which is shown in
3.3 in the simulation results. The antenna distance, D, is set
to be 5λ0 .
5.2 Eﬀectiveness of Proposed Method
Figure 17 shows the 1st and 2nd eigenvalues (λ1 and λ2 )versus the element spacing. For reference, the simulation
result with a cosn pattern is plotted in this figure. The SNRis set to be 20 dB when the optimal element spacing is used.
As can be seen in Fig. 17, we can observe the existence ofthe optimal element spacing where the ratio of λ1 and λ2
is approximately one in the measured results. Moreover,Fig. 18 BER versus element spacing when the measurement channel
matrix is considered (2×2 MIMO, D = 5λ0 ).

the ratio of the eigenvalues to the element spacing foundin the measured results is very similar to that found in thesimulation results. Hence, it is clarified that the simulation
model is eﬀective for the modeling of an SR-MIMO system
when using a directional antenna.
Figure 18 shows the BER versus array element spacing,d, when the measured channel matrix is considered. For thecomparison, the results of the proposed method and ZF areplotted in this figure. As can be seen in Fig. 18, the degradation of the BER using the simple decoding method is verysmall compared to the BER using the proposed method in
the simulated results when considering the optimal element
spacing. On the other hand, the BER using the proposed
method is greatly degraded at element spacings other thanthe optimal element spacing. Hence, the measurement results show that the usage of the optimal element spacing isessential.
In the previous results, we evaluated the BER and channel capacity at only a single frequency. However, broad-IEICE TRANS. COMMUN., VOL.E97–B, NO.3 MARCH 2014

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Fig. 19 BER versus SNR when the bandwidth is considered (2×2
MIMO, D = 5λ0 ).

band transmission is essential for future wireless communications. Figure 19 shows the BER versus SNR when the
fixed weight given at 5.0 GHz is applied for the weights at
4.95 and 5.05 GHz, respectively. As can be seen in Fig. 19,
although a degradation of 1.5 dB exists at BER=10−3 when
4.95 and 5.05 GHz are used compared to 5.0 GHz, it isshown that the wideband characteristics can be observed using the proposed simple decoding method if we can prepare
the wideband 90-degree phase shifter.
6.

Conclusion

In this paper, a novel analog decoding method with only ananalog circuit is proposed to simplify the decoding method
for SR-MIMO transmission. The proposed method does notneed any digital signal processing, which is required in conventional MIMO signal decoding. Because the weight matrix found using ZF at the optimal element spacing is expressed as a unitary matrix, it was shown that the weight matrix can be realized by using dividers and 90-degree phaseshifters in a 2×2 SR-MIMO system. In this study, the channel capacity using the proposed method is derived to evaluate the limitation on the proposed method. Moreover, it wasclarified that simple decoding when using the directional antennas can be configured by using dividers, 90-degree phaseshifters, and attenuators.
It was verified that the degradation of the BER using asimple decoding method is very small compared to the BER
using ZF when considering the optimal element spacing,
dopt . Only 1 dB of SNR degradation exists when BER=10−3
compared to ZF, when using the proposed method with dopt .
On the other hand, it was shown that the BER using the
proposed method is greatly degraded at all other element
spacings except the optimal element spacing. Hence, theuse of the optimal element spacing is essential for the given
transmit distance when employing the proposed method andcircuit. We clarified that the optimal and worst element
spacings are the same for the BER and capacity evaluations.
Hence, our derivation of the channel capacity is eﬀective

for evaluating the upper bound on the transmission performance. Moreover, it was shown that the simple decoding
method can be applicable for 4×4 MIMO. Finally, in order to verify the eﬀectiveness of the proposed method in areal propagation environment, the channel matrix was measured when considering the environment during SR-MIMO
transmission. It was shown that the simulated and measured
results agree well with each other, and the wideband characteristics can be observed with the proposed simple decoding method if we can prepare the wideband 90-degree phaseshifter.
Although ideal phase shifters are assumed in this paper, there are phase error on the phase shifter when applying
the proposed method. The influence on weight errors on
capacity when using the simple decoding scheme is evaluated by a computer simulation [27]. As the future work, theevaluation using actual phase shifters is essential. Moreover,calibration techniques are required to obtain the accurate thechannel state information by the proposed method. Hence,
actual hardware implementation should be employed for thefurther development of the proposed method.
In this study, the geometrical optics approximation andcosine pattern were used as the propagation characteristic
and antenna pattern in the simulation. Although the simulated and measured results agree with each other from apoint of view in BER when the transmit distance is 5λ0 , thisassumption may not be applied when considering very nearfield. As the future work, we should evaluate the limitation
regarding the minimum transmit distance that the proposed
method can be applicable and a new model in very near field.
Acknowledgments
The part of this work is supported by KAKENHI, Grant-inAid for Scientific Research (C) (25420362).
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Ryochi Kataoka
received the B.E. and
M.E. degrees from Niigata University, Niigata,Japan, in 2011 and 2013, respectively. Currently, he works for the D.E. degree at the Electrical and Information Engineering in Graduate School of Science and Technology, Niigata
University. His main research interests include
MIMO and digital signal processing.

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.

Takefumi Hiraguri
received the M.E. and
Ph.D. degree from the University of Tsukuba,
Ibaraki, Japan, in 1999 and 2008, respectively.
In 1999, he joined the NTT Access Network
Service Systems Laboratories, Nippon Telegraph and Telephone Corporation in Japan. He
has been engaged in research and developmentof MAC protocol for the high speed and the highcommunication quality in wireless systems. He
is now associate professor in Nippon Institute ofTechnology. He is a member of IEEE.

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, and theBest Paper Award of IEICE Communication Society in 2006, respectively. His current research interest is planar antennas
for high-speed wireless communication systems. He is a member of IEEE.

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Tomohiro Seki
was born in Tokyo, Japan,
in 1967. He received the B.E., M.E., andDr. Eng. degrees in electrical engineering from
Tokyo University of Science, Tokyo, in 1991,
1993, and 2006, respectively. In 1993, he joined
Nippon Telegraph and Telephone Corporation(NTT), Japan, and has been engaged in researchon planar antennas and active integrated antennas for millimeter-wave and microwave bands.
He is currently interested in system-on-package
technologies for millimeter-wave communication systems and antenna for wide-area ubiquitous wireless access systems.
Dr. Seki is a member of the IEEE and a senior member of the Institute ofElectronics, Information and Communication Engineers (IEICE) of Japan.
He has been served in the IEEE Radio and Wireless Symposium (IEEE
RWS) technical program committee member (2008–2013), the IEEE International Microwave Workshop Series (IEEE MTT-S IMWS) technical program committee member (2009, 2011–2013) and IEICE International Symposium on Antennas and Propagation (ISAP) executive committee member(2004, 2007, 2012). He is also an associate editor of the IEICE Trans. on
Electronics (2008–2011). He received the 1999 Young Engineer Award
from the IEICE and the 2006 Best Paper Award of the communication society of the IEICE.

Ken Hiraga
received the B.E., M.E., andPh.D. degrees in electronics and information engineering from Hokkaido University, Sapporo,in 2003, 2005, and 2013 respectively. Since
2005, he has been engaged in research and development on wireless systems at Nippon Telegraph and Telephone Corporation. He received
the Young Engineers Award from the IEICE in2010 and Young Engineer Award from IEEE
AP-S Japan Chapter in 2012. He is a memberof IEEE and IEICE.

Hideo Makino
graduated from the Department of Electronic Engineering, Niigata University, in 1976, completed the M.S. program in
1978, and joined the staﬀ of the Department ofInformation Engineering. He became an associate professor in 1990 and a professor in 1995.
He was on leave at the Research Institute of Applied Electrical Engineering, Hokkaido University, in 1983 and at the Medical School, University of Toronto, in 1989. He has been engaged
in research on medical information and assistiveequipment. He holds a D.Eng. degree, and is a member of the Japan ME
Society, the Institute of Electrical Engineers of Japan, and IEEE. He is acouncil member of the Japan Heart Rhythm Society and a councilor of theGeographical Information Systems Society.