IEICE TRANS. COMMUN., VOL.E96–B, NO.7 JULY 2013

1945

PAPER

Non-iterative Algorithm of MIMO Adaptive Array Based on
Correlation Matrix Including Parasitic Antennas
Naoki HONMA†a) , Member, Kentaro NISHIMORI†† , Senior Member, Takefumi HIRAGURI††† ,and Yoshitaka TSUNEKAWA† , Members

SUMMARY
Parasitic antenna elements with tunable terminations canbe used for interference suppression in multi-antenna systems without using the degrees of freedom. The authors have proposed a fast non-iterativealgorithm for optimizing the termination conditions. However, this method
cannot be used for suppressing the interference from unknown systems
since it requires the channel state information. In this paper, a fast noniterative algorithm based on the correlation matrix, which can be obtainedeven from unknown interference sources, is proposed for the multi-antenna
system with parasitic antenna elements. The correlation matrix including
both receiving and parasitic antennas can be estimated from a few observations of the signals even without receiving signals at the parasitic antenna.
By using this correlation matrix, the power of the interference with thearbitrary termination conditions can be easily estimated. Therefore, the termination condition, which minimizes the interference power, can be calculated without knowledge of the channel state information or additional estimations. The results of a numerical analysis indicate that proposed method
works well in suppressing the interference without the perfect channel state
information.
key words: adaptive array, tunable reactance device, MIMO, correlation
matrix1.

Introduction

It is well known that antenna-systems exploiting tunable
parasitic antennas can enhance a wireless communication
quality, such as the reception power improvement, interference cancellation, and so on [1]–[4]. These antennas canbe recognized as a kind of analog adaptive antenna, but thearbitrary excitation weight at the antenna element cannot begiven since the current at the antenna element strongly depends on the mutual coupling. This deteriorates the performance in interference suppression compared to that of thedigital adaptive array antenna. Nevertheless, they have relatively simple hardware compared with the digital adaptivearray antennas. This feature allows to use many more parasitic antennas, and the eﬀective degree of freedom can begreatly increased [5], [6].
However, it is diﬃcult to predict the channel behavior against the termination conditions at the parasitic antennas, since the relationship between the channel response andManuscript received October 1, 2012.
Manuscript revised March 11, 2013.
†
The authors are with Iwate University, Morioka-shi, 020-8551
Japan.
††
The author is with Niigata University, Niigata-shi, 950-2181
Japan.
†††
The author is with Nippon Institute of Technology, Saitamaken, 345-8501 Japan.
a) E-mail: honma@iwate-u.ac.jp
DOI: 10.1587/transcom.E96.B.1945

the termination impedance are known to be non-linear. The
steepest gradient algorithm is commonly used for optimizing the termination condition of the parasitic antennas [1],[2]. In this algorithm, the gradient of the evaluation function, e.g. signal-to-interference ratio (SIR), is estimated byvarying the termination conditions. This scheme requires
significant numbers of iterative measurements to obtain optimum radiation patterns or desired channels. The work
[7] presented a fast control method of the parasitic antennas by measuring the impedance matrix of the array antenna including the termination ports at the parasitic elements. Though the fast control of the radiation pattern canbe achieved, this method cannot be applied to the interference suppression since the response of unknown interference cannot be estimated.
Authors have proposed a deterministic solution forcontrolling analog adaptive antenna, which requires only a
few channel observations [8], [9]. In this method, the ideaof a ‘parasitic channel’, which is observed at the parasitic
antenna, is newly introduced. The parasitic channel is aninvisible channel but can be estimated by using this method.
However, this method requires the channel state information (CSI) between the receiving antenna and interference
source for suppressing the interference. Since the CSI estimation requires the known training signal whose information is shared between the transmitter and receiver in advance, it is diﬃcult to obtain the CSI from unknown signalsthat can arrive from other wireless systems.
In this paper, a fast non-iterative algorithm basedon correlation matrix for multiple-input multiple-output(MIMO) adaptive array is proposed. This method does not
require the CSI but the correlation matrix, which is obtained
from the received signals. The correlation matrix including
both receiving antennas and parasitic antennas can be estimated from a few observations of the signals even without
receiving signals at the parasitic antenna. It is shown how
this method works in suppressing the interference, and thesimulations are conducted to validate this method.
Section 2 describes the system model of the multiantenna, which is considered in this paper. Also, the proposed algorithm is described in detail. In Sect. 3, the simulation results are indicated, and show this method is eﬀectivein enhancing the channel data rate even without any iterative
channel measurements.

c 2013 The Institute of Electronics, Information and Communication Engineers
Copyright IEICE TRANS. COMMUN., VOL.E96–B, NO.7 JULY 2013

1946

2.

System Model and Proposed Algorithm

The method shown in [9] is the easiest and most secure way
to predict the channel response with arbitrary termination
conditions in the parasitically steerable arrays. However,this method cannot be applicable to the interference fromother wireless systems since the CSI between the interference source and the receiving antennas is not available. Although the CSI is not available, the stochastic characteristicsof the interference can be observed.
In the proposed method, the correlation matrix calculated from the received signals at the receiving antennas isobserved and exploited instead of using the CSI. The correlation matrix including both receiving antennas and parasitic
antennas can be estimated from several training rounds. If
this adaptive antenna is used for suppressing the interference, the correlation matrix must be observed during theabsence of the desired signal. Also, the same interference
signals must arrive repeatedly. This precondition can be obtained in the various wireless systems. For example, a guard
time is set in the actual systems in order to avoid the collision between the desired users. The interference cancellation method with adaptive array by using such guard is
proposed [10]. In the proposed method, guard time can be
exploited to obtain the correlation matrix of the interference
signals.
2.1 System Model
Figure 1 shows the configuration of the multi-antenna system considered in this paper. The number of the receiving
and parasitic antennas are Mr and M p , respectively. The antennas shown in this figure are dipoles, but the following discussion can be applied to arbitrary configurations. Each parasitic antenna is terminated by a tunable reactance, zi . Here,i is the index number of the parasitic antenna. These arrays
are placed close together since the mutual coupling between
the receiving and parasitic elements is needed to form theradiation pattern by controlling the termination condition ateach parasitic element. In this model, the intereference signals arriving at the receiving antenna system are considered.
Figure 2 shows the circuit model used in this discussion.
This model considers the receiving and parasitic elements.
Term SR is the S -parameter matrix, including the receiving
and parasitic elements. SR can be defined as,


S
SRP
SR = RR,(1)
SPR SPP
where R and P represents the receiving element and parasitic element ports, respectively. SR is assumed to be known
and stable. In an actual operation, this can be measured inadvance of the following process. b0 denotes the complex
vector that represents the interference signalsat the antenna
elements including the parasitic elements, and it can be observed only when all ports are terminated by the reference
impedance, z0 . b0 can be divided into vectors bR0 and bP0

Fig. 1

Fig. 2

Antenna system configuration.

Equivalent circuit model of the multi-antenna system.

at the receiving and parasitic elements, respectively. bR represents the complex output vector observed at the antenna
ports when the antennas are terminated and connected to thereceivers. bR can also be divided into vectors bRR and bPPobserved at the receiver ports and parasitic element ports,
respectively. aR denotes signals that are reflected from thereceivers and terminations to the antenna elements, and canbe divided into aRR and aPP . These matrices and vectors
must satisfy     
SRP aRR
S
b
bRR
= RR
+ R0
(2)
bPP
SPR SPP aPP
bP0
aPP = ΓbPP .
(3)
Γ is the termination condition and defined as,
⎛
⎞
0 ⎟⎟
⎜⎜⎜Γ1
⎟⎟⎟
⎜⎜
..
⎟⎟⎟⎟ ,
Γ = ⎜⎜⎜⎜
.
⎜⎝
⎟⎠
0
ΓM p

(4)

where Γi is the reflection coeﬃcient of the i-th reactive termination; it is defined as Γi = (zi −z0 )/(zi +z0 ), ( z0 : reference
impedance ). When the internal impedance of the receivers
is ideal, i.e. equal to the reference impedance, z0 , aRR can beassumed to be 0. From (2) and (3), the observed vector at
the receiving ports can be expressed as,
bRR = bR0 + SRP Γ(I M p − SPP Γ)−1 bP0= Ab0 ,
where,(5)

HONMA et al.: NON-ITERATIVE ALGORITHM OF MIMO ADAPTIVE ARRAY

1947

⎞
⎞
⎡⎛
⎤
⎤ ⎛ ⎞
⎡⎛
⎢⎢⎢⎜⎜⎜ bRR,1 ⎟⎟⎟⎥⎥⎥⎥⎥⎥ ⎜⎜⎜ A1 ⎟⎟⎟⎢⎢⎢⎜⎜⎜ A1 b0 ⎟⎟⎟⎥⎥⎥⎥⎥ ⎜⎜ ⎟⎟⎢⎢⎢⎜⎜⎜ . ⎟⎟⎟ H H⎢⎢⎢⎢⎜⎜⎜⎜ .. ⎟⎟⎟⎟ H
H
H
H
E ⎢⎢⎜⎜ . ⎟⎟ (bRR,1 , . . . , bRR,K )⎥⎥⎥ = E ⎢⎢⎢⎜⎜⎜ .. ⎟⎟⎟ (b0 A1 , . . . , b0 AK )⎥⎥⎥⎥ = ⎜⎜⎜⎜ ... ⎟⎟⎟⎟ E[b0 b0H ]( A1H , . . . , AH
K)
⎟⎠
⎟⎠
⎢⎣⎜⎝
⎥⎦
⎥⎦ ⎜⎝ ⎟⎠
⎢⎣⎜⎝
bRR,K
AK b0
AK
⎞
⎛ ⎞+ ⎡⎛⎤⎜⎜⎜ A1 ⎟⎟⎟⎢⎢⎢⎜⎜⎜ bRR,1 ⎟⎟⎟
⎥⎥⎥
⎥⎥
⎟⎟ H
⎜⎜ ⎟⎟
⎢⎢⎜⎜
H
+
R0 = E[b0 b0H ] = ⎜⎜⎜⎜ ... ⎟⎟⎟⎟ E ⎢⎢⎢⎢⎜⎜⎜⎜ ... ⎟⎟⎟⎟ (bRR,1, . . . , bRR,K)⎥⎥⎥⎥ ( A1H , . . . , AH
K)
⎟⎠
⎜⎝ ⎟⎠
⎢⎣⎜⎝
⎥⎦
AK
bRR,K


A = I Mr SRP Γ(I M p − SPP Γ)−1 .

(6)Here, I Mr and I M p are Mr × Mr and M p × M p identity matrices, respectively. A transfers the signal arriving at theantennas to the observed signal at the receivers, and depends on the termination condition, Γ. The size of A is
Mr × (Mr + M p ). The correlation matrix observed at thereceiver is,H] = AE[b0 b0H ] AH
E[bRR bRR
= AR0 AH ,(7)

Hwhere, (·) and E[·] are Hermitian transposition and ensemble averaging, respectively. R0 is the correlation matrix including the components of both receiving and parasitic antennas. It can be seen that the correlation matrices with arbitrary termination conditions can be obtained from (7) if
R0 is known. Since the sum of the diagonal component ofH] corresponds to the received power, the terminaE[bRR bRRtion condition that minimizes the received power, is needed
to suppress the interference when the received signal contains only the interference components.

In this subsection, technique for estimating the correlation
matrix, R0 , is described. Let us assume that SR is known.
First step is giving the various termination conditions andobserving the signals at the receiver. K sets of non-identicaltermination conditions, defined as A1 , . . . , AK , are given by(6) and they are assumed to be known. The received signal vectors corresponding to the termination conditions aredefined as bRR,1 , . . . , bRR,K . Second step is estimation of thecorrelation matrix. The correlation matrix can be written as(8). From this equation, the correlation matrix, R0 can be estimated from the received signal vectors by using (9), where(·)+ represents a pseudo inverse operation.
In (9), the size of the matrices, i.e. ( A1H , . . . , AHK ) andits Hermitian transpose, needs to be considered to obtain
the desired R0 in terms of the validity of the pseudo inverse
operations. Since the size of (A1H , . . . , AHK ) is (Mr + M p ) ×
K Mr , K Mr needs to be equal to or larger than (Mr + M p ) toobtain the correct solution. Therefore, the condition,
K≥

Mp
+ 1,
Mr

(10)

must be fulfilled. This means K sets of measurements with

(9)

non-identical termination conditions are required. If thetransmitted signal is interference, the termination condition
that minimizes the interference power can be calculated byusing the typical optimization methods, like [1], [2].
As described above, the interference power can be suppressed without any knowledge of the CSI. However, thesame interference signal must arrive repeatedly since (9) assumes E[b0 b0H ] is always constant thruough K times observations. It is natural that the same signals are transmitted
many times since many wireless systems employ frame formats that use identical preambles, and this feature can beused for obtaining (9).
2.3 Eﬀect of Noise on Estimation Accuracy of Correlation
MatrixHere, it is also assumed that the noise caused by the receiveris much greater than the external noise arriving at the antenna elements [11]. When this noise is taken into account,the received signal observed at the receiver can be described
as,bRR = Ab0 + n,

2.2 Estimation Method of Correlation Matrix

(8)

(11)

where, n represents the noise vector observed at the receivers. When the noise is modeled as zero-mean Gaussian
white, the correlation matrix derived in (9) can be modified
as,
R0e = R0 + Rn ,(12)

where, R0e is the estimated correlation matrix with errors.
Rn is the component caused by the noise, and is describedas (13), where n1 , . . . , nK corresponds to the observed noise
vector when K sets of termination conditions are applied.
When the number of received symbols for each training
round is large enough, (13) can be rewritten as,⎛ ⎞+⎜⎜⎜ A1 ⎟⎟⎟
⎜ ⎟⎟
2⎜
+
(14)
Rn = σ ⎜⎜⎜⎜ ... ⎟⎟⎟⎟ ( A1H , . . . , AH
K) ,
⎜⎝ ⎟⎠
AK
where σ2 is the expected noise power. Since the interference
signals and noise are uncorrelated, the first two terms in E[·]of (13) become zero. In the following consideration, theestimation error is defined as,
J = ||Rn ||F ,where || · ||F represents a Frobenius norm.

(15)

IEICE TRANS. COMMUN., VOL.E96–B, NO.7 JULY 20131948

⎛ ⎞+ ⎡⎛⎛ ⎞⎛ ⎞⎤⎞⎜⎜⎜ A1 ⎟⎟⎟⎢⎢⎢⎜⎜⎜ bRR,1 ⎟⎟⎟⎜⎜⎜ n1 ⎟⎟⎟⎜⎜⎜ n1 ⎟⎟⎟⎥⎥⎥⎜⎜⎜ . ⎟⎟⎟⎢⎢⎢⎜⎜⎜ . ⎟⎟⎟ H
⎜
⎜
⎥⎥
⎟
⎟
⎜
⎜
⎟
⎟
.
.
H
H
H
H
H
+
⎜
⎜
⎟
⎟
Rn = ⎜⎜⎜ .. ⎟⎟⎟ E ⎢⎢⎢⎜⎜⎜ .. ⎟⎟⎟ (n1 , . . . , nK ) + ⎜⎜⎜ .. ⎟⎟⎟ (bRR,1 , . . . , bRR,K ) + ⎜⎜⎜ .. ⎟⎟⎟ (n1 , . . . , nK )⎥⎥⎥⎥ ( A1H , . . . , AH
K)
⎢⎣⎜⎝
⎜⎝ ⎟⎠
⎜⎝ ⎟⎠
⎥⎦
⎟⎠
⎝⎜ ⎠⎟
AK
bRR,K
nK
nK

3.

Simulation

3.1 Simulation Model
To verify the fundamental performance of the proposed estimation method, a simple antenna model was studied. Table 1 shows the antenna configurations considered in thisnumerical analysis. Here, ‘Rx1 ’, ‘Rx2 ’ and ‘zi ’ (i = 1 ∼ 4)mean receiving antennas, #1, #2, and parasitic antennas, respectively. In the model (A) named as MIMO adaptive, allantennas are half-wavelength dipole, and, and this linear array antenna comprises two receiving and four parasitic antennas (Mr = 2, M p = 4). The antenna distance is 0.1λ0 ,where λ0 is the wavelength in a vacuum. The receiving antennas are placed at both sides of the array, and the parasitic
antennas are placed between the receiving antennas. The
model (B) is array without the parasitic antenna, and other
Table 1

Antenna configuration for numerical analysis.

(13)

dimensions are set to identical to model (A). The distance
between receiving antennas is set to 0.5λ0 to oﬀer the same
aperture size.
For antenna (B), two schemes are adopted to compare
the performances to antenna (A). One is no interference
suppression, and the other is interference suppression using MMSE (Minimum Mean Squared Error) algorithms. In
the MMSE algorithm, the weight matrix, W MMS E , is determined to minimize the error in the desired signals. The number of the training symbols for MMSE is set to 12, and is
identical to that for observing bRR in antenna (A).
Figure 3 shows the channel model and sketch of thetransmitting and interference antennas. As a transmitter,
two dipoles with spacing of one wavelength were used, andthe interference signal was transmitted from a single dipole.
The geometry-based statistical model was used for this calculation [12]–[14]. Around all of the antennas, the scatterers are arranged in the horizontal direction; this assumption
comes from measurements in an actual environment [15].
To consider the statistical characteristics of the channel, 500
Monte Carlo simulations were performed in each condition.
The S -parameters and radiation patterns of the receiving array are calculated by moment method, and they were taken
into account in the following simulation. The operation frequency was set to 2.4 GHz.
3.2 Sheme of Proposed Algorithm
Figure 4 explains the flowchart of the actual proceduresin this scheme. This scheme is applied only for antenna(A). Before observing the interference signals, we need toknow S -parameter of the antenna. After evaluation of the
S -parameter, A1 , . . . , AK must be determined. They correspond to the termination conditions for K observations

Fig. 3Channel model and antenna arrangement.

HONMA et al.: NON-ITERATIVE ALGORITHM OF MIMO ADAPTIVE ARRAY1949

Fig. 5

Fig. 4

Estimation error, J, versus INR.

Flowchart of proposed algorithm.

and must be non-identical to each other. They are chosen
so as to minimize (15). In this simulation, we chose thebest one out of randomly generated 100 sets of the termination conditions under the constraint of the reactance range,−100 j ≤ zi ≤ 100 j, where the insertion resistance was neglected. It should be noted that these first two procedures
are required only for the first operation since S -parameterand A1 , . . . , AK are independent of the propagation characteristics.
The antenna observes the interference signals,
b1 , . . . , bK , corresponding to the predetermined termination
conditions, A1 , . . . , AK . Then, the correlation matrix, R0 ,is estimated by using (9). After this observation process,the reactance values of the terminations were optimized tominimize the interference power, and finally the desired termination condition, Aopt , is obtained. In the simulation forantenna (A), the steepest gradient algorithm [2] is used as
an optimization algorithm.
This scheme can work independently to the numberof the interference sources since R0 can be obtained in thesame manner as in (9). The analog adaptive antenna is effective in suppressing the multiple interferences [6], and thisadvantage is also obtained even when proposed scheme isused for such environment. However, the single interferencecase is studied in this paper for simplicity.
3.3 Result
Figure 5 indicates the estimation error of the correlation matrix shown in (15) versus INR. Here, it is assumed that only
the interference signal is observed for this calculation, andthe estimation error is normalized by Frobenius norm of theideal correlation matrix, R0 . The number of the trials is 500,
and Rician factor is set to −∞ dB. It can be seen that theestimation error decreases when the INR and the training
rounds, K, are increased. From this result, the minimal number of training rounds in (10) is not suﬃcient for estimating
the correlation matrix accurately. Therefore, the number ofFig. 6 Radiation patterns of MIMO adaptive antenna, (A), in xy-plane
under interference condition: (a) single interference wave (U: φ = 90◦ ), (b)single interference wave (U: φ = 45◦ ), (c) multiple interference waves (U:φ = 30◦ , 40◦ , 50◦ , 160◦ , 220◦ , 225◦ , 230◦ , 240◦ , 250◦ , and 300◦ ).

the training rounds is set to K = 12 in the following discussion.
Figure 6 shows the radiation patterns of antenna, (A),in xy-plane under the various interference conditions. Here,the letter, ‘U’ represents interference wave, and the INR
is 30 dB, K is set to 12. Figures 6(a) and (b) indicate

IEICE TRANS. COMMUN., VOL.E96–B, NO.7 JULY 2013

1950

Fig. 7

CDF of SINR.

the patterns when a single interference wave arrives at
the antenna from angles, 90◦ , and 45◦ , respectively. It
can be clearly seen that nulls are formed at the angle ofthe interference wave for both Rx1 and Rx2 . The reception power of the interference signal is lowered by atleast 10 dB in these cases. Figure 6(c) shows the patternwhen 10 interference waves arrive at the antenna from various angles, i.e. 30◦ , 40◦ , 50◦ , 160◦ , 220◦ , 225◦ , 230◦ , 240◦ ,250◦ , and 300◦ . Note that these 10 waves are same signals
with diﬀerent directions of arrivals. It can be seen that theradiation patterns for Rx1 and Rx2 do not have deep nulls.
Nevertheless the observed interference power suppression
by the proposed algorithm was about 10 dB in this case. Thismeans the radiation pattern can be formed so as to suppress
the synthesized interference signals.
Figure 7 shows the cumulative distribution function(CDF) of signal-to-interference-plus-noise ratio (SINR).
The median signal-to-noise ratio (SNR) of the desired signal
is determined to be 30 dB. The median value of the interference power is equal to that of the desired signal power. The
path distribution is uniform in the horizontal plane. Other
parameters are given identically to that in Fig. 5. Two typesof the algorithms, i.e. the proposed and previous [9] ones,
are tested and compared for the antenna (A). The number of
the training rounds, K, is set to 12 for both two algorithms.
For each training round, the termination set is given to be
diﬀerent to that for other training rounds. It can be seen
two algorithms for (A) yield almost identical results. Thismeans that the proposed method can oﬀer the deterministic
antenna control without any knowledge of the channel of theinterference signal. Also, it is found that 50% values of the
SINR in (B) with and without MMSE are lower by 13 dB
and 6 dB, respectively, than that in (A).
Figure 8 shows the cumulative distribution function(CDF) of achievable rate. The achievable rate is approximately calculated by,


σ2


(16)
R = log2  I + HH H 2 s 2
(σn + σi )Mt 
where, σ2s , σ2i , and σ2n represent the received powers of thedesired and interference signals, and noise, respectively. Mt
represents the number of the transmitting antennas. Though
the capacity under the interference can be analyzed more in

Fig. 8

CDF of achievable rate.

detail [16], the asymptotic capacity can be easily approximated if the interference can be recognized as Gaussian andthe propagation environment is random [9]. For MMSE algorithm in antenna (B), the rate is also calculated by,
R MMS E =


σ2s


H
H
log2  I+W MMS E HH W MMS E  2  2,
(σ n+σ )Mt 

(17)

i

where, σ 2n and σ 2i are the received noise and interference
powers after the MMSE filtering.
By comparing the results of (A) with proposed algorithm and [9], it is found that the two algorithms yield identical performances. Also, the MIMO adaptive antenna, (A),achieves three times higher rate than (B) without MMSE.
Though (B) with MMSE can suppress the interference, significant improvement in the achievable rate is not observed.
Since (B) has only two degrees of freedom, the rate is seriously degraded even when the interference is suppressed by
the digital adaptive array.
Figure 9 shows 50% bitrate versus raw SIR. Where,
Figs. 9(a) and (b) represent the results with Rayleigh environment (Rician factor = −∞ dB) and Rician environment(Rician factor = 10 dB), respectively. The raw SIR represents the SIR for (B) without MMSE. The SNR is always
set to 30 dB, and only the interference power is varied. It
can be seen that the proposed algorithm can provide same
performance to the previous work [9] over wide range of
the SIR. In the Rayleigh environment, antenna (A) with theproposed algorithm yields higher bitrate than (B) does evenwhen MMSE algorithm is applied to (B). On the other hand,the antenna, (B), with MMSE yields higher rate than antenna (A) especially when SIR is low in Rician environment.
From these results, it can be seen that existence of the direct
path aﬀects the performance of the MIMO adaptive array.
Also, it can be seen that the overall rate in Fig. 9(b) is lower
than that in Fig. 9(a). This is because this channel is highly
correlated and the rate enhancement eﬀect of MIMO is not
suﬃciently obtained. That is, saving the degree of freedom
is not eﬀective in enhancing the rate for Rician environment.
Nevertheless, the antenna, (A), outperforms antenna, (B),when SIR is higher than 0 dB. From these results, it can beseen that the proposed algorithm can oﬀer satisfactory per-

HONMA et al.: NON-ITERATIVE ALGORITHM OF MIMO ADAPTIVE ARRAY1951

Fig. 9 50% rate versus SIR: (a) Rician factor = −∞ dB, (b) Rician factor= 10 dB.

formance even without knowledge of the CSI.
4.

Conclusion

In this paper, a fast non-iterative algorithm based on correlation matrix has been proposed and studied. The proposed algorithm does not need any knowledge of the CSI and avoids
iterative training. The correlation matrix of the received interference signal at the antenna elements including the parasitic elements can be estimated by several training roundswith non-identical termination conditions. The performanceof the proposed algorithm has been studied based on thesimulation. It is shown the MIMO adaptive antenna withthe proposed method can suppress the interference powerby at least 10 dB in this simulation model, and enhances thebitrate greatly with the deterministic control scheme. Also,
the MIMO adaptive antenna with the proposed algorithm
oﬀers satisfactory performance identical to that of the previous work [9]. From these results, it is found that the proposed algorithm is eﬀective in reducing the time to control
the MIMO adaptive antennas.
Acknowledgements
This research was partially supported by JSPS KAKENHI(22760261) and Murata Science Foundation.
References[1] R.J. Dinger, “Reactively steered adaptive array using microstrip
patch elements at 4 GHz,” IEEE Trans. Antennas Propag., vol.34,
no.3, pp.423–431, March 1986.
[2] T. Ohira and K. Gyoda, “Electronically steerable passive array radiator antennas for low-cost analog adaptive beamforming,” 2000

IEEE International Conference on Phased Array Systems and Tech.,
pp.101–104, May 2000.
[3] M.D. Migliore, D. Pinchera, and F. Schettino, “Improving channel
capacity using adaptive MIMO antennas,” IEEE Trans. Antennas
Propag., vol.54, no.11, pp.3481–3489, Nov. 2006.
[4] S. Smith and D.V. Thiele, Switched parasitic antennas for cellularcommunications, Artech House, 2001.
[5] T. Ohira, “Analog smart antennas: an overview,” IEEE Int. Symp.
Personal, Indoor Mobile Radio Commun. (PIMRC), vol.4, pp.1502–
1506, Sept. 2002.
[6] E. Kataoka, M. Morishita, H. Yamada, M. Taromaru, and T. Ohira,“Interference cancellation performance of adaptive array of ESPAR
antennas,” Int. Symp. Antennas Propagat (ISAP), pp.760–763, Aug.
2007.
[7] Q. Han, B. Hanna, K. Inagaki, and T. Ohira, “Mutual impedance
extraction and varactor calibration technique for ESPAR antennacharacterization,” IEEE Trans. Antennas Propag., vol.54, no.12,
pp.3713–3720, Dec. 2006.
[8] N. Honma, K. Nishimori, R. Kudo, Y. Takatori, and K. Okada, “Using MIMO approach to get out of many iterations in analog adaptive
beamforming,” 2008 IEEE Antennas and Propagation Society International Symposium, no.304.3, July 2008.
[9] N. Honma, K. Nishimori, R. Kudo, Y. Takatori, and M. Mizoguchi,“Fast control method of parasitic antennas using non-iterative algorithm in multi-antenna system,” IEEE Trans. Antennas Propag.,vol.60, no.4, pp.2044–2051, April 2012.
[10] K. Nishimori, K. Cho, Y. Takatori, and T. Hori, “Adaptive array for
reducing high-power CCI on asynchronous TDD systems,” IEICE
Trans. Commun., vol.E84-B, no.7, pp.1727–1734, July 2001.
[11] J.W. Wallace and M.A. Jensen, “Mutual coupling in MIMO wirelesssystems: A rigorous network theory analysis,” IEEE Trans. WirelessCommun., vol.3, no.4, pp.1317–1325, July 2004.
[12] W.C. Jakes, Microwave Mobile Communications, IEEE, New York,1993.
[13] B.K. Lau, J.B. Andersen, G. Kristensson, and A.F. Molisch, “Impact of matching network on bandwidth of compact antenna arrays,”
IEEE Trans. Antennas Propag., vol.54, no.11, pp.3225–3238, Nov.
2006.
[14] A.F. Molisch, “A generic model for MIMO wireless propagation
channels in macro- and microcells,” IEEE Trans. Signal Process.,
vol.52, no.1, pp.61–71, Jan. 2004.
[15] K. Nishimori, N. Tachikawa, Y. Takatori, R. Kudo, and K.
Tsunekawa, “Frequency correlation characteristics due to antennaconfigurations in broadband MIMO transmission,” IEICE Trans.
Commun., vol.E88-B, no.6, pp.2438–2445, June 2005.
[16] R.S. Blum, “MIMO capacity with interference,” IEEE J. Sel. Areas
Commun., vol.21, no.5, pp.793–801, June 2003.

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.

IEICE TRANS. COMMUN., VOL.E96–B, NO.7 JULY 2013

1952

Kentaro Nishimori
received the B.E., M.E.,
and Dr.Eng. degrees in electrical and computerengineering from Nagoya Institute of Technology, Aichi, in 1994, 1996, and 2002, respectively. He joined NTT Wireless Systems Laboratories in 1996. He was a visiting researcher at
the Center for TeleInFrastruktur, Aalborg University, Denmark in 2006. He received theYoung Engineers Award from the Institute ofElectronics, Information and Communication
Engineers (IEICE) of Japan in 2001 and Young
Engineer Award from IEEE AP-S Japan Chapter in 2001. His current research interests are multi-user MIMO systems and cognitive radio systems.
He is a member of IEEE.

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 (NTT) in
Japan. He has been engaged in research and development of MAC protocol for the high speed
and the high communication quality in wirelessLANs systems. He is now associate professor in
Nippon Institute of Technology (NIT). He is amember of IEEE.

Yoshitaka Tsunekawa
received the B.E.
degree from Iwate University, Morioka, Japan,
in 1980 and the M.E. and the Doctor of Engineering degrees from Tohoku University, Sendai, Japan, in 1983 and 1993, respectively. Since
1983, he has been with the Faculty of Engineering, Iwate University, where he is now a professor at the Department of Electrical Engineeringand Computer Science. His current research interests include digital signal processing and digital control. He is a member of the IEEE.