IEICE Communications Express, Vol.1, No.7, 246–251

Decoupling technique forn-element linear array
antenna using transmission
lines between neighboringelementsNaoya Yamakia) and Naoki Honma
Graduate School of Engineering, Iwate University
4–3–5, Ueda, Morioka, 020–8551, Japana) t2311061@iwate-u.ac.jp

Abstract: In this letter, a design method of a simple decoupling
network (DN), which decouples adjacent antenna ports for n-element
linear array antenna, is presented and evaluated based on simulationand measurements. In our technique, microstrip line (MSL) is used toconﬁgure DN. MSLs work as bridge susceptances and are connected
between two adjacent antenna ports, and they decouple the antenna
ports by means of cancelling the mutual admittance. From the experimental results, it is found that the mutual coupling less than −30 dB
between adjacent antenna elements is achieved by using proposed design method.
Keywords: decoupling network, mutual coupling, transmission line,
array antenna, MIMOClassification: Antennas and Propagation
Referencesc

IEICE 2012

DOI: 10.1587/comex.1.246
Received November 09, 2012
Accepted November 21, 2012
Published December 11, 2012[1] I. E. Telatar, “Capacity of multi-antenna Gaussian channels,” Tech. Rep.,
AT&T-Bell Labs, June 1995.
[2] Q. H. Spencer and M. Haardt, “Capacity and downlink transmission algorithms for a multi-user MIMO channel,” The Thirty-Sixth Asilomar
Conference on Signals, Systems and Computers, vol. 2, pp. 1384–1388,
Nov. 2002.
[3] B. K. Lau, J. B. Andersen, A. F. Molisch, and G. Kristensson, “Antenna
Matching for Capacity Maximization in Compact MIMO systems,” International Symposium on Wireless Communication Systems (ISWCS’06).
Antenna Systems., pp. 253–257, Sept. 2006.
[4] J. Weber, C. Volmer, K. Blau, R. Stephan, and M. A. Hein, “Miniaturizedantenna arrays using decoupling networks with realistic elements,” IEEE
Trans. Wicrow. Theory Tech., vol. 54, no. 6, pp. 2733–2740, June 2006.
[5] S. C. Chen, Y. S. Wang, and S. J. Chung, “A decoupling technique for increasing the port isolation between two strongly coupled antennas,” IEEETrans. Antennas Propag., vol. 56, no. 12, pp. 3650–3658, Dec. 2008.
[6] N. Yamaki and N. Honma, “Simple design of decoupling network considering mutual admittance in array antenna,” 2011 International Symposium

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IEICE Communications Express, Vol.1, No.7, 246–251

on Antennas and Propagation (ISAP 2011), Electric Proc. of ISAP 2011,Oct. 2011.

1Introduction

In order to enhance the performance of the wireless communication systems,
multi-antenna systems, such as MIMO (Multiple-Input Multiple-Output),and so on, have been studied [1, 2]. However, the communication quality
is deteriorated by the eﬀect of mutual coupling in such multi-antenna systems [3]. Therefore, the mutual coupling reduction technique is needed in
multi-antenna systems. To reduce the eﬀect of the mutual coupling, decoupling network (DN) can be used. Studies about DN have been pursued [4, 5]
and in [4], a deterministic design theory of decoupling and matching network(DMN) for n element array is denoted. However, this DMN has narrowband
property and its complexity of circuit conﬁguration dramatically increases as
the number of antenna elements increases. In [5], the circuit design methodby using transmission lines and lumped element is described. This method
can be applied only for two elements antenna conﬁguration, and the expansion of this method to n elements antenna conﬁguration has not been studied.
As explained above, simple DN which can be applicable to n elements array
antenna is needed. When we focus on a n element linear array antenna,
the mutual coupling between adjacent antenna elements is higher than thatof other antenna combinations. This means suppression of the mutual coupling just among adjacent antenna elements will eﬃciently enhance the array
antenna performance.
In this letter, a design method of a simple decoupling network suitable
for n element linear array antenna is presented. In order to simplify the DN
conﬁguration, only adjacent antenna elements are decoupled in the proposed
design. To achieve the decoupling network with simple and feasible conﬁguration, it is conﬁgured by using only MSL. In the following section, theproposed circuit design theory is explained ﬁrst. Next, the circuit characteristic is evaluated based on simulation and measurement.

2

Circuit design theory

Fig. 1 shows the sketch of the antennas and DN conﬁguration [6]. In Fig. 1,Y a , Y l , Y d , Y are the admittance matrices of the array antenna, transmission line, DN and synthesized circuit observed at the reference plane 1,
respectively. Since the antenna and DN are connected in parallel, the synthetic admittance matrix, Y  , can be written as
Y  = Y + Y d.

(1)

Decoupling between two neighboring antenna ports is realized by forcingc

IEICE 2012

DOI: 10.1587/comex.1.246
Received November 09, 2012
Accepted November 21, 2012
Published December 11, 2012

Yd,k+1,k = −Yk+1,k ,(2)247

IEICE Communications Express, Vol.1, No.7, 246–251

Fig. 1. Proposed DN conﬁguration
where k is integer number, 1 ≤ k ≤ n − 1. The mutual coupling between
two neighboring antenna elements can be cancelled by connecting a reactanceelement between these antenna ports if the mutual admittance is purely imaginary. However, the antenna mutual admittance has generally not only theimaginary value but also real value. To obtain the purely imaginary value ofthe mutual admittance, the serial transmission lines for phase rotation whoselengths are ll are used. Assuming MSL is lossless transmission line, the admittance matrix elements of i-th (1 ≤ i ≤ n) transmission line are expressedas
1 cos βl ll,
Zl j sin βl ll−11,Yln+i,i = Yli,n+i =Zl j sin βl ll
Yli,i = Yln+i,n+i =(3)(4)

where, Zl and βl are the characteristic impedance of the transmission line
and the phase constant, respectively. These parameters are given identicallyfor all of the serial lines. Therefore, Y l is deﬁned as 2n × 2n matrix and canbe partitioned into four matrices asY l11 Y l12Yl =,(5)
Y l21 Y l22
where, the size of each partitioned matrices are n × n. Each of partitioned
matrix is diagonal matrix deﬁned by (3), (4). By using these partitioned
matrices and Y a , the observed matrix,Y , at the reference plane 1 is expressedas [6]Y = Y l11 − Y l12 (Y a + Y l22 )−1 Y l21 .

c


IEICE 2012

DOI: 10.1587/comex.1.246
Received November 09, 2012
Accepted November 21, 2012
Published December 11, 2012(6)

By using (3), (4) and (6), the line length ll which achieves purely imaginary
mutual admittance can be determined. Therefore, the mutual coupling can becancelled by connecting a reactance element. In our technique, the reactanceelement is conﬁgured by using a bridge MSL as a bridge susceptance. Thebridge susceptance can be realized by using the bridge MSL if its length
satisﬁes βd ld = π/2 + mπ, (m ≥ 0). Where, βd and ld are the phase constant
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IEICE Communications Express, Vol.1, No.7, 246–251

and length of the bridge MSL, respectively. Structurally, the length of bridge
susceptance must be longer than the antenna space, d. Therefore,
ld = λg /2(1/2 + m) ≥ d(7)must be satisﬁed, where, λg is eﬀective wavelength in the bridge susceptance. Similarly to (4), mutual admittance of the bridge susceptance can beexpressed as
Yd,i+1,i = Yd,i,i+1 =j(−1)m .
Zd,i(8)To satisfy (2), (7), m and characteristic impedance of the bridge MSL must
be properly determined. The characteristic impedance of the bridge MSL isderived by considering the transformed mutual admittance of the antennas
shown in (6). From the absolute value of the antenna’s mutual susceptance,
Yi+1,i , the characteristic impedance of bridge line is derived asZd,i =j(−1)m.
Yi+1,i(9)Note that, m must be chosen to satisfy Zd,i > 0.

3

Measurement and simulation

3.1 Fabricated antenna and DN
Fig. 2 (a) shows the fabricated antenna. The antenna is 4-elements E-plane
patch array. The operation frequency, f0 , is 2.085 GHz. The dimension of theantenna is described as follows; W1 = 140 mm, L1 = 280 mm, W2 = 65 mm,
L2 = 47.1 mm, G = 14.5 mm, D = 140 mm and H = 1.6 mm. The antenna is
conﬁgured on the Polytetraﬂuoroethylene (PTFE) substrate, and its relative
permittivity is 2.2. Fig. 2 (b) shows the fabricated DN. The same substrateis used for the DN. The DN was designed by using the circuit design theory
described in Section 2 and its design value was calculated based on measured
antenna admittance matrix, that is, we assume this antenna admittance matrix as Y a . From calculation result, the length of serial transmission line,c

IEICE 2012

DOI: 10.1587/comex.1.246
Received November 09, 2012
Accepted November 21, 2012
Published December 11, 2012

Fig. 2. Fabricated antenna and DN249

IEICE Communications Express, Vol.1, No.7, 246–251

ll , is 23.2 mm from (3), (4) and (6). The length of the bridge MSL is determined as 3λg /4 (βd ld = 3π/2) from (7). The characteristic impedances of thebridge MSLs are calculated by using (9) and calculated values are as follows;
Zd1 = 101.3 Ω, Zd2 = 98.2 Ω and Zd3 = 102.7 Ω. By determining characteristic impedance of the bridge MSL, the width of the bridge line which achieves
desired impedance is determined. It should be noted that ll is determined byconsidering the phase delay of the connector.

3.2 Results
3.2.1 Simulation result
Fig. 3 (a) shows simulated S-parameter. The frequency characteristics of theDMN in [4], which decouples all the antenna elements are also indicated inFig. 3 (a) for comparison. Here, the reﬂected characteristics of only |S11 | and|S22 | are shown since the antenna structure is symmetric. From Fig. 3 (a), it
can be seen that the fractional bandwidth (|S11 | ≤ −10 dB) with proposed
DN and with [4] are 1.247% and 0.0959% respectively. |S21 | and |S32 | can be
decreased to about 30 dB at resonant frequency by using proposed DN. It canbe seen that the impact of the proposed DN on |S31 |, |S41 | is negligible. Thisis because the proposed DN decouples only two adjacent antenna elements.
3.2.2 Measurement resultFig. 3 (b) shows measured S-parameter. From Fig. 3 (b), it can be seen thatthe operation frequency with fabricated DN is slightly shifted. The reason ofthis is considered that self admittance of the fabricated bridge line was not
zero, and it aﬀects the self-admittance observed at the feed port. That is, themanufacturing error of bridge MSL length can aﬀect the reﬂection coeﬃcient.
By using proposed DN, the mutual coupling between two adjacent antenna
ports, |S21 | and |S32 |, was decreased to less than −30 dB at the operationfrequency. From Fig. 3 (b), the levels of |S21 |, |S32 |, |S31 | and |S41 | around2.1 ∼ 2.2 GHz are higher than that of Fig. 3 (a). The reason of this isconsidered the bridge susceptances between antenna ports deteriorate themutual coupling around this frequency band. Fig. 3 (c) shows measured
E-plane radiation pattern. Since the antenna structure is symmetric, theradiation patterns of 1st and 2nd antenna are only shown. From Fig. 3 (c),radiation patterns with and without DN diﬀer slightly, and radiation pattern
distortion can be seen. It is considered this distortion is caused by change ofantenna port current resulted from connecting DN.
4c

IEICE 2012

DOI: 10.1587/comex.1.246
Received November 09, 2012
Accepted November 21, 2012
Published December 11, 2012Conclusion

In this letter, the design method of the simple DN, which decouples adjacentantenna ports in n-element linear array antenna has been presented. The
design method of the DN using MSL is explained. Decoupling is realized byconnecting MSLs between adjacent antenna ports as a bridge susceptance.
From simulation results, the impact of proposed DN on bandwidth is negligible. From experimental results, by using proposed DN, the mutual coupling

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IEICE Communications Express, Vol.1, No.7, 246–251

Fig. 3. Frequency characteristics of S-parameter andmeasured radiation pattern
between two neighboring antenna ports is suppressed less than −30 dB at theresonant frequency. These results prove that the proposed design method iseﬀective in achieving DN with low circuit complexity.

Acknowledgments
This research was partially supported by MEXT KAKENHI (22760261). Theauthors thank Prof. Chen Qiang of Tohoku University for supporting themeasurement in this work.

c

IEICE 2012

DOI: 10.1587/comex.1.246
Received November 09, 2012
Accepted November 21, 2012
Published December 11, 2012251