IEICE Communications Express, Vol.7, No.3, 101–106

Numerical study on arotationally-symmetrical
dipole array antenna position
for a MIMO full-duplex system
Yoshiyuki Yamamoto1a), Masakuni Tsunezawa2, Kentaro Murata3,Naoki Honma2, and Qiang Chen1
1

Graduate School of Engineering, Tohoku University,6–6–5 Aramakiaza-Aoba, Aoba-ku, Sendai, Miyagi 980–8579, Japan
2

Graduate School of Engineering, Iwate University,4–3–5 Ueda, Morioka, Iwate 020–8551, Japan
3

Graduate School of Engineering, National Defense Academy,

1–10–20 Hashirimizu, Yokosuka, Kanagawa 239–8686, Japana) yamamoto-y@ecei.tohoku.ac.jp

Abstract: In this letter, a rotationally-symmetrical array (RSA) arrangement of a receiving dipole array antenna is optimized to maximize theperformance of the null-beamforming method for the suppression of selfinterference. The optimum RSA for a receiving dipole array with fourelements is clariﬁed. Through numerical simulations, we found that theoptimized RSA arrangement suppressed the self-interference signiﬁcantly.
Keywords: MIMO full-duplex, self-interference, antenna arrangement,
null-beamforming
Classiﬁcation: Antennas and PropagationReferences© IEICE 2018
DOI: 10.1587/comex.2017XBL0182
Received November 25, 2017
Accepted December 22, 2017
Publicized January 15, 2018
Copyedited March 1, 2018

[1] J. I. Choi, M. Jain, K. Srinivasan, P. Levis, and S. Katti, “Achieving singlechannel, full duplex wireless communication,” Proc. 2010 ACM MobiCom.,
pp. 1–12, Sep. 2010.
[2] I. E. Telatar, “Capacity of multi-antenna Gaussian channels,” Tech. Rep., AT&TBell Labs, June 1995.
[3] D. Bharadia, E. McMilin, and S. Katti, “Full-duplex radios,” Proc. ACM
SIGCOMM Comp. Commun. Rev., pp. 375–386, Oct. 2013.
[4] S. Zhou and G. B. Giannakis, “Optimal transmitter eigen-beamforming andspace-time block coding based on channel mean feedback,” IEEE Trans. on Sig.
Proc., vol. 50, no. 10, pp. 2599–2613, Oct. 2002. DOI:10.1109/TSP.2002.
803355[5] Y. Yamamoto, R. Takahashi, M. Tsunezawa, N. Honma, and K. Murata,“Experimental evaluation of interference reducation eﬀect; Eigen-beamformingand digital subtraction by using MIMO-OFDM signals,” IEICE Commun.
Express, vol. 6, no. 2, pp. 71–76, Feb. 2017. DOI:10.1587/comex.
2016XBL0175[6] M. Tsunezawa, N. Honma, K. Takahashi, K. Murata, and K. Nishimori,“Rotationally-symmetrical array for self-interference reduction in full-duplex

101

IEICE Communications Express, Vol.7, No.3, 101–106

MIMO,” IEICE Commun. Express, vol. 6, no. 6, pp. 363–368, Jun. 2017.
DOI:10.1587/comex.2016SPL0040

1Introduction

Full-duplex system and multiple-input multiple-output (MIMO) technology arepromising technologies that can improve communication capacity without using
additional frequency bands [1, 2]. The full-duplex system enables simultaneous twoway wireless communication in the same frequency band while the MIMO technology improves frequency utilization eﬃciency using multiple antennas. Thecombination of the MIMO technology and the full-duplex system is called theMIMO full-duplex system. However, it is well-known that the full-duplex systemsuﬀers from the so-called self-interference [3]. The self-interference problem leads
to the saturation of the radio frequency (RF) front-end because the level of thetransmitting signal is considerably higher than that of the receiving signal. Consequently, the RF front-end suﬀers from undesired nonlinearity and can be damaged.
In addition, the eigen-beamforming (EBF) method is a technique to improve thecommunication quality by controlling the radiation pattern at the transmitter sideusing transmission weight vector [4]. The control of the radiation pattern at thetransmitter side can be also eﬀective in circumventing the self-interference because
the interference cannot reach the receiving antennas ideally. The null-beamforming(NBF) method is deﬁned as the EBF method used to suppress self-interference
using transmission weight vectors obtained by singular value decomposition (SVD)of the self-interference channel [5]. The performance of the NBF method is strongly
aﬀected by the nature of self-interference channel, in terms of spatial correlation. Ingeneral, high spatial correlation leads to higher performance of the NBF method.
Previously, an array antenna arrangement such as rotationally-symmetricalarray (RSA) has been proposed to increase the spatial correlation and improve
the performance of the NBF method [6]. In RSA, the NBF method can considerably
suppress the self-interference if all antennas are point wave sources. However, theactual antenna has mutual coupling from other antennas.
Due to the highly symmetric arrangement of the RSA, the self-interference
can be suppressed but the inﬂuence of asymmetry of mutual coupling between thearray antenna elements can negatively impact its performance. The mutual coupling
between the array antenna depends on the position of the array antenna.
In this letter, the receiving antenna arrangement for the RSA is optimized fromthe viewpoint of self-interference channel between the transmitting and receivingarray antenna elements. Both transmitting and receiving antennas are array antennaconsisting of four-element dipole antennas.
2© IEICE 2018
DOI: 10.1587/comex.2017XBL0182
Received November 25, 2017
Accepted December 22, 2017
Publicized January 15, 2018
Copyedited March 1, 2018

Antenna arrangement suitable for NBF method

Fig. 1 shows a system model of our proposed MIMO full-duplex system. N and M
are the number of transmitting antenna (Tx) and receiving antenna (Rx), respectively. H is the self-interference channel, i is the i-th singular value of H in102IEICE Communications Express, Vol.7, No.3, 101–106

Fig. 1.

System modeldescending order, and vi is the i-th transmission weight vector obtained by SVD ofH. By arranging the array antenna so that the rank of H becomes 1, the singularvalues other than the ﬁrst singular value degenerate. The NBF method uses thetransmission weight vectors excluding the ﬁrst singular value. The magnitude of
the self-interference channel norm using NBF method is given by
kHV~1 k2F ¼minðM;NÞ
X

2i ;

ð1Þ

i¼2

© IEICE 2018
DOI: 10.1587/comex.2017XBL0182
Received November 25, 2017
Accepted December 22, 2017
Publicized January 15, 2018
Copyedited March 1, 2018

where V~1 is the transmission weight matrix excluding the ﬁrst singular value,
V~ 1 ¼ ½v2 ;    ; vN . This means that Tx weighted by V~1 forms a null in Rx direction
to suppress 1 using the NBF method.
Fig. 2 shows the antenna arrangement to gain high spatial correlation. The Tx
linear array is located on the z-axis. The Rx circular array is located on thecircumference around the z-axis. D is the distance from the end of the Tx arrayto the origin of the Rx array, de is the element spacing of the Tx array, and re is theradius in the Rx array. We assume that all antennas are point wave sources and there
is no mutual coupling.
In RSA, Line-of-sight paths from the arbitrary transmitting element to all of Rx
elements are the same strength and phase because the distance between an arbitrarytransmitting point and all of receiving point wave sources are equal. Therefore, allelements in each column vector of the self-interference channel matrix, H, areidentical, and the rank of self-interference channel H equals 1.
The self-interference power Pw=NBF and Pw=oNBF are deﬁned as103

IEICE Communications Express, Vol.7, No.3, 101–106

Fig. 2.

Antenna arrangement

XP minðM;NÞ
Pw=NBF ¼
2i ;N  1 i¼2

ð2ÞXP minðM;NÞ
2i ;
N i¼1

ð3Þ

Pw=oNBF ¼

where P is the sum of the transmission power. The singular value of the selfinterference channel becomes 0 except for ﬁrst singular value if the rank of H is 1.
Therefore, the self-interference power with and without NBF method arePw=NBF ¼ 0 and Pw=oNBF ¼ P21 =N. Therefore, the NBF method can suppress theself-interference by excluding only the ﬁrst singular value.
However, the gain of each Rx antenna varies if the mutual coupling of the Rx
array antenna is asymmetric due to the mutual coupling among Rx. In this letter, thesymmetry of the mutual coupling of the RSA antenna is evaluated from themagnitude of the mutual coupling of each Rx antenna.
3© IEICE 2018
DOI: 10.1587/comex.2017XBL0182
Received November 25, 2017
Accepted December 22, 2017Publicized January 15, 2018
Copyedited March 1, 2018

Numerical analysis results

3.1 Simulation setup
The antenna arrangement used for numerical analysis is shown in Fig. 2. Theantenna is a half-wavelength dipole antenna. The distance from the end of the Tx
array to the origin of the Rx array, the element spacing of the Tx array and the104

IEICE Communications Express, Vol.7, No.3, 101–106

radius of the Rx array are set to D ¼ 10, de ¼ 0:5 and re ¼ 0:5, respectively(λ: wavelength in a vacuum). e is the rotation angle of the receiving antennas
moving in the direction from x-axis to y-axis. In this numerical analysis, wechanged the rotation angle e from 0° to 90°.
3.2 Simulation results

Fig. 3.

Simulation results

Fig. 3(a) shows the singular value characteristics. The ﬁrst singular value wasalmost the same at all rotation angles, the second singular value become smaller as
it approaches e ¼ 45°. We found that the second singular value at e ¼ 45° was, atmaximum, 48 dB lower than that at e ¼ 0°. From the results, we found that thespatial correlation become higher as approach at e ¼ 45°.
Fig. 3(b) shows the mutual coupling of the Rx antenna versus rotation angle.
The mutual coupling of i-th Rx antenna Ci is given as
Ci ¼

N
XjSi;k j2

ði ≠ kÞ;ð4Þ

k¼1© IEICE 2018
DOI: 10.1587/comex.2017XBL0182
Received November 25, 2017
Accepted December 22, 2017
Publicized January 15, 2018
Copyedited March 1, 2018

where Si;k is S-parameter from k-th Rx antenna to i-th Rx antenna. The mutualcoupling diﬀerence of each Rx antenna become smaller as it approaches e ¼ 45°.
In particular, all mutual coupling at e ¼ 45° were almost equal. The sum of mutual105

IEICE Communications Express, Vol.7, No.3, 101–106

coupling from the adjacent antenna (e  90°) is equal if the directivity of theRSA antenna is point-symmetric. Therefore, Ci is aﬀected by the mutual couplingof the diagonal RSA antenna (e þ 180°). The dipole antenna is omnidirectionalon the xz-plane perpendicular to the element axis (y-axis) and forms a null at theend of element on the xy-plane. Thus, the mutual coupling C1 and C3 were large,
and C2 and C4 were small at e ¼ 0°. However, mutual coupling between Rxantennas at e ¼ 45° were almost equal because the mutual coupling of the dipole
antennas on the diagonal was equal. Therefore, the mutual coupling at e ¼ 45° wassymmetrical.
Fig. 3(c) shows the self-interference power versus rotation angle. The selfinterference power without NBF method (Pw=oNBF ) was −37 dB at all rotation
angles. In other hand, the self-interference power with NBF method (Pw=NBF )was suppressed by more than 95 dB at all rotation angles. In particular, the selfinterference power was suppressed by 143 dB at e ¼ 45°. This shows that the NBFmethod at e ¼ 45° suppresses the self-interference signiﬁcantly because the selfinterference channel including the inﬂuence of mutual coupling was symmetrical.
4Conclusions

Numerical analysis conﬁrmed that the self-interference power with NBF method
varies with the rotation angle of the receiving dipole array antenna of RSA. The
self-interference power was changed according to the rotation angles because themutual coupling of the receiving dipole array antennas alters the symmetry. The
self-interference power with NBF method (Pw=NBF ) was suppressed by 143 dB at
e ¼ 45°. Therefore, we found that the most eﬃcient arrangement of the dipole
array antenna in RSA is at e ¼ 45°.
Acknowledgments
This research and development work was supported by the MIC/SCOPE#155002002.

© IEICE 2018
DOI: 10.1587/comex.2017XBL0182
Received November 25, 2017
Accepted December 22, 2017
Publicized January 15, 2018
Copyedited March 1, 2018106