Browse > Article
http://dx.doi.org/10.4218/etrij.2018-0455

Array pattern synthesis using semidefinite programming and a bisection method  

Lee, Jong-Ho (School of Electronic Engineering, Soongsil University)
Choi, Jeongsik (Intel Labs, Intel Corporation)
Lee, Woong-Hee (Department of Communication Systems, KTH Royal Institute of Technology)
Song, Jiho (School of Electrical Engineering, University of Ulsan)
Publication Information
ETRI Journal / v.41, no.5, 2019 , pp. 619-625 More about this Journal
Abstract
In this paper, we propose an array pattern synthesis scheme using semidefinite programming (SDP) under array excitation power constraints. When an array pattern synthesis problem is formulated as an SDP problem, it is known that an additional rank-one constraint is generated inevitably and relaxed via semidefinite relaxation. If the solution to the relaxed SDP problem is not of rank one, then conventional SDP-based array pattern synthesis approaches fail to obtain optimal solutions because the additional rank-one constraint is not handled appropriately. To overcome this drawback, we adopted a bisection technique combined with a penalty function method. Numerical applications are presented to demonstrate the validity of the proposed scheme.
Keywords
array pattern synthesis; bisection method; semidefinite programming; semidefinite relaxation;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. M. Razavizadeh, M. Ahn, and I. Lee, Three-dimensional beamforming: a new enabling technology for 5G wireless networks, IEEE Signal Process. Mag. 31 (2014), no. 6, 94-101.   DOI
2 C. L. Dolph, A current distribution for broadside arrays which optimizes the relationship between beam width and sidelobe level, Proc. IRE. 34 (1946), 335-348.   DOI
3 O. M. Bucci et al., Antenna pattern synthesis: a general approach, Proc. IEEE. 82 (1994), no. 3, 358-371.   DOI
4 P. Y. Zhou, M. A. Ingram, and P. D. Anderson, Synthesis of minimax sidelobes for arbitrary arrays, IEEE Trans. Antennas Propag. 46 (1998), no. 11, 1759-1760.   DOI
5 P. Y. Zhou and M. A. Ingram, Pattern synthesis for arbitrary arrays using an adaptive array method, IEEE Trans. Antennas Propag. 47 (1999), no. 5, 862-869.   DOI
6 H. Lebret and S. Boyd, Antenna array pattern synthesis via convex optimization, IEEE Trans. Signal Process. 45 (1997), no. 3, 526-532.   DOI
7 B. Fuchs and J. J. Fuchs, Optimal narrow beam low sidelobe synthesis for arbitrary arrays, IEEE Trans. Antennas Propag. 58 (2010), no. 6, 2130-2135.   DOI
8 B. Fuchs, A. Skrivervik, and J. R. Mosig, Synthesis of uniform amplitude focused beam arrays, IEEE Antennas Wireless Propag. Lett. 11 (2012), 1178-1181.   DOI
9 Y.-H. Nam et al., Full-dimensional MIMO (FD-MIMO) for next generation cellular technology, IEEE Commun. Mag. 51 (2013), no. 6, 172-179.   DOI
10 P. Rocca, R. J. Mailloux, and G. Toso, GA-based optimization of irregular subarray layouts for wideband phased arrays design, IEEE Antennas Wireless Propag. Lett. 14 (2015), 131-134.   DOI
11 S. Todnatee and C. Phongcharoenpanich, Iterative GA optimization scheme for synthesis of radiation pattern of linear array antenna, Int. J. Antennas. Prop. 2016 (2016), 7087298.
12 O. M. Bucci, L. Caccavale, and T. Isernia, Optimal far-field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions, IEEE Trans. Antennas Propag. 50 (2002), no. 11, 1539-1554.   DOI
13 P. J. Kajenski, Phase only antenna pattern notching via a semidefinite programming relaxation, IEEE Trans Antennas Propag. 60 (2012), no. 5, 2562-2565.   DOI
14 B. Fuchs, Application of convex relaxation to array synthesis problems, IEEE Trans Antennas Propag. 62 (2014), no. 2, 634-640.   DOI
15 Z. Luo et al., Semidefinite relaxation of quadratic optimization problems, IEEE Signal Process. Mag. 27 (2010), no. 3, 20-34.   DOI
16 S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge, Cambridge University Press, 2004.
17 H. M. Wang et al., Hybrid cooperative beamforming and jamming for physical-layer security of two-way relay networks, IEEE Trans. Inf. Forensics Security. 8 (2013), no. 12, 2007-2020.   DOI
18 J. F. Sturm, Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones, Optim. Methods Softw. 11-12 (1999), 625-653.   DOI
19 J. Lofberg, YALMIP: A toolbox for modeling and optimization in MATLAB, Proc. the CACSD Conf., New Orleans, LA, USA, 2004.
20 F. Wang et al., Optimal array pattern synthesis using semidefinite programming, IEEE Trans. Signal Process. 45 (1997), no. 3, 526-532.   DOI
21 C. Sun and R. Dai, Rank-constrained optimization and its applications, Automatica. 82 (2017), 128-136.   DOI
22 J.-H. Lee, Confidential multicasting assisted by multi-hop multiantenna DF relays in the presence of multiple eavesdroppers, IEEE Trans. Commun. 64 (2016), no. 10, 4295-4304.   DOI
23 P. Rocca, N. Anselmi, and A. Massa, Optimal synthesis of robust beamformer weights exploiting interval analysis and convex optimization, IEEE Trans. Antennas Propag. 62 (2014), no. 7, 3603-2612.   DOI
24 E. Karipidis, N. D. Sidiropoulos, and Z.-Q. Luo, Quality of service and max-min fair transmit beamforming to multiple cochannel multicast groups, IEEE Trans. Signal Process. 56 (2008), no. 3, 1268-1279.   DOI
25 T. Isernia et al., A hybrid approach of the optimal synthesis of pencil beams through array antennas, IEEE Trans. Antennas Propag. 52 (2004), no. 11, 2912-2918.   DOI