Optimizing beamforming power in multi-antenna transmission with eavesdroppers
Keywords:
Beamforming, QCQP, Physical layer security, Semi-definite programmingAbstract
The problem of minimizing transmit power of a multi-antenna base station is usually considered a form of beamforming problems in multi-antenna radio transmission and is currently attracting the attention of researchers, especially in the context of physical layer security – with the existence of an eavesdropper. In fact, power minimization problems with non-convex SNR constraints belong to the class of NP-hard problems which normally introduce high computational complexity and are often difficult to derive the optimal solution. Conventional solutions are to formulate the quadratic constraint quadratic problem (QCQP) to a reduced semi-definite programming (SDP) problem tailored by randomization technique, or can be solved by a sequence of SDPs. Both methods significantly increase the number of auxiliary variables leading to increased computational complexity. In this paper, the QCQP problem is modeled as a series of quadratic problems that can be solved directly without up-converting the vector to SDP matrix. Simulation result shows that this method can provide near-optimal results while significantly reducing the computational complexity compared to both traditional methods.
References
Z. Xiao, “Suboptimal Spatial Diversity Scheme for 60 Ghz Milimeter-Wave WLAN”, IEEE Commun. Lett., vol. 17, no. 9, pp. 1790-1793, Sep. 2013
Z. Xiao, C. Zhang, D. Jin, and N. Ge, “GLRT Approach for Robust Burst Packet Acquisition in Wireless Communications,” IEEE Trans. Wireless Commun., vol. 12, no. 3, pp. 1127–1137, Mar. 2013
P. Apkarian, D. Noll, A. Rondepierre, “Mixed control via nonsmooth optimization”, SIAM J. Control Optimz., vol. 47, no. 3, pp. 1516-1546, 2008.
P. Apkarian, H.D. Tuan, “Concave programming in control theory”, J. of Global Optimization 15(1999), 243-270.
E. Karipidis, T. N. Davidson, and Z.-Q. Luo, “Transmit beamforming for physical-layer multicasting,” IEEE Trans. Signal Processing, vol. 54, no. 6, pp. 2239-2251, June 2006.
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 Processing, vol. 56, no. 3, pp. 1268-1279, March 2008.
H. H. Kha, H. D. Tuan, and T. Q. Nguyen, “Efficient design of cosine- modulated filter banks via convex optimization,” IEEE Trans. Signal Processing, vol. 57, no. 3, pp. 966-976, March 2009.
A.H. Phan, H.D. Tuan, H.H. Kha, “New optimized solution method for beamforming in cognitive multicast transmission”, Vehicular Technology Conference (VTC Fall), 2010.
T. Phan, A. Vorobyov, N. D. Sidiropoulos, and C. Tellambura, “Spectrum sharing in wireless networks via qos-aware secondary multicast beamforming,” IEEE Trans. Signal Processing, vol. 57, no. 6, pp. 2323 - 2335, June 2009.
N.D. Sidiropoulos, T.N. Davidson, Z.-Q. Luo, “Transmit bemforming for physical-layer multicasting”, IEEE Trans. Signal Processing, vol. 54, no. 6, pp. 2239-2251, 2006.
H.D. Tuan, P. Apkarian, S. Hosoe, H. Tuy,” D.C. optimization approach to robust controls: the feasibility problems”, International Journal of Control 73(2000), 89-104.
H. Tuy, “Convex Analysis and Global Optimization”, Kluwer Academic, 2000.
L. Dong, Z. Han, A. Petropulu, and H. V. Poor, “Secure wireless communications via cooperation,” in Proc. 46th Annu. Allerton Conf. Commun., Control, Comput., pp. 1132–1138, Sep. 2008
Y. Yang, Q. Li, W. K. Ma, J. Ge and P. C. Ching, “Cooperative Secure Beamforming for AF Relay Networks With Multiple Eavesdroppers,” IEEE Signal Process. Lett, vol. 20, no. 1, pp. 35– 38, Jan. 2013.
Sanenga, Abraham, Galefang A. Mapunda, Tshepiso M.L. Jacob, Leatile Marata, Bokamoso Basutli, and Joseph M. Chuma, "An Overview of Key Technologies in Physical Layer Security" Entropy 22, no. 11: 1261, 2020.
A. H. Phan, H. D. Tuan, H. H. Kha and D. T. Ngo, "Nonsmooth Optimization for Beamforming in Cognitive Multicast Transmission," 2010 IEEE Global Telecommunications Conference GLOBECOM 2010, 2010, pp. 1-5, doi: 10.1109/GLOCOM.2010.5683915.
A. H. Phan, H. D. Tuan, H. H. Kha and D. T. Ngo, "Nonsmooth Optimization for Efficient Beamforming in Cognitive Radio Multicast Transmission," in IEEE Transactions on Signal Processing, vol. 60, no. 6, pp. 2941-2951, June 2012, doi: 10.1109/TSP.2012.2189857.
J. Lofberg, "YALMIP: a toolbox for modeling and optimization in MATLAB," 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), 2004, pp. 284- 289, doi: 10.1109/CACSD.2004.1393890.
Jos F. Sturm, “Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones”, Optimization Methods and Software, 11:1-4, 625-653, DOI: 10.1080/10556789908805766. Nghiên cứu khoa học công nghệ
Trần Hoàng Linh, Nguyễn Huy Hoàng, Phan Huy Anh, Trần Đình Thông, “Ứng dụng kỹ thuật tối ưu hóa cho bài toán Beamforming trong truyền dẫn vô tuyến với bối cảnh đảm bảo an ninh lớp vật lý”, Tạp chí Khoa học và Công nghệ, Tập 56, Số 5, tháng 10 – 2020
