A dual perspective on separable semidefinite programming with applications to optimal downlink beamforming

IEEE Transactions on Signal Processing

Volumn 58, Issue 8, 2010, Pages 4254-4271

  Huang, Yongwei ^a   Palomar, Daniel P ^a  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Downlink beamforming; LP approach; rank constrained solution; SDP relaxation

Indexed keywords

CLOSED FORM SOLUTIONS; DOWNLINK BEAMFORMING; EFFICIENT ALGORITHM; LINEAR PROGRAMS; OPTIMAL BEAMFORMING; OPTIMAL DOWNLINK; OPTIMAL SOLUTIONS; OPTIMIZATION PROBLEMS; PERRON-FROBENIUS THEOREM; PURIFICATION PROCESS; QUADRATICALLY-CONSTRAINED QUADRATIC PROGRAMS; RANK REDUCTION; RELAXED PROBLEM; SDP RELAXATION; SEMI-DEFINITE PROGRAMMING; SIGNAL TO INTERFERENCE PLUS NOISE RATIO; STRONG DUALITY; TOTAL TRANSMISSION;

ALGORITHMS; MATHEMATICAL PROGRAMMING; QUALITY OF SERVICE; SPACECRAFT;

BEAMFORMING;

EID: 77954571092     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2010.2049570     Document Type: Article

References (19)

1. A. B. Gershman, N. D. Sidiropoulos, S. Shahbazpanahi, M. Bengtsson, and B. Ottersten, "Convex optimization-based beamforming: From receive to transmit and network designs," IEEE Signal Process. Mag., vol.27, no.3, pp. 62-75, 2010.
2. M. Bengtsson and B. Ottersten, "Optimal and suboptimal transmit beamforming," in Handbook of Antennas inWireless Communications, L. C. Godara, Ed. Boca Raton, FL: CRC, 2001, ch. 18.
3. M. Bengtsson and B. Ottersten, "Optimal transmit beamforming using semidefinite optimization," in Proc. 37th Ann. Allerton Conf. Commun., Contr., Comput., Sep. 1999, pp. 987-996.
4. D. Hammarwall, M. Bengtsson, and B. Ottersten, "On downlink beamforming with indefinite shaping constraints," IEEE Trans. Signal Process., vol.54, pp. 3566-3580, Sep. 2006.
5. Y. Huang and D. P. Palomar, "Rank-constrained separable semidefinite programming with applications to optimal beamforming," IEEE Trans. Signal Process., vol.58, pp. 664-678, Feb. 2010.
6. F. Rashid-Farrokhi, K. R. Liu, and L. Tassiulas, "Transmit beamforming and power control for cellular wireless systems," IEEE J. Sel. Areas Commun., vol.16, pp. 1437-1450, Oct. 1998.
7. M. Schubert and H. Boche, "Solution of the multiuser downlink beamforming problem with individual SINR constraints," IEEE Trans. Veh. Technol., vol.53, no.1, pp. 18-28, 2004.
8. Z.-Q Luo and T.-H Chang, "SDP relaxation of homogeneous quadratic optimization: Approximation bounds and applications," in Convex Optimization in Signal Processing and Communications, D. P. Palomar and Y. Eldar, Eds. Cambridge, U.K.: Cambridge Univ. Press, 2010, ch. 4.
9. N. Sidiropoulos, T. Davidson, and Z. Q. Luo, "Transmit beamforming for physical-layer multicasting," IEEE Trans. Signal Process., vol.54, pp. 2239-2251, Jun. 2006.
10. E. Karipidis, N. Sidiropoulos, and Z.-Q. Luo, "Quality of service and max-min fair transmit beamforming to multiple cochannel multicast groups," IEEE Trans. Signal Process., vol.56, pp. 1268-1279, Mar. 2008.
11. T.-H. Chang, Z.-Q. Luo, and C.-Y. Chi, "Approximation bounds for semidefinite relaxation of max-min-fair multicast transmit beamforming problem," IEEE Trans. Signal Process., vol.56, pp. 3932-3943, Aug. 2008.
12. Z.-Q. Luo, W.-K. Ma, A. M.-C. So, Y. Ye, and S. Zhang, "Semidefinite relaxation of quadratic optimization problems," IEEE Signal Process. Mag., vol.27, no.3, pp. 20-34, 2010.
13. A. Pascual-Iserte, D. P. Palomar, A. Pérez-Neira, and M. Lagunas, "A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization," IEEE Trans. Signal Process., vol.54, pp. 346-360, Jan. 2006.
14. G. Scutari, D. P. Palomar, and S. Barbarossa, "Cognitive MIMO radio: Competitive optimality design based on subspace projections," IEEE Signal Process. Mag., vol.25, no.6, pp. 46-59, Nov. 2008.
15. M. H. Er and B. C. Ng, "A new approach to robust beamforming in the presence of steering vector errors," IEEE Trans. Signal Process., vol.42, pp. 1826-1829, Jul. 1994.
16. A. Nemirovski, Lectures on Modern Convex Optimization, Class Notes Georgia Inst. Technol., 2005 [Online]. Available: http://www2.isye. gatech.edu/nemirovs/Lect-ModConvOpt.pdf
17. Y. Huang and S. Zhang, "Complex matrix decomposition and quadratic programming," Math. Operat. Res., vol.32, no.3, pp. 758-768, 2007.
18. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: The Johns Hopkins Univ. Press, 1996.
19. M. Grant and S. Boyd, CVX: Matlab Software for Disciplined Convex Programming Dec. 2008 [Online]. Available: http://stanford. edu/∼boyd/cvx