Low-dimensional SDP formulation for large antenna array synthesis

IEEE Transactions on Antennas and Propagation

Volumn 55, Issue 6 II, 2007, Pages 1716-1725

  Hoang, Hung Gia ^a   Tuan, Hoang Duong ^a   Vo, Ba Ngu ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Array signal processing; Beam pattern design; Optimization; Semi definite programming (SDP)

Indexed keywords

BEAMFORMING; CONSTRAINT THEORY; DIRECTIONAL PATTERNS (ANTENNA); LINEAR MATRIX INEQUALITIES; POLYNOMIALS;

SEMI-DEFINITE PROGRAM (SDP); SEMI-INFINITE PROGRAM (SIP);

ANTENNA ARRAYS;

EID: 34250797384     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2007.898573     Document Type: Article

References (22)

1. D. H. Johnson and D. E. Dudgeon, Array Signal Processing: Concepts and Techniques. Englewood Cliffs, NJ: Prentice-Hall, 1993.
2. B. D. V. Veen and K. M. Buckley, "Beamforming: A versatile approach to spatial filtering," IEEE ASSP Mag., pp. 4-24, Apr. 1988.
3. A. van Ardenne and F. Smits, "Technical aspects for the square kilometer array interferometer," in ESTEC Workshop on Large Antennas in Radio Astronomy, Feb. 1996, p. 117.
4. G. A. Hampson, R. de Wild, and A. B. Smolders, "Efficient multi-beaming for the next generation of radio telescopes," in Perspectives on Radio Astronomy: Technologies for Large Antenna Arrays, Apr. 1999.
5. A. Cantoni, X. Lin, and K. Teo, "A new approach to the optimization of robust antenna array processors," IEEE Trans. Antennas Propag., vol. 41, no. 4, pp. 403-411, Apr. 1993.
6. H. Lebret and S. Boyd, "Antenna array pattern synthesis via convex optimization," IEEE Trans. Signal Process., pp. 526-532, Mar. 1997.
7. B. Vo, A. Cantoni, and K. L. Teo, Filter Design with Time Domain Mask Constraints: Theory and Applications. Boston, MA: Kluwer Academic, 2001.
8. S. Nordebo and Z. Zang, "A semi-infinite quadratic programming algorithm with applications to array pattern synthesis," IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 48, no. 3, pp. 225-232, Mar. 2001.
9. T. Davidson, Z.-Q. Luo, and J. Sturm, "LMI formulation of spectral mask constraints with applications to FIR filter design," IEEE Trans. Signal Process., vol. 50, no. 11, pp. 2702-2715, Nov. 2002.
10. F. Wang, V. Balakrishnan, P. Zhou, J. C. R. Yang, and C. Frank, "Optimal array pattern synthesis using semi-definite programming," IEEE Trans. Signal Process., vol. 51, no. 5, pp. 1172-1183, May 2003.
11. J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimiz. Methods Softw., pp. 625-653, 1999.
12. O. M. Bucci, D. D'Elia, G. Mazzarella, and G. Panatiello, "Antenna pattern synthesis: A new general approach," Proc. IEEE, vol. 82, no. 3, pp. 358-371, Mar. 1994.
13. R. Hettich and K. O. Kortanek, "Semi-infinite programming: Theory methods and applications," SIAM Rev., vol. 35, no. 3, pp. 380-429, Sep. 1993.
14. R. Reemptsen and J.-J. Ruckman, Eds., Semi-Infinite Programming. Boston, MA: Kluwer Academic, 1998.
15. M. G. Krein and A. A. Nudel'man, "The Markov moment problem and extremal problems," Transl. Math. Monographs, vol. 50, 1977.
16. H. D. Tuan, T. T. Son, B. Vo, and T. Q. Nguyen, "LMI characterization for the convex hull of trigonometric curves and applications," IEEE Trans. Signal Process., to appear.
17. R. T. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1970.
18. S. Zohar, "Toeplitz matrix inversion: The algorithm of W. F. Trench," J. Assoc. Comput. Machin., vol. 16, no. 4, pp. 592-601, 1969.
19. A. H. Sayed and T. Kailath, "A survey of spectral factorization methods," Numer. Linear Algebra With Appl., vol. 8, pp. 467-496, 2001.
20. T. N. T. Goodman, C. A. Micchelli, G. Rodriguez, and S. Seatzu, "Spectral factorization of Laurent polynomials," Adv. Comput. Math. vol. 7, no. 4, pp. 429-454, 1997.
21. H. G. Hoang, H. D. Tuan, B. Vo, and H. H. Kha, "Beam pattern synthesis for large symmetric arrays with bounds on sidelobe and mainlobe levels," in Proc. Asia-Pacific Conf. Commun., Oct. 2005, pp. 1014-1018.
22. B.-N. Vo and A. Cantoni, "Continuous-time envelope constrained filter design with input uncertainty," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 10, pp. 1445-1454, Oct. 2000.