Spectral factorization for integer-interval sampled sequence and its applications in array processing

Spectral factorization (SF) has been well developed for a uniformly sampled sequence (USS). Our recent study found important applications of SF for a non-uniformly sampled sequence (NUSS) in array processing, especially considering arbitrary arrays. Since SF for an arbitrarily sampled sequence is intractable, in this paper, we propose a new SF method for an integer-interval sampled sequence (IISS). Its applications in robust adaptive beamforming and array pattern synthesis for a non-uniform linear array (NULA) are studied. Simulation results show the outstanding performance of the proposed method.

[1]  Ali H. Sayed,et al.  A survey of spectral factorization methods , 2001, Numer. Linear Algebra Appl..

[2]  Ba-Ngu Vo,et al.  Mask constrained beam pattern synthesis for large arrays , 2005, Proceedings of the Eighth International Symposium on Signal Processing and Its Applications, 2005..

[3]  Nikos D. Sidiropoulos,et al.  Transmit beamforming for physical-layer multicasting , 2006, IEEE Transactions on Signal Processing.

[4]  Petre Stoica,et al.  On the parameterization of positive real sequences and MA parameter estimation , 2001, IEEE Trans. Signal Process..

[5]  Truong Q. Nguyen,et al.  LMI characterization for the convex hull of trigonometric curves and applications , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[6]  Paul Tseng Further Results on Approximating Nonconvex Quadratic Optimization by Semidefinite Programming Relaxation , 2003, SIAM J. Optim..

[7]  Stephen P. Boyd,et al.  Antenna array pattern synthesis via convex optimization , 1997, IEEE Trans. Signal Process..

[8]  Meng Hwa Er,et al.  A novel robust adaptive beamformer based on worst-case linear optimization , 2008, 2008 3rd IEEE Conference on Industrial Electronics and Applications.

[9]  J. Capon High-resolution frequency-wavenumber spectrum analysis , 1969 .

[10]  Ba-Ngu Vo,et al.  Low-Dimensional SDP Formulation for Large Antenna Array Synthesis , 2007, IEEE Transactions on Antennas and Propagation.

[11]  C.L. Dolph,et al.  A Current Distribution for Broadside Arrays Which Optimizes the Relationship between Beam Width and Side-Lobe Level , 1946, Proceedings of the IRE.

[12]  Stephen P. Boyd,et al.  FIR filter design via semidefinite programming and spectral factorization , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[13]  A. Cantoni,et al.  A new set of linear constraints for broad-band time domain element space processors , 1986 .

[14]  Zhi-Quan Luo,et al.  Linear matrix inequality formulation of spectral mask constraints with applications to FIR filter design , 2002, IEEE Trans. Signal Process..

[15]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[16]  G. Wilson Factorization of the Covariance Generating Function of a Pure Moving Average Process , 1969 .

[17]  Wee Ser,et al.  Novel Adaptive Antenna Array Based on Robust Semidefinite Programming , 2008, 2008 IEEE International Conference on Communications.

[18]  Z. Yu,et al.  A Novel Adaptive Beamformer Based on Semidefinite Programming (SDP) With Magnitude Response Constraints , 2008, IEEE Transactions on Antennas and Propagation.

[19]  Zhi-Quan Luo,et al.  Quasi-maximum-likelihood multiuser detection using semi-definite relaxation with application to synchronous CDMA , 2002, IEEE Trans. Signal Process..

[20]  A. Cantoni,et al.  A unified approach to the design of robust narrow-band antenna array processors , 1990 .

[21]  Lieven Vandenberghe,et al.  Convex optimization problems involving finite autocorrelation sequences , 2002, Math. Program..

[22]  D. Nunn Performance assessments of a time-domain adaptive processor in a broadband environment , 1983 .

[23]  Stephen P. Boyd,et al.  FIR Filter Design via Spectral Factorization and Convex Optimization , 1999 .

[24]  Alan V. Oppenheim,et al.  Discrete-time Signal Processing. Vol.2 , 2001 .

[25]  Bjorn Ottersten,et al.  Optimum and Suboptimum Transmit Beamforming , 2001 .

[26]  A. Papoulis Signal Analysis , 1977 .

[27]  Shuzhong Zhang,et al.  Quadratic maximization and semidefinite relaxation , 2000, Math. Program..

[28]  Jian Li,et al.  On robust Capon beamforming and diagonal loading , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[29]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[30]  Fan Wang,et al.  Optimal array pattern synthesis using semidefinite programming , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).