A semi-infinite quadratic programming algorithm with applications to array pattern synthesis

This paper presents a new extended active set strategy for optimizing antenna arrays by semi-infinite quadratic programming. The optimality criterion is either to maximize the directivity of the antenna or to minimize its sidelobe energy when subjected to a specified peak sidelobe level. Additional linear constraints are used to form the mainlobe. The design approach is applied to a numerical example that deals with the design of a narrow-band circular antenna array for the far field.

[1]  Sven Nordholm,et al.  Weighted Chebyshev approximation for the design of broadband beamformers using quadratic programming , 1994, IEEE Signal Processing Letters.

[2]  Ingvar Claesson,et al.  Optimum window design by semi-infinite quadratic programming , 1999, IEEE Signal Processing Letters.

[3]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[4]  Wei Xing Zheng,et al.  Recursive procedures for constrained optimisation problems and its application in signal processing , 1995 .

[5]  E. Anderson Linear Programming In Infinite Dimensional Spaces , 1970 .

[6]  Klaus Preuss,et al.  On the design of FIR filters by complex Chebyshev approximation , 1989, IEEE Trans. Acoust. Speech Signal Process..

[7]  Kenneth O. Kortanek,et al.  Semi-Infinite Programming: Theory, Methods, and Applications , 1993, SIAM Rev..

[8]  B.D. Van Veen,et al.  Beamforming: a versatile approach to spatial filtering , 1988, IEEE ASSP Magazine.

[9]  Robin J. Evans,et al.  Envelope-constrained filters-I: Theory and applications , 1977, IEEE Trans. Inf. Theory.

[10]  Albert H. Nuttall,et al.  A Note on the Semi-Infinite Programming Approach to Complex Approximation , 1983 .

[11]  S. Nordebo,et al.  Semi-infinite linear programming: a unified approach to digital filter design with time- and frequency-domain specifications , 1999 .

[12]  T. W. Parks,et al.  Digital Filter Design , 1987 .

[13]  Thomas W. Parks,et al.  Optimal design of FIR filters with the complex Chebyshev error criteria , 1995, IEEE Trans. Signal Process..

[14]  John W. Adams A new optimal window [signal processing] , 1991, IEEE Trans. Signal Process..

[15]  B. Wahlberg System identification using Laguerre models , 1991 .

[16]  Thomas W. Parks,et al.  Design of FIR filters in the complex domain , 1987, IEEE Trans. Acoust. Speech Signal Process..

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

[18]  Sven Nordholm,et al.  Chebyshev optimization for the design of broadband beamformers in the near field , 1998 .

[19]  M. Athans,et al.  Optimal filter design subject to output sidelobe constraints: Theoretical considerations , 1972 .

[20]  Robin J. Evans,et al.  Envelope-constrained filters-II: Adaptive structures , 1977, IEEE Trans. Inf. Theory.

[21]  J. McClellan,et al.  Complex Chebyshev approximation for FIR filter design , 1995 .

[22]  R. Wu,et al.  Array pattern synthesis and robust beamforming for a complex sonar system , 1997 .

[23]  D. Cheng Field and wave electromagnetics , 1983 .

[24]  Kok Lay Teo,et al.  Continuous-time envelope constrained filter design via orthonormal filters , 1995 .

[25]  Rainer Hettich,et al.  A Review of Numerical Methods for Semi-Infinite Optimization , 1983 .

[26]  D. Luenberger Optimization by Vector Space Methods , 1968 .

[27]  Kok Lay Teo,et al.  A Dual Parametrization Method for Convex Semi-Infinite Programming , 2000, Ann. Oper. Res..

[28]  A. H. Nuttall,et al.  A general Chebyshev complex function approximation procedure and an application to beamforming , 1982 .

[29]  Kevin G. Christian,et al.  Design and characterization of optimal FIR filters with arbitrary phase , 1993, IEEE Trans. Signal Process..