On the Optimal Synthesis of Sum or Difference Patterns of Centrosymmetric Arrays Under Arbitrary SideLobe Constraints

This paper deals with the optimal synthesis of sum or difference patterns radiated by an array of fixed geometry. The aim is to establish the most general class of arrays for which such synthesis can be reduced to a linear programming problem, extending and completing previous results regarding uniformly spaced (linear and planar) arrays. It is shown that such a class consists of the centrosymmetric arrays, whose element patterns are either equal or Hermitian symmetric with respect to the center of symmetry. The optimal solutions are also Hermitian symmetric and the corresponding patterns are real. Furthermore, it is shown that the above class of arrays coincides with that of the arrays capable of radiating real patterns. Some numerical examples are provided to give an idea of the geometries and the synthesis problems to which the achieved result successfully applies and of the achievable computational advantage.

[1]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[2]  David K. Cheng,et al.  Optimum scannable planar arrays with an invariant sidelobe level , 1968 .

[3]  O. Einarsson.  Optimization of planar arrays , 1979 .

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

[5]  J. C. Mason,et al.  THE USE OF LINEAR PROGRAMMING IN THE DESIGN OF ANTENNA PATTERNS WITH PRESCRIBED NULLS AND OTHER CONSTRAINTS , 1984 .

[6]  S. Vavasis.  Nonlinear optimization: complexity issues , 1991 .

[7]  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.

[8]  Z. Yu,et al.  Beampattern Synthesis for Linear and Planar Arrays With Antenna Selection by Convex Optimization , 2010, IEEE Transactions on Antennas and Propagation.

[9]  Tommaso Isernia,et al.  Optimal focusing of scalar fields subject to arbitrary upper bounds , 1998 .

[10]  Giovanni Toso,et al.  Sparse and thinned arrays for multiple beam satellite applications , 2007 .

[11]  G. Franceschetti,et al.  On the spatial bandwidth of scattered fields , 1987 .

[12]  A F Morabito,et al.  Optimal Synthesis of Sum and Difference Patterns With Arbitrary Sidelobes Subject to Common Excitations Constraints , 2010, IEEE Antennas and Wireless Propagation Letters.

[13]  P. Woodward,et al.  The Theoretical Precision with which an Arbitrary Radiation-Pattern may be Obtained from a Source of Finite Size , 1948 .

[14]  O. Bucci,et al.  Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples , 1998 .

[15]  A. Safaai-Jazi.  Modified Chebyshev arrays , 1998 .

[16]  D. Pinchera,et al.  A Generalized Hybrid Approach for the Synthesis of Uniform Amplitude Pencil Beam Ring-Arrays , 2012, IEEE Transactions on Antennas and Propagation.

[17]  Qing Huo Liu,et al.  Synthesis of Sparse or Thinned Linear and Planar Arrays Generating Reconfigurable Multiple Real Patterns by Iterative Linear Programming , 2016 .

[18]  J. E. Richie,et al.  Linear program synthesis for direct broadcast satellite phased arrays , 1988 .

[19]  T. Isernia,et al.  A hybrid approach for the optimal synthesis of pencil beams through array antennas , 2004, IEEE Transactions on Antennas and Propagation.

[20]  T. Isernia,et al.  Optimal far-field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions , 2002 .

[21]  A. Safaai-Jazi,et al.  A new formulation for the design of Chebyshev arrays , 1994 .

[22]  Tommaso Isernia,et al.  Optimal synthesis of difference patterns subject to arbitrary sidelobe bounds by using arbitrary array antennas , 2005 .