Beam pattern synthesis for large symmetric arrays with bounds on sidelobe and mainlobe levels

Bounding the sidelobe and mainlobe levels of a symmetric antenna array with complex weights can be posed as semi-infinite trigonometric constraints. Standard optimization techniques can be used to convert the semi-infinite trigonometric constraints into linear matrix inequality (LMI) constraints. However, the drawback of this standard technique is the large number of additional variables incurred in the LMI characterization, which in turn prohibits its use in the design of large antenna arrays that arise in many modern applications. Also, in many cases an additional structure like the symmetric one may destroy the convexity of the optimization reformulation and therefore put the applicability of LMI optimization in doubt. In this paper we propose a technique for synthesizing beam pattern of large symmetric arrays with bound constraints on sidelobe and mainlobe levels. The key lies in a novel LMI characterization of the semi-infinite trigonometric constraints that only involves additional variables of minimal dimensions. Subsequently, the design of patterns for arrays with hundreds of elements can be easily achieved on a standard personal computer using existing SDP solvers.