Mask constrained beam pattern synthesis for large arrays

Antenna array pattern synthesis with mask constraints can be formulated as a convex optimization problem with semiinfinite trigonometric polynomial constraints. The current approach uses a Linear Matrix Inequality (LMI) characterization of the semi-infinite constraints to convert the original problem into a semidefinite programming (SDP) problem. However, an important drawback of this approach is the large number of additional variables incurred in the equivalent SDP representation, which in turn prohibits its use in the design of large antenna arrays that arise in many modern applications. This paper presents an efficient method for the synthesis of large antenna arrays via a novel LMI characterization of semi-infinite constraints that only involves a minimal number of additional variables. Subsequently, the design of patterns for arrays with hundreds of elements can be easily achieved on a standard personal computer using existing SDP solvers.