Narrow and shaped beam synthesis of arbitrary arrays via linear programming

Two classes of pattern synthesis problems for arbitrary arrays are addressed: narrow beam low sidelobe and shaped beam. Both problems are transformed into a linear program (LP) and can therefore be efficiently solved by many readily available algorithms. The narrow beam low sidelobe synthesis problem is rewritten as a convex optimization problem that is then easily solved to find the optimal solution. An iterative procedure is proposed to linearize and solve efficiently the shaped beam synthesis problem with simple subroutines. Numerical applications are performed to confirm the efficiency of both approaches.