Synthesis of sparse linear array with multiple patterns based on joint sparse recovery

An innovative methodology based on joint sparse recovery is proposed for sparse linear array synthesis using a minimum number of elements to generate multiple patterns with different shapes. The synthesis is formulated as a convex problem with the minimization of mixed l
₂
/l
₁
-norm in terms of the joint sparse recovery in Compressed Sensing. Then convex optimization is properly adopted to solve the above problem efficiently. The proposed method can perform a complete optimization on the number of elements, the common element positions as well as the individual element excitations for all desired patterns simultaneously. Preliminary results are presented to show the effectiveness and flexibility of the proposed method in achieving a sparse linear array including focused, cosec-squared and flat-topped beams.