Shaped-Beam Pattern Synthesis of Sparse Linear Arrays Using the Unitary Matrix Pencil Method

In this letter, the unitary matrix pencil (UMP) method is utilized for the shaped-beam pattern synthesis of maximally sparse linear arrays. Taking advantage of the equivalent matrix pencil obtained by a unitary transformation, the UMP-based synthesis method constructs a novel relation between the element positions and the generalized eigenvalues, which contributes to the real solutions for all element positions and thereby improves the matching accuracy of shaped-beam patterns. In addition, complex computations in both the singular value decomposition and the eigenvalue decomposition procedures are converted into real ones through a unitary transformation, which significantly reduces the computational complexity. Numerical experiments assess the effectiveness and advantages of the proposed method in comparison to the state-of-the-art synthesis approaches.