Efficient unitary matrix pencil method for synthesising wideband frequency patterns of sparse linear arrays

A novel technique incorporating the unitary matrix pencil (UMP) method is extended to the case of sparse linear arrays with wideband frequency invariant (FI) patterns. Multiple pattern data at different frequencies are formulated with the same poles corresponding to the FI element positions by a new sampling strategy. The unitary transform converts the complex computations for block Hankel matrices into real ones, which contributes to the reduction of the computation complexity for the singular value decomposition and the eigenvalue decomposition procedures. Taking advantage of the equivalent matrix pencil obtained by the unitary transformation, a new relation between the element positions and generalised eigenvalues can be built by the UMP method, which contributes to the real solutions for all element positions win wideband. A new tactics is exploited to avoid small element spacing with the consideration of the size of array antennas. Multiple FI patterns are reconstructed with a higher matching accuracy by only varying the excitation distributions. A set of representative numerical examples demonstrate the efficiency and advantages of the proposed method.