Pattern Synthesis of Sparse Linear Arrays with Mutual Coupling Using Vectorial Matrix Pencil Method

A challenging research question is how to achieve a desired pattern of an antenna array with the least number of antenna elements while including mutual coupling. The matrix pencil method (MPM) simplifies the derivation by assuming that the elements are isotropic and that there is no mutual coupling. However, in practical engineering, the desired pattern is scalar while the element patterns are vectorial and different due to the presence of mutual coupling, rendering traditional MPM less applicable. Here, a vectorial MPM (VMPM) is presented that takes mutual coupling effects into account. First, a Hankel sampling matrix is constructed from the desired radiation pattern, and singular value decomposition (SVD) is performed to obtain the minimum number of elements. Next, the sampling matrix is used to construct the matrix pencil to determine the positions of the elements. Furthermore, intelligent optimization algorithms are introduced to obtain the element excitations considering mutual coupling effects. Finally, the effectiveness of the proposed method is validated by a numerical case.