Synthesis of Sparse Planar Arrays With Multiple Patterns by the Generalized Matrix Enhancement and Matrix Pencil

In recent years, the matrix enhancement and matrix pencil method (MEMP) as well as the forward-backward MEMP (FBMEMP) have been successfully applied to reduce the number of antenna elements in the single-pattern planar arrays. This article aims to extend the MEMP and FBMEMP to the synthesis of sparse planar arrays with multiple patterns. The generalized MEMP (GMEMP) first constructs an enhanced matrix for each target pattern according to their data samples, respectively, and then these enhanced matrices are used to form a composite Hankel block matrix. After that, two sets of poles corresponding to two sets of reconstructed location coordinates can be extracted from the principal eigenvectors of the composite Hankel block matrix by the matrix pencil method. The randomized singular value decomposition and Hankel matrix decomposition method are used to accelerate the above extraction process. Then, we make use of improved matching algorithm to pair the two sets of position coordinates to obtain 2-D coordinates. Finally, we use the least-square method to obtain the excitations of sparse planar array elements, which makes the reconstruction process of multiple patterns more stable and accurate. Apart from the above, the GMEMP is also extended to the synthesis of multiple shaped-beam patterns using the generalized forward-backward matrix enhancement and matrix pencil method (GFBMEMP). A series of representative numerical examples show that the proposed methods can reduce the number of elements in the planar arrays efficiently while maintaining the accuracy of all the patterns to be synthesized.