An Array Decomposition Method for Finite Arrays with Electrically Connected Elements for fast Toeplitz Solvers

A large part of the geometry of array antennas is often partially defined by finite translational symmetries. Applying the method of moments (MoM) with the RWG-like element on an appropriately structured mesh to these arrays results in an impedance matrix where the main part exhibits a multilevel block Toeplitz structure. This article introduces a memory-efficient construction method that effectively represents and reuses impedance calculations. The proposed method, applicable to electrically connected elements, also accounts for all non-symmetric parts of the array. The core idea involves nine distinct electrically connectable components from which the array can be assembled. The derived multilevel block Toeplitz matrix is further utilized by an in-house inverse solver to achieve faster and more memory-efficient MoM current vector calculations. We demonstrate the method by computing the far-field of a 32x32 array and the scattering parameters of two tightly coupled 9x9 arrays. This approach reduces the memory allocation from $\mathcal{O}(N_x^2 N_y^2)$ to $\mathcal{O}(N_x N_y)$, for an $N_x \times N_y$ array.