Block-Toeplitz fast integral equation solver for large finite periodic and partially periodic antenna arrays

Abstract

We propose a fast integral equation solver for large periodic and non-periodic finite antenna array systems. A key element of the algorithm is the rigorous block-Toeplitz method with an FFT-based matrix-vector product accelerator, which can be used in conjunction with either the conventional MoM, or with the AIM (adaptive integral method) or FMM (fast multipole method) compression techniques. We refer to the resulting algorithms as the Toeplitz-MoM, Toeplitz-AIM, or Toeplitz-FMM matrix compressions. For a periodic distribution of array elements, the algorithm exploits the block-Toeplitz structure of the impedance matrix in three dimensions and allows the implementation of matrix-vector multiplication in terms of discrete fast Fourier transforms (FFTs) in spatial variables associated with distances between the array elements. This approach generalizes to antenna arrays with boundaries, arrays located on substrates, and similar not entirely periodic systems.