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An inhomogeneous plane-wave based single-level fast direct solver for the scattering analysis of extremely large antenna arrays

A semi-analytic single-level fast direct solver is presented for the method-of-moments analysis of large planar antenna arrays with up to few thousands of complex elements on current desktop computers. Assuming a partition of the impedance matrix, the proposed scheme factorizes the near-field blocks via an SVD-based low-rank approximation and the intermediate-field blocks via an analytical inhomogeneous plane-wave expansion. The near- and intermediate-field bases are then unified to leverage Woodbury formula for the inversion. The solutions for the excitation of each array ports are obtained at once with O(N15/7 ln3 N) computational cost and O(N11/7 lnN) memory for array problems with N basis functions. The complexities are traced precisely and the error is controlled by means of analytical formulas for the required number of inhomogeneous plane waves. The fast direct solver is also combined with a macro-basis function approach to deal with antenna geometries containing many subwavelength details. This paper includes simulations of regular arrays of about 1692 3D dipoles and an irregular array composed of 7 stations of the low-frequency Square Kilometer Array telescope comprising each 256 log-periodic antennas. This technique allows the analysis of the coupling effect both within any one station but also between the stations of the telescope, a size and complexity of problem which has not been possible with existing published techniques.