The filter diagonalization method in antenna array optimization for pattern synthesis

Pattern synthesis of nonuniform antenna arrays has drawn significant attention because of its wide applications. With the aim of reducing the number of elements in linear and planar arrays, this paper introduces a novel non-iterative method based on the filter diagonalization method (FDM), which was originally applied in the problem of identifying and quantifying chemical molecules with nuclear magnetic resonance (NMR) in quantum mechanical formalism. The proposed method samples the data set from the desired discrete pattern and associates the sample data with a time autocorrelation function of a fictitious dynamical system, which is described by an effective "Hamiltonian" operator that contains the array element information. The "Hamiltonian" operator can be decomposed by a set of orthonormal eigenvectors. Therefore, the original pattern synthesis is converted into solving the general eigenvalue decomposition with Krylov bases. The number of nonuniform array elements depends on the number of the Krylov bases and the sample data. The proposed method can obtain an optimized antenna array to reconstruct the desired radiation pattern with a high accuracy. Numerical examples show that proposed FDM pattern synthesis can use less prior knowledge to achieve the desired pattern with highly sparse antenna arrays.