Beamspace direction finding based on the conjugate gradient and the auxiliary vector filtering algorithms

Motivated by the performance of the direction finding algorithms based on the auxiliary vector filtering (AVF) method and the conjugate gradient (CG) method as well as the advantages of operating in beamspace (BS), we develop two novel direction finding algorithms for uniform linear arrays (ULAs) in the beamspace domain, which we refer to as the BS AVF and the BS CG methods. The recently proposed Krylov subspace-based CG and AVF algorithms for the direction of arrival (DOA) estimation utilize a non-eigenvector basis to generate the signal subspace and yield a superior resolution performance for closely spaced sources under severe conditions. However, their computational complexity is similar to the eigenvector-based methods. In order to save computational resources, we perform a dimension reduction through the linear transformation into the beamspace domain, which additionally leads to significant improvements in terms of the resolution capability and the estimation accuracy. A comprehensive complexity analysis and simulation results demonstrate the excellent performance of the proposed algorithms and show their computational requirements. As examples, we investigate the efficacy of the developed methods for the discrete Fourier transform (DFT) and the discrete prolate spheroidal sequences (DPSS) beamspace designs.