Half-Dimension Subspace Decomposition for Fast Direction Finding With Arbitrary Linear Arrays

Abstract

It is well-known that the multiple signal classification (MUSIC) algorithm is computationally time-consuming because it requires a complex-valued full-dimension eigenvalue decomposition (EVD) and a complex-valued spectral searching. In this paper, we exploit the virtual signal model of forward/backward average of array covariance matrix (FBACM) to show that its real part (R-FBACM) is a real symmetric matrix. Based on that, we prove that by evaluating two half-dimension EVD after an orthogonally similar transformation performed on the estimated R-FBACM, we are able to reconstruct the original eigenspace whereas the maximum number of estimated sources is reduced as compared to the upper limit <inline-formula><tex-math notation="LaTeX">$\mathit{M}-\text{1}$</tex-math></inline-formula> for original MUSIC. Numerical results show that the proposed method provides satisfactory estimation accuracy and improved resolution with reduced complexity.