Direction-of-Arrival Estimation for Nonuniform Sensor Arrays: From Manifold Separation to Fourier Domain MUSIC Methods

In this paper, the problem of spectral search-free direction-of-arrival (DOA) estimation in arbitrary nonuniform sensor arrays is addressed. In the first part of the paper, we present a finite-sample performance analysis of the well-known manifold separation (MS) based root-MUSIC technique. Then, we propose a new class of search-free DOA estimation methods applicable to arrays of arbitrary geometry and establish their relationship to the MS approach. Our first technique is referred to as Fourier-domain (FD) root-MUSIC and is based on the fact that the spectral MUSIC function is periodic in angle. It uses the Fourier series to expand this function and reformulate the underlying DOA estimation problem as an equivalent polynomial rooting problem. Our second approach applies the zero-padded inverse Fourier transform to the FD root-MUSIC polynomial to avoid the polynomial rooting step and replace it with a simple line search. Our third technique refines the FD root-MUSIC approach by using weighted least-squares approximation to compute the polynomial coefficients. The proposed techniques are shown to offer substantially improved performance-to-complexity tradeoffs as compared to the MS technique.