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.

I. Introduction

The multiple signal classification (MUSIC) algorithm [1], [2] is one of the most popular subspace-based techniques for estimating the directions-of-arrival (DOAs) of multiple signal sources. As the conventional (spectral) MUSIC algorithm involves a computationally demanding spectral search step, its use can be prohibitively expensive in scenarios where real-time processing is required. To reduce the computational complexity of spectral MUSIC, a numerically efficient search-free modification of this approach has been proposed [3]. The latter algorithm is commonly referred to as root-MUSIC because it makes use of polynomial rooting instead of spectral search. Although the root-MUSIC technique enjoys a substantially improved computational complexity and threshold performance as compared to spectral MUSIC [4], it is only applicable to uniform linear arrays (ULAs) or nonuniform arrays (NUAs) whose sensors lie on a uniform grid. Another popular search-free DOA estimation method is the ESPRIT (estimation of signal parameters via rotational invariance techniques) algorithm [5]. However, the array geometry is required in ESPRIT to be shift-invariant.