Two-Dimensional DOA Estimation for Three-Parallel Nested Subarrays via Sparse Representation

Abstract

Nested arrays are considered attractive due to their hole-free performance, and have the ability to resolve normalO(N2) sources with normalO(N) physical sensors. Inspired by nested arrays, two kinds of three-parallel nested subarrays (TPNAs), which are composed of three parallel sparse linear subarrays with different inter-element spacings, are proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation in this paper. We construct two cross-correlation matrices and combine them as one augmented matrix in the first step. Then, by vectorizing the augmented matrix, a hole-free difference coarray with larger degrees of freedom (DOFs) is achieved. Meanwhile, sparse representation and the total least squares technique are presented to transform the problem of 2-D DOA searching into 1-D searching. Accordingly, we can obtain the paired 2-D angles automatically and improve the 2-D DOA estimation performance. In addition, we derive closed form expressions of sensor positions, as well as number of sensors for different subarrays of two kinds of TPNA to maximize the DOFs. In the end, the simulation results verify the superiority of the proposed TPNAs and 2-D DOA estimation method.

A 2D Nested Array Based DOA Estimator for Incoherently Distributed Sources via Sparse Representation Utilizing L1-Norm

“…The recent proposed nested arrays [25] possess larger apertures and more degree of freedoms (DOFs) compared with uniform arrays with the same number of sensors. DOA estimations for point sources under different kinds of nested arrays have been proposed in [26][27][28][29][30]. As for distributed sources, based on a linear nested array, a spatial smoothing with spectral search technique has been proposed in [8] for 1D distributed sources supposing a priori knowledge of the angular spreads is known, which is impractical in practice.…”

A Novel Nested Configuration Based on the Difference and Sum Co-Array Concept

“…The direction-of-arrival (DOA) estimation is an important topic in many applications such as radar and sonar [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ]. Many traditional high-resolution subspace-based estimators [ 11 , 12 ], which utilize the uniform linear array (ULA) as the array model, have been proposed for direction finding.…”

A Sparse-Based Off-Grid DOA Estimation Method for Coprime Arrays

“…However, a large number of sensors will increase the hardware cost and the difficulty of array calibration in practical applications. To overcome this challenge, some non-uniform array geometries, called sparse arrays, have been proposed, such as minimum redundancy arrays (MRAs) [ 10 ], nested arrays (NAs) [ 11 , 12 ] and coprime arrays (CPAs) [ 13 , 14 , 15 ]. Though MRAs can obtain more degrees of freedom (DOFs) through constructing an augmented covariance matrix, they have no closed form expressions for the optimal array configurations as well as the achievable DOFs for an arbitrary number of sensor elements.…”