Abstract
A coprime array is capable of achieving more degrees-of-freedom for direction-of-arrival (DOA) estimation than a uniform linear array when utilizing the same number of sensors. However, existing algorithms exploiting coprime array usually adopt predefined spatial sampling grids for optimization problem design or include spectrum peak search process for DOA estimation, resulting in the contradiction between estimation performance and computational complexity. To address this problem, we introduce the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) to the coprime coarray domain, and propose a novel coarray ESPRIT-based DOA estimation algorithm to efficiently retrieve the off-grid DOAs. Specifically, the coprime coarray statistics are derived according to the received signals from a coprime array to ensure the degrees-of-freedom (DOF) superiority, where a pair of shift invariant uniform linear subarrays is extracted. The rotational invariance of the signal subspaces corresponding to the underlying subarrays is then investigated based on the coprime coarray covariance matrix, and the incorporation of ESPRIT in the coarray domain makes it feasible to formulate the closed-form solution for DOA estimation. Theoretical analyses and simulation results verify the efficiency and the effectiveness of the proposed DOA estimation algorithm.
Highlights
Direction-of-arrival (DOA) estimation aims at retrieving the directional information of sources from the array received signals, and plays a fundamental role in a variety of practical application fields including radar, sonar, acoustics, radio astronomy, and wireless communications [1,2,3,4,5,6,7,8,9,10,11]
The steps of the proposed coarray ESPRIT-based DOA estimation algorithm are listed in Table 1, whose main advantages can be summarized as follows: first, we introduce ESPRIT to the coarray domain, and investigate the rotational invariance based on a pair of shift invariant uniform linear coprime coarray subarrays, such that the difficulties caused by the non-uniformity of the coprime array can be overcome, and the available DOF is effectively increased in the meantime
ESPRIT-based DOA estimation algorithm is compared to several DOA estimation algorithms exploiting coprime array, including the sparse signal reconstruction (SSR) algorithm [34], the spatial smoothing
Summary
Direction-of-arrival (DOA) estimation aims at retrieving the directional information of sources from the array received signals, and plays a fundamental role in a variety of practical application fields including radar, sonar, acoustics, radio astronomy, and wireless communications [1,2,3,4,5,6,7,8,9,10,11]. To address the basis mismatch problem, several gridless algorithms have been proposed by reconstructing the covariance matrix of the derived coprime coarray via nuclear norm minimization [36] or trace minimization [37] These MUSIC-like algorithms still estimate the DOAs from the MUSIC spatial spectrum, leading to the trade-off between the resolution performance and the computational complexity. With the incorporation of the ESPRIT in the coarray domain, neither the predefined spatial sampling grids nor the spectrum peak search process is required, indicating that the proposed coarray ESPRIT-based algorithm is capable of resolving off-grid DOAs with an increased number of DOFs. The computational complexity analyses are presented to evaluate the efficiency, and the simulations are conducted to demonstrate the effectiveness of the proposed. 0 and I respectively denote the zero vector and identity matrix with appropriate dimensions
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