Abstract
Recently, many sparse-based direction-of-arrival (DOA) estimation methods for coprime arrays have become popular for their excellent detection performance. However, these methods often suffer from grid mismatch problem due to the discretization of the potential angle space, which will cause DOA estimation performance degradation when the target is off-grid. To this end, we proposed a sparse-based off-grid DOA estimation method for coprime arrays in this paper, which includes two parts: coarse estimation process and fine estimation process. In the coarse estimation process, the grid points closest to the true DOAs, named coarse DOAs, are derived by solving an optimization problem, which is constructed according to the statistical property of the vectorized covariance matrix estimation error. Meanwhile, we eliminate the unknown noise variance effectively through a linear transformation. Due to finite snapshots effect, some undesirable correlation terms between signal and noise vectors exist in the sample covariance matrix. In the fine estimation process, we therefore remove the undesirable correlation terms from the sample covariance matrix first, and then utilize a two-step iterative method to update the grid biases. Combining the coarse DOAs with the grid biases, the final DOAs can be obtained. In the end, simulation results verify the effectiveness of the proposed method.
Highlights
Direction of arrival (DOA) estimation of multiple far-field narrowband sources is a vital and interesting topic in a signal processing field, which has wide application in many areas such as radar, sonar, radio astronomy and wireless communications, etc. [1,2,3,4]
These methods are all applied on the traditional uniform linear array and they do not utilize the increased DOFs provided by the difference coarray of coprime arrays
Remove the repeated entries of rand sort the remaining entries to get z as Equation (10); Represent z sparsely according to Equation (14) and get the noiseless received signal model according to Equations (15) and (16); Normalize the sample covariance matrix estimation error according to Equations (9), (12), (17) and (18)
Summary
Direction of arrival (DOA) estimation of multiple far-field narrowband sources is a vital and interesting topic in a signal processing field, which has wide application in many areas such as radar, sonar, radio astronomy and wireless communications, etc. [1,2,3,4]. In order to maximize the utilization of extended DOFs, some sparse representation methods for coprime arrays [20,21,22] were proposed, which can be directly applied to derive the signal power vector without requiring decorrelation and covariance matrix rank recovery operation. Technique, which is implemented in a real domain and has low computation complexity These methods are all applied on the traditional uniform linear array and they do not utilize the increased DOFs provided by the difference coarray of coprime arrays. In reference [33], an off-grid DOA estimation method based on the framework of sparse Bayesian learning was proposed for coprime arrays. CN ( a, B) denotes a complex Gaussian distribution with mean vector a and covariance matrix B
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