Abstract
The imperfect array degrades the direction finding performance. In this paper, we investigate the direction finding problem in uniform linear array (ULA) system with unknown mutual coupling effect between antennas. By exploiting the target sparsity in the spatial domain, the sparse Bayesian learning (SBL)-based model is proposed and converts the direction finding problem into a sparse reconstruction problem. In the sparse-based model, the off-grid errors are introduced by discretizing the direction area into grids. Therefore, an off-grid SBL model with mutual coupling vector is proposed to overcome both the mutual coupling and the off-grid effect. With the distribution assumptions of unknown parameters including the noise variance, the off-grid vector, the received signals and the mutual coupling vector, a novel direction finding method based on SBL with unknown mutual coupling effect named DFSMC is proposed, where an expectation-maximum (EM)-based step is adopted by deriving the estimation expressions for all the unknown parameters theoretically. Simulation results show that the proposed DFSMC method can outperform state-of-the-art direction finding methods significantly in the array system with unknown mutual coupling effect.
Highlights
In the direction finding problem, the traditional discrete Fourier transform (DFT)-based method can only find one signal in one beam-width, so the resolution of such a method is too low to estimate multiple signals
With the distribution assumptions, we theoretically derive the estimation of all unknown parameters using the expectation-maximum (EM)-based method in DFSMC, where the unknown parameters include the mutual coupling vector, the noise variance, the signals, the off-grid vector, et al the proposed DFSMC method is compared with the state-of-art methods in the direction finding performance
Since the received signals are sparse in the spatial domain, we propose a sparse-based model to estimate the directions with unknown mutual coupling effect
Summary
In the direction finding problem, the traditional discrete Fourier transform (DFT)-based method can only find one signal in one beam-width, so the resolution of such a method is too low to estimate multiple signals. A symmetric Toeplitz matrix [28,29,30] is used to describe the mutual coupling effect, and a novel direction estimation method is proposed. By exploiting the signal sparsity in the spatial domain, a novel direction finding method based on SBL with unknown mutual coupling effect, named. With the distribution assumptions, we theoretically derive the estimation of all unknown parameters using the expectation-maximum (EM)-based method in DFSMC, where the unknown parameters include the mutual coupling vector, the noise variance, the signals, the off-grid vector, et al the proposed DFSMC method is compared with the state-of-art methods in the direction finding performance. The DFSM method for direction finding estimation: With the distribution assumptions of all unknown parameters, a novel SBL-based direction finding method with unknown mutual coupling effect, named DFSMC, is proposed. For a matrix A, A:,n denotes the n-th column of A, and diag{ A} denotes a vector with the entries from the diagonal entries of A
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