  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, 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 \emph{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.
